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NATIONAL LIBRARY OF MEDICINE
        Bethesda, Maryland
  LIBRARY OF  THE  NAVY  DEPARTMENT.
     Section of Bureau of Medicine and Surgery


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  Works of this Section cannot be taken from the Library except by written
permission of the Bureau of Medicine and Surgery.
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CORRELATION  AND  CON
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 \M.d-               BY              ^      4'*  '
Peof^^OYE^ Peof. HELMHOLTZ,  Dr. MAYER, „.,_^~
       De. FARADAY, Peof. LIEBIG and
               De.  CARPENTER.
INTRODUCTION AND BRIEF BIOGRAPHICAL NOTICES OF THE
      CHIEF PROMOTERS OF THE NEW'VIEWS.
EDWARD L. YOUMANS, M. D.
»—The highest law in physical science which our faculties permit us to perceive—the
             Conservation of Force."—De. Faeaday.
              NEW  YORK:

D.  APPLETON   AND  COMPANY,
          90,-92 & 94 GRAND STREET.
                   1869. 
■KM
     Enteeed, according to Act of Congress, in the year 1864, by
              D. APPLETON AND COMPANY,
It the Clerk's Office, of the District Court of the United States for thfc
                Southern District of New Yoik, 
TO
      JOHN WILLIAM  DRAPER, M.D., LL.D.      :

   professor  of  chemistry and physiolody  in  ifle
                  cnitersiit of  new  york.

Dear Sir:—
   It seems peculiarly appropriate that this volume should be dedicated to
you.  Knowing the  eminent esteem in which you are held in the circles of
European science, I cannot doubt that the distinguished authors of the fol-
lowing essays would cordially approve this connection of your name with
their introduction to the American public.
   There is, besides, a further reason for this in that large coincidence of
purpose which is manifest in their labors and your own.  For while the per-
vading design of the present collection is to widen the range of thought by
unfolding a broader philosophy of the energies of nature, your own compre-
hensive  course  of research—beginning with an  extended series of experi-
mental investigations in chemical physics and physiology, and rising to the
consideration of that splendid problem, the bearing of science upon the His-
tory  of the Intellectual Development of Europe—has powerfully contributed
to the same noble end ; that of elevating  the aim and enlarging the scope of
scientific inquiry.
   I gladly avail myself of this  occasion to say how greatly I am indebted
to your writings, in which accurate and profound instruction is so often and
happily blended with the charms of poetic  eloquence.  That you may live
lone  to  enjoy your well-won honors, and to contribute still further to the
triumphant ad ranee  of scientific  truth, is the heartfelt wish of
 *                                          Yours truly,
                                                         E. L. Y. 
 
PREFACE.
   In his address before the British Association for the Advance-
ment of Science last year, the President remarked that the new
views of the Correlation and Conservation of Forces constitute the
most important discovery of the present century.  The  remark is
probably just, prolific as has been this period in grand scientific re-
sults.  No one  can glance through  the current scientific publica-
tions without perceiving that these views are  attracting the pro-
found attention of the most thoughtful minds.  The lively con-
troversy that has  been carried on for the last two or three years
respecting the share that different men of different countries have
had in their establishment, still further attests  the estimate placed
upon them in the scientific world.
   But little, however, has been published in this country upon the
subject; no complete work, I believe, except the admirable volume
of Prof. Tyndall  on  "Heat as a Mode of Motion,"  in which the
new philosophy is adopted, and applied to the  explanation of ther-
mal phenomena in a very clear and forcible manner.   I have, there-
fore, thought it would  be a useful service to the public to reissue
some of the  ablest presentations of these views which have ap-
peared in Europe, in a compact and convenient form.  The selec-
tion of these discussions has been determined by a desire to com-
bine clearness  of exposition with authority of statement.  In the
first of these respects the essays will speak for themselves; in re-
gard to the last I may remark that all the authors  quoted stand
high as founders of the new theory of forces.   Although I  am not 
VI
FEEFACE.
aware that Prof. Liebig has made any claims in this  direction, yet
it can scarcely be doubted that his original researches in Animal
Chemistry tended strongly toward the promotion of the science of
vital dynamics.
   The work of Professor Grove, which is here  reprinted in full,
has a high European reputation, having  passed to the fourth edi-
tion in England, and been translated into several continental lan-
guages.  It is hardly to the credit of science in our  country, that
this is the first American edition.  The  eloquent  and interesting
paper  of  Helmholtz, though  delivered as a popular lecture, was
translated for the Philosophical Magazine, and has been very highly
appreciated in  scientific  circles.   The  three articles of  Mayer,
which were also translated for the  Philosophical Magazine, will
have interest not only because of  the great ability with which the
subjects are treated, but as emanating from a man who stands per-
haps preeminent among the explorers in this new tract of inquiry.
The researches of Faraday in this field have been  conspicuous and
important, and his argument is marked hy the depth  and clearness
which characterize, in an eminent degree, the writings of this ex-
traordinary man.  The essay of Liebig forms a chapter in the last
edition of his invaluable 'Familiar  Letters on  Chemistry,' which
has not been republished here; and, as it touches the relation of the
subject to organic processes, it forms a fit introduction to the final
article of  the series by Dr. Carpenter, on the " Correlation of the
Physical and Vital Forces."   The eminent English physiologist has
worked out this branch of the subject independently, and the pa-
per quoted gives  evidence of being  prepared with his usual care
and ability.  A certain amount of repetition is of course unavoida-
ble in such a collection, yet the reader will find much less of this
than he might be inclined to look for, as each writer, in elaborating
the subject, has stamped  it with his  own  originality.
   In the introduction I  have attempted to bring forward  certain
facts  in the history of these discoveries, in which we as  Ameri-
cans have a special interest, and also to indicate several applications
of the new principles  which are not treated  in the volume.  It
seemed best to confine the general discussion to those aspects of the
subject upon which  most thought had  been expended, and which
may be regarded as  settled among advanced  scientific men.  But
there are other applications of the doctrine, of the highest interest
which though incomplete are yet certain, and  these will be found 
PREFACE.
vii
briefly noticed in the introductory observations—too briefly, I fear,
to be  satisfactory.  Those, however,  who  desire to  pursue still
further this branch of the inquiry—the correlation of the vital,
mental, and social forces—are referred to the last edition of Car-
penter's " Principles of Human Physiology; " Morell's " Outlines
of Mental Philosophy; " Laycock's " Correlations of  Consciousness
and  Organization; " Sir J. K. Shuttleworth's  address before the
Social Science Congress of 1860, on the "Correlation of the Moral
and  Physical  Forces;"  Hinton's "Life  in Nature,"  and "First
Principles " of Herbert Spencer's new  system of Philosophy.  The
first and last of these works are  the only ones, it is believed, that
have appeared in an American  form, and the last is much the
ablest of all;  I was chiefly indebted to it in preparing  the  latter
part of  the introduction.   The biographical notices, brief  and im-
perfect  as they are, it is  hoped may enhance the reader's  interest
in the volume.
   I have been  specially incited to procure the publication of a
work of this  kind, by the same  motive that  has impelled me  to
write upon the subject elsewhere; a conviction of our educational
needs in this direction.  The treatment of a vast subject like this
in ordinary school text-books, is  at best quite too limited for the
requirements of the active-minded teacher; to such, a volume like
the present may prove invaluable.
   But a more serious difficulty is that, until compelled by the de-
mands  of intelligent teachers, the compilers  of school-books will
pass new views entirely by, or give them a mere hasty and  careless
notice, while continuing to inculcate the old erroneous doctrines.
And thus it is that from inveterate habit, or intellectual sluggish-
ness, or a shrewd calculation of the indifference of  teachers, out-
worn and effete ideas continue to drag  through school-books for
half a century after  they have been exploded in the world of liv-
ing science.  He who continues to teach the hypothesis of  caloric,
falsifies  the present truth of science as absolutely as he would do
in teaching the hypothesis of phlogiston; in fact, the  reasons of-
fered for persisting in the  erroneous notions of the materiality of
heat—convenience of teaching, unsettledness of the new vocabu-
lary, &c, are precisely those that were offered for clinging to phlo-
giston,  and rejecting  the  Lavoiserian chemistry of combustion.
Both conceptions have no doubt been of service, but both were
transitional, and having done their work  they become  hindrances 
viii
PEEFACE.
instead of helps.  We can now see that when the true chemistry
of combustion was once reached, the  notion of phlogiston was of
no further  use, and if retained could  only produce confusion and
prevent the reception of correct ideas.   So with caloric, and those
false conceptions of the materiality of forces, which it implies: not
only are  they errors, but the ideas they involve are radically in-
compatible with the higher truths to which science has advanced
so that while the errors are retained the truths cannot be received.
   Nor will  it answer  merely to mention  the new views while
adopting the old, on the plea that the facts  are the same in both
cases.  The facts are very far from being the same in both cases.   It
is precisely because the old ideas are out of harmony with the facts,
and can no longer correctly explain and express them, that new ideas
are sought.   Was not phlogiston abandoned because it no longer
agreed with the facts?   So with the conception of the materiality
of the forces; it contradicts the facts, and therefore, for  scientific
purposes, can no longer  represent them.  In the workshop it may
perhaps be very well to magnify facts, and depreciate their theoreti-
cal explanations, but not in the school-room; the business is here not
working, but thinking.  It is the aim of art to use facts, but of sci-
ence to understand them.  And it is simply because science goes
beyond the fact to its explanation, and is ever striving after  the
highest truth, that it is fitted to discipline the thinking and reason-
ing faculties, and therefore has imperative educational claims.
   In therefore bringing forward these  able and authoritative  ex-
positions in a form  readily accessible  to teachers, I trust I am  not
only doing  them a helpful service, but that they will be led to re-
quire of the preparers of school-books a more  conscientious per-
formance of their tasks, and that  the  interests of sound education
will be thereby promoted.
New Yobk, Oct. 1,1864 
CONTENTS.
                                                       PA8B
Preface,           .....                v
Introduction,    ......             xi

THE CORRELATION OF PHYSICAL FORCES, By W. R  Grove.
         Preface,  .......    3
         I.—Introductory Remarks,   ....       9
         II.—Motion,     .     .      .      .            .   25
        HI.—Heat,......39
        IV.—Electricity,  .     .      .      .      .      .83
         V.—Light,......110
        VI.—Magnetism,  ......  142
       VII.—Chemical Affinity,       ....     152
      VIDI.—Other Modes of Force,       .      .      .      .169
        LX.—Concluding Remarks,    ....     178
         Notes and References,          ....  200

ON   THE  INTERACTION OF  NATURAL  FORCES, By Prof.
           Helmholtz,       ,      .      .      .      .211

REMARKS ON THE FORCES OF INORGANIC  NATURE, By  Dr.
           J. R. Mayer,  .      .      .      .      .      .251 
X                        CONTENTS.
                                                        pag a
ON CELESTIAL DYNAMICS, Br Dr. J. B. Mayek,   .      .     259
         I.—Introduction,       .      .      .      .      .259
        IL—Sources of Heat,.....261
        III.—Measure of the Sun's Heat,  ....  264
        TV—Origin of the Sun's Heat,       .      .      .276
        V.—Constancy of the Sun's Mass,       .      •      •  282
        VI.—The Spots on the Sun's Disc,     .      .      .286
       VII—The Tidal Wave,.....291
      VIII.—The Earth's Interior Heat,       .      .      .     -'JOC

REMARKS ON THE MECHANICAL EQUIVALENT OF HEAT, By
           Dr. J. R. Mayer,    .      .      .      .      .316

SOME THOUGHTS ON THE  CONSERVATION OF FORCE, By Dr.
           Faraday, ......     359

THE CONNECTION  AND EQUIVALENCE OF FORCES, By Prof.
           Liebig,       ......  387

ON THE  CORRELATION  OF  THE PHYSICAL AND  VITAL
           FORCES, By Dr. Carpenter,     .      .      .401
         I.—Relation of Light and Heat to the Vital Forces of Plants, 401
        II.—Relation of  Light and Heat to the Vital Forces of Ani-
              mals,    ......  420 
INTRODUCTION.
   There are many who deplore what they regard as the material-
izing tendencies of modern science.  They maintain that this pro-
found and increasing engrossment of the mind with material ob-
jects is fatal to all refining and  spiritualizing influence.  The cor-
rectness of this conclusion is open to serious question: indeed, the
history of scientific thought not only fails to justify it, but proves
the reverse to be true.   It shows that the tendency of this kind of
inquiry is ever from the material, toward the abstract, the ideal, the
spiritual.
   We may appeal to the oldest and most developed of the sciences
for confirmation of this statement.  The earliest explanations of
the celestial movements were thoroughly and grossly material, and
all astronomic progress has been toward more refined  and ideal
views.   The heavenly bodies were at first thought to be  supported
and carried round in their courses by solid revolving  crystalline
spheres to which they were attached.  This  notion was  afterward
replaced by the more  complex  arid mobile mechanism of epicy-
cles.  To this succeeded the hypothesis of Des Cartes', who rejected
the clumsy mechanical explanation  of revolving wheelwork, and
proposed the more subtile conception of ethereal currents, which
constantly whirled around in vortices, and bore along the heavenly
bodies.  At length the labors of astronomers,  terminating with 
Xll
INTEODUCTTON.
Newton, struck away these crude devices, and substituted the action
of a universal immaterial force.  The course of astronomic science
has thus been on a vast scale to withdraw attention from the mate-
rial and sensible, and to fix it upon the invisible and supersensuous.
It has shown that a pure principle forms the immaterial foundation
of the universe.  From the baldest materiality we rise at last to a
truth of the spiritual world, of so exalted an order that it has been
said 'to connect the mind  of man with the Spirit of God.'
   The  tendency thus illustrated by  astronomy is characteristic in
a marked degree of all modern science.  Scientific inquiries are
becoming  less and  less  questions of matter, and more  and more
questions  of  force; material ideas are giving  place  to  dynamical
ideas.  While the great agencies of change with which it is the
business of science to deal—heat, light, electricity, magnetism, and
affinity,  have been  formerly regarded as kinds of matter ' impon-
derable  elements,'  in distinction from other  material elements,
these notions must now be regarded as outgrown and abandoned,
and in their place we have an order of  purely immaterial forces.
   Toward the  close of the last century the  human mind reached
the great  principle of the indestructiblity of matter.  What the
intellectual activity of ages  had failed  to establish by all  the re-
sources  of reasoning and philosophy, was  accomplished by the in-
vention  of a mechanical implement,  the balance  of  Lavoisier.
When nature was tested  in the chemist's  scale-pan, it was first
found that never an atom is  created  or  destroyed; that  though
matter  changes form with protean facility, traversing a thousand
cycles of  change, vanishing and reappearing incessantly, yet  it
never wears out or lapses into nothing.
   The  present  age will be memorable in the history  of science for
having demonstrated that  the same great principle applies also to
forces, and for the establishment of a  new philosophy concerning
their nature and relations.  Heat, light, electricity, and magnetism
are now no longer regarded  as substantive and independent exist-
ences—subtile fluids with  peculiar properties, but simply as modes 
THE NEW DOCTRINE OF  FORCES.
xiii
of motion in ordinary matter; forms of energy which are capable
of mutual conversion.  Heat is a mode of energy manifested by
certain effects.  It  may be transformed into electricity, which is
another form of force producing different effects.   Or the process
may be reversed; the electricity disappearing and the heat reap-
pearing.   Again, mechanical motion, which is a motion  of masses,
may be transformed into heat or electricity, which is held to be a
motion of the atoms of matter, while, by a reverse process, the mo-
tion of atoms, that is, heat or electricity, may be turned back again
into mechanical motion.  Thus a portion of the heat generated in
a locomotive is converted into the motion of the train, while by
the  application of the brakes the motion of the  train is changed
back again into the heat of friction.
    These mutations are rigidly subject to the laws of quantity.  A
given amount of one force produces a definite quantity of another.
so that power or energy, like matter, can neither be created nor
destroyed: though  ever changing form, its total quantity in the uni-
verse  remains constant and unalterable.   Every manifestation of
force must have come from a preexisting equivalent force, and must
give rise to a subsequent and equal amount of some other force.
When, therefore, a force or effect appears, we are not at liberty to
assume that it was  self-originated, or came from nothing; when  it
disappears we are forbidden to conclude that it is annihilated: we
must search and find whence it came and whither it has  gone; that
is, what produced it and what effect it has itself produced.  These
relations among the modes of energy are currently known by the
phrases  Correlation and Conservation of Force.
    The  present condition of the philosophy of forces is perfectly
 paralleled by  that of the philosophy of matter toward the close of
 the last  century.   So long as it was  admitted  that  matter in its
 various  changes may be created or destroyed, chemical progress
 was impossible.  If, in his processes, a portion of the material dis-
 appeared, the chemist had a ready explanation—the matter was
 destroyed; his analysis was  therefore worthless.  But when  he 
xiv
INTRODUCTION.
started with the axiom that matter is indestructible, all disappear
ance of material during his operations was chargeable to their im-
perfection.   He was therefore compelled to improve them—to ac-
count in his result for every thousandth of a grain with which he
commenced;  and  as a consequence of this  inexorable condition,
analytical chemistry advanced to a high perfection, and  its conse-
quences to the world are incalculable.   Precisely so with the anal-
ysis of forces.  So long as they are considered  capable  of being
created and destroyed, the quest for them will be careless and the
results valueless.  But the moment they are determined to be in-
destructible, the investigator becomes  bound to account for them;
all problems of power are at once affected, and the  science of dy-
namics enters upon a new era.

   The views here briefly stated will be found fully and variously
elucidated in the  essays of the present volume; in these introduc-
tory remarks I propose to offer  some observations on their history
and the extended  scope of their application.
   I have spoken  of the principles of Correlation and Conservation
of Forces as established; it may be well to state the sense in which
this is to be taken.  They have been accepted by the leading scien-
tific minds of all nations with remarkable unanimity; their discus-
sion forms a leading element in scientific literature, while they oc-
cupy the thoughts and guide the investigations of the most philo-
sophical inquirers.  But while science holds securely her new pos-
session as  a fundamental principle, its various  phases  are by no
means completely worked out.  Not only has there been too little
time for  this, even if the views were far less important, but the
questions started lie at the foundation of all branches of science,
and can only be fully elucidated as these advance in their develop-
ment.  The  new doctrine of forces is now in much the  same con-
dition as was the new astronomy of Copernicus.  It is not with-
out  its difficulties, which time  alone must be trusted to remove;
but it simplifies so many problems, clears  up so many obscurities- 
          THE  HISTORY OF SCIENTIFIC  DISCOVERY.       XV

opens so extended a range of new investigations, and contrasts so
strongly with the complexities and incongruities of the older doc-
trines, as to leave little liberty of choice between the opposing theo-
ries. Not only does the reception of these views mark a signal epoch in
the progress of science, but from their comprehensive hearings and
the luminous glimpses which they open into the most elevated re-
gions of speculative  inquiry, they have a profound interest for
many thinkers who give little attention to the specialties of exact
science.
    In the history  of human  affairs there is a growing conception
of the action of general causes in the production of events, and a
corresponding conviction that the part played by individuals has
been much exaggerated, and is far less controlling and permanent
than has been hitherto supposed.  So also in the history of science
it is now acknowledged that the progress  of discovery is much
more independent  of the labors of particular persons than has been
formerly admitted.  Great discoveries belong not so much to indi-
viduals  as to humanity; they are less inspirations  of genius than
births of eras.   As there has been a definite intellectual progress,
thought has  necessarily been limited to the subjects successively
reached.  Many minds have  been thus occupied at the same time
with similar ideas, and hence the simultaneous discoveries of inde-
pendent inquirers,  of which the history of science is so full. Thus
at  the  close of the sixteenth century, philosophers had  entered
upon the investigation of, the laws of motion, and  accordingly we
find Galileo,  Benediti, and Piccolomini proving independently that
all bodies fall to the earth with equal velocity, whatever  their size
or  weight.  A century after, when  science had advanced to the
systematic application of the higher  mathematics to general phys-
ics, Newton and Leibnitz discovered independently  the differential
calculus.  A hundred years  later questions of molecular physics
and chemistry were reached, and oxygen was  discovered simulta-
neously by Priestley and Scheele, and the composition of water by
Cavendish and  Watt.   These discoveries were made because the 
XVI
INTRODUCTION.
 periods were ripe for them, and we cannot doubt that if those who
 made them had never lived, the labors of others would have speed
 ily attained  the  same results.  The  discoverer is, therefore, in a
 great degree, but the mouthpiece of his time.  Some discern clearly
 what is dimly shadowed forth to many; some work out the results
 more completely than others, and some seize the coming thought
 so long before it is developed in the general consciousness, that
 their announcements are unappreciated and unheeded.  This view
 by no means robs the discoverer of his honors,  but it enables us to
 place upon them a juster  estimate, and to pass  a more  enlightened
 judgment upon the rival claims which are constantly arising in the
 history of science.
   Probably the most important event in the general  progress of
 science was the transition from the speculative to the experimental
period.  The ancients were prevented from  creating science by a
 false intellectual  procedure.  They believed they could  solve all the
problems  of the universe by thought alone.  The  moderns have
found that for this purpose meditation is futile unless accompanied
by observation and experiment.  Modern science, therefore, took its
rise in a change of method, and the adoption of the principle that
the discovery of  physical truth consists not in its mere logical but
in its experimental establishment.   It is now an axiom that not he
who guesses, though he guess aright, is to be adjudged the true dis-
 coverer, but he who demonstrates the new truth, and thus compels
its acceptance into the body of valid knowledge.
   Now the later doctrines of the constancy and relations of forces,
and that heat is a kind of motion among the minuter parts  of mat-
ter, have had their twofold phases of  history, corresponding to the
two methods of inquiry.   They had an early and vague recognition
among many philosophers, and  may be traced  in the writings  of
 Galileo, Bacon, Newton,  Locke, Leibnitz,  Des  Cartes, Bernoulli,
 Laplace, and others; but they were held by these thinkers as un-
verified and fruitless speculations, and the subject awaited the gen-
ius that could deal with it according to the more effective methods
 of modern science. 
      SKETCH OF  THE  CAREER  OF COUNT  EOIFORD.    XVH

   It was this country, widely reproached for being over-practical,
which produced just that kind of working ability that was suited
to translate this profound question from the barren to the fruitful
field of inquiry.  It is a matter of just national pride that the two
men who  first demonstrated  the capital propositions of pure sci
ence, that lightning is but a case of common electricity, and that
heat is but a mode of motion—who first converted these proposi-
tions from conjectures of fancy to  facts of science, were not only
Americans by birth and education,  but men eminently representa-
tive  of the peculiarities of American  character—Benjamin Frank-
lin and Benjamin Thompson, afterwards known as Count Rumford.
The  latter philosopher is less  known than the former, though his
services to science and society were probably quite as great.  The
prominence which his name now occupies in connection with tho
new views of heat, and the relations of forces, make it desirable to
glance briefly  at his career.

   Benjamin  Thompson was born at  Woburn, Mass., in  1753.  Ho
received the rudiments of a common school education; became a
merchant's apprentice  at twelve, and subsequently taught school.
Having a strong-taste for mechanical  and chemical  studies, he cul-
tivated them assiduously during his leisure time.  At seventeen he
took charge of an  academy in the village of Rumford  (now Con-
cord), N. H., and  in 1772  married  a wealthy widow, by whom  he
had  one daughter.   At the outbreak of revolutionary hostilities he  ^
applied  for a  commission in  the American  service, was charged
with toryism, left the country in  disgust, and went  to England,
His talents were there  appreciated,  and he took a responsible  posi-
tion under the government, which he held for some years.
   After  receiving the honor of knighthood he left England and
entered the service of the elector  of Bavaria,  ne settled in Mu-
nich in 1784,  and was appointed  aide-de-camp and chamberlain to
the Prince.  The labors which he now undertook were of the most
extensive  and  laborious character, and could never have been ac- 
xvm
INTRODUCTION.
complished but for the rigorous habits of order which he  carried
into all his pursuits.  He reorganized the entire military establish-
ment of Bavaria, introduced not only a simpler code of tactics, and
a new system of order, discipline, and  economy among the troops
and industrial schools for the soldiers' children, but greatly im-
proved the construction and modes of manufacture of arms and
ordnance.  Ho suppressed the system of beggary which had grown
into a recognized profession in Bavaria, and become an enormous
public evil—one of the most remarkable social reforms on  record.
He also  devoted himself to various ameliorations, such as improv-
ing the construction and arrangement of the dwellings of the work-
ing classes, providing for them a better education, organizing houses
of industry, introducing superior breeds of horses and cattle, and
promoting landscape-gardening, which he did by converting an old
abandoned hunting-ground near Munich into  a park, where, after
his departure, the inhabitants erected a monument to his honor.
For these services Sir  Benjamin Thompson received  many distinc-
tions, and among others was made Count of the holy Roman Empire.
On receiving this dignity he chose a title  in  remembrance of the
country of his nativity, and was thenceforth  known as  Count of
Rumford.
   His health failing from excessive labor and what he considered
the unfavorable climate, he came back to England in 1798, and had
serious thoughts of returning to the  United  States.  Having re-
ceived from the American government the  compliment of a formal
invitation to revisit  his  native land, he wrote to an  old friend re-
questing him to look  out for a " little quiet retreat" for  himself
and daughter in the vicinity of Boston.  This intention, however,
failed, as he shortly after became involved in the enterprise of
founding the Royal Institution of England.
    There was in Rumford's character a happy combination of phi-
lanthropic impulses, executive power in carrying out great projects
and versatility of talent in physical research.  His scientific inves-
tigations were largely guided and determined by his philanthropic 
          SCIENTIFIC  LABORS OF COUNT RUMFORD.      XIX

plans and public duties,   nis interest in the more needy classes led
him to the assiduous study of the  physical wants of mankind, and
the best  methods of relieving them;  the laws and domestic  man-
agement  of heat accordingly engaged a largo share of his attention.
Ho determined the amount of heat arising from the combustion of
different  kinds of fuel, by means  of a calorimeter of his  own in-
vention.  He  reconstructed the  fireplace,  and so improved the
methods  of heating apartments and cooking food as to produce a
saving in the precious element, varying from one-half to seven-
eighths of the fuel  previously consumed.  He improved  the con-
struction of stoves, cooking ranges, coal  grates, and chimneys;
showed  that the non-conducting  power of cloth  is  due to the  air
enclosed  among its fibres, and first pointed out that mode of action
of heat called convection;  indeed he was the first  clearly to dis-
criminate between the three modes of propagation of heat—radia-
tion, conduction, and convection.   He determined the almost per-
fect non-conducting properties of liquids, investigated the produc-
tion of light,  and invented a mode  of measuring it.  He was the
first to  apply steam generally to the warming of fluids and the
culinary  art;  he experimented upon the use of gunpowder, the
strength  of materials, and the maximum density of water, and
made many valuable and original  observations upon an extensive
range of subjects.
   Prof. James D. Forbes, in his  able Dissertation  on the recent
Progress of the Mathematical  and Physical  Sciences, in the last
edition of the Encyclopedia Britannica, gives a full account of  Rum-
ford's contributions to science, and remarks:
   " All  Rumford's experiments were made with admirable precis-
ion,  and  recorded with elaborate fidelity, and in the plainest lan-
guage.   Every thing with him was reduced to weight and  meas-
ure,  and  no pains were spared to attain the best results.
   " Rumford's name will be ever connected with the progress of
science in England  by two circumstances:  first, by the foundation
of a perpetual  medal  and prize in the  gift of the  council of the
              B 
XX
INTRODUCTION.
Royal Society of London, for the reward of discoveries connected
with heat and light; and secondly, by the establishment in 1800 of
the Royal Institution in London, destined, primarily, for the pro
motion of original discovery, and, secondarily, for the diffusion of a
taste for  science among the educated classes.   The plan was con-
ceived with the sagacity which characterized Rumford, and its suc-
cess has been greater than could have been anticipated.  Davy was
there brought into notice by Rumford  himself, and furnished with
the means of prosecuting his admirable experiments.   He and Mr.
Faraday have given to that  institution its just  celebrity with little
intermission for half a century."
    Leaving England, Rumford took up his residence in France, and
the estimation in which he  was held may be judged of by the fact
that he was  elected one of the eight foreign  associates of the Acad-
emy of Sciences.
    Count Rumford bequeathed to  Harvard  University the funds
for endowing its professorship of the Application of Science to the
Art of Living, and instituted a prize to be awarded by the Ameri-
can Academy of Sciences, for the most important discoveries and
improvements relating to heat and  light.   In 1801 he married the
widow of the celebrated chemist Lavoisier, and with her retired
to the villa of Auteuil, the residence of her former husband, where
he died in 1814.

    Having thus glanced briefly  at his career, I now pass to the dis-
covery upon which Count Rumford's fame in the future will chiefly
rest.   It is described in a paper published in the transactions of the
Royal Society for 1798.
    He was  led to it while superintending the operations of the
Munich arsenal, by observing the large amount of heat generated
in boring brass cannon.  Reflecting upon this, he proposed to him-
 self the following questions: " Whence comes the heat  produced
 in  the mechanical operations above mentioned ?"  " Is it furnished
 by the metallic chips which are separated from the metal ?" 
        RUMFORD'S  EXPERIMENTAL INVESTIGATIONS.      xxi

   The common hypothesis affirmed  that the heat produced had
been latent in the metal, and had been forced out by condensation
of the chips.  But if this were the case the capacity for heat of the
parts of metal so reduced to chips ought not only to be changed,
but the change undergone by them should be sufficiently great to
account for all the heat produced.  With a fine saw Rumford then
cut away slices of the unheated metal, and found that they had ex-
actly the same capacity for heat as the metallic chips. No change
in this respect had occurred, and it was thus conclusively proved
that the  heat generated could  not  have been held  latent in the
chips.  Having settled this preliminary point, Rumford proceeds to
his principal experiments.
    With the intuition  of the true  investigator, he remarks that
" very interesting philosophical  experiments may often be made,
almost without trouble or expense, by means of machinery con-
trived for mere mechanical purposes of the arts and manufactures."
Accordingly, he  mounted a metallic cylinder  weighing  113.13
pounds avoirdupois, in a horizontal position.  At  one end there was
a cavity three and a half inches in diameter, and into this was in-
troduced a borer, a flat  piece of hardened steel,  four inches long,
0.63 inches thick, and nearly as wide as the cavity, the area of con-
tact of the borer with the cylinder  being two and a half inches.
To measure the heat developed, a small  round hole was  bored in
the cylinder near the bottom of the  cavity, for the  insertion of  a
small mercurial thermometer.  The borer was pressed against the
base of the cavity with a force of 10,000 pounds, and the cylinder
made to revolve by horse-power at the rate of thirty-two times per
minute.  At  the beginning of the experiment tne temperature of
the air in the shade  and also in the  cylinder was 60°F. at the end
of thirty minutes, and after the cylinder had made 960 revolutions
the temperature was found to be 130'F.
    Having taken away the borer, he found that  839  grains  of me-
tallic dust had been cut away.   " Is it possible," he exclaims, " that
the very considerable quantity of heat produced in this experiment 
XXII
INTRODUCTION.
—a quantity which actually raised the temperature of upward uf
113 pounds of gun metal at least 70', could have been furnished by
so inconsiderable a quantity of metallic dust, and this merely in
consequence of a change in the capacity for heat? "
   To  measure more precisely the heat  produced, he next  sur-
rounded his cylinder by an oblong wooden box in such a manner
that it  could turn water-tight in the centre of the box, while the
borer was pressed against the bottom.  The box was  filled with
water until the entire cylinder was covered, and the apparatus was
eet in action. The temperature of the water on commencing was
60'.  He remarks, " The  result of this beautiful  experiment was
very striking, and the pleasure it afforded amply repaid me for all
the trouble I had taken in contriving and arranging the complicated
machinery used in making it.   The cylinder  had been in motion
but a short time when I perceived, by putting  my hand  into the
water and touching the outside of the cylinder, that heat was gen-
erated."
   As  the work continued the temperature gradually rose; at two
hours and twenty minutes  from the beginning of the operation, the
water  was at 200°, and in ten minutes more  it actually boiled 1
Upon this result Rumford observes, "It would  be difficult to de-
scribe the surprise and astonishment expressed in the countenances
of the  bystanders, on seeing so large  a  quantity of water heated
and  actually made to boil without  any fire.  Though  there was
nothing that could be considered very surprising in  this matter,
yet I acknowledge fairly that  it afforded me  a  degree of childish
pleasure which, were I ambitious of the reputation of a grave phi-
losopher, I ought most certainly rather to hide than to discover."
   Rumford estimated the total heat generated as sufficient to raise
26.58 pounds of ice-cold water 180°, or to its boiling point; and he
adds, " from the results of these  computations, it appears  that the
quantity of heat produced equally or in a continuous stream, if I
may use  the expression, by the friction of the  blunt steel borer
against the bottom of the hollow metallic  cylinder, was greater 
     rumford's lnferences from nis experiments,   xxiii

 than that produced in the combustion of nine wax  candles, each
 three-quarters of an inch in diameter, all  burning together with
 clear bright flames."
    " One horse would have been equal  to the work  performed,
 though two were actually employed.  Heat may thus be produced
 merely by the strength of a horse,  and in a case  of  necessity this
 might  be used in cooking victuals.   But no  circumstances could bo
 imagined in which this method of producing heat could be advan-
 tageous,  for more heat might be obtained by using the fodder ne-
 cessary for the support of the horse, as fuel.
    " By  meditating on the results of all these experiments, we are
 aaturally brought to that great question which has  so often been
 the subject of speculation  among  philosophers, namely, What is
 heat?  Is there such a thing as an igneous fluid?   Is there any
 thing that with propriety can be called caloric ?
    " We have seen that a very considerable quantity of heat may
 be excited by the friction of two metallic surfaces, and given off in
 a constant stream or flux in all directions, without interruption or
 intermission, and without any signs of diminution or exhaustion.
 In reasoning on this subject we must not forget that most  remark
 able circumstance, that the source of the heat generated by friction
 in these experiments appeared  evidently to be inexhaustible.  (The
 italics  are  Rumford's.)   It is hardly necessary to add, that any
 thing which  any insulated body or system of bodies  can  continue
 to furnish without  limitation, cannot possibly be a material sub-
stance ; and it appears to me to be extremely difficult, if not  quite
impossible, to form any distinct idea of any thing capable  of being
excited and communicated in  those experiments, except it be mo-
tion."
   No one  can  read the remarkably able  and lucid paper from
which  these extracts are taken, without being struck with the per-
fect distinctness with which the problem to be solved was pre-
sented, and the systematic and conclusive method of its treatment.
Rumford kept strictly within the limits of legitimate inquiry, which 
XXIV
INTRODUCTION.
no man can  define better  than he did.  "I am very far from pre-
tending to know how, or by what means or mechanical contri-
vances, that particular kind of motion in bodies, which has been
supposed to  constitute heat, is exerted, continued, and propagated.
and I shall not presume to trouble the  Society with  new conjec-
tures.  But  although the mechanism of heat should in part be one
one of  those mysteries of  nature, which are beyond the reach of
human intelligence, this ought by no means to  discourage us, or
even lessen our ardor in our attempts to investigate the laws of its
operations.  How far can we  advance in any of the  paths which
science has  opened to us, before we  find ourselves enveloped in
those thick  mists, which on every side bound the  horizon of the
human intellect."
   Rumford's experiments completely annihilated the  material hy-
pothesis of heat, while the modern doctrine was stated in explicit
terms.   He  moreover advanced the question to its quantitative and
highest stage, proposing to find the  numerical  relation  between
mechanical power and heat, and  obtained a result remarkably near
to that finally established.  The English unit of force is the foot-
pound, that is, one pound falling through one foot of space; the
unit of heat is one pound of water heated 1° F.  Just fifty years
subsequently to the experiment  of Rumford, Dr. J. P. Joule,* of
Manchester, England, after a most  delicate and elaborate  series of
experiments, determined that 772 units of force  produce  one unit
of heat;  that is, 772 pounds falling through one  foot produces suf-
ficient  heat  to raise one pound of water 1° F.  This law is known
as the mechanical equivalent of heat.  Now, when we throw Rum-
ford's results into these terms, we find that about 940 units of force
produced a unit of heat, and that, therefore, on  a large scale and
at the very first trial, he came within twenty per  cent, of the truo

  * James I'kescott Joule, born December 24th, 1818, at Salford, near Manchester,
England, •where he pursued the  occupation of  a brewer.  Long and deeply devoted
to scientific investigation, he became a member of the Manchester Philosophical So-
ciety in 1842, and of the Eoyal Society of London in 1850. 
              SUMMARY  OF RUMFORD S CLAIMS.         XXV

statement.  No account was taken  of the heat lost by radiation,
which, considering the high temperature  produced, and the dura-
tion of the experiment, must, have been  considerable;  so  that as
Rumford himself noticed, this value must be too high.  The  ear-
liest numerical results in science are rarely more than rough ap-
proximations,  yet  they may guide to the establishment  of great
principles.  Certainly no one could question Dalton's claim to the
discovery of the law of definite  proportions,  because of the inac-
curacy of the  numbers upon which he first rested it.
   We are called further  to note that Rumford's ideas upon the
general subject of forces were far in advance of his age.  He saw
the relation of all friction to heat, and.suggested that of fluids, by
churning processes, as  a  means of producing it—precisely the
method finally employed by Joule in  estabhshing the mechanical
equivalent  of heat.  He furthermore regarded  animals  dynami-
cally, considering  their force as the derivative of then* food, and
therefore as not created.  That  Rumford held these views in the
comprehensive and matured sense in which they are  now enter-
tained is, of course, not asserted.  The  advance from his day to
ours has  been prodigious.  Whole sciences have been created,
which afford  the most  beautiful exemplifications of the new doc-
trines.  Those doctrines have received their subsequent  develop-
ment in various directions by many minds, but we may be allowed
to question if  the contributions of any of their promoters will sur-
pass, if indeed they will equal, the value and importance which we
must assign to the first great experimental step in the new direc-
tion.
   The claims of Rumford may be summarized as follows:

   I. no was  the man who first took the question of the nature
        of heat out of the domain of motaphysics, where  it had
        been  speculated upon  since the time of Aristotle, and
        placed it upon the true basis of physical experiment.

   II. Ho first proved  the insufficiency of the current explanations 
XXVI
INTRODUCTION.
       of the sources of heat, and demonstrated the falsity of the
       prevailing view of its materiality.

 in. He first estimated the quantitative relation between the heat
       produced by friction and that by combustion.

 IV. He first showed the quantity of heat produced by a definite
       amount of mechanical work, and arrived at a result re-
       markably near the finally established law.

  V. He pointed out other methods to be employed in determining
       the amount of heat produced by the expenditure  of me-
       chanical  power, instancing  particularly the  agitation  of
       water, or other liquids, as in churning.

 VI. He regarded the power of animals as due to their food, there
       fore as having a definite  source and not created, and thus
       applied his views of force to the organic world.

VII. Rumford was the first to demonstrate the quantitative con-
       vertibility of force in an important case,  and the  first to
       reach, experimentally, the fundamental conclusion that heat
       is but a mode of motion.

   In his late work upon  heat,  Prof. Tyndall, after quoting co-
piously from Rumford's paper, remarks: " When the history of the
dynamical theory of heat is written, the man who in opposition to
the scientific belief of his time could experiment, and reason  upon
experiment, as did Rumford in the investigation here referred to,
cannot be lightly passed over."   nad other  English writers been
equally just, there would have been less necessity for the foregoing
exposition of  Rumford's labors and  claims;  but there has  been a
manifest disposition in various quarters to obscure and depreciate
them.  Dr. Whewell, in his history of  the Inductive Sciences,
treats the subject of thermotics without mentioning him.  An em-
inent Edinburgh  professor, writing recently in the Philosophical
Magazine, under the confessed  influence of  'patriotism,'  under- 
           DAVY'S  RELATION TO THE QUESTION.      XXVli

takes to make the dynamical theory of heat an English monopoly,
due  to  Sir  Isaac  Newton,  Sir Humphry  Davy, and  Dr. J. P
Joule;  while an able writer in a late number of the North  British
Review, in sketching the historic progress of the new views, puts
Davy forward as  their founder, and assigns  to Rumford a minor
and subsequent place.
   Sir Humphry  Davy, it is well known, early rejected the caloric
hypothesis.  In 1799, at the age  of twenty-one, he published  a
tract at Bristol, describing some ingenious experiments upon the
subject.  It was the  publication  of this pamphlet which brought
him  to Rumford's notice, and resulted in his subsequent connection
with the Royal Institution.  But Davy's ideas upon the question
were far from  clear,  and will bear no  comparison with those of
Rumford, published the year before.  Indeed his eulogist remarks:
"It is certain that even Davy himself was led astray in his argu-
ment by using  the hypothesis of change of capacity as the basis
of his reasoning, and that he might have been met successfully by
any able calorist, who, though maintaining the materiality of heat,
might have been willing to throw overboard one or two  of the less
essential tenets of his school of philosophy."  It was not till 1812
that  Davy wrote  in  his Chemical Philosophy, " The immediate
cause of the phenomena of heat then is motion, and the laws of its
communication are precisely the same as those of the communica-
tion  of motion."  When, therefore, we remember that Davy's first
publication was subsequent to that  of Rumford's, that he confined
himself to the narrowest point of the subject, the simple question
of the existence of caloric;  and that he  nowhere gives evidence
of having the slightest notion of the quantitative relation between
mechanical force and heat, the futility of the claim which would
make him the  experimental founder of the  dynamical  theory, is
abundantly apparent.
   The inquiries opened by Rumford and Davy were not formally
pursued by the  succeeding generation.  Even the powerful adhe-
Bion of Dr. Thomas Young—perhaps the  greatest mind in science 
XXV11I
INTRODUCTION.
since Newton—failed to give currency to the new views.   But the
salient and impregnable demonstration of Rumford, and the ingen-
ious experiments of Davy, facts which could neither be evaded nor
harmonized with the prevailing errors, were not without influence.
That there was a general, though unconscious tendency toward a
new philosophy of forces, in the early inquiries of the present cen-
tury, is shown by the fact that various  scientific men  of different
nations, and with no knowledge  of each other's labors, gave ex-
pression to  the same views at about the same time.  Grove and
Joule of England,  Mayer of Germany,  and Colding of Denmark,
announced the general doctrine of the mutual relations of the forces,
with more  or less  explication,  about 1842, and Seguin of France,
it is claimed, a little earlier. From this time the subject was closely
pursued, and the names of Helmholtz, Holtzman, Clausius,* Faraday,
Thompson, Rankine,t Tyndall, Carpenter, and others are intimately
associated with its advancement.  In this country Professors Henry J
and Leconte § have contributed to illustrate the organic phase of the
doctrine.
    I cannot here  attempt an  estimate of the  respective shares
which  these men have had in constructing the new theories; the
reader will  gather various intimations  upon  this point from the
succeeding essays.  The foreign periodicals, both scientific and lit-
erary,  show that the question is being thoroughly sifted, and mate-
rials accumulating for the future history of the subject.  The para-
mount claims are, however, those of Joule, Mayer,  and Grove.
   * Classics, Rudolph Julius Immanuel -was born at COslin, Pommern, January
22,1822.  lie became Professor of Philosophy and Physics in the Polytechnic School
at Zurich in 1855, and then Professor of the Zurich University (1857). He was after-
wards teacher of Physics and Artillery in the School of Berlin, and then private
teacher of the University of that place.
   t Eankine, William John  Macqttoen was born at Edinburgh, July 5,1820.  He
is a civil engineer in Glasgow, a member of the Philosophical Society at that place,
and of the Royal Society of London.
   % See the article " Meteorology," in the Agricultural Report of the Patent Office, for
t8DT.
   § See the American Journal of Science for Nov. 1859. 
           CLAIMS OF JOULE, GROYE, AND MATER.      XXIX

    According to the strict rule of science, that in all those cases
 where experimental proof is possible, he who first supplies it is the
 true discoverer, Dr. Joule must be assigned the foremost place
 among the modern investigators of the subject.  He dealt with the
 whole question upon the basis of experiment.  He labored with
 great perseverance and skill to determine the mechanical equivalent
 of heat—the corner-stone of the edifice; and in accomplishing  this
 result in 1850, he may be said to have matured the work of Rumford,
 and finally established upon an experimental basis the great law of
 thermo-dynamics,  to remain a demonstration of science forever.
    Professor Grove has also worked out the subject in his own in-
 dependent way.   Combining original experimental  investigations
 of great acuteness, with the philosophic employment of  the gen-
 eral results of science, he was the first to give complete and system-
 atic expression to the new views.  His  able work, which  opens
 the present series, is an authoritative exposition, and an acknowl-
 edged classic upon the subject.
    Again,  the claims of Dr. Mayer to an eminent  and  enviable
 place among the pioneers of this great scientific movement, are  un-
 questionable.  There has evidently been, on the part  of some Eng-
 glish  writers, an  unworthy inclination  to depreciate his merits,
 which has given rise to a sharp and, searching  controversy.  The
 intellectual rights of the German  philosopher have, however, been
 decisively vindicated by the chivalric pen of Prof. Tyndall; and it
 is to the public interest thus excited, that we are indebted for  the
 translation of Mayer's papers, which appear in this volume.  Mayer
 did not experiment to the extent of Joule  and Grove, yet he well
 knew its importance, and made such investigations as his apparatus
 and the duties of a laborious profession would  allow.   Yet  his
 views were not therefore mere ingenious and probable conjectures.
 Master of the results of modern science, and of the  mathematical
methods of dealing with them,  possessing a  broad philosophic
grasp, and  an extraordinary mental pertinacity,  Dr. Mayer entered
early upon the inquiry, and not only has he developed many of its 
XXX
INTRODUCTION.
prime  applications in advance  of any other thinker, but he has
done his work under circumstances  and  in a manner which  awa-
kens the highest admiration for his genius.*

    An eminent authority has remarked (that tl ese discoveries open
a region which  promises  possessions richer  than  any hitherto
granted to the intellect of man.'   Involving as they do a revolution
of fundamental  ideas, their  consequences must  be as comprehen-
sive as the range of human thought.   A principle has been devel-
oped of all-pervading application, which brings  the diverse and
distant branches of knowledge into more intimate and harmonious
alliance, and affords a profounder insight into the universal order.
Not only is science itself deeply affected by the presentation of its
questions,  in new and  suggestive lights, but its method is at once
made universal.   There is a  crude notion in many minds, that it jg
the  business of  science to  occupy itself merely with the study of
matter. When, hitherto, it has pressed its inquiries into the higher

  * Prof. Tyndall remarks: "Mayer  probably had not the means of making experi-
ments himself, but he ransacked the records of experimental science for his data, and
thus conferred upon his writings a strength which mere speculation can never possess.
From the extracts which I have given,  the reader may infer his strong desire for quan-
titative accuracy, the clearness of his insight, and the firmness of his grasp.  Regard-
ing the recognition which will be ultimately accorded to Dr. Mayer, a shade of trouble
or doubt has never crossed my mind.  Individuals may seek to pull him down, but
their efforts will be unavailing as long as such evidence of his genius exists,  and as
long as the general mind of humanity is influenced by considerations of justice and
truth.
  " The paucity of facts in  Mayer's time has  been urged as if it were a reproach to
him; but it ought to be remembered that the quantity of fact necessary to a generaliza-
tion is different for different  minds. 'A woid  to the wise is sufficient for them,'' and
a single fact  in  some minds bears fruit that  a hundred cannot produce in others.
Mayer's data were comparatively scanty, but his genius went far to supply the lack of
experiment, by enabling him to see  clearly the bearing of such facts as he possessed.
They enabled him to think out the law of conservation, and his conclusions received
the stamp of certainty from the subsequent experimental labors of Mr. Joule.   In ref-
erence to their comparative merits, 1 would say that as Seer and Generalize^ Mayer,
In my opinion, stands first—as experimentalphiloi opher, Joule," 
THE TRUE  SCOPE OF  SCIENCE.
xxxi
region of life, mind, society, history, and education, the traditional
custodians of these subjects have bidden it keep within its limits
and  stick to matter.  But  science is not to be hampered by this
narrow conception; its office is nothing less than to investigate the
laws  and universal relations of force, and its domain is therefore
coextensive with the display of power.  Indeed, as we know noth-
ing of matter, except through its manifestation of forces, it is ob-
vious that the  study of matter itself is at last resolved into  the
study of forces.   The establishment of a now philosophy of forces,
therefore, by its vast  extension of the scope and  methods  of  sci-
ence, constitutes a momentous event of intellectual progress.
   The discussions  of the present volume will make fully apparent
the importance of the new doctrines in relation to physical science,
but their higher implications are but  partially unfolded.  In  the
concluding article Dr. Carpenter has shown the applicability of the
principle of correlation to vital phenomena.  His argument is of
interest, not only because of the facts  and principles established,
but as opening an  inquiry which must lead to still  larger results:
for, if  the  principle  be found operative in fundamental  organic
processes, it will undoubtedly be traced in those which are higher;
if in the lower sphere of life, then throughout that sphere.   If  the
forces are correlated in organic growth and nutrition, they must be
in organic  action;  and thus human activity, in all its forms, is
brought within  the operation of the law.  As a creature of or-
ganic nutrition, borrowing matter and force  from the outward
world;  as a being of feeling and sensibility, of intellectual power
and multiform activities, man must be regarded as  amenable to  the
great law that forces  are convertible and indestructible; and as
psychology and sociology—the science of mind and  the science of
society—have to deal  constantly with different phases and forma
of human energy, the new principle must be  of  the  profoundest
import in relation to these great subjects.
   The forces manifested in the living system are of the most
varied and unlike character, mechanical, thermal, luminous, electric, 
xxxn
INTRODUCTION.
chemical, nervous, sensory, emotional, and intellectual.  That these
forces are perfectly coordinated—that there is some definite relation
among them which explains the marvellous dynamic unity of tho
living organism, does not admit of question.  That this relation is
of the same nature as that which is found tc exist among tho
purely physical forces, and which is expressed by the term ' Correl-
ation,' seems also  abundantly evident.   From the great complex-
ity of the conditions, the samo exactness will  not,  of course, be
expected here as in the inorganic field, but this is one of the neces-
sary limitations of all physiological and psychological inquiry; thus
qualified  the proofs of the correlation of the nervous and mental
forces with the physical, are as clear and  decisive a3 those for the
physical forces alone.
   If a current of electricity is  passed through a small wire it
produces heat, while if heat is applied to a certain combination of
metals, it reproduces a  current  of electricity; those  forces  are,
therefore, correlated.  A current of electricity passed through a
small portion  of a motor or sensory nerve will excite the nerve
force in the  remainder, while, on the other hand, as is shown in the
case of  the torpedo,  the nerve-force  may generate  electricity.
Nerve-force may produce heat, light, electricity, and, as  we con-
stantly experience, mechanical power, and these in their turn may
also excite nerve-force.  This form of energy is  therefore clearly
entitled to a place in the order of correlated agencies.
    Again, if we take the highest form of mental action, viz.:  will-
power, we find that while it commands  the movements of the sys-
tem, it does  not act directly upon the muscles, but upon the cerebral
hemispheres of the  brain.  There is a dynamic chain  of which
voluntary power is but one link.   The will  is a power which excites
nerve-force in the brain, which again excites mechanical power in
the muscles.  Will-power is therefore correlated with nerve-power
in the same manner as the  latter is with  muscular power.  Dr.
Carpenter well observes:  "It is difficult to see  that the dynamical
agency which we term will is more removed from nerve-force on 
     CORRELATION OF NERVOUS AND MENTAL FORCES.  XXX111

the one hand than nerve-force is removed from motor force on the
other.  Each, in giving origin  to the next, is  itself expended or
ceases  to exist as such, and each bears, in  its own intensity, a pre-
cise relation to that of its antecedent and its consequent."  We have
here only space  briefly to trace the principle in its application to
Bensations,  motions, and intellectual operations.
   The physical agencies  acting upon inanimate objects  in the
external world, change  their form and state,  and we regard theso
changes as transformed manifestations of the forces in action.  A
body is heated by hammering; the heat is but transmuted mechani-
cal force;  or a body is put in motion by heat, a certain quantity
being transformed into mechanical effect, or motion of the mass.
And so it is held that no force can arise except by the  expenditure
of a preexisting force.  Now, the living system is acted upon by
tho  same agencies and under  the same  law.  Impressions made
upon the organs of sense  give rise to sensations, and we have the
same warrant in this, as in the former  case, for regarding the effects
as  transformations of  the forces  in action.  If the change  of
molecular state in a melted body represents the heat  transformed
in fusing  it, so the sensation  of warmth in a living body  must
represent the heat transformed in producing it.  The impression on
the retina,  as well as that on the  photographic  tablet,  results from
the transmuted impulses of fight.  And thus impressions made
from moment to moment on all  our  organs  of sense,  are directly
correlated with external physical  forces.   This correlation, further-
more,  is quantitative as well as  qualitative.    Not only does the
light-force produce its peculiar sensations, but the intensity of these
sensations  corresponds with the intensity of the force; not only is
atmospheric vibration transmuted into the sense of sound,  but the
energy of  the vibration determines its loudness."  And so in all
other  cases; the quantity of sensation depends upon the quantity
of the force  acting to produce it.
    Moreover, sensations do not  terminate in themselves, or come
to nothing;  they produce  certain correlated and equivalent effects. 
XXXIV
INTRODUCTION.
The feelings of light, heat, sound, odor,  taste,  pressure, are im-
mediately followed by physiological effects, as secretion, musculai
action, &c.  Sensations increase the contractions of the  heart, and
it has been lately maintained that every sensation contracts the
muscular fibres throughout the whole vascular system.   The  res-
piratory muscles also respond to  sensations;  the rate of breathing
being increased by both pleasurable and painful nerve-impressions.
The quantity of sensation, moreover, controls the quantity of emo-
tion.  Loud sounds produce violent starts,  disagreeable tastes cause
wry faces, and  sharp  pains give rise  to violent  struggles.  Even
when groans and cries are suppressed, the clenched hands and set
teeth  show that the muscular excitement is only taking another
direction.
   Between  the emotions and bodily actions the correlation and
equivalence are also equally clear.  Moderate actions, like moderate
sensations, excite the  heart, the vascular system, and the glandular
organs.  As  the emotions rise in strength,  however, the various
systems of muscles are thrown into action; and when they reach a
certain  pitch of intensity, violent convulsive movements  ensue.
Anger frowns and stamps; grief wrings its hands; joy dances and
leaps—the amount of sensation determining the quantity of correla-
tive movement.
   Dr. Carpenter, in his Physiology, has brought forward numerous
exemplifications of this principle of the conversion of emotion  into
movement, as seen in the common workings of human nature.
Most persons have experienced the difficulty of sitting still  under
high excitement of the feelings, and also the relief afforded by
walking or active exercise; while, on the other hand, repression of
the movements  protracts the emotional excitement. Many irascible
persons get relief from their irritated feelings by a hearty explosion
of oaths, others by a violent slamming of the door, or a prolonged
fit of grumbling.   Demor strative  persons habitually expend their
feelings in action, while those who manifest them less retain them
longer:  hence  the former are more weak and  transient in their 
    CORRELATION OF  PHYSICAL  AND MENTAL FORCES.  XXXV

attachments than the latter, whose unexpended  emotions become
permanent elements of character.  For the same reason, those wno
are loud and vehement  in their lamentations seldom die of grief;
while the  deep-seated  emotions of sorrow  which others cannot
work off in.violent demonstrations, depress the organic functions,
and often wear out the life.
   Tho intellectual operations  are also directly correlated with
physical  activities.  As in the inorganic world we know nothing
of forces except as exhibited by matter, so in the higher intellectual
realm we know nothing of mind-force except through its material
manifestations.  Mental operations are  dependent upon material
changes in the nervous system;  and it  may  now be regarded as a
fundamental physiological principle, that " no idea or feeling can
arise, save  as the result of some physical  force expended in pro-
ducing it."  The directness of  this dependence  is proved by the
fact that any disturbance  of the train of cerebral transformations
disturbs mentality,  while  their arrest destroys it.  And here, also,
the correlation is quantitative.   Other things being equal there is a
relation between  the  size of the nerve apparatus and the amount
of mental  action of which it is capable.  Again, it  is dependent
upon the vigor of the  circulation; if this is arrested by the cessation
of the heart's action, total  unconsciousness results; if it is enfeebled,
mental action is low;  while if it is quickened, mentality rises, even
to delirium, when the cerebral activity becomes excessive.  Again,
tho rate of brain  activity  is dependent upon the special chemical
ingredients of the blood, oxygen and  carbon.  Increase of oxygen
augments cerebral action,  while  increase  of carbonic acid depresses
it.  The degree of mentality is also dependent upon the phosphatic
constituents of the nervous system.   The proportion of phosphorus
in the brain is smallest in  infancy, idiocy, and old age, and greatest
duriug the prime of fife; while the quantity of alkaline phosphates
excreted by the kidneys rises and falls with the variations of mental
activity.   The equivalence of physical agencies and  mental effects
is still further seen in the action of various substances, as alcohol, 
XXXVI                 INTRODUCTION,
opium, hashish, nitrous oxide, etc., when  absorbed into the blood,
Within the limits of their peculiar action upon the nervous centres,
tho effect of each  is strictly proportionate to the quantity taken.
There is a constant ratio between the antecedents and consequents.
   " How this  metamorphosis  takes place—how a force existing
as motion, heat, or light, can become a mode of consciousness—
how it is possible  for aerial vibrations to generate the sensation
we call sound, or for the forces liberated by chemical changes in the
brain, to give rise to emotion, these are mysteries which it is im-
possible to fathom.  But they are not profounder mysteries than
the transformation  of the physical forces into each other.  They
are not  more  completely  beyond  our comprehension than the
natures of mind and matter.   They have  simply the same  insolu-
bility as all other ultimate questions.  We can learn nothing more
than that here is one of the uniformities in the  order  of  phe-
nomena."
   The law  of correlation being thus applicable to human energy
as well as to the powers of nature, it must  also apply to society,
where we constantly witness the conversion of forces on a compre-
hensive scale.  The powers of nature are transformed into the activ-
ities of society; water-power, wind-power, steam-power, and electri-
cal-power are pressed into the social service, reducing human labor,
multiplying  resources, and  carrying  on numberless industrial pro-
cesses : indeed, the conversion  of these forces into social activities
is one of the chief triumphs ot  civilization.  The universal forces
of heat and light  are transformed by the vegetable kingdom into
the vital energy of organic compounds, and then, as food, are  again
converted into human  beings  and human power.  The very exist-
ence as well as the activity of society are obviously dependent upon
the operations of vegetable growth.   When that is abundant, popu-
lation may  become dense,  and  social activities  multifarious and
complicated, while a scanty vegetation entails  sparse population
and enfeebled  social action.    Any universal disturbance of tho
physical forces, as excessive rains or drouth,  by reducing  the har- 
      CORRELATION OF  VITAL  AND SOCIAL FORCES.  XXX Vli

vest, is  felt throughout the entire social organism.  Where this
effect is marked, and not counteracted by free communication with
more fertile regions, the means of the community become restricted,
business declines, manufactures are reduced, trade slackens,  travel
falls off, luxuries are diminished, education is neglected, marriages
are fewer, and a thousand kindred results indicate decline of enter-
prise and depression of the social energies.
   In a dynamical point of view there is a strict  analogy between
tho  individual  and the social economies—the same law  of force
governs the development  of both.  In the case of the individual,
the  amount of energy which he possesses at any time is limited,
and  when consumed for one purpose it cannot of course be had for
another.   An undue demand in one direction involves  a  corre-
sponding  deficiency elsewhere.   For  example, excessive action of
tho  digestive system exhausts the muscular and cerebral  systems,
while excessive action of the muscular system is at the expense of
the cerebral and  digestive  organs;  and again, excessive action of
the brain depresses the digestive and muscular  energies.   If the
fund of power in the growing constitutions of children is overdrawn
in any special channel, as is often the  case by excessive stimulation
of the brain, the undue abstraction of energy from other  portions
of the system is sure to entail  some form of physiological  disaster,
So with the social organism; its forces being limited, there is but a
definite amount of power to be consumed in the' various  social
activities.  Its appropriation in one way  makes impossible its  em-
ployment in another, and  it  can only gain power to perform one
function by the loss of it in other directions.  This fact, that social
force cannot bo created by enactment, and that when dealing with
the producing, distributing, and commercial activities of the com-
munity, legislation can do little more than interfere with their
natural  courses, deserves to be more thoroughly appreciated by the
public.
   But  tho law in question has  yet  higher  bearings.   More  and
more we are perceiving that the condition of humanity  and  tho 
XXXV1U
INTRODUCTION.
progress of civilization are direct resultants of the forces by which
men are controlled.  What we term the moral order of society, im-
plies a strict regularity in the action of these forces.  Modern sta-
tistics disclose a remarkable constancy in  the moral activities man-
ifested in  communities of men.  Crimes, and even  the modes of
crime, have been observed to occur with a uniformity which admits
of their prediction.  Each period may therefore be said  to have its
definite amount of morality and justice.  It has been maintained,
for instance, with good reason,  that  " the degree of liberty a peo-
ple is capable of in any given age, is a fixed quantity, and that any
artificial extension of it in one  direction brings about  an  equiva-
lent  limitation in some other direction.  French  revolutions show
scarcely any more respect for individual rights .than the  despotisms
they supplant; and French  electors  use their  freedom  to put
themselves again in slavery.  So in those communities where State
restraint is feeble, we may expect to find it supplemented by the
sterner  restraints of public opinion."
   But society like the individual  is progressive.   Although  at
each stage of individual growth the forces of the organism, physi-
ological, intellectual, and passional,  have each a certain  definite
amount of strength, yet these ratios are  constantly changing, and
it is in this change that development essentially consists.  So with
society; the measured action of its forces gives rise  to  a fixed
amount of morality and liberty in each age,  but  that amount in-
creases with social evolution.   The  savage is one in whom certain
classes of feelings and emotions predominate, and  he becomes civil-
ized just in proportion as these feelings are slowly replaced by oth-
ers  of a higher character.  Yet the  activities which  determine
human  advancement  are various.  Not  only must we  regard the
physiological forces, or those which  pertain to man's physical or-
ganization and capacities,  and the psychological, or those resulting
from his intellectual and emotional constitution, but the influences
of the external world, and those of the social state, are  likewise to
be considered.  Man and society, therefore, as viewed  by  the eye 
         SPENCER'S CONTRIBUTION  TO THE INQUIRY.   XXXIX

of science, present a series of vast and complex dynamical problems,
which are  to be studied in the future in  the  light of the great
law by which, we have reason to believe, all forms and phases of
force are governed.
   A further aspect of the subject remains still to be noticed.   Mr.
Herbert Spencer has the honor of crowning this sublime inquiry by
showing that the law of the conservation, or as he prefers to term it
the ' Persistence of Force,' as it is the underlying principle of all be-
ing, is also the fundamental truth of all philosophy.  With masterly
analytic skill he has shown that  this principle of which the human
mind has just become fully conscious, is itself the profoundest  law
of the human mind, the deepest foundation of consciousness.  Ho
has demonstrated that the law of the Persistence of Force, of which
the most piercing intellects of past times had but partial  and un-
satisfying glimpses, and  which  the  latest  scientific research has
disclosed as a great principle of nature, has a yet more transcendent
character;  is, in fact, an d ]iriori truth of the highest order—a
truth which is necessarily involved  in our mental organization;
Which is broader than any possible induction, and of higher validity
than  any other truth whatever.  This principle,  which is at once
the highest  result  of  scientific investigation  and  metaphysical
analysis, Mr. Spencer has made  tho basis of his new and  compre-
hensive System of Philosophy; and in the first work of the series,
entitled " First Principles, " he  has  developed  the doctrine in its
broadest philosophic  aspects.  The  lucid reasoning by which he
reaches his conclusions cannot be presented here; a brief extract
or two will, however, serve to indicate the important place  assigned
to the law by this acute and profound inquirer:
    " We might, indeed, be certain, even in the absence of any such
analysis  as the foregoing, that  there must exist some  principle
which, as being the basis of science, cannot be established by sci-
ence.   All  reasoned out  conclusions whatever must rest  on some
postulate.  As before  shown, we cannot go on merging derivative
truths in these wider  and wider truths from which  they are do- 
xl
INTRODUCTION.
rived, without reaching at last a widest truth which can be merged
in no other, or derived from no other.   And whoever contemplates
the relation in which it stands to the truths of science in general,
will see that this truth, transcending demonstration, is the Persist-
ence of force." * * *
   " Such, then, is the foundation of any possible system  of posi-
tive  knowledge.   Deeper than  demonstration—deeper even than
definite cognition—deep as  the very nature of mind,  is the postu-
late at which we have arrived.  Its authority transcends all others
whatever; for not only is it given in the constitution of our own
consciousness, but it is impossible to imagine a consciousness so
constituted as not to give it.   Thought, involving simply the  estab-
lishment of relations, may be readily conceived to go on while yet
these relations have not been organized into  the abstracts we  call
space and time; and so there is a conceivable kind of consciousness
which  does  not  contain  the  truths commonly called d priori, in-
volved in the organization of these forms of relations.  But thought
cannot be conceived to go on without some element between which
its relations may be established; and  so there is no conceivable
kind of consciousness which does  not imply continued existence as
its datura.  Consciousness without this or that particular form is
possible; but consciousness without contents is impossible.
   " The sole truth which transcends experience by underlying it, is
thus the Persistence  of force.  This being the basis of experience,
must be the  basis of any scientific organization of experiences.  To
this an ultimate  analysis brings us down;  and on this a rational
synthesis must be built up."
   To  the question, What then is the value of experimental  inves-
tigations upon the subject, if the truth sought cannot  be  estab-
lished  by inductions from them?  Mr. Spencer replies: "They are
of value as disclosing the many particular implications which  the
general truth does not specify; they are of value as teaching us how
much of one mode of force is the equivalent of so much of another
mode;  they are of value as determining  under what conditions each 
             STUPENDOUS  REACH OF THE LAW.           xll

metamorphosis occurs;  and they are of value as leading us to in-
quire in what shape the remnant of force has  escaped, when the
apparent results are not equivalent to the cause."  And it may bo
added, that it is to these investigations that we are indebted for the
clear and comprehensive establishment of the principle as a law of
physical nature;  psychological analysis having only shown that it
extends much further than it is the business of experimental science
to go.
   Thus the law characterized by Faraday as the highest in phys-
ical science which  our  faculties permit us  to  perceive, has  a far
more  extended sway;  it might  well  have been proclaimed the
highest law of all  science—the most  far-reaching  principle  that
adventuring reason has discovered in the universe.   Its stupendous
reach spans all orders of existence.   Not only does it govern the
movements of the heavenly bodies, but it presides over the genesis
of the constellations; not only does it control those radiant floods
of power which fill the eternal spaces, bathing, warming, illumining
and vivifying our planet, but it rules the actions and  relations of
men, and regulates the march of terrestrial affairs.   Nor is its do-
minion limited to physical  phenomena;  it provails  equally in the
world of mind, controlling all the faculties and processes of thought
and feeling.  The star-suns of the remoter  galaxies dart their ra-
diations across the universe; and although the distances are so pro-
found that hundreds of centuries may have been required to traverse
them, the impulses of force enter the eye, and impressing an atomic
change  upon  the nerve, give  origin to the sense of sight.  Star
and nerve-tissue are parts of the same system—stellar and nervous
forces are correlated. Nay  more; sensation awakens  thought and
kindles emotion,  so that this wondrous dynamic chain  binds into
Uving  unity the realms of matter and mind through  measureless
amplitudes of space and time.
   And if these high  realities are but faint  and  fitful  glimpses
which science has obtained in the dim dawn of discovery,  what
must  be the glories of the coming day?  If indeed  they are but 
xlii
INTRODUCTION.
'pebbles'  gathered from the shores of the great  ocean of truth,
what are the mysteries still hidden in the bosom of the mighty un-
explored?   And how far transcending all stretch of thought that
Unknown  and Infinite Cause of all to which the human spirit turns
evermore in solemn and mysterious worship!
   It remains only to observe, that so immense a step in the pro-
gress of our knowledge of  natural agencies as the following pages
disclose, cannot  be without effect upon the  intellectual  culture
of the  age.  To the  adherents of that  scholastic and verbal edu-
cation  which prefers words to  things, and  ancient to modern
thought; which ignores the study of nature, and regards the pro-
gress of science  with indifference or hostility, it matters little what
views of the world are entertained, or  what changes these views
may undergo. But there is another, and happily an increasing class,
who hold  that  it is the true destiny of mind  to comprehend the
vast order of existence in the midst of which it is placed, and that
the faculties of man are divinely adapted to this sublime task; who
see that the laws of nature must be understood before they can be
obeyed, and that only through this understanding  can man rise to
the mastery of  its powers, and bring himself into final harmony
with his conditions.   These will recognize that the discovery of
new principles which  expand, and elevate, and harmonize our views
of the  universe—which involve  the workings  of  the mind itself,
open a new chapter in philosophy, and  touch the very foundations
of knowledge, cannot be without a determining influence upon the
future  course and development  of thought,  and the  spirit  and
methods of its acquisition. 
                     THE




               CORRELATION





OF  PHYSICAL  FOECES.



         By W. R. GROVE,  Q.C., M.A., F.R.S.



 FIEST AMEEI0AN', FROM THE FOURTH ENGLISH EDITION. 
   William Robert Grove, an English lawyer and physicist, was  born at
Swansea, July 14,  1811.   He graduated at Oxford in 1834, and during the
next five years was Professor  of Natural  Philosophy at  the  London Insti-
tution.  Professor Grove is a rare example of the ability which has achieved
a distinguished eminence in different fields of effort.  While pursuing with
marked success the profession of an advocate, he has devoted his leisure to
original scientific researches, and obtained a high distinction both 13 u dis-
coverei and  a philosophic writer upon scientific subjects.  In 1852 he waa
made Queen's Counsel, and afterwards Vice-President of the Royal Society.
He is the inventor of the powerful galvanic battery known by his name, and
his chief researches have been in the field of electricity.  Many of his ex-
perimental  results  are  referred to in the following pages, which will  also
attest  his high  position  among the founders of the  new  philosophy of
forces. 
PREFACE
rrUJE Phrase ' Correlation  of Physical Forces' in the sense in
J.   wnich I have used it, having become recognized by a large
number of scientific writers, it would produce  confusion were I
now to  adopt another title.  It would, perhaps, have been better
if I  had in the first instance "used  the term Co-relation, as the
words ' correlate,' ' correlative,' had acquired a peculiar metaphys-
ical  sense somewhat differing from  that which  I attached to the
substantive correlation.  The passage in the text (p. 183) explains
the meaning I have given to the term.
   Twenty years  having elapsed since I promulgated  the views
contained in this Essay, which were first advanced in a lecture at
the  London Institution in January 1842, and subsequently more
fully developed in a course of lectures in 1843,1 think it advisable
to add a little to the Preface with reference to other labourers in
the same field.
   It has happened with  this subject as with many others, that
similar ideas have independently presented themselves to differ-
ent minds about  the same  period.  In May 1842 a paper was
published by M. Mayer which I had not read when my last edition
was  published, and indeed  only now know imperfectly by the
ticd-voce translation of a friend.  It  deduces very much the same
conclusions to which I had  been led, the author starting partly
from A priori reasoning and partly from an experiment by which
water was heated by agitation, and from another, which had, how-
ever, previously been made by Davy, viz. that ice can be melted
by friction, though kept in a medium which is below the freezing
point of water.
   In 1843 a paper by Mr. Joule on the mechanical equivalent of 
4
PREFACE.
heat appeared, which, though not in terms touching on the mutual
and necessary dependence of all the Physical Forces, yet bears
most importantly upon the doctrine.
    While my third edition was going through  the  press I  had
the  good fortune to make the  acquaintance of M. Seguin, who
informed me that his uncle, the eminent Montgolfier, had long
entertained  the  idea that force was indestructible, though, with
the exception of one sentence, in his paper on the hydraulic ram,
and where he is  apparently speaking of mechanical force, he has
left nothing in print on the subject.   Not so, however, M. Seguin
himself, who in 1839, in a work on the ' Influence of Railroads,'
has  distinctly expressed his uncle's and his own views on the
identity of heat and mechanical force, and has given a calculation
of their equivalent relation, which is not far from the more recent
numerical results of Mayer, Joule, and others.
    Several of the great mathematicians of a much earlier period
advocated the idea of what they termed the Conservation of Force,
but  although they considered that  a body in motion would so
continue for ever, unless arrested by the impact of another body,
and, indeed, in the latter case, would, if elastic, still continue to
move (though deflected from its course) with a force proportion-
ate  to  its elasticity, yet with inelastic bodies the general, and, as
far as I am aware, the universal  belief was, that the  motion was
arrested and the  force  annihilated.  Montgolfier went a step far-
ther, and his hydraulic ram was to him a proof of the truth of
his preconceived idea, that the shock or impact of bodies left the
mechanical force undestroyed.
   Previously, however, to the discoveries of the voltaic battery,
electro-magnetism, thermo-electricity,  and photography, it was
impossible for any mind to perceive what, in the greater number
of cases,  became of the force which was  apparently lost.  The
phenomena of heat, known from the earliest times, would have
been a mode of accounting for the resulting force in many cases
where  motion was arrested, and we find Bacon announcing  a
theory that motion was the form, as he quaintly termed it, of
heat.   Rumford  and Davy adopted  this view, the former with a
fair approximate attempt at  numerical calculation, but no one of
these philosophers seems to have connected  it  with the inde-
structibility of force.   A passage in  the writings of Dr. Roget, 
PREFACE.
5
combating the theory that mere contact of dissii lilar bodies was
the source of voltaic electricity, philosophically supports his argu-
ment by the idea of non-creation of force.
   As I have introduced into the  later editions of my Essay ab-
stracts of the different discoveries  which I have found, since my
first lectures, to bear upon the subject, I have been regarded by
many rather as the historian of the progress made in this branch
of thought than as one who has  had anything to do with its ini-
tiation.  Everyone is but a poor judge where he is himself  inter-
ested, and I therefore write with  diffidence, but it would be affect-
ing  an indifference which I do not feel if I did  not state that I
believe myself to have been the first who introduced this subject
as a generalised system of philosophy, and  continued to enforce
it in my lectures  and writings for many years, during which it
met with the opposition usual and  proper to novel ideas.
   Avocations necessary to the well-being of others have prevent-
ed my following it up experimentally, to the  extent  that I once
hoped; but I trust and believe that this Essay, imperfect though
it be, has helped  materially to impress on that portion of the
public which  devotes its  attention rather to  the philosophy of
science than to what is now termed science, the truth of the thesis
advocated.
   To show that the work of  to-day is not substantially different
from the thoughts I first  published on the subject, at a period
when I knew little  or nothing of what had been thought before,
I venture to give  a few extracts from the printed copy of my
lecture of 1842 :—
   Physical Science  treats of Matter, and what I shall to-night term ita
Affections; namely, Attraction, Motion, Heat, Light, Electricity, Magnet-
ism,  Chemical-Affinity. When these  re-act upon matter, they constitute
Forces.  The present tendency of  theory seems to lead to the opinion that
all these Affections are  resolvable into one, namely, Motion; however,
should the theories on these  subjects be ultimately so effectually gener-
alised as to become laws, they cannot  avoid the necessity for  retaining dif-
ferent names for these different Affections; or, as they would then be called,
different modes of Motion.....
   (Ersted proved that Electricity and Magnetism are two forces which act
upon each  other; not in straight lines, as all other known forces do, but in
a rectangular direction: that is, that bodies invested with electricity, or the
conduits of an electric-current, tend to place magnets at right angles to
them ; and, conversely, that magnets teud to place bodie3 conducting dec-
iricity at right angles to them.  .... 
6
PREFACE.
   The discovery  of CErsted, by which electricity was  made a source ol
Magnetism, soon led philosophers to seek the converse effect; that  is, to
educe Electricity from a permanent magnet:—had these experimentalists
succeeded in their expectations of making a stationary magnet a source of
electric-currents, they would have realised the ancient dreams of perpetual
motion, they would have converted statics into dynamics, they would have
produced power without expenditure;  in other words, they would have be-
come creators.  They failed, and Faraday saw their error; he proved that
to obtain Electricity from Magnetism it was necessary to superadd  to this
latter, motion; that magnets while in motion induced electricity  in  con-
tiguous conductors; and that the direction of such  electric-currents was
tangential to the polar direction of the magnet; that as  Dynamic-electricity
may  be made the source of Magnetism and Motion, so Magnetismconjoined
with Motion may be made the source of  Electricity.  Here originates the
Science of Magneto-electricity,  the true  converse  of Electro-magnetism;
and thus  between Electricity and Magnetism is shown to exist a reciprocity
of force such that,  considering either as the primary agent,  the other be-
comes  the re-agent; viewing one in the relation of cause, the other is the
effect.....
   The Science of  Thermo-Electricity connected heat with electricity, and
proved these, like  all  other natural forces, to be capable of mutual reac-
tion.....
   Voltaic action is Chemical action taking place at a distance or trans-
ferred  through a chain of media;  and the  Daltonian equivalent numbers
are the exponents of the amount of voltaic action for corresponding chemi-
cal substances.   .  .  .
   By regarding the quantity of electrical, as directly proportional to the
efficient chemical action, and by experimentally tracing this principle,  I
have been fortunate enough to  increase the  power  of the Voltaic-pile
more than sixteen times, as compared with  any combination previously
known.....
   I am  strongly disposed to consider that the facts of Catalysis depend
upon voltaic action, to generate which  three heterogeneous substances are
always necessary.  Induced by this belief I made some experiments on the
subject, and succeeded in forming a voltaic combination by gaseous-oxygen,
gaseous-hydrogen, and  platinum; by which a galvanometer  was deflected
and  water decomposed.....
   It appears to me that heat and light may be considered  as affections;
or, according to the Undulatory-theory, vibrations of matter  itself,  and not
of a  distinct etherial fluid permeating  it:  these vibrations would be  prop-
agated, just as sound is propagated bj vibrations of  wood or as waves by
water.   To my mind,  all the consequences of the  Undulatory-theory flow
as easily from this, as froir the hypothesis of a specific ether;  to suppose
which, namely, to suppose a fluid sui generis,  and of  extreme tenuity  pene-
trating solid bodies, we must assume, first, the existence of the fluid itself;
secondly, that bodies are without  exception  porous;  thirdly, that  these
pores  communicate;  fourthly, that  matter  is limited  in  expansibility.
None of  these difficulties apply to the modification of this theory which  I
venture to propose; and no other difficulty applies  to it which does not
equally apply to tho received hypothesis.  With regard to  the planetary
Bpaces, the diminishing periods of comets is a strong argument for the ex-
istence of an universally-diffused matter: this has the function of res'ut- 
PKEFACE.
7
ance, and there appears to be no reason to divest it of the functions com-
mon to all  matter, or superficially to appropriate it  to certain affections.
Again, the phenomena of transparency and opacity are, to my mind, more
easily explicable by the former than by the latter theory;  as resuliiuy from
a difference in the molecular arrangement of the matter  affected.  In re-
gard  to  the effects of  double-refraction and polarisation, the molecular
gives at once a reason for the effects upon the one theory, while upon the
other we must, in addition to previous assumptions, further assume a dif-
ferent elasticity of the  ether in different directions within  the doubly-
refracting medium.  The same theory is applicable  to Electricity and
Magnetism; my own experiments on the influence of the elastic intermedium
on  the voltaic-arc, and  those of Faraday on electrical induction, furnish
strong arguments in support of it. My inclination would lead me to de-
tain you on this subject much longer than my judgment deems advisable:
I therefore  content myself with offering it to your consideration,  and,
should my avocations permit, I may at a future period more fully develope
it.  ...  .
   Light, Heat, Electricity, Magnetism, Motion, and  Chemical-affinity, are
all convertible material affections;  assuming either  as the cause, one of
the others will be  the effect: thus heat may be said to produce electricity,
electricity to produce heat;  magnetism  to  produce  electricity, electricity
magnetism; and so of the rest.  Cause  and  effect, therefore,  in  their ab-
stract relation to  these forces, are words solely of  convenience: we are
totally unacquainted with the ultimate generating power of each and all
of them, and probably shall ever remain so; we can  only ascertain the
norma? of their action: we must humbly refer their causation to one omni-
present influence, and content  ourselves with studying their effects and
developing  by experiment their mutual relations.

    I have  transposed the passages  relating to  voltaic  action and
catalysis, but  I  have not added a word  to the above quotation,
and, as  far as I am now aware, the theory that the so-called im-
ponderables  are  affections of  ordinary matter, that they are re-
solvable into motion, that they are to be regarded in their action
on matter as forces, and not as specific entities, and that they are
capable of mutual reaction, thence alternately acting as cause  and
effect, had not at that time been publicly advanced.
   My original Essays being a record of lectures, and being pub-
lished by the managers of the  Institution, I  necessarily adhered
to the form and matter which I  had orally communicated.  In
preparing  subsequent editions  I found that, without destroying
the identity of the work, I could  not alter the style ; although it
would have been less difficult and more satisfactory to me to have
done so, the work would not have  been  a republication; and  I
was for obvious  reasons anxious to preserve as far as I could the
original text, which, though added to, is but little altered.
   The form of  lectures has  necessarily continued the  use of tho 
8
PREFACE.
first person, and I would beg my readers not to attribute  to me,
from the modes of expression used, a dogmatism which is far from
my thought.  If my opinions are expressed broadly, it is that, if
opinions are always hedged in by qualifications, the style becomes
embarrassed and the meaning frequently unintelligible.
   As  a course of lectures can only be useful by inducing the
auditor to consult works on the subject he hears treated, so tho
object of this Essay is more to in luce a particular train of thought
on the known facts of physical science than to enter with minute
criticisms into each separate branch.
   In one or two of the reviews of previous  editions the general
idea of the work was objected to.  I believe, however, that will
not now be the case; the. mathematical labours of Mr. Thompson,
Clausius, and others, though  not suitable  for insertion  in  an
Essay such as this, have awakened an interest for many portions
of the subject, which promises much for its future progress.
   The short and irregular-intervals which my profession permits
me to  devote to science so prevent the continuity of attention
necessary for the proper evolution of a train of thought, that I
certainly should not now have courage to  publish for the first
time such an Essay; and  it is only the favour it has received
from those whose opinions I highly value, and the, I trust pardon-
able, wish not to let some favourite thoughts of my youth lose all
connection with my name, that have induced me to reprint it.
   My scientific readers will, I hope, excuse the very short notices
of certain branches of science which  are introduced, as without
them the work would be  unintelligible to many for whom it is
intended.   I have endeavoured so to arrange my matter that each
division should form an introduction to those which follow, and
to assume no more preliminary knowledge to be possessed by my
readers than would be expected from persons acquainted with the
elements of physical science.
   The notes contain references to the original memoirs in which
the branches of science  alluded to  are to be found, as well as to
those which bear on the main arguments; where these memoirs
are numerous, or not easy of access, I have referred to treatises iu
which they are collated.  To prevent the reader's attention being
interrupted, I have in the notes referred to the pages of the text,
instead of to interpolated letters. 
          COKRELATION

                  OF

PHYSICAL  FOPtOES
          I.—INTRODUCTORY REMARKS.

       HEN natural phenomena are for the first ti nc ob-
       served,  a tendency immediately  developes itself to
refer  them to something previously known—to bring them
within the range of acknowledged sequences.  The mode of
regarding new  facts, which is most favourably received by
the public, is that which  refers them to  recognised views-
stamps them into the mould in which the mind has been al-
ready shaped.  The new fact may be far removed from those
to which it  is referred, and may belong  to a different order
of analogies, but this cannot then be known, as its co-ordi-
nates  are wanting.   It may be questionable whether  the
mind  is not so moulded by past events that it is impossible
to advance an entirely new view, but admitting such possi-
bility, the new view, necessarily founded on insufficient data,
is likely to be more incorrect and prejudicial than even a
strained attempt to reconcile the  new discovery with known
facts.
   The theory consequent upon  new facts,  whether it be a
co-ordination of them with known ones, or the more difficult
w 
10         CORRELATION OF PHYSICAL FORCES.

and  dangerous attempt at remodelling the public ideas,  is
generally enunciated by the  discoverers  themselves of the
facts, or by those to whose authority the world at the period
of the discovery defers; others are not bold enough,  or if
they be so, are unheeded.  The earliest theories thus enuncia-
ted obtain the firmest hold upon the public mind, for at such
a time there is no power of testing, by a sufficient range of
experience, the  truth of the theory;  it is accepted solely or
mainly upon  authority: there  being no means of contradic-
tion, its reception is, in the first instance, attended with  some
degree of doubt, but as the time in which it can fairly be in-
vestigated far exceeds that of any lives then in being, and as
neither the individual  nor the public mind will long tolerate
a  state of  abeyance,  a  theory shortly becomes,  for  want
of a better,  admitted as an established truth: it is handed
from father to  son, and gradually takes  its place in edu-
cation.   Succeeding  generations, whose minds  are  thus
formed to an established view,  are much less likely to aban-
don  it.  They have  adopted it in the  first instance, upon au-
thority, to them unquestionable, and subsequently to yield up
their faith  would involve a laborious  remodelling of ideas, a
task which  the  public as a body will and can rarely under-
take, the frequent occurrence of which is indeed inconsistent
with the very existence of man in a social state, as it would
induce an anarchy of thought—a  perpetuity  of mental  revo-
lutions.
   This necessity has its good;  but the prejudicial  effect
upon the advance of science is, that by this means, theories the
most immature  frequently become the  most permanent; for
no theory can be more immature, none is likely to be so in-
correct,  as that which is formed at the first flush of a new
discovery;  and though  time  exalts the  authority of those
from whom it emanated, time  can never give to the illustri-
ous  dead  the means  of  analysing and  correcting erroneous
vicT?s which subsequent discoveries confer. 
INTRODUCTORY REMARKS.              U
   Take for instance the Ptolemaic System, which we may
almost literally explain  by the expression of Shakspeare:
' He that is  giddy thinks the world turns round.'  Yf e now
Bee the error of this  system, because Ave have all  an immedi-
ate opportunity of refuting  it; but this identical error was
received as a truth for  centuries, because, when first promul-
gated,  the  means  of refuting it were  not at hand, and when
the means of its  refutation  became attainable, mankind had
been so educated to the supposed truth, that they rejected the
proof of its fallacy.
   I have premised the above for two reasons :  first to obtain
a  fair  hearing, by requesting as  far as possible  a dismissal
from the  mind of my readers  of preconceived views by and in
favour of which all are liable to be prejudiced ; and secondly,
to defend myself from the charge of undervaluing authority,
or treating lightly the opinions of those  to whom and  to
whose memory mankind looks with reverence.   Properly to
value authority, Ave should estimate it together with its means
of information : if' a dwarf on the shoulders of a giant can
see further than the giant,' he is no less a dAvarf in compari-
son •with the giant.
   The subject on which I am about to treat—viz., the rela-
tion of the affections of matter to each other and to matter—
peculiarly demands an unprejudiced regard.   The different
aspects under Avhich these agencies have been contemplated ;
the different views which have been taken of matter itself;
the metaphysical subtleties to which these views unavoidably
hod, if pursued beyond fair inductions from existing expe-
rience, present difficulties almost insurmountable.
   The extent of claim which my views on this subject may
have to  originality has been stated in the  Preface ;  they be-
came strongly impressed upon my mind at a period when I
was  much engaged in experimental research, and were, as I
then believed, and ^till believe, regarding  them as a system,
new : expressions  in the works of different authors, hearing 
12         CORRELATION  OF PHYSICAL FORCES.
more or less on the subject, have subsequently been pointed
out to  me. some of which go back to a distant period.  An
attempt to analyse these in detail, and  to  trace how far I
have been anticipated by others,  would  probably but little
interest the reader, and in the course of it  I should constantly
have to make  distinctions showing wherein I differed, and
wherein I agreed with others.  I might cite authorities which
appear to me to oppose,  and others which appear to coincide
with certain  of the  views I have put forth; but this would
interrupt the  consecutive  developement of  my own ideas, and
might render me liable to the charge of misconstruing those of
others ; I therefore think it better to avoid such discussion in
the text;  and in addition to the sketch given in the  Preface,
to  furnish in the notes at the conclusion  such  references
to  different authors as bear upon the  subjects treated  of,
which I have discovered, or which have been  pointed out to
me since  the delivery of the lectures  of AA-hich  this essay
is a record.
    The more extended  our  research becomes, the  more we
find that  knowledge is a thing of slow  progression, that the
very notions  which  appear to ourselves  new, have arisen,
though perhaps in a  very indirect manner, from successive
modifications of traditional opinions.  Each word we utter,
each thought we think, has in it the  vestiges, is in itself the
impress, of antecedent words and thoughts.  As  each ma-
terial form,  could we rightly read it, is a book, containing in
itself the  past  history of the world;  so, different though our
philosophy may now appear to be from that of our progeni-
tors, it is but theirs added to or subtracted from, transmitted
drop by drop through the filter of  antecedent, as ours will be
through that of subsequent, ages.—The relic is to the past as
is the germ to the future.
    Though many valuable facts, and correct deductions from
them,  are to be  found  scattered  amongst  the  voluminous
works of the  ancient philosophers ; yet, giving  them  tho 
INTRODUCTORY REMARKS.
13
credit which they pre-eminently deserve for having devoted
their  lives to purely intellectual  pursuits, and for having
thought, seldom  frivolously, often profoundly, nothing can be
more  difficult than to seize and apprehend the ideas of those
who reasoned from abstraction to abstraction—who, although,
as we noAV believe, they must have depended upon  observa-
tion for their first inductions, afterwards raised upon them
such a complex superstructure of syllogistic deductions, that,
without following the same paths, and tracing the same sinu-
osities which led  them to their conclusions, such conclusions
are to  us  unintelligible.  To think as another thought, we
must  be placed  in the same situation as he was placed: the
errors of commentators generally arise from their reasoning
upon the arguments of their text, either in blind obedience to
its dicta, Avithout considering the circumstances under which
they were  uttered, or in viewing the images presented to the
original writer from a different point to that from which he
viewed them.  Experimental philosophy keeps in check the
errors both of « priori  reasoning and of commentators,  and,
at all  events, prevents  their becoming cumulative;  though
the theories  or explanations of a fact be  different, the fact
remains the same.  It is, moreover, itself the exponent of its
discoverer's thought: the observation of known phenomena
has led him to elicit from nature the new phenomena :  and,
though he may be wrong in his deductions  from this after its
discovery, the reasonings which conducted him to it are them
selves  valuable, and, having led  from  known to  unknown
truths, can seldom be uninstructive.
   Very different views existed amongst the ancients as to tho
aims to be pursued by physical investigation, and as to the obj ects
likely to be attained by it.  I do not here mean the moral ob-
jects,  such as the  attainment  of  the summum bonum,  &c.
—but the  acquisitions in knowledge  which such investiga-
tions were  likely to confer.  Utility Avas one object in view,
and this was to some extent attained by the progress made in 
14         CORRELATION OF  PHYSICAL  FORCES.
astronomy and mechanics ;  Archimedes, for instance, seema
to have constantly had this end in vieAV; but, -while pursuing
natural knowledge for the sake of knowledge  and the power
Avhich it brings with it, the greater number  seemed  to enter-
tain an expectation of arriving at some ultimate goal, some
point of knowledge, which Avould give them a mastery  over
the  mysteries of nature, and would  enable them to  ascertain
what Avas the  most intimate structure  of matter, and the
causes of the changes it exhibits.  Where they could not dis-
cover, they speculated.   Leucippus, Democritus, and others,
have given us their notions of the ultimate atoms of which
matter was formed, and of the modus agendi of nature in the
various transformations which matter undergoes.
   The expectation of arriving at ultimate causes or essences
continued long after the speculations of the ancients had been
abandoned, and continues even to the present day to be a very
general notion  of  the  objects to be ultimately attained by
physical  science.  Francis Bacon,  the  great  remodeller of
science, entertained this notion, and thought that, by experi-
mentally testing natural phenomena, we should be enabled to
trace them to certain primary essences or causes Avhence the
various  phenomena  flow.   These  he  speaks of  under the
scholastic name of ' forms '—a term derived from the ancient
philosophy, but differently applied.  He appears to  have un-
derstood by ' form' the essence of quality—that in Avhich, ab-
stracting everything extraneous, a given quality consists, or
that Avhich, superinduced on any body, would  give  it its pe-
culiar  quality:  thus  the  form of transparency, is  that
which constitutes transparency, or that  by which, when dis-
covered, transparency  could be produced or superinduced.
To take a  specific example of what I may  term the  syn-
thetic  application of his philosophy:—' In gold there  meet
together yelloAvness, gravity, malleability, fixedness in the fire,
a determinate way of solution, which are the  simple natures
in gold: for he who understands form, and  the  manner of 
INTRODUCTORY REMARKS.
15
superinducing this  yelkrwne.:;,  gravity,  ductility, fixedness.
faculty of fusion, solution, &c, with their particular degrees
and proportions, Aviil consider how to join them  together in
some body, so that  a transmutation into gold shall folloAv.'
   On the other hand, the analytic method, or, ' the enquiry
from what origin gold or any other metal or stone is generated
from its first fluid matter or rudiments, up to a perfect min-
eral,' is to be perceived by Avhat Bacon calls  the  latent pro-
cess, or a search for ' what in  every generation or transfor-
mation of bodies, flies off,  what remains behind, what is add-
ed, Avhat separated, &c. ;  also, in  other  alterations and mo-
tion?, Avhat  gives  motion, what  governs  it,  and the like.'
Bacon appears to have thought  that  qualities  separate from
the substances themselves were attainable, and if  not capable
of physical isolation, were at all events capable of physical
transference and superinduction.
    Subsequently to'Bacon a belief has generally existed, and
now to a  great  extent  exists, in what are called secondary
causes,  or consequential steps, wherein  one  phenomenon is
supposed necessarily to hang on another, until at last Ave ar-
rive  at  an essential  cause,  subject immediately to the First
Cause.  This notion is generally prevalent both on the Con-
tinent and in this country: nothing is more familiar than the
expression ' study the effects  in order to arrive at  the causes.'
   Ii! Lead of regarding the proper object of physical science
as a  search after essential causes, I believe it "ought to be, and
must be, a search after facts  and relations—that although the
word Cause may be used in a secondary and concrete  sense,
as meaning antecedent forces, yet in an abstract sense it is to-
tally inapplicable ; we cannot predicate of  any physical agency
that  it is abstractedly the cause of another ;  and if, for the sake
of convenience,  the language of secondary causation be per-
missible, it should be only with reference to the special phe-
nomena referred to, as it can never be generalised.
   The misuse,  or  rather varied uee, of the term Cau.-o, hag 
16         CORRELATION OF PHYSICAL FORCES.

been a source  of great  confusion in physical theories, and
philosophers arc even now by no means agreed  as  to theii
conception of causation.  The most generally received view
of causation, that of Hume, refers it to invariable antecedence
—i. e., we call that a cause  which invariably precedes, that
an effect which invariably succeeds.  Many instances of in-
variable sequence might however be selected, which do  not
present the relation of cause and effect: thus as Reed observes,
and  Brown  does not satisfactorily answer, day invariably
precedes night and yet day is not the cause of night.  The seed,
again, precedes the plant, but is not the cause of it; so that when
we study physical phenomena it becomes difficult to separate the
idea of causation from that of force, and these have been regarded
as identical by some philosophers.   To take an example which
will contrast these two views : if a floodgate be raised, the water
flows out; in ordinary parlance,  the water is said to  flow be-
cause the floodgate is raised:  the sequence  is invariable ; no
floodgate, properly so called, can be raised without the water
flowing out,  and yet in another, and perhaps more strict, sense,
it is  the gravitation of the water which causes it to flow.  But
though we  may truly say that, in  this  instance,  gravitation
causes the water to flow, we cannot in truth abstract the pro-
position, and say, generally, that gravitation is the cause of
water flowing, as water may flow from other causes, gaseous
elasticity, for instance, which will cause water to flow from a
receiver full of air into one that is exhausted ;  gravitation may
also, under certain circumstances, arrest instead of cause the
flow  of  water.
   Upon neither view, however, can we get at anything like
abstract causation.   If we regard causation as invariable se-
quence, we can find no case in which a given antecedent  is
the only antecedent to a given sequent:  thus if  water could
floAv from no other cause than the withdrawal of a floodgate,
we might say  abstractedly that this was the cause of water
flowing. If, again, adopting the view which looks to causa- 
INTRODUCTORY REMARKS.
17
tion as a force, Ave could say that water  could  be caused to
flow only by gravitation, we might say abstractedly that grav-
itation was the cause of water floAving—but this  wTe cannot
say; and if  we seek  and examine any other example, we
shall find that causation is only predicable of it in the partic-
ular case, and cannot be supported as an abstract proposition ;
yet this is constantly attempted.  Nevertheless, in each par-
ticular case Avhere Ave speak of Cause, we habitually refer to
some antecedent power or force : we never see  motion or any
change in matter take  effect Avithout regarding  it as produced
by some previous change ;  and when we cannot trace it to its
antecedent, Ave mentally refer it to one ; but whether this hab-
it be philosophically correct is by no means clear.   In other
words, it seems questionable, not only whether cause  and ef-
fect are convertible terms with antecedence and sequence, but
Avhether in fact cause does precede effect, Avhether force does
precede the change in matter of which it is said to be the
cause.
    The actual priority of cause to effect has been doubted,
and their simultaneity argued with much ability.  As an  in-
stance of this argument it may be said, the  attraction which
causes iron to approach the magnet is simultaneous with and
ever accompanies the movement of the iron ;  the movement
is evidence of the co-existing cause or force, but there is no
evidence of any interval in time between the one and the oth-
er.  On this  vieAv time would cease to be a necessary element
in causation ;  the idea of cause, except perhaps as referred to
a primeval creation, would cease to exist; and the same  ar-
guments which apply to the simultaneity of  cause with  effect
would apply to the simultaneity of Force Avith  Motion.   We
could not, however, even if we  adopted this  vicAv,  dispense
with the element of time in the sequence of phenomena;  the
effect being thus regarded as ever accompanied simultaneous-
ly by its appropriate cause, Ave should still refer it to some an-
tecedent effect; and our reasoning as applied  to the succes-
sive production of  all  natural changes would be the same. 
18
CORRELATION  OF PHYSICAL FORCES.
    Habit and the identification of thoughts with phenomena
so compel the use of recognised terms, that Ave cannot avoid
using the word cause even in the sense to which  objection is
taken ;  and if we struck it out  of our vocabulary, our lan-
guage, in speaking of successive changes, would be unintelli-
gible to the present generation.   The common error, if I am
right in supposing it to be such, consists in the abstraction of
cause, and in  supposing in  each case  a general  secondary
cause—a something which is not the first cause, but which, if
we  examine it carefully, must have^ill the attributes of a first
cause, and an existence independent of, and dominant over,
matter.
    The relations of electricity and magnetism  afford us a
very instructive example of  the belief in secondary causa-
tion.  Subsequent to the discovery by Oersted of electro-mag-
netism,  and prior to that by Faraday of magneto-electricity,
electricity and magnetism were believed by the highest author-
ities to stand in  the  relation of  cause and effect—i.  e.  elec-
tricity was regarded as the cause, and magnetism as the effect;
and where magnets existed without any  apparent electrical
currents to  cause  their magnetism, hypothetical  currents
were supposed,  for  the purpose of carrying out the caus-
ative view;  but magnetism may  now  be said with equal
truth to be the cause of electricity, and electrical  currents
may be  referred to hypothetical magnetic lines :   if therefore
electricity cause magnetism, and magnetism cause electricity,
Avhy then electricity causes  electricity, which becomes, so to
speak, a reductio ad absurdum of the doctrine.
    To take another instance, which may render these posi-
tions more intelligible.  By heating bars of  bismuth and anti-
mony in contact, a current of electricity is produced; and if
their extremities be united by a  fine wire, the wire is heated.
Now here the electricity in the metals is said to be caused
by  heat, and the heat in the wire to be caused by electricity.
and in a concrete sense  this is true ; but can  we thence  say 
INTRODUCTORY REMARKS.
19
abstractedly that heat is the cause of electricity, or that elec-
tricity is the cause of heat ?   Certainly not; for if either be
true, both must be so, and the effect then becomes the cause
of the cause, or, in other words, a thing  causes  itself.  Any
other proposition on this subject will be found to involve sim-
ilar  difficulties, until, at length, the mind  will become con-
vinced that abstract  secondary causation  does not exist,  and
that a search after essential causes is vain.
    The position Avhich  I seek to establish  in this Essay is,
that the various affections of matter which  constitute the
main objects of experimental physics, viz., heat, light, elec-
tricity, magnetism, chemical affinity, and motion, are all cor-
relative, or have a reciprocal  dependence ; that neither, taken
abstractedly, can be said to be the essential cause of  the  oth-
ers, but that cither may produce or  be convertible into,  any
of the others : thus heat may mediately or immediately produce
electricity, electricity may produce heat; and so of the rest,
each merging itself  as the force  it produces becomes  devel-
oped : and that the same must  hold good of other forces, it be-
ing an irresistible inference from observed phenomena  that a
force cannot originate otherwise than by devolution from some
pre-existing force or forces.
    The term force, although used in very different senses by
different authors, in  its  limited sense may be 'defined as  that
Avhich produces or resists motion.  Although strongly inclined to
believe that the other affections of matter, which I have above
named,  are, and will ultimately be  resolved into, modes of
motion, many arguments for  Avhich will be given in  subse-
quent parts, of  this Essay, it would be going too  far,  at  pre-
sent, to assume their identity with it; I therefore use  the term
force in reference to them, as meaning that active principle
inseparable from matter which is supposed to induce its vari*
ous changer.
    The word force and the idea it aims at  expressing might
be objected to by the purely physical philosopher on similar 
 20         CORRELATION OF PHYSICAL FORCES.

 grounds to those which apply to the Avord cause, as it repre-
 sents a subtle mental conception, and not a sensuous  percep-
 tion or phenomenon.  The objection would take something
 of this form.  If the string of a bent  bow  be cut, the  bow
 will straighten itself; we thence say there  is an elastic force
 in the bow which straightens it; but if we applied our expres-
 sions to this experiment alone, the use  of the term force
 would be superfluous, and would not add to our knowledge
 on the subject.   All the information which  our minds could
 get would be as  sufficiently obtained  from the expression,
 when the string is cut, the bow becomes straight, as from the
expression,  the  bow becomes straight by its elastic force.
Do we know more of the phenomena,  viewed Avithout refer-
ence to other phenomena, by saying it is produced by force?
Certainly not.   All we know or see is  the effect; Ave do not
see force—Ave see motion or moving matter.
    If now Ave  take a piece of caoutchouc and stretch it, Avhen
 released it returns to its original length.   Here, though the
subject-matter is very different, we see some analogy in the
 effect or phenomenon to that of the strung bow.   If again
we suspend an apple by a string, cut the string, the apple falls.
Here, though it is less striking, there  is still an analogy to
the strung bow and the caoutchouc.
    Now when the Avord force is employed as comprehending
these  three different phenomena we find some use in the term,
 not by its explaining or rendering more intelligible the modus
 agendi of matter, but as conA-eying to the mind something
 which is alike in the three phenomena, however distinct they
 may be in other respects : the word becomes an abstract or
 generalised expression, and regarded in this  light* is of hi^h
 utility.  Although I have given  only  three examples, it  is
 obvious that the  term would equally apply to 300 or 3,000 ex-
 amples.
    But it will be said, the term force is used not as  express-
 ing the effect, but as that Avhich produces the effect.   This is 
INTRODUCTORY REMARKS.
21
  true, and in this its ordinary sense I shall use it in these pages.
  But though the term has a potential meaning, to depart from
  which Avould render language unintelhgible,  we must  guard
  against supposing that we know essentially more of the phe
  nomena by saying they  are  produced by  something,  which
  something is only a word  derived from the  constancy and
  similarity of the phenomena we seek to explain by it.   The
  relations of  the phenomena to which the terms force or forces
• are applied  give us real knowledge ; these relations may be
  called relations of forces ; our knowledge of them is not there-
  by lessened, and the convenience  of expression is greatly in
  creased, but the separate phenomena  are not more intimately
  known ; no  further insight  into Avhy the apple falls is acquired
  by saying it is forced to fall, or it falls by the force of gravita
  tion; by the latter expression we are enabled to relate  it
  most usefully to other phenomena, but we still know no more
  of the particular phenomenon than that under certain circum-
  stances the  apple does fall.
      In the  ahpve  illustrations, force has  been treated as the
  producer of motion, in which case the evidence of the force is
  the motion produced ; thus we estimate the force used to pro-
  ject a cannon ball in terms of the mass of matter, and the
  velocity with which  it is projected.   The evidence of force
  when the term is applied to resistance to motion is of a some-
  what different character ; the matter resisting is molecularly.
  affected,  and has  its  structure*more or less changed; thus a
  strip of caoutchouc to which a weight is suspended is elonga-
  ted, and its  molecules are displaced as compared with their
  position when unaffected  by the gravitating force.  So a piece
  of glass bent by an appended Aveight has  its whole structure
  changed; this internal change is made evident by transmit-
  ting through it a beam of polarised  light: a relation thus
  becomes established between the molecular state  of bodies
  and the external forces or motion of masses.   Every particle
  of the caoutchouc or glass must be acting and contributing to 
22        CORRELATION OF  PHYSICAL  FORCE?.

resist or arrest the motion of the mass of matter  appended
to it.
    It is difficult, in such cases, not to recognise a reality in
force.   We need some word to express this state of tension ;
we know that it produces an effect, though the effect be nega-
tive in character : although  in this effort  of inanimate matter
we can  no more trace the mode of action to its ultimate ele-
ments  than we can follow out  the  connection of  our own
muscles with the  volition which calls them into action, we m
are experimentally convinced  that matter  changes  its state
by  the  agency of other matter,  and this  agency we  call
force.
    In  placing  the Aveight  on the glass, we have moved the
former  to an extent equivalent to that which it would again
describe if  the  resistance were removed, and this motion of
the mass becomes an exponent or measure of the force exert-
ed  on  the  glass;  wrhile this  is  in the state of tension, the
force is ever existing,  capable  of reproducing the original
motion, and while in a state of abeyance  as to#actual motion,
it  is really acting  on the glass.  The motion is suspended,
but the force  is not annihilated.
    But it may be objected, if tension or static force be thus
motion  in  abeyance, there is at all times a large amount of
dynamical action subtracted from the  universe.   Every stone
upon a hill, every spring that is  bent, and has required force
to upraise  or bend it, has  for a time, and possibly for ever,
withdrawn  this force, and  annihilated  it.   Not so; what
takes place when we raise a weight and  leave it at the point
to which it has been elevated ?  we have changed the  centre
of gravity of the earth, and consequently the earth's position
with reference  to the sun, planets, and  stars; the effort we
nave made pervades  and shakes  the universe;  nor can we
present  to the mind any exercise of force, which is thus not
permanent in its dynamical effects.  If, instead of one Aveight
being raised, we raise  two weights, each  placed at a point 
INTRODUCTORY REMARKS.
23
diametrically opposite the  other, it  would be said, here you
have compensation,  a balance,  no change  in the  centre of
gravity of the earth ; but Ave have increased the mean diame-
ter of the earth, and a perturbation of our planet, and of all
other celestial bodies necessarily ensues.
   The force may be said to be in abeyance with reference
to the effect  it would  have produced,  if  not arrested, or
placed in a state of tension ; but in  the  act of imposing this
state, the relations of equilibrium with other bodies have
been changed, and these move in their  turn, so that motion
of the same amount would seem to be ever affecting matter
conceived in its totality.
   Press  the  hands violently together;  the  first notion may
be that this is  poAver locked up, and that no change ensues.
Not so ;  the blood courses more quickly, respiration is accele-
rated,  changes Avhich we may not be able to trace, take place
in the muscles and  nerves, transpiration is increased;  we
have given off  force in various ways, and must, if the effort
be prolonged, replenish our sources of power, by fresh chemi-
cal action in the stomach.
   In  books which treat of statics and  dynamics, it is com-
mon and  perhaps necessary to isolate the subjects of consid-
eration ;  to  suppose, for instance, two bodies gravitating, and
to ignore the rest of the universe.  But no such isolation ex-
ists in reality, nor could we predict the result if it did exist.
Would two bodies gravitate  towards each other in empty
space,  if space can be empty ? the notion that they would is
founded on  the theory of attraction, which NeAvton himself
repudiated,  further than  as  a  convenient means of regard-
ing the subject.  For purposes of instruction or argument it
may be convenient to assume  isolated  matter:  many con-
clusions  so  arrived  at  may be true,  but  many will  be
erroneous.
   If,  in producing  effects of tension fir of static force, the
effort made pervades the universe, it may be said, when the 
24         CORRELATION  OF PHYSICAL FORCES.
 bent  spring is freed, when the raised Aveight falls, a converse
 series of motions must be effected, and this theory Avould lead
 to a mere reciprocation, which Avould  be equally unproduc-
 tive of permanent change with the annihilation of force.  If
 raising  the  weight has  changed the centre of gravity of the
 earth, and thence  of the universe, the  fall of the weight, it
 will be said, restores the original centre of gravity, and every-
 thing comes back to its original status.  In this argument we
 again, in thought, isolate  our experiment; we neglect sur-
 rounding  circumstances.  Between the time  of the raising
 and falling of the  weight, be the  interval never so  small,
 nay, more, during the rising and during the  fall, the earth
 has been going on revolving round its axis  and round  the
 sun, to  say nothing  of other  changes,  such as temperature,
 cosmical magnetism,  &c, which we may call  accidental, but
 which, if  Ave kneAV all,  would  probably be found  to  be as
necessary and as reducible to law as the motion of the earth.
A change having taken place, the fall of the weight does
not bring back  the status quo, but other changes  supervene,
and  so  on.  Nothing repeats  itself,  because nothing can
be placed again in  the  same  condition:  the past is irre-
vocable. 
II.—MOTION.
      MOTION—which has  been taken as the main exponent
       of force  in the above examples—is the most obvious,
 the most distinctly conceived of all the affections of matter.
 Visible motion,  or relative  change of position in space, is a
 phenomenon so  obvious  to  simple  apprehension, that to at-
 tempt to define it would be to render it more obscure ;  but
 Avith  motion, as with all physical appearances, there are cer-
 tain Aanishing gradations or undefined limits, at which the
 obvious  mode of action fades away ; to detect  the continu-
 ing existence of the  phenomena we  are obliged to have re-
 course to other  than ordinary methods of investigation, and
 we frequently apply other and different names to the effects
 so recognised.
    Thus sound  is motion;  and although in the earlier pe-
 riods of philosophy the identity of sound and motion was not
 traced out,  and  they were  considered distinct affections of
 matter—indeed,  at the close  of the last century a theory was
 advanced that sound was transmitted by the vibrations of an
 ether—we now  so readily resolve sound into motion, that to
 those  who are  familiar  with acoustics, the  phenomena of
 sound immediately present  to the mind the idea of motion,
J, e. motion of ordinary matter.
   Again, Avith  regard to light: no doubt  now  exists  that
li°ht moves or is accompanied  by motion.   Here  the phe-
             2 
20         CORRELATION OF PHYSICAL FORCES.
 nomena of motion are not made evident by the ordinary sen-
 suous perception, as for instance the motion of a visibly mov-
 ing projectile would be, but by an  inverse  deduction  from
 known relations of motion to time and space :  as all observa-
 tion teaches us that bodies in moA-ing from one point in space
 to another occupy time, we conclude that,  whereA*er a con-
 tinuing  phenomenon is  rendered  evident in two  different
 points of space at different times, there is motion, though we
 cannot see the progression.   A similar  deduction convinces
 us of the motion of electricity.
   As we  in common parlance  speak of sound moving,
 although sound is  motion, it  requires  no great stretch of
 imagination to conceive light and electricity as motion?, and
 not as things moving.  If one end of a long bar of metal be
 struck, a sound is  soon perceptible at the other end.   This
 we now know to be a vibration of the bar ; sound is but a word
 expressive of the mode of motion impressed on the bar;  so
 one end of a column of air or glass subjected to a luminous im-
 pulse gives a perceptible effect of hght at the other end : this
 can equally be conceived to be a  vibration or transmitted
 Snotion of particles in the transparent column : this question
 Ivill, however, be further discussed hereafter ;  for the present
Ave Avill confine ourselves to motion Avithin the limits to which
 the term is usually restricted.
   With the  perceptible phenomena of  motion the mental
conception has been invariably associated to  which  I have
before  alluded, and to  which  the  term force is given__
the which conception, when  atc analyse  it,  refers us to
some  antecedent motion.  If  we except the production of
motion by heat, light, &c, Avhich Avill be considered in tho
sequel, A^hen we see a body moving  Ave look to motion  hav-
ing been communicated to it by matter which has previously
moved.
   Of absolute rest Nature gives us no evidence :  all matter,
 as far as  we can ascertain, is ever in movement, not  merely 
MOTION.
27
in masses, as  with the planetary spheres, but  also mole-
cularly, or throughout its most intimate structure :  thus every
alteration  of  temperature  produces  a  molecular  change
throughout  the whole substance  heated or  cooled;  slow
chemical  or  electrical actions,  actions of light or- invisible
radiant forces, are always at play, so that as a fact we can-
not predicate of any portion of matter that it i3 absolutely at
rest.   Supposing, hoAveA-er, that motion is not an indispensa-
ble function of matter, but that matter can be at rest, matter
at rest would neA-er of itself cease to be at rest; it would not
move  unless impelled to such motion by some other moving
body,  or  body Avhich  has moved.   This  proposition applies
not merely to  impulsive motion, as Avhen a ball  at rest is
struck by a  moving body, or pressed by  a spring which  has
previously been moAred, but to  motion caused by attractions
such as magnetism or  gravitation.  Suppose a piece of iron
at rest in contact Avith a magnet at rest; if it be desired to
moAre the iron by the attraction of the magnet, the magnet or
the iron  dk::-t first be moved ; so before  a body falls it must
first be rai.cd.  A body at rest would therefore  continue so
for ever, and  a body once in motion would continue so for
ever, in  the same direction and with the same velocity,  un-
less  impeded by some other body, or affected by some other
force  than that which originally impelled it.  These propo-
sitions may seem somewhat arbitrary, and it has been doubted
Avhether they are necessary truths ; they have for a long time
been  received  as  axioms,  and there can at all events be no
harm in  accepting them as postulates.   It is however very
generally believed that if the Aisibie or palpable motion of
duo  body be arrested by impact on another body, the mo-
tion ceases,  and the  force  Avhich produced it is annihi-
lated.
    Now  tlie view which I  A-enture to submit is, that force
cannot  be annihilated, but L  merely subdivided or altered in
direction  or  character.  First, as  to direction.  Wave your 
 28         CORRELATION OF  PHYSICAL FORCES.

 hand: the motion, which has apparently ceased, is taken up
 by the  air, from the air by the walls of the room, &c,  and
 so by direct and reacting Avaves, continually comminuted, but
 never destroyed.   It is true  that, at a certain point, Ave lose
 all means of detecting the motion, from  its minute  subdivi-
 sion, which defies our most delicate  means of appreciation
 but Ave  can indefinitely extend our power of  detecting it ac-
 cording as we confine  its direction, or increase the delicacy
 of our examination.  Thus, if the hand be moved in uncon-
 fined air, the motion of the air  would not be sensible to a per-
 son at a few feet distance ; but if a piston of the same extent
 of surface  as the hand be moved Avith the same rapidity in a
 tube, the  blast of air may be distinctly felt at several yards
 distance.   There is no greater absolute amount of  motion in
 the air  in  the second than in the first case, but its direction
 is restrained, so to make the means of detection more facile.
 By carrying  on this  restraint, as  in  the air-gun,  we get a
 power of detecting the motion, and of moving  other bodies at
 far greater distances.   The puff  of air  which Avould in the
 air-gun project a bullet  a quarter of a mile, if allowed to es-
 cape without its direction being restrained, as by the bursting
 of a  bladder, Avould not be  perceptible  at a  yard distance,
 though the same absolute amount of motion be impressed on
 the surrounding air.
    It may, however, be asked, what becomes  of force Avhen
 motion is arrested or impeded by the counter-motion of another
 body ?  This is generally believed to produce rest, or entire
 destruction of motion, and  consequent annihilation of force:
 so indeed it may, as regards the mo'tion of the  masses, but a
new force, or new character of force, noAV ensues, the expo-
nent of which, instead of visible motion,  is heat.   I venture
to regard the  heat Avhich results  from friction or percussion
as a continuation of the  force which was  previously associa-
ted Avith the moving body, and which, when this impinges on 
MOTION.
29
another body, ceasing to exist as gross, palpable motion, con
tinues to exist as heat.
    Thus, let two bodies, A and B, be supposed to move in
opposite directions (putting for the moment out of question
all resistance, such as that of the air, &c), if they pass each
other without contact each  Aill move on for ever in its re-
spective direction with  the  same velocity, but if they touch
each  other the velocity of the movement of each is reduced,
and each becomes heated : if this contact be slight, or such as
to occasion but a slight diminution of  their velocity, as when
the surfaces of the bodies are oiled, then the heat is  slight;
but if the  contact be such as to occasion a great diminution
of  motion, as in percussion, or as Avhen the surfaces are
roughened, then the heat is great, so that in all cases the re-
sulting   heat  is  proportionate  to  the diminished  velocity.
AY here,  instead  of resisting and consequently impeding the
motion  of  the body A, the body B gives Avay, or itself takes
up the  motion originally communicated to A, then avc haATe
less heat in proportion to the motion of the body B, for  here
the operation of  the  force continues in the form of palpable
motion : thus the heat resulting from friction in the axle of a
Avheel is lessened by surrounding it by rollers ; these  take up
the primary motion of the axle, and the less, by this means,
the initial  motion is  impeded, the less is the  resulting heat.
Again, if a body move in a fluid, although some heat is pro-
duced, the  heat is apparently trifling, because the particles of
the fluid themselves move, and continue the motion originally
communicated to  the moving body :  for every portion of mo-
tion communicated to  them this loses an  equivalent, and
Avherc both lose, then an equivalent of heat results.
    As the converse of this proposition, it should folloAV that
the more rigid the bodies impinging on each other the greater
should be the amount of heat  developed by friction, and so
we  find it.  Flint, steel, hard  stones, glass, and metals, are
those  bodies  which give the greatest amount of heat from 
30         CORRELATION OF PHYSICAL  FORCES.
friction or percussion ; while water, oil, &c, give little or no
heat, and from the ready mobility of their particles lessen its
developement Avhen interposed between rigid moving bodies.
Thus, if Ave oil the axles of wheels, we have more rapid mo-
tion of the bodies  themselves, but less heat; if Ave increase
the resistance to motion, as by roughening the  points of con-
tact, so that each particle strikes  against and  impedes the
motion  of others, then Ave have diminished motion, but  in-
creased heat; or if the bodies be smooth, but instead of slid-
ing past each  other  be pressed closely together and  then
rubbed, we shall in many cases evolve more heat than by the
roughened bodies,  as we get a greater number  of particles in
contact and a greater resistance to the initial motion.   I can-
not present to my mind  any case of heat resulting from fric-
tion which is not explicable by this vieAV :  friction, according
to it, is simply impeded motion.   The  greater  the impedi-
ment, the more force is required to overcome it, and the
greater is the resulting heat; this resulting heat  being a con-
tinuation of indestructible force, capable, as Ave shall pres-
ently see, of reproducing palpable motion, or motion of defi-
nite masses.
    Whatever be the  nature of the  bodies, rough or smooth,
solid or liquid, provided there be the same initial force, and
the whole motion be ultimately arrested, there  should be the
same amount of heat developed, though Avhere the motion is
carried on through a great number of points of matter avc do
not so sensibly perceive the resulting heat from its greater
dissipation.   The  friction  of  fluids  produces heat, an effect
first noticed I believe  by Mayer.  The total heat produced by
the friction of fluids should,  therefore, it will  be said,  be
equal to that produced by the  friction of solids ;  for although
each  particle produces  little heat, the  motion  being readily
taken up by the neighbouring particles, yet by the time the
whole mass has attained a state of rest there  has been the
same impeding of  the initial motion as by the friction of sol- 
MOTION.
31
ids if produced by the same initial force.   If the  heat be
Ariewed in the aggregate, and alloAvance be made for the spe
cific thermal capacity of the substances employed, it probably
is  the same, though apparently less ;  the  heat in the case of
solids being manifested at certain defined  points, while in
that of fluids it is dissipated, both the time and space during
and through which the motion is propagated differ in the two
cases, so that the heat in the latter case is more readily car-
ried off by surrounding bodies.
    If the  body be elastic,  and by its reaction the motion im-
pressed on it by the initial force be continued, then the heat
is proportionately less ; and were a substance perfectly elas-
tic, and  no resistance opposed to it by the air or other mat-
ter, then the movement once impressed would be perpetual,
and no  heat would  result.   A ball of  caoutchouc bandied
about  for  many minutes  between a racket and a wall is not
perceptibly heated, Avhile  a leaden bullet  projected by a gun
against a wall is rendered so hot as to be intolerable to the
touch:  in the  former case, the motion of the mass is contin-
ued by the reaction  due  to  its  elasticity; in the latter, the
motion of the mass is extinguished, and heat ensues.
    A pendulum  started in the exhausted receiver of an air-
pump  continues  its  oscillation  for hours or even days; the
friction at its  point of suspension and the  resistance  of the
air is minimised, and the heat is imperceptible, but these tri-
fling resistances in the end arrest the motion of the mass, the
one giving it out as heat, the other conveying the force to the
receiver, and thence to surrounding bodies.   Similar reason-
ing may be applied to the oscillation of a coiled spring and
balance wheel.
    To wind up a clock a certain amount of force is expended
by the arm;  this force is given back by the descent  of the
weight, the wheels move, the pendulum is kept oscillating,
heat is generated at each point of friction, and the surround-
ing air is set in motion, a part of  Avhich is made obvious to 
32
CORRELATION  OF PHYSICAL FORCES.
 us by the  ticking sound.  But it Avill be  said, if instead of
 alloAving the weight to act upon the machinery, the cord by
 which it is suspended be cut, the weight drops and  the  force
 is  at an end.  By no means,  for in this case the house is
 shaken by the concussion,  and thus the force and motion are
 continued, while in the former case the weight reaches the
 ground  quietly, and no evidence of force or motion is mani-
 fested by its impact, the whole having been  previously  dissi-
 pated.
    If the  injtial motion, instead of being arrested by the im-
 pact of other bodies, as in friction or percussion, is impeded
 by confinement or compression, as where the dilatation of a
 gas is prevented by mechanical means, heat equally results :
 thus if a piston is used to compress air in a closed vessel, the
 compressed air  and, from it, the sides of the vessel will be
 heated:  the  air  being unable  to take  up and  carry on the
 original motion communicates molecular motion or expansion
 to  all bodies  in contact with it; and, conversely, if we ex-
 pand air by mechanical motion, as by withdraAving the pis-
 ton, cold is produced.  So  when a solid has its particles  com-
 pressed or  brought nearer together, as Avhen a bar of iron is
 hammered, heat is produced beyond that Avhich is due to per-
 cussion alone.   In this latter case Ave cannot very easily ef-
 fect the  converse result, or produce cold by the mechanical
 dilatation  of  a  solid, though the phenomena of  solution,
 Avhere the particles of a solid are detached from each other,
 or drawn more widely asunder, give us an approximation to
 it:  in the case of solution cold is produced.
    We are from a very extensive  range of observation and
experiment entitle**! to conclude that, with  some  curious ex-
ceptions  to be presently noticed, whenever  a body is com-
pressed or  brought into smaller dimensions it is heated, i. e.
it expands  neighbouring substances.  Whenever it is dilated
or increased in volume it is cooled, or contracts neighbourin"
substances. 
MOTION.
33
   Mr. Joule has made a great number of experiments for
the purpose of ascertaining what quantity of heat is produced
by a given mechanical action.   His mode of experimenting
is as follows.  An apparatus formed of floats or paddles of
brass or iron is made to rotate in a bath of Avater  or mercu-
ry.  The  power Avhich  gives rise to this rotation is a weight
raised  like a  clock-weight to a certain height; this  by acting
during  its fall on a spindle and  pulley communicates motion
to the  paddle-Avheel, the  Avater or mercury serving as a fric-
tion  medium and calorimeter ; and the heat is measured by a
delicate mercurial thermometer.  The  results of his experi-
ments  he considers  prove that  a fall of 772  lbs. through a
space of one foot is able to  raise  the temperature of one
pound  of water through one degree of Fahrenheit's thermon>
eter.   Mr. Joule's experiments  are of extreme delicacy—he
tabulates to the thousandth part of a degree  of Fahrenheit,
and  a  large number  of his  thermometric data are  compre-
hended within the  limits of a single degree.   Other experi-
menters have given very different numerical results, but the
general opinion seems to be that the numbers  given by  Mr.
Joule are  the nearest approximation to the truth yet obtained.
   Hitherto  I  have taken no distinction as  to the physical
character  of the bodies impinging on each other; but Nature
gives us a remarkable difference in the  character or mode of
the force  eliminated by friction,  accordingly as the bodies
which  impinge  are  homogeneous or heterogeneous: if the \
former, heat alone is produced ;  if the latter, electricity.
   We find, indeed, instances given by authors, of electricity
resulting from the friction of homogeneous bodies ; but,  as I
stated  in my original Lectures,  I have  not found  such facts
confirmed by my OAvn experiments, and this  conclusion  has
been corroborated by some experiments of Professor Erman,
communicated  to the meeting of  the British Association in
the year 1845, in which he found that no electricity resulted
from the  friction of  perfectly homogeneous substances ; as, 
34
CORRELATION  OF PHYSICAL  FORCES.
 for instance, the ends of a broken bar.  Such experiments as
. these will, indeed, be seldom free from slight electrical cur-
 rents, on account of the  practical  difficulty of fulfilling the
 condition of perfect homogeneity in the substances themselves,
 their size, their  temperature, &c.;  but the effects produced
 are very trifling and vary in direction, and the resultant effect
 is nought.  Indeed, it would be difficult to conceive  the con-
 trary.  How could we possibly image to  the  mind  or de-
 scribe the direction of a current from the same body to the
 same body, or give instructions for a repetition of the  exper-
 iment ?  It would be unintelligible to  say that in rubbing to
 and fro two  pieces of bismuth, iron, or glass, a current of
 electricity circulated  from bismuth  to bismuth, or  from iron
 to iron, or from glass to glass ; for the question  immediately
 occurs—from  which  bismuth to which  does it  circulate?
 And should this  question be answered by calling one piece
 A, and the other B, this  would only apply to the particular
 specimens  employed, the  distinctive  appellation denoting a
 distinction in fact, as  otherwise A could be substituted for B,
 and the bar to which the positive electricity flowed would in
 turn become the bar to which the negative electricity flowed.
 We may say that it circulates from  rough glass to smooth,
 from cast iron to wrought, for here there is not homogeneity.
 It is moreover conceivable, that when the motion is contin-
 uous  in a  definite direction, electricity may result  from the
 friction of  homogeneous bodies.   If A and  B rub against
 each  other, revolving in opposite directions, concentric cur-
 rents of positive  and negative electricity may be conceived
 circulating within the metals, and be described  by reference
 to the direction of their motion ; this indeed would be a dif-
 ferent phenomenon from those we have been considering; but
 without some distinction between the two substances in qual-
 ity or direction, the electrical effects are indescribable, if not
 inconceivable.
    When,  however,  homogeneous bodies  are  fractured  or 
MOTION.
35
even rubbed together, phenomena are observed to Avhich the
term electricity is apphed;  a flash or line of light appears at
the point of friction which  by some is called electrical, by
others phosphorescent.
   I have myself observed a remarkable case of the kind in
the caoutchouc fabric now  commonly  used for Avaterproof
clothing :  if two  folds of this substance be alloAved to cohere
so as partly to  unite and present a difficulty of separation,
then, on stripping the one  from the other, or  tearing them
asunder, a line of light will  follow the line of separation.
   If this class  of  phenomena be electrical, it is electricity
determined as it  is generated ; there is  no dual character im-
pressed on the matter acting, the flash is electrical as a spark
from the percussion of flint is electrical, or as the slow  com-
bustion of phosphorus, or any other case of the development
of heat and light.   It seems to be  better to class this phe-
nomenon under the categories of heat  and Hght than  under
that of electricity, the latter word  being  retained for those
cases where a dual or polar  character of force is manifested.
In experiments which have been made  by the friction of sim-
ilar  substances  where the   one appears positively  and the
other negatively electrical, there will be  found some  differ-
ence in the mode of  rubbing by which the molecular  state of
the bodies is in all probability changed, making one a dissim-
ilar  substance from the  other ; thus it is said by Bergmann,
that when two pieces of  glass are rubbed so that all the parts
of one pass over one part of the other, the former is positive
and  the latter negative.  It is obvious that  in this  case the
rubbing  in one is confined to a line, and that must be more
altered in molecular structure at the hue of friction than the
one where  the friction is spread over the whole surface: so
if a ribbon be drawn transversely over another ribbon, the
substances  are  not, qua  the  rubbing action, identical; so
again, in the rupture of crystals, we  are dealing with  sub-
stances having a polar arrangement of particles—the surfaces 
36         CORRELATION OF PHYSICAL  FORCES.
 of the fragments cannot be assumed to be molecularly identi-
 cal.
    The developement of electricity by the common electrical
 machine arises, as far as I can understand it, from the sepa«
 ration or rupture of contiguity between  dissimilar bodies ;  a
 metallic  surface, the  amalgam of the cushion, is in contact
 with glass ; these two bodies  act upon  each other by the force
 of cohesion; and  when, by an  external  mechanical force,
 tins is ruptured, as it is at each moment of the motion of the
 glass  plate or cylinder, electricity is deA-eloped in each; were
 they similar bodies, heat only would be developed.
   According to the experiments of Mr. Sullivan electricity
 may be produced by vibration alone if the substance vibra-
 ting be composed either of dissimilar metals, as a wire partly
 of iron and partly of brass caused to  emit a musical sound ;
 or of the  same  metal, if its  parts be not homogeneous, as a
 piece  of iron, one  portion of which is hard  and  crystallised
 and the other soft and fibrous; the current resulting appears
 to be  due to the vibration, and not to heat engendered, as  it
 ceases immediately with the \ribration.
   We may say, then, that in our present state of knowledge,
 where the mutually impinging bodies are homogeneous, heat
 and not electricity is the result of friction and percussion;
 where the bodies impinging are heterogeneous, we may safely
 state that electricity is always produced by friction or percus-
 sion, although heat in a greater or less  degree  accompanies
it; but when we come to the question of ratio in Avhich fric-
tional  electricity is produced, as determined by the different
 characters of the substances employed, we find very complex
results.  Bodies may differ in so many particulars which in-
fluence more or less the developement of electiicity, such as
their  chemical constitution, the state of their surfaces, their
state  of aggregation,  their  transparency or opacity, their
power of conducting electricity, &c, that the normce of their
action are very difficult of attainment.   As a general rule,  it 
MOTION.
37
may be said that the developement of electricity is greater
when the substances employed are broadly distinct in their
physical and chemical qualities, and more particularly in their
conducting poAvers ; but up to the present time the laws gov-
erning such developement haAre not been even approximately
determined.
    I have said, in reference to the various forces or affections
of matter, that either of them may, mediately or immediately,
produce the others ;  and this is all I can venture to predicate
of them in the present state of science ; but after much con-
sideration I incline strongly to the opinion that science is rap-
idly progressing towards  the establishment of immediate  or
direct  relations between all these forces.   Where  at present
no  immediate  relation  is  established between  any of them,
electricity  generally forms the interA'ening link  or middle
term.
    Motion, then, will  directly produce heat and electricity,
and electricity, being produced by it, will produce  magnetism
—a force which is always developed by electrical currents at
right angles to the direction of those currents, as will be sub-
sequently more fully explained.  Liglvt also is readily pro-
duced by motion, either directly, as when  accompanying the
heat of friction,  or  mediately, by electricity resulting from
motion ; as in the electrical spark, which has most of the  at-
tributes of  solar light, differing from it only in those respects
in which light differs wdien emanating from different sources
or seen through different media ; for instance, in the position
of the fixed lines  in the spectrum or in the ratios of the spaces
occupied by rays of different refrangibility.  In the decom-
positions and compositions Avhich the terminal points proceed-
ing from the conductors of an electrical machine develope
when immersed in different chemical  media, we get the pro-
duction of chemical affinity by  electricity, of which  motion is
the  initial source.   Lastly, motion  may be again reproduced
by the forces which  have emanated from  motion; thus, tho 
38         CORRELATION OF PHYSICAL  FORCES.

divergence of the electrometer, the revolution of the electri-
cal  wheel, the deflection of the  magnetic needle, arc, when
resulting from frictional electricity, palpable movements re-
produced  by the  intermediate modes of force,  which  have
themselves been originated by motion. 
III. —HEAT.
  IF Ave now take Heat as our starting point, Ave shall find
   that the other modes of force may be readily produced by
it.  To take motion first: this is so generally, I think I may
say invariably, the immediate effectof heat,thatwe mayalmost,
if not entirely, resolve heat into motion, and  view it  as  a
mechanically repulsive force, a force antagonist to attraction
of cohesion or aggregation, and tending to move the particles
of all bodies, or to separate them from each other.
   It may be well here to premise, that in  using the terms
' particles ' or  ' molecules,' which will be frequently employed
in this Essay, I do not use them in the sense of the atomist,
or mean to assert that matter consists of inckVisible particles
or atoms.  The words will be used for the necessary purpose
of contradistinguishing the action of the indefinitely minute phy-
sical elements of matter from that of masses having a  sensi-
ble magnitude, much in the same way as the term ' lines' or
' points' may be used, and  with  advantage in  an abstract
sense ; though there does not exist, in fact, a thing which has
length and breadth without thickness, and though a thing with-
out parts  or dimensions is nothing.
    If Ave put aside the sensation which heat produces in our
own bodies, and regard heat simply as to its effects upon in-
organic matter, we find that, with a very few exceptions, which I 
  40         CORRELATION OF PHYSICAL  FORCES.

  shall presently notice, the effects  of what is  called heat ara
  simply an expansion of the matter  acted upon, and that the
  matter so expanded has the power by its own contraction of
  communicating expansion to  all bodies in contiguity with it.
•  Thus, if the body be a solid, for  instance, iron, a  liquid, say
  water, or a gas, say atmospheric air—each  of these, when
  heated, is expanded in every direction;  in  the two former
  cases, by increasing the heat to a certain point,  we  change
  the physical character  of the substance, the solid  becomes a
  liquid, and the liquid becomes  a  gas ; these, however, are
  still expansions, particularly  the  latter,  when, at a certain
  period, the expansion becomes rapidly and indefinitely greater.
  But what is, in fact, commonly done in order to  heat a sub-
  stance, or to increase the heat of a substance? it is  merely
  approximated to some  other heated, that is, to some  other
  expanded substance, Avhich latter is cooled or contracted as
  the former expands.  Let us now divest the mind of the impres-
  sion that heat is in  itself anything substantive, and suppose
  that these phenomena  are regarded for  the  first  time, and
  without any preconceived notions on the subject;   let us in-
  troduce no hypothesis,  but merely express as simply as Ave
  can the facts of which  we have become cognisant; to  what
  do they amount?  to this, that matter has pertaining to it a
  molecular repulsive poAver, a power of  dilatation, which is
  communicable by contiguity or proximity.
     Heat thus viewed, is motion,  and this molecular  motion
  Ave may readily change into the motion of masses, or motion
  in its most ordinary and palpable  form  :  for example, in the
  steam engine, the piston and  all  its concomitant  masses  of
  matter are moved by the molecular dilatation of the vapour of
  water.
     To produce continuous motion there must be an alternate
  action of heat and cold; a given  portion of air, for instance,
  heated beyond the temperature of the  circumambient  air, is
  expanded.  If now it be made to act on  a movable piston, it 
nEAT.
41
moves this to a point at which the tension or elastic force of
the confined air equals that of the  surrounding air.  If the
confined air be kept at this  point, the  piston would remain
stationary;  but if it be  cooled, the external  air exercising
then a greater relative degree of pressure, the piston returns
toAvards its original position ; just as it will be seen, when we
come to the magnetic force, that a magnet placed in a partic-
ular position produces motion in iron  near it,  but to  make
this motion continuous, or to obtain  an available mechanical
power, the magnet must be demagnetised, or a  stable equili-
brium is obtained.
   In the case of the piston moved  by heated air the motion
of the mass becomes the  exponent of the amount of heat—
i. e. of the expansion or separation  of the molecules ; nor do
we, by any of our ordinary methods, test heat  in any other
way than  by its purely dynamical action.  The various modi-
fications of the thermometer and pyrometer are all measur-
ers of heat by motion: in these instruments liquid or solid
bodies are expanded and elongated,  i. e. moved in  a definite
direction,  and, either by their own visible motion, or by  the
motion of an attached index, communicate to our senses  the
amount of the force  by which they moved.   There are, in-
deed, some delicate experiments Avhich tend to  prove that a
repulsive action between separate masses is produced by heat.
Fresnel found that mobile bodies heated in an  exhausted re-
ceiver repelled each  other to sensible distances; and Baden
Powell found that the coloured rings usually called Newton's
rings change their breadth and position, when the glasses be-
tween Avhich they appear are  heated, in a manner  which
ehoAved that the glasses repelled each other.   M. Faye's the-
ory of comets is based on some such repellent force.  There
is, however, some difficulty in presenting these phenomena to
the mind in the same aspect as the molecular repulsive action
of heat.
   The phenomena of what is termed latent heat have beep 
42         CORRELATION OF  PHYSICAL FORCES.
generally considered as strongly in favour of that view which
regards heat either as  actual matter, or, at  all events, as a
substantive entity, and not a motion or  affection of ordinary
matter.
   The hypothesis of latent matter is, I venture  Avith  diffi-
dence to think, a dangerous one—it is something like the old
principle of Phlogiston, it is not tangible, visible, audible;
it is, in fact, a mere  subtle mental  conception,  and ought, I
submit, only to be received on  the ground of absolute neces-
sity, the more so as these subtleties are  apt  to be  carried on
to other natural phenomena, and so they add to the hypothe-
tical scaffolding Avhich is seldom  requisite,  and  should  be
sparingly used, even in the early stages of discoA'cry.  As an
instance, I think a striking one, of the injurious  effects  of
this, I Avill mention the analogous doctrine of ' invisible light;'
and I do this, meaning no disrespect to  its distinguished au-
thor, any more than in discussing the doctrine of latent heat,
I can be supposed, in the slightest degree, to aim at detract-
ing from the merits of the illustrious investigators of the facts
which that doctrine seeks to explain.  Is not' invisible light,'
a contradiction in terms ?  has not light ever been regarded as
that  agent which affects our visual   organs ?   Invisible Hght,
then, is darkness, and if it exist, then  is  darkness light.   I
know it may be said, that one eye can detect light where
another cannot; that a cat may see  where a man cannot; that
an insect may see where  a cat cannot;  but then it is not
invisible light to those  who see it: the light, or rather  the
object seen by  the cat, may be  invisible  to the man, but it
is  visible to  the cat,  and, therefore, cannot abstractedly be
said  to be invisible.   If we go further, and find an agent
which affects certain substances  similarly to light, but does
not, as far as we are aware, affect  the  visual organs of any
animal, then is it not an erroneous  nomenclature which calls
such an agent light ?   There are many cases in which a de-
viation from the once accepted  meaning of words has so grad- 
HEAT.
43
ually entered into common usage as to be unavoidable, but I
venture to think that additions to such  cases should as far
as possible be avoided, as injurious to  that precision  of lan-
guage which is one  of the safest guards to knowledge, and
from the absence of which physical  science has materially
suffered.
   Let us now shortly examine the question of latent heat,
and  sec  whether the phenomena cannot be as well,  if not
more  satisfactorily, explained without the hypothesis of la-
tent matter, an  idea presenting many similar  difficulties to
that of invisible hght, though  more  sanctioned  by usage.
Latent heat is supposed to be the matter  of heat, associated,
in a masked or dormant state, with ordinary matter, not ca-
pable of being detected by any test so long as the matter with
which it is associated remains in the same physical state, but
communicated to or absorbed from other  bodies, when the
matter writh Avhich it is  associated changes  its  state.   To
take a common example : a pound or  given weight of  water
at 172°, mixed with an equal weight  of water at 32°, will
acquire a mean temperature, or 102° ; Avhile water at 172°,
mixed with an equal weight of ice at 32°, AArill be reduced to
32°.  By the theory of latent heat this phenomenon is thus
explained:—In the  first case, that of the mixture  of water
with water, both the bodies being in the same physical state,
no latent heat is rendered  sensible, or sensible heat latent;
but in the second, the ice  changing its condition from the solid
to the liquid state abstracts from the liquid as much heat  as
it requires to maintain it  in the liquid  state, which it renders
latent, or retains associated with itself, so long as it remains
liquid, but of which heat no evidence  can be  afforded by any
thermoscopic test.
   I believe  this and similar phenomena, where heat is con-
nected with a  change of state,  may be explained and dis-
tinctly comprehended without recourse to the conception of
latent heat, though  it requires some effort of the  mind to di» 
44
CORRELATION  OF PHYSICAL FORCES.
vest itself of this idea, and to view the phenomena simply in
their dynamical relations.   To assist us in so vie-wing them,
let  us first  parallel  with purely mechanical actions, certain
simple effects of heat, where change of state (I mean such
change  as from the solid to the liquid,  or liquid to the gase-
ous state) is not concerned.  Thus, place within a receiver a
bladder, and  heat  the air  within to a higher temperature
than that without it, the bladder expands;  30, force the air
mechanically into it by the  air-pump, the bladder expands ;
cool the air on the  outside,  or remove its pressure mechani-
cally by an exhausting pump, the bladder also  expands ; con-
versely, increase the external repellent force, either by heat
or mechanical pressure, and the bladder contracts.   In the
mechanical  effects,  the force  which produced the distension
is derived from, and at the expense of, the mechanical power
employed, as from muscular force, from gravitation, from the
reacting elasticity of springs,  or any similar force by which
the air-pump may be worked.   In the  heating effects,  the
force is  derived  from the  chemical action in the  lamp or
source of heat employed.
    Let us next consider the experiment so arranged  that the
force, which produces  expansion in the  one case, produces a
correlative contraction  in the other: thus, if two bladders,
Avith a connecting neck between them, be half-filled with air,
as the one is made to contract by pressure the other  will di-
late, and vice versa ;  so a bladder partly filled writh cold air,
and contained within  another filled with hot air, expands,
while the space between the bladders contracts, exhibiting a
mere transfer of the same amount of repulsive  force, the
mobility of  the particles, or their mutual attraction, being
the same in each body; in other words, the repulsive force
acts in the  direction of least resistance until equilibrium is
produced ; it then becomes  a static or balanced, instead of a
dynamic or  motive force.
    Let  us  now consider the  case where  a  solid is to  bo 
HEAT.
45
changed to a liquid, or a liquid to a gas ; here a much great*
er amount of heat or repulsive force is required, on account
of the cohesion of the particles to be separated.   In order to
separate  the particles of the  solid,  precisely as  much force
must be  parted Avith by the warmer liquid body as keeps an
equal quantity of it in its liquid state ; it is, indeed, only with
a more striking line of demarcation, the case of the hot and
cold bladder—a part of the repellent poAver  of the hot parti-
cles is transferred to the cold particles, and separates them in
their turn, but the antagonist force of cohesion or aggregation
necessary to be overcome, being in this case much stronger,
requires  and exhausts  an exactly proportionate  amount of
repellent force mechanically to overcome it;  hence the differ-
ent effect  on a body such as the  common thermometer, the
expanding liquid of which does not undergo a similar change
of state.   Thus, in the example above given, of the mixture
of cold  Avith hot water, the  hot  and cold  water and  the
mercury of the  thermometer being all in a liquid state before,
and remaining  so after contact, the resulting temperature is
an exact  mean ; the  hot water contracts to a certain extent,
the cold water  expands to the same extent, and the ther-
mometer  either sinks or rises the same^ number of degrees,
accordingly as it had been previously immersed in the  cold
or in the hot solution, its mercury gaining or losing an equiva-
lent of repellent force.  In the second instance, viz. the mix-
ture of ice with hot  water, the substance we use  as an indi-
cator, i.  e. mercury, does  not undergo the same physical
change as those  whose relations of volume we are examining.
The force—viewing heat simply as mechanical force—which
is employed in loosening or tearing  asunder the particles of
the sohd ice, is abstracted  from the liquid water, and from
the liquid mercury of the thermometer, and in proportion as
this  force meets with  a greater  resistance in  separating
the particles  of a solid than  of a liquid, so  the  bodies
which  yield the force suffer proportionately a greater con-
traction.                                 • 
 48         CORRELATION OF PHYSICAL  FORCES.

    If we compare the  action of heat on the two substances,
 water and mercury, alone, and throw out of our consideration
 the ice, we shall be able  to apply the same view:  thus, if a
 given source of heat be applied to water containing a mercu-
 rial  thermometer, both  the Avater and mercury gradually ex-
 pand, but in different degrees ; at a certain point the attrac-
 tive  force of  the  molecules of the Avater is so far overcome
 that the water becomes vapour.   At this point, the heat or
 force, meeting Avith much less resistance from the  attraction
 of the particles of steam than from those of the mercury, ex-
 pends itself upon the  former; the mercury does  not further
 expand,  or expands in an infinitesimally  small  degree, and
 the steam expands greatly.  As soon  as  this arrives at a
 point Avhere circumambient  pressure causes its resistance to
 further expansion to  be equal to the resistance to expansion
 in the mercury of the  thermometer, the latter  again rises,
 and  so both  go  on expanding in an inverse ratio to their
 molecular attractive force.   If the circumambient pressure be
 increased, as by confining the water at the commencement
 of the experiment within  a  less expansible body than itself,
 such as a metallic  chamber, then the mercury of  the  ther-
 mometer continues  to rise ; and if the experiment were con-
 tinued, the v/ater being  confined and not the  mercury, until
 we have arrived at a degree  of repulsiAre force Avhich is able
 to overcome the cohesive poAver of the mercury, so  that  this
 expands into  vapour,  then we get the converse  effect; the
force  expends  itself upon the  mercury, which expands  in-
 definitely, as the water did  in the first case, and the water
 does not expand at all.
   Another  very usual  mode  of regarding the subject may
cmbarras  at first sight, but  a little  consideration will sIioav
that it is explicable by the same doctrine.   Water which has
ice floating in  it will give, when measured by the thermo-
meter, the same temperature as the  ico ; i. e.  both the Avater
nnd ice contract the mercury of the thermometer to the point 
HEAT
47
conventionally marked as 32°.  It may be said, how is this
reconcileable with the  dynamical doctrine, for, according to
that, the solid  should take  from  the  mercury of the ther-
mometer more  repulsive  poAver  than  the liquid;  conse-
quently, the ice should contract the mercury more than the
water?
   My ansAver is, that in the proposition as thus stated, the
quantities of the water, ice, and mercury are not taken into
consideration, and hence  a  necessary dynamical element is
neglected:  if the element of  quantity be included, this objec-
tion will not apply.   Let the thermometer, for instance, con-
tain 13  oz. of mercury, and stand at 100° ; if placed in con-
tact  with an unlimited quantity of ice  at 32°, the mercury
will  sink to  32°.  If the same thermometer be immersed in
an unlimited quantity of Avater at 32 °, the mercury sink3 also
to 32 5; not absolutely, perhaps, because, however great tho
quantity of  water or ice, it will be someAvhat raised in tem-
perature by the warmer mercury.   This elevation of tempera-
lure above 32° will be smaller in proportion as the  quantity
of water or ice is larger than the quantity of mercury ;  and,
as we know of  no intermediate state between ice and water,
the contact  of a thermometer at  a temperature above the
freezing point with any quantity of ice exactly at the freezing
point  would, theoretically speaking,  liquefy the Avhole, pro-
vided it had sufficient time ;  for as every portion of that ice
would in time have its temperature raised by the contact of
the warmer body, and as any elevation of temperature above
the freezing point liquefies ice, every portion should be lique-
fied.   Practically speaking, howeA-er, in both cases, that of
the water and  of the ice,  when the quantity is indefinitely
great the thermometer falls to 32°,
   Now place  the same thermometer  at 100 °, successively
in one oz. of water at 32°, and in one of ice  at 32°; Ave shall
find in the former case it will be lowered only to 54°, and in
the latter to  32° ; apply to this the doctrine of repulsive force,
and Ave get a satisfactory explanation. 
48
CORRELATION OF PHYSICAL FORCES.
    In the first case, the  quantities both of ice and water be-
 ing indefinitely great in respect to the  mercury, each reduces
 it to its own temperature, ATiz. 32°, and the ice cannot reduce
 the mercury below 32°, because it would receive back repul-
 sive power  from the newly formed water, and this would be-
 come ice ; in the second case, where the quantities are limited,
 the mercury does lose more repulsive power by the ice than by
 the water, and the observations made in reference to the first
 illustration apply.
    The  above doctrine is beautifully instanced in the experi-
 ment of  Thilorier, by which carbonic acid is solidified.  Car-
 bonic acid gas,  retained in a strong vessel under great pres-
 sure, is  allowed to escape from a small orifice ;  the sudden
 expansion requires so great a supply of force, that in furnish-
 ing the  demands of the expanding gas certain other portions
 of the gas contract to such an extent as to solidify:  thus, we
 have  reciprocal expansion and contraction going on in one
 and  the  same substance, the time  being too limited for the
 whole to assume a uniform temperature, or in  other words, a
 uniform extent of expansion.
   It has been observed with reference to heat thus viewed,
 that it would  be as correct to say, that heat is absorbed, or
 cold produced by motion, as that heat  is produced by it. This
 difficulty ceases  Avhen  the mind has been accustomed to re-
 gard heat and cold as themselves, motion ; i. e. as correlative
 expansions and contractions, each being evidenced by relation,
 and being inconceivable as an abstraction.
   For instance, if the  piston of an air-pump be drawn down
by a weight, cold is produced in the receiver.  It may be here
 said that a mechanical  force, and the motion consequent upon
it, produces  cold; but  heat is  produced on the opposite side
 of the piston, if a receiver be adapted so as to retain the com-
pressed  air.  Assuming them to equivalise each other, the
force of the falling weight would be expressed by the heat of
friction of the piston against its tube,  and by the tension or 
HEAT.
49
 power of reaction of the compressed  against the dilated air.
 If the heat due to compression be made to perform mechani-
 cal work, it Avould pro tanto be consumed, and could  not
 restore the temperature to the dilated air ;  but  if it perform
 no work, no heat  is lost.   Mr. Joule has experimentally
 proved this proposition.
    In commencing the subject of heat, I asked  my reader to
 put out of consideration the  sensations which heat produces
 in  our own bodies; I  did this because these sensations are
 likely to deceive, and haA-e deceived many as to  the nature of
 heat.   These sensations are  themselves occasioned by simi-
 lar expansions to those Avhich we have been considering;  the
 liquids of the body are expanded, i. e.  rendered  less viscid by
 heat, and from their more ready flow, we obtain  the sensation
 of agreeable Avarmth.  By a greater degree of heat, their ex-
 pansion becomes too great, giving rise  to a sense of pain, and,
 if pushed to  extremity,  as with the heat which  produces a
 burn, the liquids of the body are  dissipated in vapour, and an
 injury or destruction of the organic structure takes place.  A
 similar though  converse effect may be produced by intense
 cold; the application of frozen mercury to the animal body
 produces a burn similar  to that produced  by great heat, and
 accompanied with a similar sensation.
    Doubtless other actions than those above mentioned inter-
 fere in producing the sensations of heat and cold ; but I think
 it will be  seen that these will not affect the arguments as to
 the  nature of  heat.  The phenomenal effects will be four d
 unaltered : heat will still be found to be expansion, cold to be
 contraction ; and the expansion and contraction are, as with
 the  two bladders of air,  correlative—i. e. we cannot  expand
 one body,  a, without  contracting some other body, b ;  we
cannot contract a without expanding b, assuming that we view
the  bodies Avith relation to heat alone, and suppose no other
force to be manifested.
   I have said that there are few exceptions as to heat bein«
             3 
50
CORRELATION  OF PHYSICAL FORCES.
always manifested by an expansion of matter.   One class of
these exceptions i3  only apparent:  moist clay,  animal or
vegetable fibre, and other substances  of a  mixed  nature,
which contain matter of different characters, some of which is
more and some less volatile, i. e. expansible, are contracted
on the application of heat; this arises from the more volatile
matter being dissipated in the form of vapour or gas ;  and the
interstices of the less volatile being thus emptied, the latter
contracts by its own cohesive attraction, giving thus a prima
facie appearance of  contraction by heat.  The pyrometer of
Wedgwood is  explicable  on this principle.
   The second class of exceptions, though much more limited
in extent,  is  less easily explained.  Water,  fused bismuth,
and  probably  some  other  substances (though  the fact as to
them is  not clearly estabhshed),  expand as they approach
very near to  the  freezing or solidifying point.  The most
probable explanation of these exceptions is, that at the point
of maximum  density the molecules of these bodies assume  a
polar or crystalline condition;  that by the  particles being
thus  arranged in linear  directions like chevaux de frise,
interstitial  spaces are left, containing matter of less  den-
sity, so that the specific density of the  Avhole mass i3 dimin-
ished.
    Some recent experiments of Dr. Tyndall on the physical
properties  of  ice seem to favour  this  A'iew.  When a sun-
beam, concentrated by a lens, is  allowed to fall  on a piece
of apparently homogeneous ice  the path  of the rays is in-
stantly studded with numerous luminous spots like minute air
bubbles, and  the planes of  freezing are  made manifest by
these and  by small fissures.   Stars or  flower-like figures of
six petals appear parallel to the  plane3 of freezing, and seem-
ingly spreading out from a central bubble.   These  flowers
are formed of water.  When the ice is melted in warm water
no air is given off from the bubbles, so they seem to be va-
cuous ; it  h,  however,  possible that extremely minute parti' 
HEAT.
51
cles of air sufficient to form foci for the melting points of ice
might be dissolved by the Avater as soon as they came in con-
tact with it.  Be this as it may, the existence of these points
throughout the kv, where it gh'es way to the heat of the solar
beam, if it does not prove actual vacuous or aeriform spaces
to exist in ice, proves  that it  is not homogeneous, that its
structure  is  probably definitely crystalline, and  that the
matter composing it is in different degrees of aggregation, so
that its mean specific  gravity might well be less than that of
water.
    We cannot examine  piecemeal the ultimate structure of
matter, but  in  addition  to  the  fact that the  bodies which
evince this peculiarity are bodies which, when solidified, ex-
hibit a very marked  crystalline character, there are experi-
ments which shoAv that water between the  point of maximum
density and its point of solidification polarises light circularly ;
showing, if these experiments be correct, a structural altera-
tion in Avater, and one analogous to that possessed by certain
crystalline solids, and  to that possessed by water itself, where
it is forcibly made to assume a polarised condition by the in-
fluence of magnetism.
    The accuracy of these results has, however, been doubted,
and the experiments  have not succeeded Avhen repeated by
very experienced  hands.  Whether this  be so or not, and
whether the  above  explanation of the exception to the other-
wise invariable effect of expansion by heat be or be not re-
garded as  admissible, must  be left to the  judgment  of each
individual  who thinks upon the subject; at  all events, no
theory of heat yet proposed removes the difficulty, and there-
fore  it equally opposes every other  view  of  the  phenom-
ena of heat, as it  does  that which I  have  here   consid-
ered, and which  regards heat  as communicable  expansive
 force.
    As certain bodies expand in freezing, and  indeed, under
 some circumstances, Defore they arrive at the temperature at 
 52 .        CORRELATION OF PHY'SICAL  FORCES.

 which they solidify, we  get the  apparent anomaly that tho
 motion or mechanical force generated by heat or change of
 temperature is reversed in direction when we arrive at the
 point of change from the  solid to the liquid state.   Thus a
 piece of ice  at the temperature of Zero, Fahrenheit, would
 expand by heat, and produce a mechanical force by such ex-
 pansion  until it arrives at 32°; but then by an increment of
 heat it contracts, and if the first expansion had moved a pis-
 ton upwards, the subsequent contraction Avould bring it back
 to a certain extent, or move it doAvnwards, an apparent nega-
 tion of the force of heat.
    Again  with  water above  40°,  i. e, above its point  of
 maximum density, a progressive increment of cold or decre-
 ment  of heat would  produce  contraction to a certain point,
 and then expansion or a mechanical force in an opposite direc-
 tion.   Thus not only heat  or  the  expansive force given  to
 other bodies by a  body cooling wrould be given out by water
 freezing, but also the force due to the converse expansion in the
 body itself, and force would thus seem  to be got out of noth-
 ing : but if water in a confined space be gradually cooled, the
 expansion attendant on its cooling as it approaches the freez-
 ing point would occasion pressure amongst its particles, and
 thence tend to antagonise the force of dilatation produced in
 them  by cooling, or to resist their tendency to freeze ; or in
 other words, the pressure would tend to liquefaction, and con-
 versely to the usual effect of pressure, produce cold instead
 of heat, and thus neutralise some of the  heat yielded by the
 cooling  body.  Hence we  find that it requires a lower tem-
 perature to freeze  water  under pressure than when exempt
 from it, or that the freezing point is lowered as the pressure
increases for bodies which expand in freezing—an effect first
predicted by Mr.  J. Thompson, and experimentally verified
by Mr.  W.  Thompson ; Avhile  as shown by M. Bunsen, the
converse effect takes  place  with bodies which  contract in
freezing.  Here the pressure cooperates Avith  the effects  of 
HEAT.
53
cold, both tending to approximate the particles, and such sub-
stances solidify at a higher  temperature in proportion as the
pressure is greater ; so that we might expect a body of this
class, which under  the  ordinary pressure of the  air is at a
temperature  just  above its freezing point,  to  solidify  by
being submitted  to  pressure  alone, the  temperature being
kept constant.
    A  similar class of exception to the general  effect  of
heat in expanding bodies  is  presented by vulcanised caout-
chouc.  This has been observed by Mr. Gough, and,  in-
deed,  Avas  pointed  out to me many years ago by Mr.
Brockedon to be heated Avhen stretched, and cooled Avhen
unstretched.
    Mr. Joule  finds that its  specific gravity is lower when
stretched  than when  unstretched, and that when  heated
in  its  stretched  state it shortens, presenting in  this par-
ticular  condition a  similar series  of converse  relations to
those which are presented by water near or at its freezing
point.
    With  the exception of this class of phenomena, Avhich
offer difficulties to any theory which has been proposed, the
general phenomena of heat may, I believe, be explained upon
a purely dynamical  A'ieAV, and  more satisfactorily than  by
having recourse to the hypothesis of latent matter.   Many,
howeA'er, of the phenomena of heat are  involved  in much
mystery, particularly those  connected Avith specific heat  or
that relative proportion of heat Avhich equal weights of differ-
ent bodies require to raise them from a given temperature to
another given temperature, which appear to depend in some
way hitherto  inexphcable upon the molecular  constitution  of
different bodies.
    The view of heat which  I have taken, viz. to  regard it
simply as  a communicable molecular  repulsive force, is sup-
ported by many of the phenomena to which the term specific
or  relative heat  is apphed; for example, bodies as they in- 
54         CORRELATION OF PHYSICAL FORCES.

crease in temperature increase in specific heat.   The ratio
of this increase in specific heat is  greater with sohds than
with  liquids, although  the latter  are  more  dilatable ;  an
effect probably  depending upon the commencement of fusion.
Again, those metals Avhose rate of expansion increases most
rapidly whe~ they are heated, increase most in specific heat ;
and  their specific heat is reduced by percussion, which, by
approximating  their particles,  makes them specifically more
dense.   When, however, we  examine  substances  of very
different  physical characters, we find that their specific heata
have  no  relation  to their  density or rate of expansion  by
heat; their  differences of specific  heat must  depend upon
their  intimate molecular  constitution in a manner accounted
for (as far as  I am  avrare) by no  theory of heat  hitherto
proposed.
   In the greater number, probably in all sohds and liquids,
the expansion by heat is relatively greater as the temperature
is higher; or, preserving the vieAV of expansion and contrac-
tion, if two  equal portions of the same  substance be juxta-
posed at  different  temperatures, the hotter portion will con-
tract a little  more than  the colder  will expand; from this
fact, Adz.  that the coefficient of expansion increases in a given
body with the  temperature, and from other considerations,
Dr. Wood has argued, Avith much apparent reason,  that the
nearer the particles of bodies are to each other, the less they
require to move to produce a given expansion or  contraction
in those of another body.   His mode of reasoning, if  I rightly
conceive  it, may be concisely put as follows :—
   As bodies  contract by cold, it is clear that,  in  a given
body, the lower the temperature the nearer are the particles ;
and,  as  the coefficient of expansion increases Avith the tem-
perature, the lower the temperature of the substance be, the
less  the  particles require to move, or approach to or recede
from each other, so as to  compensate the correlative recession
n approach of the particles in a hotter  portion of the samo 
                          iieat.                        55

substance,  that is, in another portion of the same substance
in Avhich the particles  are  more  distant from each  other.
The amount of approximation or recession of the particles of
a body, in other Avords, its change of bulk by a given change
of temperature, being thus in a given substance an index of
the relative proximity of its particles, may it not be so of all
bodies?  The proposition is very ingeniously argued by Di\
Wood, but the argument is based upon certain hypotheses as
to the size3 and  distances of atoms, which must be admitted
as  postulates by  those Avho adopt his  conclusions.   Dr.
Wood seeks by means of this theory to explain the heat pro-
duced by chemical combination, and I shall endeavour to give
a sketch of his mode of reasoning Avhen I arrive at that part
of my subject.
    Although the comparative effects of specific heat may not
be satisfactorily  explicable by any known theory, the absolute
effect of heat upon each separate substance is simply expan-
sion, but when  bodies  differing in  their  physical characters
are  used, the rate of expansion varies,  if measured by  the
correlative  contractions  exhibited by the substances produc-
ing it.   Though I  am obliged, in  order to be intelligible, to
talk of heat as an entity, and of its conduction, radiation, &c,
yet these expressions  are, in fact, inconsistent with the dyna-
mic theory Avhich  regards heat as motion and nothing else ;
thus conduction would be simply a  progressive  dilatation or
motion of the particles of the conducting substance, radiation
an \mdulation or motion  of the particles of  the  medium
through which the heat is said to be transmitted,  &c.; and it
is a strong  argument in favour of this theory, that for every
diversity  in the physical character  of bodies, and for every
change in  the structure and arrangement of particles of the
same  body, a  change is apparent in the thermal effects.
Thus gold conducts heat, or transmits the motion called heat,
more readily than  copper, copper  than iron, iron than lead,
and lead than porcelain, &c. 
56
CORRELATION  OF PHYSICAL FORCES.
    So Avhen the structure of a substance is not homogeneous,
we have a change in the conduction of different parts depend-
ent upon the  structure.  This  is  beautifully  shown with
bodies Avhose structure is symmetrically arranged, as in crys-
tals.   Senarmont has shown that crystals conduct heat differ-
ently in  different directions with reference to the  axis of
symmetry, but definitely in definite directions.  His mode of
experimenting is as follows :—A plate of the crystal is cut in
a  direction, for one  set of experiments  parallel, and  for
another at right angles to the axis;  a tube of platinum is in-
serted  through  the  centre of the  plate, and  bent  at one
extremity, so as to be  capable of being heated  by a lamp
without the heat which radiates from the lamp affecting the
crystal;  the  surfaces or bases of the plate of crystal are
covered with wax.   When the platinum is heated, the direc-
tion of the heat conducted by the crystal is made known by
the melting of  the wax, and  a curved line is visible at the
juncture  of  the solid  and liquid wax.   This curve, Avith
homogeneous substances,  as glass or zinc,  is a circle ; it is
also a circle on plates of calc  spar cut perpendicular to the
axis of symmetry;  but on plates cut parallel to the axis of
symmetry, and having their plane perpendicular to one of the
faces  of the  primitive  rhombohedron,  the  curves are Avell-
defined ellipses, having their longer axes in the direction of
the axis of symmetry, showing that this axis  is a direction of
greater conductibility.   From experiments of this character
the inference is drawn, that ' in media constituted like crys-
tals of the rhombohedral system, the conducting power varies
in such  a manner, that, supposing a centre of heat to exist
within them, and the medium to be indefinitely extended in
all directions, the isothermal surfaces are concentric ellipsoids
of revolution round the  axis of symmetry, or at least surfaces
differing but little therefrom.'
    Knoblauch has further shown, that radiant heat is absorb-
ed  in  different  degrees, according as its direction is parallel
»r perpendicular to the axis of a crystal. 
HEAT.                        57
   If we select a substance of a different but also of a definite
structure, such as Avood, we find that heat progresses through
it  with more  or less rapidity, according to its direction with
reference  to the fibre of the wood:  thus Decandolle and De
la Rive found that the conduction was better in a direction
parallel to the  fibre than in one transverse to it; and Dr.
Tyndall" has added the fact, that the conduction is better in a
direction transverse to the fibres and layers of the wood than
when transverse to the fibre but parallel to the layers, though
in both these  directions the conduction is inferior to that fol-
lowing the direction of the fibre.   Thus, in the three possible
directions in  which the  structure of wood may be contem-
plated,  we have three different degrees of progression for
heat.
   In the above examples we see, as we shall see farther on
Avith reference  to  all the so-called imponderables, that the
phenomena depend upon the molecular structure of the mat-
ter  affected;  and although these facts are  not absolutely in-
consistent with  the theory which supposes them to be fluids
or entities, it will, I think, be found to be far more consistent
with that which views them as motipn.  Heat, which we are
at present considering, cannot be insulated: we cannot re-
move the heat  from a substance  and retain it as  heat;  we
can  only transmit it to another substance, either as heat  or
as some other  mode of force.  We only knoAV certain changes
of matter, for which changes heat is a generic name ; the
thing heat is unknown.
   Heat having been shoAvn to be a force capable of pro-
ducing motion, and motion to be capable  of producing the
other modes of  force, it necessarily follows that heat is capa-
ble,  mediately, of producing them ; I will, therefore, content
myself with enquiring how far heat is  capable of immediately
producing  the other modes of force.  It  will  immediately
produce electricity, as shown in the beautiful experiments  of
Seebeck, one  of which  I have already cited, which expert 
58         CORRELATION  OF PHYSICAL FORCES.
ments proved, that when dissimilar metals are made to touch,
or are soldered together .and heated at the point of contact, a
current of electricity flows through the metals having a defi-
nite direction  according to the metals employed, which cur-
rent continues as long as an increasing temperature is grad-
ually pervading the metals, ceases when the  temperature is
stationary, and flows in the contrary direction with the decre-
ment of temperature.
   Another class of phenomena which have been generally
attributed to the effects of radiant heat, and to which, from
this belief, the term thermography has  been applied, may
also, in their turn, be made to exhibit electrical  effects—ef-
fects here of Franklinic or static electricity, as Seebeck's ex-
periments showed effects of voltaic or dynamic electricity.
   If polished discs of dissimilar metals—say, zinc and cop-
per—be  brought into  close proximity, and kept there for
some time, and either of them has irregularities upon its sur-
face, a superficial outline of these irregularities is  traceable
upon the other  disc, and vice versa.  Many theories have
been framed to account for thi3 phenomenon, but whether  it
be due or not to thermic radiations, the relative temperature
of the discs,  their relative capacities  and  conducting and
radiating  powers for heat,  undoubtedly influence  the phe-
nomena.
   Now, if two such discs in close proximity be connected
with a delicate  electroscope,  and then suddenly separated,
the electroscope is  affected, showing  that the  reciprocal ra-
diation from surface to surface has produced electrical force.
I cite this experiment in treating of heat as an initial force,
because at present the probabihties  are in favour of thermic
radiation producing the phenomenon.  The origin  of these
so-called thermographic effects is, however, a question open
to much  doubt, and needs much further experiment.   When
I first published the experiment which showed that the mere
approximation of metallic discs would give rise to  electrical 
HEAT.
59
effects, I mentioned that I considered the fact of the superfi
cial change upon  the  surface of metals in proximity, and, d
fortiori, in contact, would explain the developement of elec-
tricity in Volta's original contact experiment, without having
recourse to the contact  theory, i. e. a theory which  supposes
a force to be produced  by mere contact of dissimilar metals
without any molecular or  chemical  change.  I have  seen
nothing to alter this view.  Mr. Gassiot has  repeated and
verified my  experiment with  more delicate  apparatus and
under more unexceptionable circumstances ; and without say-
ing that radiant heat is the initial force  in this case, we  have
evidence,  by the  superficial  change which takes  place in
bodies closely approximated, that some molecular change is
taking place, some force is called into action by their proxim-
ity, which produces  changes  in matter as it expends, or
rather transmits itself; and, therefore, is not a force without
molecular change, as the supposed contact force would be.
The force in this, as in  all other cases, is not created, but de-
veloped by the action  of matter on  matter, and  not annihi-
lated, as it is shown by this  experiment  to be convertible into
another mode of force.
    To say that heat will produce light, is to assert a fact ap-
parently familiar to every one, but there  may be  some  rea-
son to doubt whether the expression to produce light is  cor-
rect in this particular application ; the relation between heat
and hght is not analogous to the correlation between these
and the  other four affections of matter.   Heat  and hght ap-
pear to be rather modifications of the same  force than dis-
tinct forces mutually dependent.  The modes of action of ra-
diant heat and of hght are  so similar, both being  subject to
the same  laws of reflection,  refraction, and double refraction,
and polarisation, that their  difference appears to exist  more
in the manner in which they affect  our senses than in our
mental conception of them.
   The experiments of Melloni, which  have  mainly contrib- 
60         CORRELATION  OF PHYSICAL FORCES.
uted to demonstrate this close analogy of heat and hght, a£
ford a beautiful instance of the assistance which the progress
of one branch of physical science renders to that of another
The discoveries of Oersted and Seebeck led to the construc-
tion of an instrument for measuring temperature, incompara-
bly more  delicate than any previously  known.   To  distin-
guish it from the ordinary thermometer, this instrument is
called the  thermomultiplier.   It  consists  of a  series of small
bars of bismuth and antimony, forming one zigzag chain of
alternations arranged parallel to each other, in the shape of
a cylinder or prism ; so  that the  points of junction, which are
soldered, shall be all exposed at the  bases of the  cylinder:
the two extremities of this  series are  united to a galvano-
meter—that  is, a#flat coil  of wire surrounding a freely-sus-
pended magnetic  needle, the  direction of which is parallel to
the convolutions of the  wire.  When radiant heat impinges
upon  the  soldered ends of the  multiplier, a  thermo-electric
current is  induced in each pair;  and, as all  these currents
tend to circulate in the same  direction, the energy of  the
whole is increased by the  cooperating  forces :  this current,
traversing the helix of  the galvanometer, deflects the  needle
from parallelism by virtue of the electro-magnetic tangential
force, and  the degree of this deflection  serves as the index
of the temperature.
    Bodies  examined by these means show a remarkable dif-
ference between  their transcalescence, or poAver of transmit-
ting heat, and their transparency :  thus, perfectly transparent
alum arrests  more heat  than  quartz so dark coloured as to be
opaque ; and alum coupled with green  glass Melloni found
was capable  of transmitting a beam of brilliant light, while,
with the most delicate  thermoscope, he could detect no indi-
cations of transmitted heat:  on  the other hand, rock-salt,  the
most transcalescent body known,  may be covered with soot
until perfectly opaque, and yet be  found capable of transmit-
ting a considerable  quantity of heat.   Radiant heat, when 
HEAT.                         61
transmitted through a prism of rock-salt, is found to be une-
qually refracted, as is the  case  with light; and the rays of
heat thus  elongated into  what is, for the  sake of analogy,
called a spectrum, are found to possess similar properties to
the primary or coloured rays of hght.  Thus  rock-salt is to
heat what colourless glass  is to hght;  it transmits heat of all
degrees of refrangibility: alum is to  heat as  red glass to
light;  it transmits the least, and stops the most refrangible
rays ;  and rock-salt covered with soot represents blue glass,
transmitting the most, and stopping the least refrangible rays.
    Certain bodies,  again, reflect heat of different refrangi-
bility: thus paper, snoAV, and lime, although perfectly white
—that is,  reflecting  hght of all degrees of refrangibility, re-
flect heat only of  certain degrees; while metals, which are
coloured bodies—that is, bodies which reflect hght only of
certain degrees of refrangibility—reflect heat of all degrees.
Radiant heat  incident upon substances which doubly refract
hght is doubly refracted ; and the  emergent rays are  polar-
ised in planes at right angles to each other, as  is the case
with hght.
    The relation of radiation to absorption also holds good
with hght as  with  heat:  with the latter it has been long
known that the radiating power of different substances  is di
rectly proportional to  their absorptive and inverse to  theii
reflective poAver ; or rather, that the sum of the  heat  radia
ted and reflected is a constant quantity.   So,  as  has been
shown by  Mr.  Balfour Stewart,  the  absorption bears the
same  relation  to radiation for heat as to quality as well as
quantity.
    Light presents us with  similar relations.   Coloured glass,
when heated  so as to be  luminous, emits the same  hght
which at  ordinary temperatures it absorbs: thus  red glass
gives out or radiates a greenish hght, and green glass a red
lint.
    The flame of substances containing sodium  yields a yel- 
62        CORRELATION OF PHl'SICAL  FORCES.

low light of such purity that other colours  exposed to it ap-
pear black—a phenomenon shown by the familiar experiment
of exposing a picture of bright colours, other than yellow, to
the flame of spirits of wine Avith which common salt is mixed :
the picture  loses its colours, and appears to be black and
white.  When the prismatic  spectrum of such a flame is ex-
amined, it is found to exhibit two bright yellow hnes at a cer-
tain  fixed position.  If a source of light be employed which
gives no hnes in its spectrum, and this, being at a higher
temperature, be  made to pass through the sodium flame, two
dark  hnes will  appear in the spectrum precisely coincident
in position with the yellow lines which were given by the so-
dium flame itself.  The same relation of absorption to radia-
tion  is  therefore shown here : the  substance  absorbs that
light  A\Thich it yields when it  is itself the source  of light.
The  same is true  of other substances, the spectra of which
exhibit  respectively lines of peculiar colour and position.
Now, the  solar  prismatic spectrum is traversed by a great
number of dark  lines; and Kirchoff has deduced from con-
siderations such as  those which  I have shortly stated, that
these dark lines in the solar  spectrum are  due to metals ex-
isting in an atmosphere around the sun, which absorb the
hght from a central incandescent nucleus, each metal absorb-
ing that light which would appear as a bright line or lines in
its own spectrum.
   By comparing the position of the bright hnes in the spec-
tra of metals with that of the dark hnes in the solar spec-
trum, several of them are found to be in identically the same
place : hence it is inferred, and the inference seems reason-
able, that  the metals which show luminous lines in their spec-
tra, identical in  position with dark lines in  the solar  spec-
trum, exist in the sun, and are  diffused in a gaseous state in
its atmosphere.  It  does not seem to me necessary to this
conclusion to assume that the sun is a solid mass of incandes-
cent matter:  it may well be that what we term the  photo- 
HEAT.
63
sphere or luminous envelope of the sun has surrounding it a
more diffuse  atmosphere  containing vaporised  metals,  and
that the mass of the sun  itself may be in a different state,
and not necessarily at an incandescent  temperature ; indeed,
the protuberances and  red light seen  at the period of total
eclipses afford some  eATidence of an atmosphere exterior to
the photosphere.  It  Avould, however, be out of place here to
speculate on these  subjects: the point  Avhich concerns us is
the analogies of heat  and hght, which these discoveries illus-
trate.   Kirchoff has  carried the analogy farther by showing
that a plate of tourmaline absorbs the polarised ray which
when heated it radiates.  Thus, the phenomena of hght  are
imitated closely by those of radiant heat; and the same the-
ory Avhich is considered most plausibly to  account  for  the
phenomena  of the one, will necessarily be apphed to the other
agent, and in each case  molecular change is accompanied by
a change in the phenomenal effects.
    In certain cases  heat  appears  to become  partially con-
verted into  b'ght, by changing the matter affected by heat:
thus gas  may be heated to  a  very high point without pro-
ducing light, or producing it to a very slight degree ; but  the
introduction of solid matter—for instance, the metal platinum
into the highly-heated  gas—instantly exhibits hght.  Whether
the heat is converted  into hght, or Avhether it is concentrated
and increased in intensity by the solid matter so as to become
visible, may be open to some doubt: the fact of sohd matter,
when ignited  by the  oxyhydrogen jet decomposing water, as
will be presently explained, would  seem to indicate that  the
heat was  rendered more intense by condensation in the solid
matter, as water is in this case decomposed by a heated body,
which body  has itself  been  heated by the combining elements
of water.  The apparent effect, however, of the introduction
of solid incombustible matter into heated gas, is a conversion
of heat into light.
    There is another  method by which  heat would probably 
64         CORRELATION OF  PHYSICAL FORCES.
be made to produce  luminous effects, though I am not aAvare
that the experiment has ever been made.
    If we concentrate into a focus by a large lens a dim hght,
we increase the intensity of the light.  Now if a heated body
be taken, which, to the unassisted eye, has just  ceased to be
visible, it seems probable that by coUecting and condensing
by a lens  the  different rays  which have so ceased to be visi-
ble, light would  reappear at  the  focus.  The experiment is,
for reasons obvious to  those acquainted with optics, a difficult
one, and,  to be  conclusive, should be made on a large scale,
and with a very perfect lens  of large diameter and short fo-
cus.  I have obtained an approximation to the result in  the
following  manner:—In  a dark  room a  platinum  wire is
brought just to the point of visible ignition by a constant vol-
taic  battery ;  it is then viewed, at a short  distance, through
an opera-glass of large aperture applied to one eye, the other
being kept open.  The wire will be  distinctly visible to that
eye which regards it through the opera-glass, and at the same
time totally invisible to the other and naked eye.   It  may be
said with some justice that such experiments proAre little more
than the  fact  already known, viz. that by increasing the in-
tensity of heat, hght is produced: they however  exhibit this
effect in a more  striking form, as bearing on the  relations of
heat and hght.
    With  regard to  chemical  affinity and magnetism, perhaps
the only method by which in  strictness the force of heat may
be said to produce them is through the medium of electricity,
the thermo-electrical current, produced, as  before described,
by heating dissimilar metals, being  capable of deflecting  the
magnet, of magnetising iron, and  exhibiting the other mag-
netic effects, and also of  forming  and  decomposing chemical
compounds, and this in proportion to the progression of heat:
this has not, indeed, as yet been proved to bear a measurable
quantitative relation to the other  forces thus produced by it,
because so little of the heat is utilised or converted into eleo« 
HEAT.
65
tricity, much being dissipated, without change, in the form of
heat.
    Heat, however, directly affects and modifies both the mag-
net and chemical compounds ; the union of certain chemical
substances is induced by heat, as, for instance, the formation
of water by the union of oxygen  and hydrogen gases: in
other cases this union is facilitated by heat, and in many  in-
stances, as in ammonia and its salts, it is weakened or antag-
onised.   In many of these cases, however, the force of heat
seems more a determining than a producing influence ;  yet to
be  this, it  must have  an immediate relation with the  force
whose reaction  it  determines:  thus,  although gunpowder,
touched Avith an ignited wire, subsequently carries on its own
combustion or  chemical combination, independently of the
original source of heat, yet the chemical  affinities of  the first
portion  touched must  be  exalted by, and at the cost of, the
heat of  the wire ; for to disturb even an unstable equilibrium
requires a force  in direct relation with  those which maintain
equihbrium.
    Since the first edition of this  essay was pubhshed, I haA*e
communicated to  the  Royal Society some experiments  by
which an important exception to  the general effect of heat on
chemical affinity is removed, and the results of which induce
a hope that a generalised  relation will ultimately be estab-
lished between heat, chemical affinity, and physical attraction.
I find that if a  substance  capable of supporting an intense
heat, and incapable of being acted upon  by water or either
of its elements—such, for instance, as platinum, or iridium—
be raised to a high  point of ignition and then  immersed in
water, bubbles of permanent gas ascend  from  it, which  on
examination are found  to consist of mixed oxygen and hydro-
gen in the proportions in which they form water.   The  tem-
perature at which this is  effected is,  according to Dr. Robin-
son, Avho has since written a valuable  paper on the  subject,
«s 23860.   Now, when mixed oxygen and hydrogen are ex- 
36         CORRELATION OF PHYSICAL FORCES.

posed to a temperature of about 800°, they combine and forir
water; heat therefore  appears to act differently upon  these
elements according to its intensity, in one case producing
composition, in  the other decomposition.  No  satisfactory
means of reconciling this  apparent anomaly have been pointed
out: the best approximation to a theory which I can frame in
by assuming that the constituent  molecules of water are, be-
low a certain temperature, in  a state of stable equilibrium;
that the molecules of mixed or oxyhydrogen gas are, above a
certain temperature, also in a state of stable equihbrium, but
of an opposite  character;  while  below this latter tempera-
lure  the molecules of mixed gas are in  a state of unstable
equilibrium, somewhat similar to that  of the  fulminates or
similar bodies, in which  a slight derangement subverts the
nicely-balanced forces.
   If, for instance, we  suppose four  molecules, A, B, C, D,
to be in a balanced state of equilibrium  between attracting
and repelhng forces, the  application of a repulsiAre  force be-
tween B and C, though it may still farther separate B and C,
will  approximate B to A and C  to D, and may bring  them
respectively within the  range of attractiAre  force;  or,  sup-
posing the repulsive force to be in the centre of an indefinite
sphere of particles, all these,  excepting  those immediately
acted on by the force, will be approximated, and having from
attraction assumed a state of stable equihbrium, they will re-
tain this, because the repulsive force divided by the mass  is
not capable of overcoming it.  But if the  repulsive  force be
increased in quantity and of sufficient intensity, then the at-
tractive force of aU the molecules may be overcome, and de-
composition ensue.   Thus, water or  steam below a certain
temperature, and mixed  gas  above a  certain temperature,
may be supposed to be in a state of stable equihbrium, whilst
below this limiting temperature, the equihbrium of oxyhy-
irogen gas is unstable.
   This, it must be confessed, is but a crude mode of explain* 
HEAT.
67
ing the phenomena, and requires  the  assumption, that the
particles of a gas exercise an attraction  for each other as do
the particlej^of a solid, though different  in degree, perhaps in
kind.   Whether this be so or not, there  can be no doubt that
both gases and sohds expand or contract according to  the in-
verse  contraction or expansion of other  neighbouring  bodies,
and so far resemble each other in their relations to  heat and
cold.   The extent to which such  expansion or contraction
can be  carried, seems to be limited  only by the correlative
state  of other bodies; these again, by others, and so on, as
far as Ave may judge, tliroughout the universe.
   Adopting the explanation above given of the decomposi-
tion of  water by heat, heat would have  the same relation to
chemical affinity as it has  to physical attraction; its  imme-
diate  tendency is antagonistic to both, and it is only by a sec-
ondary action that chemical affinity is  apparently  promoted
by heat.  This view Avould explain how heat may promote
changes of the equilibrium of chemical  affinity among mixed
compound substances, by decomposing certain compounds and
separating elementary constituents  whose affinity is greater,
Avhen they are brought within the sphere of attraction for the
substance with  which they are mixed, than for those with
which they Avere originally chemically united : thus an intense
heat  being applied to a mixture of chlorine  and the vapour
of Avater, occasions the  production of  muriatic acid, libera-
ting oxygen.
    Carrying out this view, it would  appear  that a sufficient
intensity of heat might yield indefinite powers of decomposi-
tion ; and there seems some probability of bodies  noAV sup-
posed to be elementary, being  decomposed or resolved into
further elements by the application  of heat of sufficient inten-
sity ; or,  reasoning conversely, it  may fairly be anticipated
that bodies, Avhich will not enter into combination at a certain
temperature, will enter into combination if their temperature
be lowered, and that thus new compounds may be'formed by 
68         CORRELATION OF PHYSICAL FORCES.
a proper disposition of their constituents when  exposed to an
extremely low temperature, and the more so if compression
be also employed.
   In considering the effect of heat as a mechanical force, it
would be expected, a priori, and independently of any theory
of heat which may be adopted, that a given amount of heat
acting on a given material must produce a given amount of
motive power; and the next question which  occurs  to the
mind is, whether the same amount of heat would produce the
same amount of mechanical power, whatever be the material
acted on or affected by the heat.   I will endeavour to reason
this out on the view of heat which I have advocated.  Heat
has been considered in this essay as itself motion or mechan-
ical power, and  quantity  of heat as measured by motion.
Thus, if  by a given contraction of a body (say mercury) air
witliin a  cylinder  having a moveable piston be  expanded, the
piston moves, and in this case the  expansion or motion of the
material  (say iron) of the  cylinder itself and of the air sur-
rounding it is commonly neglected.  As the air dilates it be-
comes colder ; in other words, by undergoing expansion itself,
it loses  its power of making neighbouring bodies expand;
but if the piston be forcibly kept down, the expansive power
due to the mercury continues to  communicate itself to the
iron  and to the surrounding air, which become  hotter than
they would if the piston had given way.
   Now, in the above case, if the  air be  confined and its
volume unchanged, will the expansion of the iron, assuming
that it can be utilised, produce an exactly equivalent mechan-
ical effect to that which the expansion of the air would pro-
duce if the heat be entirely confined to it ?
   Assuming  that (with the  exception of bodies which ex-
pand in freezing, where, through a limited range of tempera-
ture, the converse effects  obtain) whenever a body is com-
pressed it is heated, i. e. it expands neighbouring substances ;
whenever it is dilated or increased in volume it is cooled, i. e 
HEAT.
69
it  contracts  neighbouring  substances—the conclusion ap-
pears to me inevitable  that  the mechanical power  produced
by heat will be definite, or the same for a given  amount and
intensity  of heat, whatever be the substance acted on.
   Thus, let  A be a definite source of  heat, say a pound of
mercury  at the temperature of 400° ;  let B be another equal
and similar source of heat: suppose A be  employed to raise
a piston  by the  dilatation of ah, and  B to  raise  another pis-
ton by the  dilatation of the vapour of Avater.  Imagine the
pistons attached to a beam, so that they oppose each other's
action, and thus  represent a sort of calorific balance.   If A
being applied to air could conquer  B, which is applied to
water, it would depress or throw back the piston of the latter,
and, by  compressing the A'apour,   occasion an  increase  of
temperature;  this, in  its turn,  Avould raise the temperature
of the source of heat,  so that we should  have the anomaly
that a pound of mercury at 400° could heat another pound
of mercury at 400° to 401°, or to some point higher than its
original  temperature, and this without any adventitious aid:
it  will be  obvious  that this is impossible,  at least contradic-
tory to the whole range of our experience.
   The  above experiment is ideal, and stated for the object
of giving a more precise form to the reasoning;  to bring the
idea more  prominently into relief, aU statements as to quan-
tities, specific heats, &c, so as to yield comparative results
for given  materials, are omitted.  The  argument may be
thus stated in another form,  viz. that by no  mechanical appli-
ance or  difference of material acted  on can a given source
of heat  be made to produce more  heat  than  it originally
possessed; and that, if  all be converted into  mechanical
power, an  excess cannot be supposed, for  that could be con-
verted into a surplus of heat, and be a creation of force ;  and
a deficit  cannot be  supposed, for that would be annihilation
of force.   I cannot, however, see how the theoretical concep-
tion  could  be verified by experiment; the  enormous weights 
70        CORRELATION  OF PHYSICAL FORCES.

and the  complex mechanical contrivances requisite to give
the measure of power yielded by matter in its less dilatable
forms, would  be far beyond our present experimental re-
 ources.  It would also be difficult to prevent the interference
of  molecular  attractions,  inertia, &c, the overcoming of
which expends a part of the  mechanical  power  generated,
but which could hardly be made to appear  in  the  result.
We could not, for instance, practically reahse the  above con-
ception by the construction of a machine which should act by
the expansion  and contraction of a bar of iron, and produce a
power equal to that of a steam engine, supphed with an equal
quantity  of heat.
    Carnot, who wrote in 1824 an essay on the motive power
of heat, regarded the mechanical  power produced by heat as
resulting from a transfer of heat from one point  to another,
without any ultimate loss of heat.  Thus, in the action of an
ordinary steam engine, the heat from the furnace having ex-
panded the water of  the  boiler  and raised  the  piston,  a
mechanical motion is produced ; but this cannot be continued
without the removal  of the heat, or the contraction of the ex-
panded v/ater.   This is done by the condenser, and the piston
descends.  But then  we have apparently transferred the heat
from the  furnace to the condenser, and in the transfer effected
mechanical motion.
    Should the mechanical motion produced by heat be  con-
sidered as the  effect of a simple transference of heat from one
point to another, or as the result of a conversion of heat into
the mechanical force  of which this motion is the result ?  This
question leads  to the  following :  does the heat which generates
the mechanical poAver return to the thermal machine as heat,
or is it conveyed away by the work performed ?
    If a definite quantity of  air be heated it is  expanded, and
by its  expansion it cools or loses  some of  its poAver of com-
municating heat to  neighbouring bodies.  That  which we
should have called heat if the expansion of the air had been 
                          HEAT.                        71

prevented, we call mechanical effect, or may A'iew as converted
into  mechanical effect ceasing to be heat;  but, throwing  out
of the question nervous sensation, this expansion or mechani-
cal effect is all the evidence we have  of heat, for if the air is
alloAved to expand freely, this expansion  becomes the index
of the heat;  if the  air be  confined, the expansion  of  the
matter of the vessel confining it, or of the mercury  of a ther-
mometer in contact Avith it, &c, are the indices of the heat.
    If, again, the air which has been expanded be, by mechani-
cal pressure or by other means, restored to its original bulk,
it is capable of heating or  expanding other substances to a
degree to which it would not be equal, if it had remained in
its  expanded  state.  To produce  continuous motion, or the
up and down stroke of a piston, we must  heat and cool, just
as Avith a magnetic machine we must magnetise and demagne-
tise  in -order to produce a continuous mechanical effect;  and
although, from the impossibility of insulating heat,  some heat
is apparently lost in the process, the  result may be said to be
effected by the transfer of heat from the hot to the  cold body,
from the furnace to the condenser.   But Ave may equally well
say that the  heat has  been  converted into mechanical force,
and the mechanical  force back into heat;  the  effects  are
always correlative,  as are the  mechanical  effects of an air
pump,  Avith  which, as Ave dilate the air on one side, we con
dense it on  the  other; and as Ave cannot dilate Avithout the
reciprocal condensation, so avc cannot heat without the recip-
rocal cooling, or vice versa.
    Hitherto the resistances of the piston or of any superim-
posed weight have been thrown out of consideration, or, Avhat
amounts to  the same thing, it has  bee,i assumed that  the
weight raised by the piston has descended  Avith ii.  The heat
ha3  not merely been employed in dilating the air or vapour,
but  in  raising the piston with its weight.   If, as the  vapour
is cooled, the  weight be permitted to descend, its mechanical
force restores the heat lost by the dilatation ;  but in this case 
72
CORRELATION OF PHYSICAL FORCES.
 no part of the  power  can be abstracted so as to be employed
 for any practical purpose:  this question then follows, what
 takes place with regard to the initial heat, if,  after the ascent
 of the piston, the weight be  removed so as not to help the pis-
 ton in its descent, but to fall  upon a lever or produce some
 extraneous mechanical effect?
   To answer this question, let us suppose a weight to rest
 an a  piston which confines air at a definite temperature, say
 for example 50°, in  a  cyhnder,  the  whole  being  assumed
 to be  absolutely non-conducting for heat.   A part of the heat
 of this  confined  air will be  due to the pressure,  since, as
 we have  seen, compression  of  an  elastic  fluid produces
 heat.
   Suppose, now, the  confined air to be heated to 70°, the
 piston with its superincumbent weight wiU ascend, and the
 temperature, in consequence of the dilatation  of the air, will
 be somewhat lowered, say to 69° (we will assume, for the
 sake of simplicity, that the heat engendered by the  friction of
 the piston compensates the force lost by friction).
   The piston  having reached its maximum of elevation, let
a cold body or condenser take away 20° from the temperature
of the confined air ; the piston will noAV descend, and by the
compression which the weight on it produces, will restore the
 1° lost by dilatation, and when the piston reaches its original
position the temperature of the  air will be restored to 50°.
Suppose this experiment repeated up to the rise of the piston ;
but when the piston is at its full elevation, and the cold body
apphed, let the weight be removed, so as drop upon a wheel,
 or to be used for other mechanical purposes.  The descend-
ing piston will not noAV reach its  original point without more
heat being abstracted;  in consequence of the removal of the
weight, there will not be the same force to restore the 1°, and
the temperature will be 49°, or  some fraction short of the
original 50°.  If  this were  otherwise, then, as the weight in
falling may be  made  to produce  heat by friction,  we should 
HEAT.
73
have more heat than at first, or a creation of heat out of noth-
ing—in other Avords, perpetual motion.
   Let us now assume that this 20° supplied in  the first in-
stance Avas yielded by a body at 90°, of such size and material
that its total  capacity for heat is equal to that of the mass of
confined  air': this body would be reduced in temperature to
70°, in other Avords, our furnace  would have lost 20° of her.t.
Let the  cold body of the same  size and material, used as a
condenser, be at  30°.  In  the  first experiment,  the body at
30° Avould bring back the piston to its original point;  but in
the second experiment, or  that  where the Aveight has been
removed, the body at 30° Avould not suffice to restore the  pis-
ton :  to effect this, the cold body or condenser must be at a
lower temperature.
   The question in Carnot's theory,  which is  not experi-
mentally resolved, and  which presents extreme experimental
difficulty, is  the following:  Granted  that  a piston with a
superimposed weight be raised by the thermic expansion of
confined gas or vapour bcloAV it; if the  elastic  medium be
restored to its original  temperature by cooling, the weight in
depressing the  piston  -will  restore that portion of the heat
which has been lost by the expansion, and by the  mechanical
effect consequent thereon ; but if the weight be removed when
at its maximum of elevation, and the piston be brought back
to its  starting point by a necessarily cooler body than could
restore it if the weight Avere not removed, would the return of
the piston now  restore the heat which had been lost by the
dilatation, or, in other  words, would pulling the piston down
by cold restore the heat equally with the pressing it down by
mechanical force?  The argument from the impossibility of
perpetual motion  would  say no,  for  if all the heat were
restored,  the mechanical  effect  produced by the fall of the
weight, or  the  heating  effect  which might be  made to
result  from  this  mechanical power,  would be got from
nothing.
             4 
    74         CORRELATION OF  PHYSICAL  FORCES.

       Then follows another question, A-iz. Avhether, where an ex-
    ternal or derived  mechanical effect has been obtained, Avould
    the return of the piston, effected Avithout  the Aveight or exter-
    nal force  to assist it, but solely by the  colder body, give to
    this latter the same number of thermometric degrees as had
    been lost by the hot body in the first instance?   Suppose, for
    instance, the cold body in our experiment to be at 20° instead
   of 30°, would this body gain  20°, and then reach the tempera-
    ture of 40° when the  piston  is brought back,  or would its
   temperature be  higher  or lower than 40° ?   The argument
   from the  impossibility of perpetual motion does not apply
   here, for it  doe3 not necessarily follow that 20°,  on the ther-
   mometric scale from 20° to 40°, represents an equal amount
   of force to 20° on the scale from 70° to 90°, and therefore it
   is quite conceivable  that we may lose 20° from  the furnace,
 . and gain 20°  in the condenser, and yet have obtained a cer-
   tain amount of derived mechanical power.  It w7ill also folloAV,
   upon  a  consideration of the  above imaginary experiments,
   that the greater the mechanical poAver required, the greater
    should  be  the difference between  the  temperature of the
   furnace  and that of the  condenser ;  but the exact relation in
-  temperature between these, for a given mechanical effect, has
   not, as  far  as I am aware, been satisfactorily estabhshed by
   experiment,  though it has been shown  that steam  at  high
   pressure produces,  comparatively,  a  greater  mechanical
   effect  for  the  same  number of degrees  than steam at Ioav
    pressure.
      Carnot, assuming the number of degrees of temperature
   to "be restored, but at a loAver point of the thermometric scale,
   termed this the fall (chute) of caloric.  The mechanical effect
    cf heat, on  this view, may be likened  to that of a series of
    cascades on Avater-whcels.   The highest  cascade  turns  a
    wheel,  and  produces a given mechanical effect;  the Avater
    which has produced this cannot again  effect it at the samo
    level without being carried back to  its original elevation, i. e. 
HEAT.
75
wilhout an  extra force  being employed  equivalent to, or
ra her a fraction more  than the  force  of the descending
water ;  but  though its poAver is spent Avith reference ta-the-
first wheel, the  same water may, by falhug  over a new
precipice upon a second whee^, again reproduce the same
mechanical  effect (strictly speaking, rather more, for it has
approximated the centre  of gravity), and so  on,  until no
lower fall can be attained.   So Avith heat:  it involves no
necessity of assuming perpetual motion to suppose that, after
a given mechanical effect, produced by a certain loss of heat,
the number of degrees  lost from  the  original  temperature
may be restored to the condenser, but at a lower point of the
thermometric scale.
    If work has  been done, i. c. if force  has  been parted
with, the original temperature itself cannot be restored, but
there is no a priori impossibility  in  the  same number of
degrees of heat as have been converted into Avork  being con-
veyed to a condensing body so cold that, when it receives this
heat, it will still  be beloAV the original temperature to which
the Avork-producing heat  was added.
    In the theory of the steam-engine, this subject possesses
a  great practical interest.  Watt supposed that  a given
weight  of water  required the   same  quantity of  Avhat is
termed  total heat (that  is, the  sensible added  to the latent
heat) to keep it  in the  state of vapour, Avhatcver  Avas the
pressure to  Avhich it was subjected, and, consequently, 1ioaat-
eA-er its expansive force varied.   Clement Desormes  Avas
also supposed to have experimentally verified this laAv.   If
this were so, vapour raising a piston with a weight attached
Avould produce mechanical power; and yet, the  same heat
existing as  at  first, there  would be  no expenditure of the
initial force ; and if Ave suppose that the heat in  the condens-
er  was the   real representative of the original heat, Ave
should get perpetual motion.  Southern supposed that the
latent heat  was  constant,  and that  the heat of v;i;-xir under 
 76        CORRELATION OF PHYSICAL FORCES.

 pressure increased as the sensible  heat.   M. Despretz, in
 1832,  made some experiments, Avhich led  him to the  con-
 clusion that the increase was not  in the same ratio  as the
 sensible heat,  but that  yet there  Avas an increase ; a result
 confirmed and  A'erified with great accuracy by M. Regnault,
 in some recent and elaborate  researches.  What seems to
 have  occasioned the error in Watt and Clement Desormcs'
 experiments was, the idea invoked in the term latent heat;
 by which, supposing the phenomenon of the  disappearance of
 sensible heat to be due to the  absorption of a material  sub-
 stance, that substance, ' caloric,' was thought to be restored
 when the  vapour was condensed by water, even though the
 water  was not subjected to pressure ;  but to  estimate the
 total heat of vapour  under pressure the  vapour should be
 condensed while subjected to the same pressure as that under
 which  it is  generated, as was done in M.  Despretz and M.
 Regnault's experiments.
   M. Seguin,  in 1839, controverted the position that derived
 power could be got  by the mere  transfer of heat, and by
 calculation from certain known data, such as the law of Mar-
 iotte, viz. that the elastic force of gases and vapours increas-
 ed directly with the pressure ; and assuming that for vapour
between 100° and ISO11 centigrade, each degree  of  elevation
 of temperature  was produced by a thermal  unit, he deduced
 the equivalent of mechanical work capable of  being perform-
ed by a given decrement of heat;  and thus concluded that,
for ordinary pressures, about one  gramme  of water losing
one degree centigrade Avould produce a force capable of rais-
ing a weight of 500 grammes through a space of one metre  :
this estimate is a little beyond that given by the converse ex-
periments  of Mr. Joule, already stated, in which  the heat
produced by a given amount of mechanical  action is estimat-
ed.   I am not aware that the  amount of  mechanical Avork
 which is produced by a given quantity of heat has  been di-
 rectly established by experiment, though some approximative 
HEAT.
77
results in particular cases have been given.   TheoreticaUy it
should be  the same—that is to say, if a  fall of 772 lbs.
through a space of one foot will raise the temperature of 1 lb.
of Avater through one degree  of  Fahrenheit, then the  fall in
the temperature of 1 lb: of water through one degree of Fah-
renheit should be able to raise 772 lbs.  through a  space  of
one foot.  The calculations of M. Seguin are  not  far  from
this, but since the elaborate experiments of M. Regnault he
has expressed some doubt of the correctness  of  his  former
estimate, as by these experiments it appears that, Avithin cer-
tain limits, for elevating the temperature of  compressed va-
pour by one degree, no more than about three-tenths of a de-
gree of total heat is required ;  consequently, the equivalent
multiplied in this ratio would be 1,6G6 grammes, instead of
500.   Other investigators have  given numbers more or less
discordant;  so that, Avithout giving any opinion on  their dif-
ferent results, this question may be considered at present far
from settled.  M. Regnault himself does not give the law by
which the ratio of heat varies Avith reference to the pressure,
and is still belieA-ed to be engaged in researches on the sub-
ject—one involving questions of  which experiments  on the
mechanical effects of elastic fluids seem to offer the  most pro-
mising means of  solution.
    I have  endeavoured  to  give  a proof (by showing the
anomaly to which the contrary conclusion would lead) that,
whatever amount of mechanical poAver  is produced by one
mode of application of heat,  the  same should,  in  theory, be
equally produced by any other mode.   But  in practice the
difference is immense ; and therefore it becomes a question
of great interest practically  to  ascertain what is  the  most
convenient medium on which to  apply the heat employed, and
the best machinery for economising it.   One  great problem
to be solved is the saving of  the heat which the steam in or-
dinary engine?, after having done  its work,  carries into the
condenser, or, in  the high-pressure engine, into the air.  It 
 78         CORRELATION  OF PHYSICAL FORCES.

 is argued you have a large amount of fuel consumed to raise
 water to the boiling point, at Avhich its efficiency as a motive
 agent commences.  After it has done a small portion of work,
 and while it still retains a A'ery large portion of the  heat  ori-
 ginally communicated to it, you reject it, and  have to start
 again with a fresh portion of steam which  has similarly ex-
 hausted fuel—in other words, you throw away aU, and  more
* than all  the heat which has been employed in raising  the
 water to the boiling point.   Various plans have been devised
 to remedy this.  Using again the warm water  of the conden-
 ser to feed the boiler regains a part, but a very small part, of
 the heat.   Employing the  steam first for a high pressure,  and
 then before its rejection or condensation using  it for  a  low
 pressure, cyhnder, is a second  mode; a  third  is to use  the
 steam, after it has done  its work on the piston, as a  source of
 heat or second furnace, to boil ether, or  some  hquid which
 evaporates at a lower temperature than Avater.  These plans
 have certain advantages;  but the  complexity  of apparatus,
 the  danger  from combustion  of ether,  and  other reasons,
 haAre hitherto precluded their general adoption.   Under  the
 term  regenerating  engine  various ingenious  combinations
 have  lately  been suggested,  and  some experimental engines
 tried, with Avhat success it is perhaps too  early at present to
 pronounce an opinion.  The fundamental  notion on which
 this class of engine is basecl is that the A-apour or air,  when
 it has performed a certain amount  of work, as  by raising a-
 piston, should, instead of being condensed  or  blown off,  be
 retained and again heated to its original high temperature,
 and then used de novo;  or that it should impart its heat to
 some other substance, and the latter in turn impart  it to  the
 fresh vapour about to act.   The latter plan has been proposed
 by  Mr.  Ericsson:  he  passes the  air which  has  done  its
 Avork through layers of  Avire gauze, Avhich are heated by the
 rejected air, and through  which the  next  charge  of  air ia
 made to pass.  M.  Seguin and Mr. Siemens have  construct 
HEAT.
79
ed machines upon the former principle, which are  said  to
have given good experimental results.   There  is, however,
a theoretical difficulty in all these, not affecting their capabil-
ity of acting,  but affecting the question of economy, which it
does not seem easy to escape from.  Whether the heated aii
or vapour be retained, or whether it yield its heat to a metal-
lic or other substance, this heat must exercise its usual repul-
sive force, and this must re-act either against the returning
piston or against the incoming vapour, and require a  greater
pressure in that to neutralise it.   Vapour raising a piston and
producing mechanical force effects this with decreasing power
in proportion  as the piston is moved.   At a certain point the
piston is arrested, or the stroke, as it is termed, is completed,
but there is still compressed vapour in the  cyhnder  capable
of doing work, but so little that it is, and  must in practice
be neglected ; if this compressed vapour be retained, the pis-
ton cannot be depressed without an extra  force  capable  of
over coming the resistance of this, so to speak, semi-compress-
ed vapour, in addition to that which is  requisite to produce the
normal work of the machine ; and in whatever  way the resi-
dual force be  retained, it must either be antagonised at a loss
of power for the initial  force, or at most can  only yield Jhe
more feeble power which it would have originally given if it
had been alio Ave d to act for a longer stroke  on the piston.  It
may be that a portion of this  residual force may be  econo-
mised ; indeed, this is done when the boiler is charged  with
warm water from the condenser, instead of  with cold water;
but some, indeed a notable loss, seems inevitable.
   Without farther discussing the various inventions and the-
ories  on this subject, which are daily receiving increased de-
A'elopment, it  may be well to point out how far nature dis-
tances art in its present state.   According to some careful es-
timates, the most economical of our furnaces consume  from
ten to tAA-enty  times as much fuel to produce the same quantity
of heat as an animal produces;  and  Matteucci found  that. 
SO         CORRELATION OF  PHYSICAL FORCES.

from a given consumption of zinc in a voltaic battery,  a far
greater mechanical effect could be produced by making it act
on the limbs  of  a recently-killed  frog,  notAvithstanding the
manifold defects of such an arrangement and  its inferiority
to the action  of the hving animal, than Avhen the same bat-
tery Avas made to produce mechanical poAver, by acting on an
electro-magnetic or other artificial motor apparatus.  The ratio
in hi3 experiments Avas nearly six to one.  Thus in all our arti-
ficial combinations Ave  can but apply natural forces, and Avith
far  inferior mechanism to  that  A\Thich  is perceptible  in the
economy of nature.

                Nature is made better by no mean ;
          But nature makes that mean;  so o'er that art,
          "Which you say adds to  nature, is an art
          That nature makes.

    A speculation has been  thrown  out  by Mr.  Thompson,
that, as a certain amount of heat results from mechanical ac-
tion, chemical action, &c, and this heat is radiated into space,
there  must be a  gradual diminution  of temperature  for  the
earth, by AA'hich expenditure, however  slow, being continuous,
it would ultimately be  cooled to  a degree incompatible Avith
the  existence of  animal and A~egetable life—in short, that the
earth  and the planets of our system are parting with more
heat than they receive, and are therefore progressively cool-
ing.  Geological researches support to some extent this A'iew,
as they show that the climate of many portions of the terres-
trial surface Avas atjremote periods hotter than at the  present
time :  the animals whose fossilised remains are found  in  an-
cient strata have their  organism  adapted to  Avhat  we  should
noAV term a hot climate.  There are, hoAvever, so many  cir-
cumstances  of  difficulty  attending cosmical speculations,
that but httle reliance  can be placed upon the most profound.
We knoAv not the  original  source of  terrestrial heat;  still
less that of the solar heat;  we know not whether or not sys- 
HEAT.
81
tenis of planets may be so  constituted as  to  communicate
forces, inter se, so  that forces  which have hitherto  escaped
detection may be in a continuous or recurring state of  inter
change.
   The moA'ements produced by mutual gravitation  may be
the means of  calling into existence molecular forces  Avithin
the substances of the planets themselves.   As neither from
observation, nor from deduction, can we fix or conjecture any
boundary to the universe of stellar orbs, as each advance  in
talescopic poAver  gives us  a new shell, so  to speak, of
stars, Ave may regard our globe, in the limit, as surrounded by
a sphere of matter radiating heat, light, and possibly other,
forces.
   Such stellar radiations would not, from the evidence Ave
have at present, appear sufficient to supply the loss  of  heat
by terrestrial radiations ; but it is quite conceivable that the
whole solar system may pass through portions of space  hav-
ing different temperatures,  as Avas suggested, I believe, by
Poisson;  that as Ave have a terrestrial summer  and  winter,
so there may be a solar or systematic summer and Avinter, in
which case the heat lost during the latter period might be re-
stored during the former.  The amount of the radiations of
the celestial bodies may again, from changes in their positions,
vary through epochs Avhich are of enormous duration as re-
gards the existence of the human species.
   The views of Mr. Thompson differ from those of Laplace,
recently enforced by M. Babinet,  which suppose the  planets
to have been formed by a gradual condensation of nebulous
matter.  A modification of this view might, perhaps, be sug-
gested, viz.  that worlds or systems, instead of being  created
as wholes at definite periods, are gradually changing by at-
mospheric additions or subtractions, or by accretions or  dim-
inutions  arising from nebulous  substance or from meteoric
bodies, so that no star or planet could at any time be  said to
be created or destroyed, of to be  in a state of absolute stabii- 
82          CORRELATION OF PHYSICAL  FORCES.

ity, but that some may be increasing, others dAvindling away,
and so throughout the universe, in the past as in  the future.
When, hoAvever, questions relating to cosmogony, or  to tho
beginning or end of Avorlds, are contemplated from  a  physi-
cal point of view, the period of time over which our experi-
ence,  in its most enlarged sense,  extends, is so  indefinitely
minute with reference to that which must be required for any
notable  change, even in our oAvn planet, that a variety of the-
ories  may be framed equally incapable of proof or of dis-
proof.   We have no means  of ascertaining whether  many
changes, which endure in the  same  direction  for a term be-
yond the range of human experience, are really continuous or
only secular variations, which may be  compensated for at
periods far beyond our ken, so that in  such cases the  ques-
tion of comparative stability or  change  can at best  be only
answered as to a term which, though enormous Avith  refer-
ference to our computations, sinks into nothing Avith reference
to cosmical time, if cosmical time be not eternity.  Subjects
such as  these, though of a kind on which the mind  delights
to speculate, appear, with reference to any hope of attaining
reliable knowledge, far  beyond the reach of  any  present  01
immediately prospective capacity of man. 
IV.   ELECTRICITY.
     ELECTRICITY is  that  affection  of matter or mode of
       force which most distinctly and beautifully relates other
modes of force, and exhibits, to a great extent in a quantita-
ti\-e form, its  own  relation Avith them, and their reciprocal
relations  Avith  it and with each other.   From the manner
in  Avhich the  peculiar force called  electricity i3  seemingly
transmitted through  certain bodies,  such as metallic wires,
the term current  is  commonly used to denote its apparent
progress.   It  is very difficult to present to the  mind  any
theory which will  give  a  definite conception  of  its  modus
ajendi: the early theories  regard its  phenomena as produced
either  by a single  fluid idio-repulsfve,  but attractive of all
matter, or else  as produced by two fluids, each idio-repulsive
but attractive of the  other.  No substantive theory has been
proposed other than these two ; but although this is the case,
I think I shall  not be unsupported by many who have atten-
tively studied electrical  phenomena,  in  viewing them as re-
sulting, not from the  action of a fluid or fluids, but as a mole-
cular polarisation of ordinary matter, or as matter acting by
attraction and  repulsion in a definite direction.  Thus,  the
transmission of the  Aroltaic current in  liquids  is viewed by
Grotthus  as a series of chemical affinities acting in a definite
direction : for  instant e,  in the electrolysis of water, i. e. its
decomposition  when placed betAveen the poles or electrodes 
84
CORRELATION  OF PHYSICAL FORCES.
of a voltaic battery, a molecule of oxygen is supposed to be
displaced by the exalted attraction of the neighbouring elec-
trode ;  the hydrogen liberated by this displacement  unites
with the oxygen of the contiguous molecule of water ;  this in
turn liberates  its  hydrogen, and so on; the  current being
nothing else than  this  molecular transmission of chemical
affinity.
   There  is strong reason  for believing that, Avith some ex-
ceptions, such  as  fused metals, liquids do not conduct elec-
tricity without  undergoing decomposition ; for even in those
extreme cases  where a trifling effect of conduction is  appar-
ently produced Avithout  the usual elimination of substances at
the electrodes, the latter when detached from the  circuit
shoAV, by the counter-current which they are  capable of pro-
ducing when immersed  in a fresh liquid, that their superficial
state has  been changed,  doubtless by the determination to
the surfaces of minute  layers of substances  having opposite
chemical characters.  The question Avhether or not a minute
conduction in liquids can take place unaccompanied by  chemi-
cal action, has however been much agitated, and may  be re-
garded  as inter apices of the science.
   Assuming  for  the  moment electrolysis to be the only
known electrical phenomenon, electricity would appear to con-
sist in  transmitted chemical action.   All the evidence we
have is, that a certain affection of matter or chemical change
takes place at certain distant points of space,  the change at
one  point having  a  definite  relation to  the  change  at the
other, and being capable of manifestation at any intermediate
points.
   If, now, the electrical  effect called induction be examined,
the phenomena will be found equally opposed to the theory of
a  fluid, and  consistent with that of molecular polarisation.
When an electrified conductor is brought near  another which
is not electrified, the latter becomes electrified by influence or
induction, as  it is termed, the nearest parts of each of these 
ELECTRICITY.
85
two  bodies exhibiting states  of electricity of the contrary
denominations.  Until this subject Avas investigated by Fara-
day, the intervening non-conducting  body or dielectric was
supposed to  be purely negative, and the effect Avas attributed
to the repulsion at a distance  of the  electrical fluid.   Fara-
day showed that these effects differed greatly according to the
dielectric that Avas interposed.   Thus they were more  exalted
with sulphur  than Avith shellac ; more with shellac than with
glass,  &c.   Matteucci,  though differing  from Faraday as  to
the explanation he gave, added some experiments which proArc
that the intervening dielectric is molecularly polarised.   Thus
a number  of thin plates of  mica are superposed like a pack
of cards ;  metallic plates are applied to the outer facings, and
one of them electrified, so that the  apparatus is charged like
a Leyden phial.   Upon separating the plates Avith insulating
handles, each  plate is  separately electrified,  one side  of  it
being  positive and the  other  negative, showing  very neatly
and decisively a polarisation throughout the intervening sub-
stances by the effect of induction.
    Indeed, chemical  action or electrolysis may,  as  I  have
shown, be transmitted by induction across a  dielectric sub-
stance, such as glass, but apparently only while the glass  is
being charged with electricity.   A  Avire passing through and
hermetically sealed into a glass tube, a short portion only pro-
jecting,  is made  to dip into  water contained in a Florence
flask;  the  flask is immersed in water to an equal depth with
that Avithin  it; the wire  and another  similar Avire  dipping
into the outer Avater  are made to  communicate metallically
with the powerful electrical machine known as Rhumkorf s
coil; bubbles of gas instantly ascend from the exposed por-
tions of the wires, but cease after a certain time, and are
reneAved Avhen, after an  interval  of separation, the coil  is
pgain  connected with the wires.
    The  following interesting experiment by Mr.  Karsten
Toes a step farther in corroboration of the molecular changes 
83         CORRELATION OF  PHYSICAL FORCES.

consequent upon electrisation: A coin is placed on a pack of
thin plates of glass, and then electrified.  On removing the
coin and  breathing  on the  glass plate, an impression of the
coin is perceptible ; this show3 a certain molecular change on
the  surface of the glass opposed to the plate, or of the vapours
condensed on such surface.   This effect might, and has been
interpreted as arising from a film of greasy deposit, supposed
lo exist on  the plate;  the  impressions, however, have been
proved to  penetrate to certain depths below the surface, and
not  to be removed by polishing.
    The following experiment, hoAvever, goes farther:  On
separating carefully the glass plates, images of the coin can
be developed- on each of the surfaces, shoAving that the mole-
cular change has been  transmitted through the substance of
the   glass;  and we may thence  reasonably suppose  that a
piece of glass, or other  dielectric body, if it could be  split up
while under the influence of electric induction, Avould exhibit
some molecular change  at each side of each lamina, hoAvever
minutely subdivided.  I have succeeded in farther extending
this experiment, and in permanently fixing the  images  thus
produced by electricity.   BetAveen two carefully-cleaned glass
plates is placed a word or device cut out of paper or tinfoil;
sheets  of  tinfoil a  little smaller than the glass plate3 are
placed on the  outside  of each plate,  and these coatings are
brought into contact with the terminals of Rhumkorf s coil.
After electrisation for a few  seconds, the glasses are sepa-
rated, and their interior surfaces  exposed to the vapour of
hydrofluoric acid, which acts chemically on glass;  the por
tions of the glass not protected by the paper  device are cor-
roded, while  those  so protected  are  untouched  or less
affected by the acid, so that a  permanent etching  is  thus
produced, which nothing but  disintegration of the glass will
efface.
    Some  further  experiments of mine on this subject bring
out  in a  still more  striking manner these curious molecular 
ELECTRICITY.
87
changes.  One of the plates of gla33 havh.gbeen electrified
in the manner just mentioned, is coated, on the side impressed
with the inATisible electrical image,  with a film of iodised
collodion in the manner usually adopted  for  photographic
purposes; it is then in a dark room immersed in a solution
of nitrate of silver; then  exposed to diffuse light for a few
seconds.  On pouring  over the  collodion the usual solution
of pyrogalhc  acid,  the  invisible electrical  image  is brought
out as a dark device on a light ground, and can be permanently
fixed by hyposulphite of soda.   The  point worthy of obser-
vation in this experiment is, that this permanent image exists
in the collodion film, which can be stripped off the glass, dried,
and placed on any other surface, so that the molecular change
consequent on electrisation has  communicated, by contact or
close proximity,  a  change to the  film of  collodion corres-
ponding in form Avith that on the glass, but being undoubtedly
of a chemical nature.  Electricity has, moreover,  in this ex-
periment  so modified the  surface of glass, that it can, in its
turn, modify the structure  of another substance so  as to alter
the relation of the latter to light.  It would require a curious
complication of hypothetic fluids to explain this ; but if elec-
tricity and light be supposed to be affections of  ordinary pon-
derable matter, the  difficulty is only one of detail.
    If, again, we examine  the  electricity of the atmosphere,
when, as is usually the case, it is positive with respect to that
of the earth, we find that  each successive stratum is positive
to those below it and negative to those above it; and the con-
verse is the case when the electricity of the  atmosphere is
negative with respect to that of the earth. %
    If another electrical phenomenon  be selected, another sort
of change will be found to  have taken place.  The electric
spark, the brush, and similar phenomena, the old theories
regarded  as actual  emanations of the matter or fluid, Elec-
tricity ; I venture to regard them as produced by an emission
of the material itself from whence they issue, and a molecular 
88
CORRELATION OF PHYSICAL  FORCES.
action of the gas, or intermedium, through or across Avhich
they are transmitted.
   The colour of the electric spark, or of the voltaic  arc  (i.
e. the  flame which plays  between the terminal points of a
poAverful voltaic battery), is dependent upon the substance of
the metal, subject to certain modifications of the intermedium :
thus, the electric spark or arc from zinc is blue ;  from silver,
green ;  from iron, red and scintillating ; precisely the colours
afforded by these metals in their  ordinary combustion.  A
portion  of the metal is also found to  be actually transmitted
with every electric or voltaic discharge :  in the latter  case,
indeed,  Avhere the  quantity of matter acted upon  is greater
than in  the former, the metallic particles emitted by the elec-
trodes or terminals can be readily  collected, tested, or  even
weighed.   It Avould thus appear that the  electrical discharge
arises, at least in part,  from an  actual repulsion and  sever-
ance of the electrified matter itself, which flies off at the points
of least resistance.
    A careful examination of the  phenomena attending the
electric  spark or the voltaic arc,  which  latter  is the electric
disruptive  discharge  acting  on  greater portions of matter,
tends to modify  considerably our previous idea of the nature
of the electric force as a producer of ignition and combustion.
The voltaic arc  is perhaps, strictly speaking, neither ignition
nor combustion.   It is not simply ignition ; because the mat-
ter of the terminals is not merely brought to a state of incan-
descence, but is  physically separated and partially transferred
from one electrode to another, much of it being dissipated  in
a vaporous state.  .It is not combustion ;  for the phenomena
will take place independently of atmospheric air, oxygen gas,
or any  of the bodies usually called supporters of combustion,
combustion being in fact chemical union attended with heat
and light.  In the voltaic arc we may have no chemical union ;
for if the experiment be performed in an exhausted receiver, or
in nitrogen, the  substance forming the electrodes  is condensed. 
ELECTRICITY.
89
and precipitated upon the interior of the vessel in, chemically
speaking, an unaltered state.   Thus, to take  a very striking
example, if the voltaic discharge be taken between zinc ter-
minals in an exhausted receiver, a fine black  powder of  zinc
io deposited on the sides of the receiver ;  this can  be collect-
ed, and takes fire readily in the air by being  touched with a
match, or ignited wire, instantly burning into white oxide of
zinc.   To an ordinary observer, the zinc would appear to be
burned twice—first in the  receiver,  where the phenomenon
presents all the appearance of combustion,  and secondly in
the real  combustion in  air.   With  iron the  experiment is
equally instructive.   Iron is volatilised by the voltaic  arc in
nitrogen or  in an exhausted receiver;  and Avhen  a scarcely
perceptible film has lined the receiver, this is  Avashed with an
acid, Avhich then gives, Avith ferrocyanide of potassium, the prus-
sian-blue precipitate.  In this case Ave readily distil iron, a
metal by ordinary means fusible only at a A-ery high tempera-
ture.
   Another strong evidence that  the A-oltaic discharge  con-
sists of the  material itself of Avhich the terminals are compos-
ed,  is  the peculiar rotation which is observed in the light
when iron is employed, the magnetic character of  this metal
causing its molecules to rotate  by the  influence of  the voltaic
current.
   If Ave increase the number  of  reduplications  in a voltaic
series, Ave increase the length of the arc, and  also increase its
intensity or  power of overcoming  resistance.   With a battery
consisting of a limited number, say  100 reduplications, the
dire-barge Avill not pass from one terminal to  the other Avith-
out first  bringing them into contact,  but  if  Ave  increase the
number of cells to  400 or 500, the discharge  will  pass from
one terminal to the other before they are brought into contact.
The difference between Avhat is called Franklinic electricity, or
that produced by an ordinary electrical machine, and voltaic elec-
tricity, or that produced by the ordinary voltaic battery, is that 
00        CORRELATION OF PHYSICAL FORCES.

the former is of much greater intensity than the latter, or has a
greater power of overcoming resistance, but acts upon a much
smaller quantity of matter.   If, then, a voltaic battery be
formed with a vieAv to increase the intensity  and lessen the
quantity, the character of the electrical phenomena approxi-
mate those of the electrical machine.   In order to effect this,
the sizes  of the plates  of the battery and thence the quantity
of matter acted on  in  each  cell, must be reduced,  but the
number of reduplications increased.  Thus if in a battery of 100
pairs of plates each plate be divided, and the battery be arranged
so as to form 200 pairs, each being half the original size, the
quantitative effects are diminished, and the effects of intensi-
ty increased.   By carrying on this  sub-division,  diminishing
the sizes  and increasing the number, as is the case in the vol-
taic piles of Deluc and Zamboni, effects are  ultimately pro-
duced similar to those  of Franklinic electricity, and we thus
gradually pass from the voltaic arc to  the spark or electric
discharge.
   This  discharge,  as  I have already stated, has a colour de-
pending in part upon the nature of the terminals employed.
If these terminals be highly polished, a spot will be observed,
even in the case of  a small electric  spark, at the points from
which the discharge emanates.   The matter of the terminals
is itself affected; and a transmission of this matter across
the intervening space is detected by the deposition of minute
quantities of the metal or substance composing the one, upon the
other terminal.
   If  the gas or elastic  medium between the terminals be
changed, a change takes place in the length or colour of the
discharge,  showing  an affection of the intervening matter.
If the  gas be rarefied, the discharge gradually changes with
the degree of rarefaction, from a spark to a luminous gloAv or
diffuse light,  differing in colour in different gases, and capable
of extending to a much greater distance than Avhen  it takes
place in air of the ordinary density.  Thus, in highly attenu- 
ELECTRICITY.
91
ated air a discharge may be made to pass across six or seven
feet of space, Avhile in air of the ordinary density it Avould
not pass across an inch.   An obserA'cr regarding the beauti-
ful phenomena exhibited by this electric discharge in attenua-
ted gas, which, from some degree  of similarity in  appear-
ance to the Aurora Borealis, has been called the electric  Au-
rora, would have some  difficulty in believing  such effects
could be due to an action of ordinary matter.   The  amount
of gas present  is extremely small;  and the terminals,  to a
cursory examination, shoAv  no change after long  experiment-
ing.  It is therefore not to be wondered at that the first ob-
servers of this  and similar phenomena, regarded electricity
as in itself something—as a specific existence or fluid.  Even
in this extreme case, hoAvever, upon a more careful examination
we shall find that a change does take place, both as regards the gas
and as regards the terminals.   Let one of these consist of a high-
ly-polished metal—a silver plate is one of the best materials for
the purpose—and let the discharges in attenuated atmospheric
air take place froma point, say a common sewing needle, to the
surface of the polished silver plate ;  it will be found that this
is gradually changed in appearance opposite the point—it is ox-
idated, and gradually more and more corroded as the discharge
is continued.
    If noAV the gas be changed, and highly-rarefied hydrogen
be substituted for the rarefied air, all other things remaining
the same, upon passing the discharges  as before  the oxide
aviU be cleared off the plate, and the polish to a great extent
restored—not entirely, because the silver has been disinte-
grated by the oxidation—and the portion which has been af-
fected by the discharge will present a somewhat different ap-
pearance from  the remainder of the  plate.
    A question Avill probably here occur to the reader:—What
will be the effect if there be not an oxidating medium  pres-
ent, and the experiment be first performed in a rarefied gas,
which possesses no power of chemically acting on the plate? 
92         CORRELATION OF  PHYSICAL  FORCES.
In this case there will stiU be a molecular change  or disinte-
gration of the plate ;  the portion of it  acted  on by the  his-
charge will present a  different appearance from that which is
beyond its reach, and a AAiiitish film,  someAvhat  similar to
that seen on the mercurialised portions  of a  daguerreotype,
will gradually appear on the portion of  the plate affected by
the discharge.   If the gas be a compound, as carbonic oxide,
or a mixture, as oxygen andhyarogen, and consequently contain
elements capable of producing oxidation and reduction,  then
the effect upon the plate Avill depend upon whether it be pos-
itive or negatiATe ;  in the former case it  wiU be  oxidated, in
the hitter the oxide, if existing,  will be  reduced.   This effect
Avill also  take place in atmospheric  air,  if it be  highly rare-
fied, and can hardly be explained otherwise than  by a mole-
cular polarisation of the compound  gas.  If, again, the metal
be reduced to a small point, and be of such material that the
gas cannot act chemically upon it, it can yet be  shown  to be
disintegrated by the electric spark.  Thus, let  a fine  plati-
num wire be hermetically scaled in  a glass tube, and the  ex-
tremity of the tube and the wire ground to a flat surface, so as to
expose a section only of the wire ;  after taking the discharge
from this for some time, it will be  found that the platinum
wire is worn away, and that its termination is sensibly below
the level  of the glass.  If the discharges from such a  plati-
num wire be taken in gas  contained in a narrow tube, a cloud
or film consisting of a deposit of platinum will be  seen on
the part of the tube surrounding the point.
    Another curious effect which, in addition to the  above, I
have detected in the electrical discharge in attenuated media,
is that when passing between terminals  of a certain form, as
from a wire placed at right angles to a polished plate, the dis-
charge possesses certain phases or fits of an alternate character,
so that, instead  of impressing an uniform mark on a polished
plate, a series of concentric rings is formed.
    Priestley observed that, after the discharge of a Leyden 
ELECTRICITY.
93
battery,  rings  consisting of fused globules of  metal were
formed on the terminal plates ; in my experiments  made in
attenuated media, alternate rings of  oxidation and  deoxida-
tion are formed.   Thus,  if  the plate be  polished,  coloured
rings of oxide will alternate with ring? of polished or unoxi-
dated surface ;  and if the plate be previously coated with  an
uniform film of oxide, the oxide will  be  removed in concen-
tric spaces,  and increased in the  alternate ones, shoAving a
lateral alternation of  positive and  negative  electricity,  or
electricity of opposite character in the same discharge.
    It  would be hasty to assert that in no case can the electri-
cal disruptive discharge take place without the terminals be-
ing affected. I have, howeA-er, seen no instance of such a re-
sult where the  discharge has been sufficiently prolonged, and
the terminals in such a state as could be  expected to render
manifest slight changes.
    The next question  Avhich Avould occur in following out the
enquiry Avhich has been indicated, Avould probably be, What
io the  action upon the gas itself? is this changed in any man-
ner ?
    In  answer to this, it must be admitted that, in the present
state  of experimental knowledge on this  subject, certain
gases only appear to leave permanent traces of their having
been changed by the discharge, while others,  if  affected by
it, which, as will be presently seen, there are reasons to be-
hove they are, return to their normal  state  immediately after
the discharge.
    In  the former class we may place  many compound gases,
as ammonia, olefiant gas,  protoxide  of  nitrogen, deutoxide
of nitrogen, and others, which are decomposed by the action
of the  discharge.   Mixed gases are also chemically combined :
for instance, oxygen and hydrogen unite  and form Avater;
common air gives nitric acid ; chlorine and aqueous A-apour
five oxygen, the  chlrvir.e uniting Aviih the   hydrogen of the
water. 
94         CORRELATION  OF PHYSICAL FORCES.

   But, further than this, in the case of certain elementary
gases a permanent change is effected by  the  electrical  dis-
charge.   Thus, oxygen submitted to the discharge is par-
tially changed into the substance now considered to be  an al-
lotypic condition of oxygen ; and there is reason to believe
that when the change takes  place, there is  a  definite  polar
condition of the gas, and that definite portions of it are affected
—that in a certain sense one  portion of  the  oxygen  bears
temporarily to the other the relation which hydrogen ordina-
rily does  to oxygen.
   If the discharge be passed through the vapour of  phos-
phorus in the vacuum of a good air-pump, a deposit of allotro-
pic phosphorus soon coats the interior of the receiver, show-
ing an analogous change to that produced in oxygen ; and in
this case a series of transverse bands or stratifications appears
in the  discharge, showing a most striking alteration  in its
physical character, dependent on the medium across which it is
transmitted.  These  effects were  first  observed by  me in
the year  1852.  They have  since  been much  examined by
continental philosophers, and much extended by Mr. Gassiot;
but no satisfactory rationale of them has yet been gi\-en.
   There are many gases which either do not  show any per-
manent change, or (which is  more  probably  the  case)  the
changes produced in them by the electrical discharge have
not yet been detected.   Even with these gases, however, the
difference of  colour, of length, or of  the different position of
a certain dark space or spaces which appear in the discharge,
show that the discharge differs for different media.   We neA'-
er find that the discharge has itself added to or subtracted
from the  total weight of the substances acted on: we find no
evidence  of a fluid but the visible phenomena themselves;
and those we may account for  by the  change Avhich takes
place in the matter affected.
   I have here, as elsewhere, used words of common accep-
tation, such as ' matter affected by the discharge,' &c. though 
                       ELECTRICITY.                     05

upon the vieAV  I am suggesting,  the  discharge is itself this
affection of matter : and the writing these  passages affords,
to me  at least, a striking  instance of hoAv much ideas are
bound up in Avords,  when, to express a vieAV differing  from
the received one, Avords involving the receired one are neces-
sarily used.
    Passing now to the  effect of the transmission  of electri-
city by the class of the best conducting bodies,  such as the
metals and carbon, here, though we cannot at present give the
exact character of the  motion impressed upon the particles,
there are yet many experiments which shoAV that a  change
takes place in such substances when they arc affected by elec-
tricity.
    Let discharges from a Leyden jar or battery  be passed
through a platinum  wire, too thick to be fused by the dis-
charges, and free  from constraint, it Avill be found  that the
wire is shortened ; it has undergone a molecular change, and
apparently been acted on by a force tranverse to  its length.
If  the  discharges be continued,  it gradually gathers up in
small irregular bends or convolutions.  So Avith voltaic  elec-
tricity :  place a platinum wire  in a trough of porcelain, so
that Avhen fused it shall retain its position as a wire, and then
ignite it by a voltaic battery.   As it reaches the point of fu-
sion it will snap asunder, showing  a contraction in length, and
consequently a distension or increase in its transverse dimen-
sions.   Perform the same  experiment  with a lead wire,
which can be more readily kept in a state of fusion,  and fol-
low it, as it contracts, by the terminal wires of the batter:  ;
it Avill be seen  to gather up in  nodules, which press  on each
other like a string of beads of a soft material  which  have
been longitudinally compressed.
    As we increase the thickness of the Avires in these exper-
iments with reference to the electrical force employed, we les-
ecu the perceptible effect: but even in this  case  we  shall be
enabled  safely to infer that  rnrr.o molecular change accompa- 
96         CORRELATION OF THYSICAL FORCES.
nies the transmission of electricity :  the AA'ires are heated in a
degree  decreasing  as  their thickness increases—but by in-
creasing the delicacy of our  tests as the heating effects de-
crease in intensity,  we may indefinitely detect the augmenta-
tion of temperature  accompanying  the  passage of electri-
city—and wherever there is augmentation of  temperature
there must be expansion or change of position of the mole-
cules.
    Again, it has been observed that wires Avhich have  for  a
long time  transmitted electricity, such as those  which have
served as  conductors for atmospheric electricity,  have  their
texture changed, and are rendered brittle.  In  this  observa-
tion, however, though made by a skillful electrician, M. Pel-
tier, the effects of exposure to the atmosphere, to changes of
temperature, &c, have not  been sufficiently  eliminated  to
render it worthy of entire confidence.  There are, hoAvever,
other experiments which show that the elasticity  of metals i3
changed by the passage through them of the electric current.
    Thus M. Wertheim has, from an elaborate series of ex-
periments, arrived at the conclusion that there is a temporary
diminution in the coefficient of elasticity in Avires while they
are transmitting  the electric current, which is independent of
the heating effect of the current.
    M. Dufour has  made  a considerable  number of experi-
ments with the view of ascertaining if any permanent change
in metals is effected by electrisation.   He arrives at the  cu-
rious result that  in a copper wire through Avhich a feeble \-ol-
taic current has  passed for several days, a notable diminution
in tenacity takes place; while, in an iron Avire, the tenacity
is increased; and that these  effects were more perceptible
when the wires had been electrised for a long time (nineteen
days) than for a short time  (four  days).  The  copper wire
was. in his experiment, not perfectly pure ; so that the effect,
or a portion of it, might be due  to the state of alloy: in the
case of iron, the magnetic character of the metal  would prob- 
ELECTRICITY.
97
ably modify the effects, and might  account for  the  opposite
character of the results Avith these two metals.
    Matteucci has  made  experiments  on the conduction of
electricity by bismuth in  directions  parallel or transverse to
the planes of principal cleavage, and he  finds that  bismuth
conducts  electricity and heat  better in the direction of the
cleavage planes than in that transverse to them.
    Many other experiments have been made both on the pro-
duction  of  thermo-electric currents by two  portions of the
same crystalline  metal, but Avith the planes of crystallization
arranged in  different directions relatively to each  other, and
also on the  differences in conduction of heat  and electricity
according to the direction in which they are transmitted with
reference to the planes of crystallization.
    It is  found, moreover, that the slightest difference in ho-
mogeneity in the  same metal  enables it when heated to pro-
duce a thermo-electric current, and  that metals in a  state of
fusion, in Avhich  state they may be  presumed to be homoge-
neous throughout, give no thermo-electric  current: thus, hot
in contact with cold  mercury has been sIioaati by Matteucci
to giA'e no thermo-electric current, and the same is the case
Avith portions of fused bismuth unequally heated.
    The fact that  the molecular structure or arrangement of a
body influences—indeed I may say  determines—its conduct-
ing power, is by no means explained by the theory of a fluid;
but if electricity be only a transmission of force or  motion,
the influence of the  molecular state is just what would be
expected.  Carbon, in a transparent crystalline state, as dia-
mond,  is as  perfect a non-conductor as we know; Avhile in an
opaque amorphous state, as graphite or charcoal, it is one of
the best conductors : thus, in the  one state, it transmits  light
and stops electricity, in the other it transmits  electricity and
stops light.
    It is a circumstance worthy of remark, that the arrange-
ment of molecules,  which  renders  a sohd body capable of
             5 
98         CORRELATION  OF PHYSICAL FORCE?.

transmitting hght, is most unfavourable to its transmission oi
electricity, transparent solids being very imperfect conductors
of electricity;  so all  gases readily transmit light, but  are
amongst the worst conductors of electricity, if, indeed, prop-
erly speaking, they can be  said to conduct at all.
    The conduction of electricity by different classes of bodies
has been generally regarded  as a question of degree: thus
metals Avere viewed as perfect conductors,  charcoal less  so,
Avater and other aquids as imperfect conductors, &c.  But,
in fact, though between one metal and another the mode of
transmission may be the same and the difference one  of  de-
gree, a different  molecular effect obtains, when we  contrast
metals Avith electrolytic liquids and these wTith ga- es.
    Attenuated gases may be, in one sense, regarded as non-
conductors,  in another,  as conductors ; thus  if gold-leaves be
made to diverge, by electrical  repulsion,  in air at ordinary
pressure, they in  a short time collapse ; while in highly-rare-
fied air, or what is commonly termed a vacuum, they remain
divergent for days ; and yet electricity of a certain degree of
tension passes readily across attenuated air,  and with diffi-
culty across air of ordinary density.
    Again, where  the  electrical  terminals arc brought to a
state of visible ignition, there are symptoms of the transmis-
sion of electricity of low tension across gases; but  no such
effects have been detected  at  loAArcr temperatures.   All this
presents a strong argument in favour of the transmission of
electricity across  gases  being effected by the  disruptive dis-
charge, and not by a conduction  similar to that which takes
place Avith metals or with electrolyte;-.
    The  ordinary attractions  and  repulsions  of electrified
bodies present no more difficulty when regarded as being pro-
duced by  a change in the state or relations of the matter af-
fected, than do the attractions of the earth by the sun, or of
a leaden ball  by the earth; the hypothesis of a fluid  is  not
considered necessary for the latter, and need not be so for the 
ELECTRICITY.
99
former  class of phenomena.  How the phenomena  are  pro-
duced to which  the term  attraction is applied is still a mys-
tery.   Newton, speaking of it, says, 'What I call attraction
may be performed by impulse,  or  by some other means un-
known to me.   I use that Avord here to signify only in  gen-
eral any force by which bodies tend toAvards one  another,
whatsoever be the cause.'  If we suppose a fluid to act in at*
tractions and repulsions, the  imponderable fluid must drag or
push the matter with  it: thus Avhen  we  feel a stream of
air rushing from an electrified metallic  point, each  molecule
of air contiguous  to the point  being repelled, another takes
its  place, Avhich is in  its  turn  repelled:—hoAV does a hypo-
thetic fluid assist us here ?  If we say the electrical  fluid re-
pels itself, or the  same electricity repels itself, we  must go
farther and  assert, that it not only repels itself, but  either
communicates its repulsive force to the particles of the air, or
carries wiili it the particle of air  in  its passage.  Is  it not
more easy to  assume that the particle of air is in such a state
that the ordinary forces which  keep it in equilibrium are dis-
turbed by the electrical force, or force in a definite  direction
communicated to it, and that thus each particle in  turn re-
cedes from the  point?   As this latter force is increased, not
only doe3 the particle of air Avhich was contiguous to the me-
tallic point recede, but the cohesion of the extreme  particles
of metal may be overcome to such an extent that these are
detached, and the  brush or spark may consist wholly or in
part of minute  particles of the metal itself thrown off.   Of
this there is some  evidence, though the  point can hardly bo
considered as proved.   A similar effect undoubtedly takes
place  with voltaic electricity, acting upon  a  terminal im-
mersed in a liquid ; thus if metallic terminals of a powerful
voltaic battery be  immersed in water, metal, or the  oxide of
metal, is forcibly detached, producing great heat at the point
of disruption.
    If we apply ourselves to the  effect of electricity in the 
100        CORRELATION OF PHYSICAL FORCES.

animal  economy, we find that the first rationale  given  of the
convulsive effect produced by transmission through the living
or recently killed animal was, that electricity itself, something
substantive, passed rapidly through  the  body, and gave rise
to the contractions ; step by step we are now arriving at the
conviction that consecutive particles of the nerves and mus-
cles are affected.  Thus the  contractions which the prepared
leg of a frog undergoes at the moment it is submitted to a
voltaic  current, cease  after a time if the  current  be  contin-
ued, and are renewed on breaking the circuit, i. e.  at the mo-
ment when the current ceases to traverse  it.  The excitabil-
ity of a nerve, moreover, or its power of producing muscular
contraction, is weakened or destroyed by the transmission of
electricity in one direction, while the excitability is increased
by the transmission of electricity in the opposite  direction;
showing that the fibre or matter itself of the nerATe is changed
by electrisation, and changed in a manner bearing a direct
re.ation to the other effects produced by electricity.
    Portions of muscle and of nerve present different  electri-
cal states  Avith reference to other portions of the  same muscle
or nerve ; thus the external part of a muscle bears the  same
relation to the internal  part as platinum  does to zinc in the
voltaic battery ; and dehcate galvanoscopes will  show electri-
cal effects when interposed in a conducting circuit Connecting
the surface of a nerve with its interior  portions.  Matteucci
has proved that a species of voltaic pile  may be  formed by a
series of slices of muscle, so arranged that the external part
of one  slice may  touch the  internal part  of the  next, and
so on.
    Lastly, the magnetic  effects produced by electricity &ho
show a change in  the  molecular state  of  the  magnetic sub-
stance affected; as Ave shall  see when the subject of magnet-
ism is discussed.
    I have taken in succession all  the known classes  of elec-
trical phenomena;  and, as far as I am aware, there is not an 
ELECTRICITY.
101
electrical effect, where, if a close investigation be instituted,
and  the  materials  chosen in a  state for  exhibiting minute
changes, evidence of molecular  change will not be detected;
thus, excepting those cases where infinitesimally small  quan-
tities of  matter are acted on, and our means of detection fail,
electrical effects are knoAATi to us only as changes of ordinary
matter.  It seems to me  as easy to  imagine these changes to
be  effected by a force acting in definite  directions, as by a
fluid which  has no  independent or  sensible existence, and
which, it must be assumed, is  associated with, or exerts  a
force acting upon  ordinary matter, or  matter of a different
order from the supposed fluid.  As  the idea of the hypothetic
fluid is pursued, it gradually vanishes, and resolves itself into
the idea of force.  The hypothesis of matter Avithout weight
presents in itself, as I believe, fatal  objections to the theories
of electrical fluids,  which are  entirely removed by viewing
electricity as force, and not as matter.
    If  it be said that the effects we  have been considering
may still be produced by a fluid, and that this fluid acts upon
ordinary matter in certain cases,  polarising the matter af-
fected  or arranging its particles  in a definite  direction,  whilst
in others, by its  attractive or repulsive force, it carries Avith
it portions of matter; yet, if the fluid in itself be incapable
of recognition  by any test,  if it be only evidenced  by the
changes  Avhich it operates in ponderable  matter, the  Avorda
fluid and force become identical  in meaning; we may as well
say  that the attraction of gravitation or weight is occasioned
by a fluid, as that electrical changes are so.
    When, as is constantly done  in common parlance, a  house
is said to be struck, windoAvs broken, metals fused or dissipa-
ted by the  electrical fluid, are not the expressions used such
as, if not  sanctioned  by habit, would seem absurd?   In all
the  cases of injury done  by lightning there  is  no fluid per-
ceptible  ; the so-called sulphurous  odour is either  ozone de-
veloped  by the action of electricity  on atmospheric air,  or tho 
102        CORRELATION OF  PHYSICAL  FORCES.
vapour of some substance dissipated by the discharge ; on the
other hand, it seems more consonant Avith experience to re-
gard these effects as produced by force, as we have analogous
effects produced  by admitted forces, in cases where no one
would invoke the aid of a hypothetic fluid  for explanation.
For instance, glasses may be broken by electrical discharges ;
so may they by  sonorous vibrations.  Metals  electrified  or
magnetised will emit a sound; so they will if struck, or if a
musical note with which they can vibrate in"unison be sounded
near to them.
   Even chemical  decomposition, in cases of feeble  affinity,
may be produced by purely mechanical effects.   A number  of
instances of this have been collected by M.  Becquerel; and
substances whose constituents are held together by feeble af-
finities, such as iodide of nitrogen and similar compounds, are
decomposed by the vibration occasioned by sound.
   If, instead of  being regarded as a fluid  or  imponderable
matter sui generis, electricity be regarded as the motion of  an
ether, equal difficulties are encountered.   Assuming ether to
pervade the pores of aU bodies, is the ether a  conductor  or
non-conductor ?  If the latter—that is, if the  ether be incapa-
ble of transmitting the electrical Avave—the ethereal hypothe-
sis of  electricity  necessarily falls ; but if the motion of the
ether constitute what we call conduction of electricity, then
the more porous bodies, or those  most permeable  by the
ether, should be the  best conductors.   But this is not the case.
If, again, the metal and the air surrounding it are  both per-
vaded  by ether,  Avhy  should the  electrical  wave  affect the
ether in the metal, and  not stir that in the gas?   To  support
an ethereal hypothesis of electricity, many additional and
hardly reconcilable hypotheses must be imported.
   The fracture and comminution of a non-conducting body,
the fusion or dispersion of a metallic  Avire  by the electrical
discharge,  are  effects  equally difficult to conceive upon the
hypothesis of an  ethereal Aibration, as upon that of  a  fluid, 
ELECIRICITY.
103
but are  necessary results of the  sudden subversion of mole-
cular polarisation, or of a sudden or irregular vibratory move-
ment of  the matter  itself.   A\re see  similar effects produced
by  sonorous Aibrations, which might be called  conduction
and non-conduction of sound.  One  body transmits sound ea-
sily, another stops or deadens it, as  it is termed—i. e. dis-
perses the vibrations, instead of continuing them in the same
direction as the primary impulse ; and solid bodies may,  as
has been above observed, be shivered  by sudden impulses  of
sound in those  cases where all the parts of the body cannot
uniformly carry on the undulatory motion.
    The progressive stages  in the History of Physical Philoso-
phy Avill  account in a great  measure for the  adoption by the
early electricians of the theories of fluids.
    The ancients, when they witnessed  a natural phenomenon,
removed from  ordinary analogies, and unexplained by any
mechanical  action known  to them,  referred  it to a soul, a
spiritual or preternatural poAver :  thus  amber and the magnet
were  supposed by Thales  to have a soul; the functions  of
digestion, assimilation,  &c, were supposed by Paracelsus  to
be effected by a spirit (the Archoous).   Air and gases were
also at first deemed spiritual, but subsequently became invest-
ed Avith a more material character;  and the word gas, from
geist, a ghost or spirit, affords us  an instance of the gradual
transmission of a spiritual into a physical conception.
   The establishment by Torricelli of the ponderable charac-
ter of  air and  gas, sliOAved  that  substances which had been
deemed spiritual and essentially different  from  ponderable
matter were possessed of its attributes.  A less superstitious
mode  of reasoning ensued,  and  now  aeriform fluids  were
sliOAvn to be analogous in many of their actions to liquids or
known fluids.   A behef in  the existence of other fluids, differ-
ing from air as this differed  from water, grew up, and Avhen
a new phenomenon  presented itself, recourse was had to a
hypothetic fluid for  explaining the phenomenon and connects 
104        CORRELATION  OF PHYSICAL FORCES.
 ing it Avith others ; the mind  once possessed of the idea of a
 fluid, soon invested it with the necessary powers and proper-
 ties, and grafted upon it a luxurious vegetation of imaginary
 offshoots.
    Iu what I am here  throAving out, I Avish to guard myself
 from being supposed to state that the  theory, historically
 viewed, followed exactly the  dates of the discoveries which
 were effectual  in changing its character; sometimes a dis-
 covery precedes, at other times it succeeds to a change in the
 general course of thought;   sometimes, and perhaps most
 frequently, it does both—i. e. the  discovery is the result of a
 tendency of the age and of the continually improved methods
 of observation, and Avhen made, it strengthens and extends the
 views which  have led to it.   I think the phases of thought
 which physical  philosophers have gone through, will be found
 generally such  as I have indicated, and that the gradual ac-
 cumulation of discoveries which has  taken  place  during the
 more recent periods, by showing what effects can be produced
 by  dynamical causes  alone, is rapidly  tending to a general
 dynamical theory into which that of  the imponderable fluids
 promises ultimately to merge.
    Commencing  Avith electricity as an initiating force, we
 get motion directly produced by it  in  various forms ; for in-
 stance, in the attraction and repulsion  of bodies, evidenced by
mobile  electrometers, such as that of Cuthbertson,  where
large masses are acted on;   the  rotation of  the fly-wheel,
another form of electrical  repulsion,  and the  deflection of
the galvanometer needle, are also  modes of palpable, visible
motion.
    It would  folloAV, from  the reasoning  in this essay, that
when electricity performs any mechanical wrork which does
 not return to the machine, electrical power is lost.  It would
 be unsuitable to the scope of this work to give the mathemati-
cal labours of M. Clausius and  others here ; but the follow-
 ing experiment, which I devised  for making the result evi- 
ELECTRICITY.
105
dent  to  an audience  at  the  Royal  Institution, will form a
useful iUustration:—A Leyden jar, of one square foot coated
surface, has its interior connected with a Cuthbertson's elec-
trometer, between  which and the  outer coating of the  jai
are a pair of discharging baUs  fixed at a certain distance
(about half an inch apart).  Between the Leyden jar and
the prime conductor is inserted a small unit jar of nine inches
surface, the knobs of which are 0*2 inch apart.
    The  balance of the electrometer  is  now  fixed by a stiff
wire  inserted between the attracting knobs, and the Leyden
jar charged by discharges from the unit jar.   After a certain
number of these, say twenty, the discharge of the large  jar
takes place across  the   half inch interval.   This may be
viewed  as the expression of electrical power received from
the unit jar.   The experiment is  now repeated, the wire
between the balls haATing been removed, and therefore the
' tip,' or the raising of the weight, is performed by the electri-
cal repulsion  and attraction of the two pairs of balls.   At
tAventy discharges of the  unit jar the balance is subverted,
and one  attracting knob  drops upon the other; but no dis-
charge takes place, shoAving that some electricity has been lost
or converted into the mechanical  poAver which raised the
balance.
   By another mode "'of  expression,  the electricity may be
supposed to be masked or analogous to latent heat,  and it
would be restored if the  ball were brought back without dis-
charge by extraneous force.  If the  discharge or other elec-
trical effects were the same in both cases, then,  since the
raising of the ball or  weight is an  extra mechanical effort,
and since the  weight is capable by its fall of producing elec-
tricity, heat, or other force, it would seem that force could be
got out of nothing, or perpetual motion obtained.
   The above experiment is suggestive of others of a similar
character,  Avhich may be indefinitely varied.   Thus I  have
found that two balls made to diverge by electricity do not 
106       CORRELATION OF PHYSICAL FORCES.

give to an electrometer the same amount of electricity as they
do if, whilst similarly electrified, they are kept forcibly to-
gether.   This experiment is the converse of the former one.
There is an advantage in electrical experiments of this class
as compared  witli those on heat, viz. that though there is no
perfect  insulation for electricity, yet our  means of  insula-
tion are immeasurably superior to any attainable for heat.
    Electricity directly produces heat, as shown in the ignited
wire, the electric spark,  and the  voltaic  arc: in the latter
the most intense heat writh which we are acquainted—so in-
tense, indeed, that it cannot be measured, as every sort of
matter is dissipated by it.
    In the phenomenon of electrical  ignition, as shown by  a
heated conjunctive wire, the relation of force and resistance,
and the correlative character of the two forces, electricity and
heat, are strikingly demonstrated.  Let a thin wire of plati-
num join the terminals of a voltaic battery of suitable poAver,
the Avire  will be ignited, and a certain amount of chemical
action  will take  place in the cells of the battery—a definite
quantity of zinc being dissolved and  of hydrogen eliminated
in a given time.  If now the platinum wire be immersed in
Avater,  the heat will, from the  circulating currents  of the
liquid, be more rapidly dissipated, and we shall instantly find
that the chemical action in the battery will be increased, more
zinc will be dissolved, and more hydrogen eliminated for the
same time ; the  heat being conveyed away by the  Avater,
more chemical action is required to generate it, just as more
fuel is   required  in proportion  as  evaporation is  more
rapid.
    Reverse the experiment, and instead of placing the wire
in water, place it in the flame of a  spirit lamp, so that the
force of heat meets with greater resistance to its dissipation.
We now find that the chemical  action is less than in the first
or normal experiment.  If the wire be placed in other differ-
ent gaseous or liquid media, we shall find that the chemical 
ELECTRICITY.
107
action of the battery will be proportioned to the facility Avith
which the heat is circulated or radiated by these media, and
Ave thus  establish an alternating reciprocity of action between
these two forces: a similar reciprocity may be established
between electricity and motion, magnetism  and motion, and
so of other forces.   If it  cannot be reahsed  with all, it is
probably because  we have not yet eliminated interfering ac-
tions.  If we carefully  think over the matter, Ave shall, unless
I am much mistaken, arrive at the conclusion that it cannot
be otherwise, unless it be supposed that a force can arise from
nothing—can exist without antecedent force.
   In the phenomenon of the voltaic arc, the electric spark,
&c, to which  I have  already adverted, electricity directly
produces  light of the greatest known intensity.  It directly
produces magnetism, as shoAvn by Oersted, who first distinctly
proved  the connection between electricity  and magnetism.
These two forces act upon each other, not in straight hnes,
as all other known forces do, but in a rectangular direction;
that is, bodies affected by dynamic electricity, or the conduits
of an electric current, tend to place magnets at right angles
to them ; and,  conversely,  magnets tend to  place bodies con-
ducting electricity at right angles to them.   Thus an electric
current  appears to have a magnetic action,  in  a direction
cutting its oavu at right angles;  or, supposing its section to
be a circle, tangential to it:  if, then, we reverse the position,
and make the electric current form  a series of tangents to an
imaginary cylinder, this cylinder should be a magnet.   This
is effected in practice by coiling a  Avire as a helix or spiral,
and this, when conducting  an electrical current, is to all in-
tents and purposes a magnet.   A  soft iron core placed within
such a helix has the property of concentrating its power, and
then we can, by connection or disconnection writh the source
of electricity, instantly make or unmake  a most poAverful
magnet.
   We may figure  to  the mind  electrified and  magnetised 
 10S        CORRELATION OF PHYSICAL FORCES.

 matter, as hnes  of which the extremities repel each other in
 a  definite direction;  thus,  if  a line  A B  represent a Avire
 affected by electricity, and superposed on c d a wire affected
 by magnetism, the extreme points A and B Avill be repelled to
 the farthest distances from the points c and D, and the  line A
 b be at right angles to the  line c d ;  and so, if the lines be
 subdivided to any extent, each will have two extremities or
 poles repulsive of those of the other.   If  the  line of matter
 affected by  electricity be a liquid, and  consequently have
 entire mobility of particles,  a  continuous  mo\-ement Avill be
 produced  by magnetism, each particle successively tending,
 as it were,  to fly off at a tangent from the magnet:  thus,
 place a flat dish containing acidulated v/ater on the poles of a
 powerful magnet, immerse the terminals of a voltaic battery
 in the hquid just above the magnetic  poles, so that the lines
 of electricity and  of magnetism coincide ; the Avater will now
 assume a movement at right angles to this line, floAving con-
 tinously, as  if bloAvn by an  equatorial wind, Avhich may be
 made east or west with reference to the magnetic poles by
 altering the direction of the electrical current: a similar effect
 may  be produced A\'ith mercury.  These cases  afford  an
 additional argument  to  those  previously  mentioned of the
particles of matter being affected by the forces of  electricity
 and  magnetism  in a way  irreconcilable  with the fluid  or
 ethereal hypothesis.
   The representation of transverse direction by magnetism
 and electricity appears to have led Coleridge to  parallel it by
the transverse expansion of matter, or length  and breadth,
though he injured the parallel by adding galvanism as depth :
whether a third force exists which may bear this relation to
electricity and magnetism is  a question upon which we have
no evidence.
   The ratio which the attractive magnetic force  produced
bears to the electric current producing it has been investigat-
ed by many experimentalists  and mathematicians.   The data 
ELECTRICITY.
109
are so numerous and so variable, that it is difficult to  arrive
at definite results.   Thus the relative size of the coil and the
iron, the temper or degree of hardness of  the latter, its shape,
or the proportions of length to diameter, the number of coils
surrounding it, the conducting power of the metal  of  which
the coils are formed, the size of the keeper or iron in  which
magnetism is induced, the  degree of  constancy of the  bat-
tery,  &c, comphcate the experiments.
    The most trustworthy general relation which has been as-
certained is, that the magnetic attraction is  as the square of
the electric force ;  a result due to the researches of Lenz and
Jacobi,  and also of Sir W. S. Harris.
    Lastly, electricity produces chemical affinity; and  by its
agency  Ave are enabled to obtain  effects of analysis or synthe-
sis Avith which ordinary chemistry doe3 not furnish us.   Of
these effects we have examples in the brilliant discoveries, by
Davy, of the alkaline metals, and in the  pecuhar  crystalline
compounds made known by Crosse and Becquerel. 
V.—LIGHT.
   IN' entering on the subject of Light, it Avill be avcII to dc«
     scribe briefly, and in a manner as far as may be inde-
pendent of theory, the effects to which the term  polarisation
has been applied.
   When light is reflected from the surface  of water, glass,
or many other media, it undergoes a change which disables it
from being again similarly reflected in a direction at right
angles  to that at which it has  been  originally reflected.
Light so affected is said to be polarised ;  it will  always  be
capable of being reflected in planes parallel  to the plane in
Avhich it has been first reflected,  but incapable of  being re-
flected  in planes at right  angles  to that  plane.   At  planes
having a direction intermediate between the original plane of
reflection, and a plane at right angles to it, the hght will be
capable of being partially reflected, and more or less  so ac-
cording as the direction of the second  plane  of reflection is
more or less coincident with the original plane.   Light, again,
when passed through  a crystal  of Iceland spar, is what is
termed doubly refracted, i. e. split into two divisions or beams,
each having half the luminosity of the original incident hght;
each of these beams is polarised in planes at right angles to
each other ; and if they be  intercepted by the mineral tour-
maline, one of them is absorbed, so that  only one polarised
beam emerges.  Similar effects may be produced by certain 
LIGHT.
Ill
other reflections or refractions.  A ray of hght once polaris
ed in a  certain  plane  continues  so affected throughout its
whole subsequent course ; and at any indefinite  distance from
the point Avhere it originally  underwent the  change, the  di-
rection  of  the plane  will be  the same, proATided the media
through which it is transmitted be air, water, or certain other
transparent substances Avhich  need not be  enumerated.   If,
hoAvever, the polarised ray, instead of passing through water,
be made to pass through oil of turpentine, the definite  direc-
tion in which it is polarised will be found to be changed ;  and
the  change  of  direction  will be greater according to the
length of the column of interposed liquid.  Instead of being
an   uniform plane, it  will  have  a  cur\-ilincar direction,
similar to that which a strip  of  card would have  if forced
along two  opposite grooArcs  of a  rifle-barrel.   This curious
effect is produced in different degrees by different  media.
The direction also A'aries; the rotation, as it is  termed, being
sometimes to the right hand and sometimes to the left, accord-
ing  to the peculiar molecular character of the medium through
which the  polarised ray is transmitted.
    Light is, perhaps, that mode of force the  reciprocal rela-
tions of Avhich Avith the others have  been the least traced
out.  Until the discoATeries of Niepce, Daguerre, and Talbot,
very little  could be definitely predicated of the action of light
in producing other modes of force.   Certain chemical  com-
pounds, among which stand  pre-eminent  the salts of silver,
have the property of suffering decomposition when exposed
to light.   If, for instance, recently formed  chloride of silver
be submitted to  luminous rays, a partial  decomposition en-
sues ; the  chlorine is separated and expelled by the action of
light, and  the silver is precipitated.   By this  decomposition
the  colour of the substance changes from white to blue.   If
now, paper be impregnated with chloride of silver, which can
be done by a simple chemical process, then partially covered
with an opaque substance, a leaf for example, and exposed to 
112        CORRELATION OF PHYSICAL FORCES.

a strong hght, the chloride will be decomposed in all those
parts of the paper Avhere the hght is not intercepted,  and avo
shaU have, by the action of light, a Avhite image of  the leaf
on a purple ground.  If similar paper be placed in the focus
of a lens in a camera-obscura, the objects there depicted will
decompose the chloride, just in the proportion in Avhich they
are luminous ; and thus, as the most luminous parts of the im-
age will most darken the chloride, we shall have a picture of
the objects with reversed hghts and shadows.  The picture
thus produced would not be permanent, as subsequent expos-
ure Avould darken the hght portion of the picture : to fix it,
the paper must  be immersed in  a solution Avhich has the pro-
perty of dissolving chloride of silver, but not metallic silver.
Iodide  of potassium wiU effect this;  and  the paper  being
Avashed and dried will then preserve  a  permanent image of
the depicted objects.  This was the first and simple  process
of Mr. Talbot; but it is defective as to the purposes aimed
at, in many points.   First, it is not sufficiently  sensitive, re-
quiring a strong hght and a long time to produce  an image ;
secondly, the hghts and shadows are reversed ; and  thirdly,
the coarse structure of the finest paper does  not admit  of the
delicate traces of objects being distinctly impressed.   These
defects have been to  a great extent remedied  by a process
subsequently discovered by Mr. Talbot, and  which bears his
name, and Avhich has led to the collodion process,  and others
unnecessary to  be detailed here.
   The photographs  of M. Daguerre, with Avhich all are now
familiar, are produced by holding a plate  of highly-polished
silver over iodine.   A thin film of iodide  of silver is thus
formed on the surface of the metal;  and when  these iodized
plates are exposed in the camera, a chemical alteration takes
place.  The portions of the plate on which the  hght  has im-
pinged part with some of the iodine, or are otherwise changed
—for the  theory is somewhat  doubtful—soas  to  be capable
of ready amalgamation.  When, therefore, the plate is placed 
LIGHT.
113
over the Arapour of heated  mercury, the  mercuiy attaches it
self to the portions affected by light, and gives them a wrhite
frosted appearance; the  intermediate tints are less affected,
and  those  parts  where no  light  has fallen, by retaining
their  original polish, appear dark; the iodide  of silver is
then  washed  off  by hyposulphite  of soda,  which  has  the
property  of  dissolving  it,  and there  remains  a  picture
in which the lights and  shadows are  as in nature, and  the
molecular  uniformity  of  the  metallic surface enables  the
most  microscopic details to  be depicted with perfect  accu-
racy.   By using chloride  of iodine, or  bromide  of iodine,
instead of iodine, the equilibrium of chemical forces is ren-
dered still more unstable, so that images may be taken in an
indefinitely short period—a period practically instantaneous.
   It would be foreign to the object of this essay to  enter
upon  the many beautiful  details into  which  the science of
photography has branched  out, and the many valuable discoAr-
cries  and  practical applications  to which it  has  led.   The
short statement I have given above is perhaps superfluous, as,
though they were neAV and surprising at the period when these
Lectures were delivered, photographic processes have noAV be-
come familiar, not only  to the  cultivator  of science, but to
the artist and  amateur ;  the important point for consideration
here is that light will chemically or molecularly affect mat-
ter.   Not only will the particular compounds above  selected
as instances be  changed by the  action of hght; but a vast
number of substances, both elementary and  compound,  are
notably affected by this agent, even those apparently the most
unalterable in character, such  as metals:  so numerous, in-
deed, are the substances  affected, that  it has  been  supposed,
not without reason, that matter of every description is altered
by exposure to hght.
   The permanent impression stamped on the molecules of
matter by light can be  made  to repeat itself by the  same
agency,  but  ahvays Avith  decreasing force.   Thus a phot*- 
114       CORRELATION OF PHYSICAL FORCES.

graph placed opposite a camera containing a  sensitive  plate
whl be reproduced, but if the size of the image be equal to
the picture, the second picture will be  fainter  than the first,
and so on.   Thus again,  a photograph taken  on a dull day
cannot, by being placed in bright sunshine be made to  repro-
duce a second photograph of the same  size and more distinct-
ly marked than itself; I at least have  never succeeded in
such reproduction, and I  am not aAvare that others have : the
image loses in intensity as light itself does by each transmis-
sion.   The surface of the metal or paper may give a brighter
image from its being exposed to a more intense light, but the
photographic details are limited to the intensity of the first
impression, or rather to something short of this.  A question
of theoretical interest arises from the consideration of these
reproduced photographs.   We know that the  luminosity  of
the image at the focus of a telescope is limited by the area
of the object-glass.   The image  of any given  object cannot
be intensified by throwing upon it extraneous hght; it is  in-
deed diminished in intensity, and wdien for certain purposes
astronomers illuminate the fields of their telescopes, they are
obliged to be contented with a loss of intensity in the telescopic
image.
    Now, let us suppose that the minutest details in the image
of an object seen in a given telescope, and with a given pow-
er, are noted ; that then a photographic plate is placed in the
focus of  the same telescope so as to obtain  a permanent im-
pression  of the image which has been viewed by the eye-glass.
Could the observer, by throwing a beam of condensed light
upon the photograph, enable himself to bring out fresh details ?
or in other words, could  he use with advantage a higher pow-
er apphed to the illuminated photograph ?
    It is, perhaps, hardly safe to answer a priori this question ;
but the experiment of reproducing photographs would seem to
show that more than the initial hght cannot be got, and that we
cannot expect to increase telescopic power by photography, 
LIGnT.
115
though we may render observations  more  convenient;  may
by its means fix images seen on rare and favourable occasions,
and may preserve permanent and infallible  records  of the
past state of astronomical objects.
    The effect of light on chemical  compounds  affords us a
striking instance of the extent to which a force, ever active,
may be ignored through successive  ages  of  philosophy.  If
Ave suppose the  walls of a large room covered with photo-
graphic apparatus, the small amount of light reflected  from
the face of a  person  situated in  its  centre would  simulta-
neously imprint his portrait  on a multitude of recipient sur-
faces.  Were the cameras absent, but the room coated with
photographic paper,  a change  would equally take  place in
every portion  of it, though not a  reproduction  of form and
figure.   As  other substances  not  commonly called photo-
graphic  are  knoAvn to be affected by hght, the  list of Avhich
might be indefinitely extended, it becomes a curious object of
contemplation  to consider how far light is daily operating
changes in ponderable matter—hoAv  far  a  force, for a long
time  recognised only in its visual effects,  may be constantly
producing changes in the  earth and atmosphere, in  addition
to the changes it produces in organised structures which are
now beginning to be extensively studied.  Thus CA'ery portion
of hght may be supposed to Avrite its own history by a change
more or less permanent in ponderable matter.
    The  late Mr. George Stephenson had a favourite  idea,
which would now be recognised as more philosophical than it
was  in his day, A-iz.  that the hght, which we nightly obtain
from coal or other fuel, Avas a reproduction of that which had
at one time been absorbed by vegetable structures from the
sun.   The conviction that the transient gleam leaves its per-
manent  impress on the world's history, also leads the  mind
to ponder over the many possible agencies of which we of the
present  day may be as ignorant as  the ancients were of the
chemical action of light. 
116       CORRELATION OF PHYSICAL FORCES.

    I have used the term hght, and affected by light, in speak-
ing of photographic effects; but, though the phenomena de-
rived their name  from  light, it has been  doubted by many
competent investigators  Avhether the  phenomena of photo-
graphy are not mainly dependent upon a separate agent ac-
companying light, rather than upon light itself.  It is, indeed,
difficult not to believe that a picture, taken in the focus of a
camera-obscura, and which represents to the eye  all the gra-
dations of light  and shade shown by the  original  luminous
image, is not an effect of light; certain it is, hoAvever, that
the different coloured rays exercise different actions upon va-
rious chemical compounds, and that the effects on many, per-
haps on most of them, are not proportionate in  intensity to
the effects upon  the visual organs.   Those  effects, however,
appear to be more of degree than of specific difference; and,
without pronouncing myself  positively upon the  question,
hitherto so little  examined, I think it will be safer to regard
the action  on photographic compounds as resulting from a
function of light.  So viewing it, we get hght as an initia-
ting force, capable of producing, mediately or  immediately,
the other  modes of force.  Thus, it  immediately produces
chemical action ; and haAdng this, we at once acquire a means
of producing the others.   At my Lectures in 1843, I shoAved
an experiment by which the production of all the other modes
of force by light is exhibited :  I may here shortly  describe it.
A prepared  daguerreotype plate is  enclosed in a box filled
with Avater, having a glass front with a shutter  over it.   Be-
tAveen this  glass and the plate  is a gridiron of silver wire;
the plate is connected with one  extremity of a galvanometer
coil, and the gridiron of Avire with one extremity of a Bre-
guet's helix—an elegant instrument, formed by a coil of tAvo
metals,  the unequal  expansion of Avhich  indicates slight
changes in temperature—the  other extremities  of the galva-
nometer and helix are connected by a wire, and  the  needles
brought to zero.  As soon as a beam of either  daylight or 
LIGHT.
117
the oxyhydrogen hght is, by raising the shutter, permitted to
impinge  upon  the  plate, the needles are deflected.   Thus,
hght being the initiating force, we get chemical action on the
plate, electricity circulating  through the wires, magnetism in
the coil,  heat in the helix, and motion in the needles.
    K two plates of platinum be  placed in acidulated water,
and connected with a delicate galvanometer, the  needle  of
this is always  deflected, a result due to films of gas or other
matter on the surface of the platinum, which no cleaning cau
remoA-c.   If, after the needle has returned to zero, Avhich Avill
not be the case for some hours or even days, one of the plat-
inum surfaces be  exposed to hght, a fresh  deflection  of the
needle takes place, due,  as far as I have been able to resoh-e
it, to an  augmentation of the chemical action which had occa-
sioned the original deflection, for the deviation is in the same
direction.  If, instead of white light, coloured hght be per-
mitted to impinge  on the plate, the deviation is greater Avith
blue than with  red or yellow hght, shoAving, in addition to
other tests, that the effect is not due to the heat of the sun's
rays, as  the calorific effects of hght are greater with red than
AArith blue light, while  the chemical effects are the inverse.
    There are other apparently more direct  agencies of light
in  producing electricity and  magnetism, such as those ob-
served by Morichini and  others, as well as  its effects upon
crystalhzation ; but these results have hitherto been of so in-
definite a character, that they can only be regarded as pre-
senting fields for experiment,  and not as proving the relations
of light to the other forces.
    Light Avould seem  directly to  produce heat in the phenom-
ena of what is termed absorption of light: in these we  find
that heat is  developed in some  proportion to the  disappear-
ance of light.   To take the  old experiment of placing a se-
ries of different coloured pieces  of cloth upon snow exposed
to sunshine, the black cloth absorbing the most hght, and de-
veloping the most heat,  sinks  more deeply in the  snow than 
118        CORRELATION  OF PHYSICAL FORCES.
any others;  the  other  colours or shades of colour sink the
more  deeply in proportion as they absorb or cause to disap-
pear the more hght, until we come to the Avhite  cloth, Avhich
remains upon the surface.  The heating powers of different
colours are, however, not by any means in exact proportion
to the intensity of their light  as affecting the visual organs.
Thus red light, Avhen produced by refraction from a prism of
glass,  produces greater heating effect than yelloAv light in the
phenomena  of absorption, as has been observed by Sir W.
Herschel.   The red rays appear, however, to produce a dy-
namic effect greater than any of the others ; thus they pene-
trate water to a greater depth than the other colours; but,
according  to Dr. Seebeck, we get a  further  anomaly, viz.
that when hght is refracted by a prism of water the  yellow
rays produce the greater heating effect.  The subject, there-
fore, requires much  more experiment before Ave can ascertain
the rationale of the  action of the forces of  light  and heat in
this class of phenomena.
   In a former edition of this Essay, I suggested the folioav-
ing experiment  on   this subject:—Let a  beam of light be
passed through  tA\ro plates  of tourmaline, or  similar sub-
stance, and the temperature of the  second plate, or that on
which the light last  impinges, be examined by a delicate ther-
moscope, first Avhen it is in a position  to transmit the polar-
ised beam coming from the first  plate, and secondly when it
has been turned round through an arc of 90s, and the polar-
ised beam  is absorbed.  I expected that, if the experiment
Avere carefully performed, the temperature of the second plate
would be more raised in the second case than in  the first, and
that it might afford  interesting results when tried  with light
of different colours.  I met with difficulties in procuring a
suitable apparatus,  and was endeavouring to o\'ercome them
when I found  that  Knoblauch had, to some extent, realised
this result.  He finds that, when  a solar beam, polarised in a
certain plane, is transmitted perpendicularly to the axis of n 
LIGHT.
119
crystal of brown quartz or tourmaline, the heat is transmit-
ted in a smaller proportion than when the beam passes alon"
the direction of the axis of the crystal.
    It is generally—as far as I am  aware, universally—true
that, while light continues as light, even though reflected or
transmitted by different media, httle or no heat is developed:
and, as far as we can judge, it would appear that, if a me-
dium were perfectly transparent, or if a surface perfectly re-
flected hght, not the slightest heating effect would take place j
but, wherever light is  absorbed, then heat takes its place, af-
fording us  apparently  an instance of the conversion of hght
into heat, and of the fact that the force of hght is not, in fact,
absorbed  or  annihilated, but merely changed in  character,
becoming in this instance  converted into  heat by  impinging
on solid matter, as in  the instance mentioned in treating of
heat, this force Avas shown to be converted into hght by im-
pinging on sohd matter.   As, liOA\Tever, I have before ob-
served, this correlation of light and heat is not so distinct, as
Avith the other affections of matter.  One experiment, indeed,
of Melloni, already mentioned, AArould  seem to show that
hght may exist in a condition  in Avhich  it does not produce
heat, Avhich  our instruments are able to detect;  but some
doubt has  recently been thrown on the accuracy of  this ex-
periment ;  probably the substances themselves through Avhich
the light is transmitted would be found to have been heated.
    The recipient body, or that  upon Avhich  light  -"^rpinges,
seems to exercise as important an influence  on o\^  percep-
tions of hght as the  cmittent body, or that from  Avhich the
light first  proceeds.   The  recent  experiments o.  Sir John
Herschel and Mr. Stokes show that radiant impuLes, which,
falling on certain bodies, give  no effect of light, become lu-
minous ay hen falling on other bodie3.
    Thus, let ordinary  solar hght be refracted  by i- prism (the
best material for Avhich is quartz), and the spectrum receiA-cd
on a sheet of  paper, or of white porcelain;  looVirif  jn the 
120     .   CORRELATION  OF PHYSICAL FORCES.

paper, the eye  detects no light beyond  the extreme  violet
rays.  If,  therefore, an opaque body be interposed so as just
to cut off the whole  visible  spectrum, the paper would be
dark or  invisible, with the exception of some slight iUumina-
tion  from light reflected by the air and surrounding bodies.
Substitute for  that portion of the paper Aviiich was beyond
tbe \dsible spectrum a piece of glass tinged by the oxide  of
uranium, and  the glass is perfectly \nsible ; so Avith a bottle
of sulphate of  quinine, or of the juice of horse-chestnuts, or
even paper soaked in these latter solutions.   Other substances
exhibit this  effect in different degrees; and among  the sub
stances  which have hitherto been considered perfectly analo-
gous as  to their appearance when illuminated, notable differ-
ences are  discovered.   Thus it appears  that  emanations
which give  no impression of hght to the eye, when imping-
ing on certain  bodies, become  luminous when  impinging on
others.  We might imagine  a room so constructed that such
emanations  alone are permitted to enter it, which would be
dark or light according to the substance with which the  walls
Avere coated, though in fuU  daylight the respective  coatings
of the walls would appear equally white ; or, without  alter-
ing the  coating of the waUs, the  room exposed to one  class
of rays, might be rendered dark by windoAvs which would be
transparent to another class.
    If, instead of solar light,  the  electrical hght be employed
for similar experiments, an equally striking effect can actually
be produced.   A design, draAAm on Avhite  paper with a solu-
tion of  sulphate of quinine and tartaric acid, is invisible by
ordinary hght, but appears with beautiful distinctness  when
illuminated by the electric hght.   Thus, in pronouncing upon
a luminous effect, regard must be had to the recipient as Avell
as to the emittent body.  That which is, or becomes, light
when it falls upon one body is not hght  when it falls upon
another.  Probably  the retinas of the eyes of different per-
sons differ to  some extent in a similar manner ; and  the same 
LIGHT.
121
substance, illuminated by the same spectrum, may present
different appearances to different persons, the spectrum ap-
pearing more elongated to the one than to the other, so that
what is light to the one is darkness to the other.  A depend-
ence on the recipient body may also, to a great extent, be
predicated of heat.  Let  two vessels of Avater, the contents
of the one clear and transparent, of the other tinged by some
colouring matter, be suspended in a summer's sun ;  in a very
short time a notable difference of temperature will be ob-
served, the   coloured having  become much  hotter than the
clear liquid.  If the first vessel be placed at a considerable
distance from the surface  of the earth, and the  second near
the surface,  the difference is still more  considerable.  Carry-
ing on this experiment, and suspending the first over the top
of a high mountain, and the second in a valley, we may ob
tain so great a difference of temperature, that animals whose
organization is suited for the one temperature could not hve
in the  other, and yet both arc exposed to the same  luminous
rays at the same time, and substantially at  the same distance
from the emittent body—the substance nearer the sun  is in
fact colder than the more remote.  So, Avith regard to the
medium transmitting the influence : a green-house  may have
its temperature considerably varied by changing the glas3  of
which  its roof is made.
    These effects have an important bearing on certain cos-
mical questions which have  lately been  much discussed, and
should  induce the  greatest caution in  forming opinions  on
such subjects as light and heat on the sun's surface, the  tem-
perature of the planets, &c.  This may depend as much upon
them physical constitution as upon their distance  from the
sun.   Indeed, the planet Mars gives us a highly probable ar-
gument for   this; for, notwithstanding that it is half as far
again from the sun as the earth is, the increase of the white
tracts at its poles during its winter, and their diminution dur-
ing its summer, show that the  temperature of the surface  of
             6 
122        CORRELATION OF PHYSICAL FORCES.

this planet oscillates about that of the freezing point of water,
as do the  analogous zones of our planet.  It is true, m this
we assume that the substance thus changing its state is water,
but,  considering the many close analogies of this planet Avith
the earth, and the identity in appearance of these very effects
with what takes  place on the earth, it seems a highly proba-
ble assumption.
   So it by no means necessarily follows, that because Venus
is nearer to the sun than the earth, that planet is hotter than
our globe.  The  force emitted by the sun  may  take a differ-
ent  character at  the  surface of each  different planet, and
require different organisms or  senses  for its  appreciation.
Myriads of organised  beings may exist imperceptible to our
vision, even if we were  among them ; and we might be also
imperceptible to them!
   However vain it may be, in the present state of science,
to speculate upon such existences, it is equally vain to assume
identity or close approximations to  our own forms in those
beings Avhich may people other worlds.   From  analogical
reasoning, or from final  causation,  if that be  admitted, we
may feel  convinced  that  the gorgeous globes of the universe
are not unpeopled deserts ; but whether the denizens of other
worlds are more or less powerful, more  or  less intelligent,
whether they have attributes of a higher or loAver class than
ourselves, is  at present an utterly hopeless  guessing.
    Specific  gravity and  intelligence have  no necessary con-
nexion.  On our OAvn planet five senses, and a mean density
equal to that of water, are not invariably associated with in-
tellectual or  moral greatness, and the many arguments  Avliich
have been used  to prove that suns and planets other than the
earth are uninhabited, or not inhabited by intellectual beings,
might, mutatis mutandis, equally be  used by the denizens cf
a sun  or planet to prove that this world was uninhabited.
    Men are too  apt, because  they are men,  because their
existence  is the  one thing of all importance to themselves, to 
LIGHT.
123
frame  schemes of the universe as though it was formed for
man alone : painted by an artist of the sun, a man might not
represent so  prominent  an object of creation as he does
Avhen represented by his oAvn pencil.
    Light Avas regarded, by AArhat was termed the corpuscular
theory, as being in itself matter or a specific fluid emanating
from luminous bodies, and producing the  effects of sensation
by impinging on the retina.   This theory gave way to theun-
dulatory one,  Avhich is generaUy adopted in the present day,
and which regards light as resulting from the undulation of a
specific fluid  to which the name  of ether has  been given,
which  hypothetic fluid is supposed to pervade the  universe,
and to penetrate the pores of all bodies.
    In  a  Lecture  delivered in January 1842, Avhen I first
pubhely advanced the views advocated in this Essay, I stated
that it  appeared to  me  more consistent with knoAvn facts to
regard light as resulting from a vibration or motion of the
molecules of matter itself, rather  than from a specific ether
pervading it;  jnst as  sound is propagated by the vibrations
of wood, or as waves are by water.  I am not here speaking
of the  character of the vibrations of hght,  sound, or Avater,
Avhich  are doubtless very different from each other, but am
only comparing them so far as they illustrate the propagation
of force by motion in the matter itself.
    I was not aware,  at the  time that I first adopted the
above view, and brought it forward in my Lectures, that tho
celebrated Leonard Euler had pubhshed a someAvhat similar
theory; and,  though I suggested it Avithout knowing that it
had  been previously advanced,  I  should  have hesitated  in
reproducing it had  I not found that it Avas sanctioned by so
eminent a mathematician as Euler, who cannot be  supposed
to have overlooked any irresistible argument against it—the
more so in a matter  so much controverted and discussed as
tho undulatory theory of light was in his time.
   Although this theory has been  considered defective by a 
 124       CORRELATION  OF PHYSICAL FORCE?.

 philosopher of high  repute,  I  cannot see the force of tho
 arguments by which it has been assailed ; and therefore, for
 the present, though with diffidence, I still adhere to it.   The
 fact itself of the correlation of the different modes of force is
 to my rnind a very cogent argument in favour of their being
 affections of the same matter ; and though electricity, magnet-
 ism, and heat might be viewed as produced by undulations of
 the same ether as that by means of which hght is supposed to
 be produced, yet this hypothesis offers greater difficulties with
 regard to the other affections than with regard to light: many
 of these difficulties I have already alluded to when treating of
 electricity;  thus  conduction and non-conduction are not ex-
 plained by it; the  transmission  of  electricity  through long
 wires  in preference to the air which surrounds them, and
 which must be at  least equally pervaded by the  ether,  i3
 irreconcilable  with  such an hypothesis.   The phenomena ex-
 hibited by these  forces afford, as I think, equally strong evi-
 dence with those  of light, of ordinary matter acting from par-
 ticle to particle,  and having no action at a distance.  I have
 already instanced the experiments of Faraday on  electrical
 induction, showing  it to be an action of contiguous particles,
 which are strongly in favour of this view, and  many experi-
 ments which I have made on the voltaio arc, some of which
 I have mentioned  in this Essay, are, to my  mind, confirma-
 tory of it.
   If it be admitted that one of the so-called imponderables is
 a mode of motion, then the  fact of its  being  able to produce
 the others, and be  produced by them, renders  it highly diffi-
 cult  to conceive  some as  molecular motions and  others as
 fluids or undulations of an  ether.  To the main objection of
Dr. Young, that all bodies would have the properties of solai
phosphorus if light consisted  in the  undulations  of  ordinary
matter, it may be  answered  that so many bodies have this
property, and  with so great  a variety in  its  duration, that
non constat all  may not have  it,  though for a time  so  short 
LIGHT.
125
that  the  eye cannot detect its duration.   M. E. Becquerel
has made many experiments which  support  this view; the
fact of the  phosphorescence  by insolation of a large number
of bodies, is in itself evidence of the matter of which they are
composed being throAvn  into a state of undulation, or at all
CA'cnts molecularly affected  by the impact of light, and  is
therefore an argument in support of the view  to Avhich objec-
tion  is taken.  Dr. Young admits that the  phenomena of
solar phosphorus  appear to resemble greatly the sympathetic
sound3 of musical instruments, Avhich  are agitated  by  other
sounds conveyed to them through the air, and  I am not aAvaro
that  he gives any explanation of these effects  on the ethereal
hypothesis.
   Some  curious  experiments of  M.  Niepce de St. Victor
seem also  to present an analogy  in luminous phenomena to
sympathetic sounds.  An  engraving Avhich has been kept for
some days in the dark is half covered by an  opaque screen,
and  then exposed  to the sun; it is then removed from the
light, the screen taken away, and the engraving placed  oppo-
site,  and at a short distance from, photographic paper: an
inverted  image of that portion of  the  engraving which has
been exposed to the  sun is produced on the  photographic
paper, while  the  part which had been covered by the screen
is  not reproduced.   If  the engraving,  after  exposure,  is
alloAved to remain in contact AA~ith Avhite paper  for some hours,
and the Avhite paper is then  placed upon photographic paper,
a faint image of the exposed portion of the engraving is repro-
duced.  Similar results are produced by mottled marble ex-
posed to the sun ; an invisible tracing on paper by a fluores-
cent body,  sulphate of quinine, is, after  insolation, reproduced
on the photographic paper.  Insolated paper retains the poAver
of producing an impression for a very long period, if it is kept
in an opaque tube hermetically closed.
   It is  light  to observe that these effects are  supposed by
many to be due to chemical  emanations proceeding from the 
 12G        CORRELATION OF PHYSICAL  FORCES.

 substances exposed to the sun, and which are beheved to have
 undergone some chemical change by this  exposure.   It is
 desirable to  aAA'ait further experiment before forming a decid-
 ed opinion.
    The analogies in  the progression of  sound and light are
 very numerous: each proceed in straight  hnes, until  inter-
 rupted ; each  is reflected in the same manner, the angles of
 incidence  and  reflexion being equal;  each is alternately nulli-
 fied and doubled in intensity by interference ; each  is capable
 of refraction when  passing from media of different density:
 this last effect of sound, long  ago theoretically determined,
 has been experimentally proved by Mr. Sondhauss, who con-
 structed a lens of films of collodion, which,  AAThen filled with
 carbonic  acid, enabled him to hear the ticking of a  watch
 placed in one focus of the lens, the ear of the experimenter
 being  in  the  opposite focus.  The  ticking was not heard
 when the  watch was moved aside from the focal point, though
 it remained at an equal  distance  from the ear.  An experi-
 ment of M.  Dove seems, indeed, to show an effect  of polari-
 sation  of sound.
    The phenomena presented by heat,  viewed according to
the  dynamic theory, cannot be explained by the motion of an
imponderable  ether,  but involve  the molecular actions  of
 ordinary ponderable matter.   The doctrine of propagation by
undulations of ordinary matter is A*ery generaUy admitted by
those  who support  the  dynamical theory of heat; but  the
 analogies of the phenomena presented by heat and hght  are
 so close, that  I cannot see how a theory apphed to the  one
 agent should not be applicable to the other.  When heat is
transmitted, reflected, refracted, or polarised, can we vieAV
that as an affection of ordinary matter, and Avhen  the  same
effects take  place with hght,  view the  phenomena as pro-
 duced by an imponderable ether, and by that alone  ?
    An objection that  immediately occurs  to the  mind in
 reference to the ethereal hypothesis of  hght is, that the most 
LIGHT.
127
porous bodies arc opaque ; cork, charcoal, pumice stone, dried
and moist wood, &c, all A'ery porous and very light, are all
opaque.  This objection is not so superficial as it might seem
at first sight.  The  theory which assumes  that hght is  an
undulation of an ethereal  medium perA'ading gross matter,
assumes  the  distances between the  molecules  or  atoms  of
matter to be A-ery great.  Matter has been hkened by Demo-
critus, and by many modern philosophers, to the starry firma-
ment, in which,  though the individual monads are at immense
distances from each other, yet they have in the aggregate a
character of unity, and are  firmly held by attraction in their
respective positions and at definite distances.  Xow, if matter
be built  up of separate molecules, then,  as far as our knowl-
edge extends, the lightest bodies would be those in which the
molecules are at the  greatest  distances, and those in which
any undulation of a pervading medium  would  be the least
interfered Avith by the separated particles—such bodies should
consequently be the most transparent.
    If, again, the analog}' of the  starry firmament held good,
in this case an undulation or wave proportioned to the indivi-
dual monads  would be broken up by the number of them,  and
the very appearance of continuity which results, as in the
milky way, from each  point of  A'ision being  occupied by  one
of the monads, wrould  sIioav that at some  portion of  its pro-
gress the wave is interrupted by one  of them, so that the
whole  may be ATiewed in some respect as  a  sheet of ordinary
matter interposed in the  ethereal expanse.
   Even then, if it be admitted that a highly elastic  medium
pervades the  interspaces, the separate masses as a whole must
exercise an important influence on the progress of the wave.
    Sound or vibrations of air meeting Avith a screen, or, as
it Avere,  sponge  of diffused particles, would be broken up and
dis| eised by  them ;  but if they be sufficiently continuous to
take up the vibration and propagate it themselves, the sound
continues comparatively unimpaired. 
128        CORRELATION OF  PHYSICAL FORCES.

    With regard, however, to liquid and gaseous bodies, there
are very great difficulties in viewing them  as consisting of
separate and distant moleculer.  If, for instance, we  assume
with Young that the particles in Avater are at least as distant
from each other comparatively as 100  men Avould be if dis-
persed at equal distances over the surface of England, the dis-
tance of these   particles,  Avhen  the  water is  expanded into
steam, would be increased more than forty times, so that the
100 men would be reduced to  two, and by further increasing
the temperature this distance may be indefinitely increased ;
adding to the effects of temperature  rarefaction  by  the air-
pump, Ave may again increase the distance, so  that, if Ave as-
sume any original  distance, we ought, by expansion, to in-
crease it to a point at Avhich the  distance between  molecule
and molecule should become measurable.  But no extent  of
rarefaction, Avhether by heat or the air-pump,  or both, makes
the slightest change in the  apparent  continuity of  matter;
and gases, I find, retain their peculiar character, as far a3 a
judgment of it can be formed from its effect  on the  electric
spark, throughout  any extent of  rarefaction Avliich can exper-
imentally be applied to them:  thus the electric spark in prot-
oxide of nitrogen, hoAveArer  attenuated, presents a  crimson
tint, that in carbonic oxide a greenish tint.
    Without, however, entering on the metaphysical  enquiry
as to the constitution of matter (or Avhether the atomic phil-
osophers or the followers of Boscovich are right), a  question
which probably human  apphances Avill never answer:  and
even admitting  that an ethereal  medium, not absolutely im-
ponderable as asserted by many, but of extreme tenuity, per-
vades matter, still ordinary or non-ethereal matter itself must
exercise a most important action upon the transmission of
light; and Dr.  Young, avIio opposed the tlicory of Euler, that
light was transmitted by undulations of  gross matter itself,
just as sound is, Avas afterwards obliged  to  call to his assis-
tance the vibrations of the ponderable matter of the refractr 
LIGHT.
129
ing media, to explain why rays of all colours were not equal-
ly refracted, and other difficulties.  One of his arguments in
support of the existence of a permeating ether was,  " that a
medium resembling in many properties that which has  been
denominated Ether does exist, is undeniably  proved by the
phenomena of electricity."  This seems to me, if I may ven-
ture to say so of anything proceeding from so eminent a  man,
scarcely logical: it is supporting one hypothesis by  another,
and considering that to be proved which its most strenuous
advocates admit to be surrounded by very many difficulties.
    If it be said that there is not  sufficient elasticity in  ordi-
nary matter for the transmission of undulations AA-ith such ve-
locity as light is known to travel, this may be so if the vibra-
tions be supposed exactly analogous to those of sound ; but
that molecular motion can traA*el with equal and even greater
velocity than light, is shown by the rapidity with which  elec-
tricity traverses a  metal Avire where each particle of  metal is
undoubtedly affected.  It has, moreover, been shown by the
experiments of Mr.  Latimer  Clarke  upon a  length of wire
of 7G0 miles, that whatever be the intensity of electrical cur-
rents, they are  propagated  Avith the same velocity  provided
the effects of lateral induction be the same—a striking  anal-
ogy Avith one of the effects observed in the propagation of
light and sound.  The effects  observed by MM. Fizeau and
Foucault, of the sloAver progression of hght in proportion as
the transmitting medium is more dense, seem  to me  in favour
of the view here  advocated;  as a greater degree  of heat
Avould be produced by light in  proportion to the density of
the medium, force would be thus carried off, and the molecular
system disturbed so that the progress of the motion should be
more slow ;  but so many considerations enter into this question,
and the phenomena are so extremely complex, that  it Avould
be rash to hazard any positive opinion.
    Dr. Young ultimately came to the conclusion that it was
simplest to consider the ethereal  medium, together  with the 
130       CORRELATION OF PHYSICAL  FORCES.

material atoms of the  substance, as constituting together a
compound medium denser than pure ether, but not more clas-
tic.  Ether might thus be viewed as performing the functions
which oil does with tracing  paper, giving continuity  to  the
particles of  gross  matter, and in  the interplanetary  spaces
forming itself the medium Avhich transmits the undulations.
    Since the period when Huyghens, Euler, and Young, the
fathers of the  undulatory theory, applied their great minds to
this subject, a  mass of experimental  data has  accumulated,
all tending to estabhsh the propositions, that whenever  matter
transmitting or reflecting hght undergoes a structural change,
the hght itself is affected, and that  there  is a  connection  or
paraUelism between the change in the matter and the  change
in the affection of hght, and conversely that hght Avill modify
or change the  structure of matter and impress its molecules
Avith new characteristics.
    Transparency, opacity, refraction, reflection, and  colour
were phenomena known to the ancients, but sufficient attention
does not appear to haATe been paid by them to the molecular
states of the bodies producing these effects ;  thus the  trans-
parency or opacity of a body appears to depend entirely upon
its molecular arrangement.  K strias occur in a lens or glass
through which objects are viewed, the objects are distorted:
increase the number of these striae, the  distortion is  so in-
creased that the objects become invisible, and the glass ceases
to be transparent,  though remaining translucent;  but alter
completely the molecular structure, as by slow  solidification.
and it becomes opaque.  Take, again, an example of a liquid
and a gas : a solution of soap is transparent, air is transpar-
ent, but agitate them together so  as to form a froth or  lather,
and this, though consisting of two transparent  bodies, is
opaque ;  and  the reflection of light from the surface of these
bodies, when so intermixed, is strikingly different from its re-
flection before mixture, in the one case  giving to the eye a
mere general effect of whiteness, in the other the images of
objects in their proper shapes and colours. 
LIGHT.
131
   To take a more refined instance:  nitrogen is perfectly
colourless, oxygen is perfectly colourless, but chemically uni-
ted in certain proportions they form nitrous acid, a gas which
has a deep orange brown colour.  I know not how  the  col-
our of this gas, or of  such gases as chlorine or vapour of
iodine, can be accounted for by the ethereal hypothesis, with-
out calling in aid molecular affections of the matter  of these
gases.
    Colour in many instances  depends upon the thickness of
the plate or film of transparent matter upon Avhich light is in-
cident ; as in all those cases which are termed the colours of
thin plates, of Avhich the  soap bubble affords a beautiful in-
stance.
   When Ave arrive at the more recent discoveries of double
refraction and polarisation, the effects of  light are  found to
trace out as it were the structure of the matter affected,  and
the crystalline form  of a body  can  be   determined  by the
effects which a  minute portion of it exercises on a ray of
light.
    Let a piece of good glass  be  placed in  what is  called a
polariscope, or instrument in which hght that has undergone
polarisation is transmitted through the substance to be exam-
ined, and the emergent hght is afterwards submitted to anoth-
er substance capable of polarising hght, or, as it is termed, an
analyser ; no change in effect will be observed.   Remove the
glass, heat it and suddenly or quickly cool it as to render  it
unannealed, in which  state its molecules  are in a  state of
tension or strain, and the glass highly brittle, on  replacing it
in the polariscope, a beautiful series of colours is perceptible.
Instead of subjecting the glass to heat and sudden  cooling,
let it be bent or strained by mechanical pressure, and the col-
ours Avill be equally visible, modified, according to the direc-
tion of the flexure, and indicating by their course the  curves
where the molecular state has been changed by pressure.   So
if tough glue be elongated and allowed to cool in a stretched 
 132        CORRELATION  OF PHYSICAL FOECUS.

 state, it doubly refracts hght, and the colours are shown as in
 the instance of glass.
    Submit a series of crystals to the same examination, and
 different figures will be formed by different  crystals, bearing
 a constant and definite relation to the structure  of the partic-
 ular crystal examined, and to  the direction in  Avhich, A\rith
 reference to crystalline form, the ray crosses the crystal.
    In the crystalhsed salts of paratartaric acid, M. Pasteur
 noticed two sets of crystals which were hemihedral in oppo-
 site directions, i. e. the crystals  of one set were to those of
 the other as to their oavu image reflected in  a mirror;  or
 making a separate solution of each of these classes of crys-
 tals, he found that the solution of  the  one class rotated the
 plane of  polarisation  to the right,  Avhile  that  of the other
 class rotated to the left, and that a mixture in proper propor-
 tions of the two solutions produced no deviation in the plane
 of polarisation.   Yet all these three solutions are Avhat is term-
 ed isomeric, that is, have as far as can be discovered the same
 chemical constitution.
    In the above, and in innumerable other cases,  it is seen
 that an alteration in the structure of a transparent  substance
 alters the character and effects of the transmitted light.  The
 phenomena of photography prove that hght alters the struc-
 ture of matter submitted to it;  with regard even to vision it-
 self, the persistence of images on the retina of the eye Avould
 seem to show that its structure Avas changed by the  impact
 of light, the luminous impressions being as it Avere branded
 on the retina, and the memory of the vision being the scar of
such brand.   The science of photography has reference main-
ly to solid substances, yet there are many instances of  liquid
 and gaseous bodies being changed by the action of light: thus
hydrocyanic acid, a liquid, undergoes a  chemical change  and
 deposits  a solid carbonaceous compound by the  action of
 light.  Chlorine and hydrogen  gases, when  mixed  and pre-
 served in darkness, do not  unite,  but Avhen exposed to  light
 rapidly combine, forming hydrochloric acid. 
LIGHT.
133
   The above facts—and many others might have been given
—go far to connect light with motion of ordinary matter, and
to show that many of the evidences  Avhich our senses receive
of the  existence of  light result from changes in matter itself.
When  the matter is in the solid state, these changes are more
or less permanent;  when in the liquid or gaseous state, they
are temporary in the greater number of instances, unless there
be some chemical change effected, which is, as it were, seized
upon during its occurrence, and a resulting compound formed,
which  is more  stable than  the  original compound or mix-
ture.
   I might AVeary my reader Avith  examples,  showing that,
in every case Avhich AAre can trace out, the effects of light are
changed by any and every change of structure, and that light
has a  definite connection with the structure  of the  bodies
affected by it.   I cannot but think that it is a strong assump-
tion to regard ether, a purely hypothetical creation, as chang-
ing its elasticity for each change of structure, and to regard
it as  penetrating the  pores of bodies of whose porosity Ave
have in many case's no  proof; the Avhich pores must, more-
over, have a definite and peculiar communication, also assumed
for the purpose of the theory.
   Ether is a most convenient medium for hypothesis :  thus,
if to account for a given phenomenon the hypothesis requires
that the ether be more elastic, it is said to be more elastic ;
if more  dense, it is said to be more dense ; if it be required
by hypothesis to be less elastic, it is pronounced to be less
elastic ;  and so on.
    The  advocates of the ethereal  hypothesis certainly have
this advantage,  that  the ether, being hypothetical, can have
its characters modified or changed  without any possibihty of
disproof either of its existence or modifications.
   It  may be  that  the refined  mathematical labours  on
light, as on electricity, have given an undue and adventitious
strength to the hypotheses on Avhich they are based. 
 134     .  CORRELATION OF PHYSICAL I-ORCI P.

    An objection to which the view I have been advocating ia
 open, and a formidable one, is, the necessity involved in it of
 an universal plenum ; for if hght, heat, electricity, &c, be affec-
 tions of ordinary matter, then matter must be supposed to be
 everywhere where these phenomena are apparent, and con-
 sequently there can be no vacuum.
    These  forces  are  transmitted through what are called
 vacua, or through  the interplanetary spaces, where matter, if
 it exist, must be in a highly attenuated  state.
    It  may be safely stated  that hitherto all attempts at pro-
 curing a  perfect  ATacuum have failed.   The ordinary air-
 pump gives us only highly rarefied air ;  and, by the principle
 of construction,  even of the  best, the operation depends upon
 the indefinite expansion of the volume of air in the receiver;
 even in the  vacuum which  is formed in this, so  great is the
 tendency of matter to fill up space, that I have observed dis-
 tilled water contained in a vessel within the exhausted receiv-
 er of a good air-pump has a  taste of tallow, derived from the
 grease, or an essential oil  contained in it, which is used to
 form an air-tight junction between the  edges of the receiver
 and the pump-plate.
   The Torricellian vacuum, or that of the  ordinary baro-
 meter, is filled with the vapour of mercury ; but it might be
 worth  the trouble  to ascertain what would be the effect of a
 good Torricellian  vacuum, when the mercury in the tube is
 frozen, which might, Avithout much difficulty, be now effected
 by the  use of solid carbonic acid and ether ; the  only proba-
 ble difficulty would be  the  different rates of contraction of
 mercury and glass, at such a degree of cold,  and more par-
 ticularly the contraction of  mercury at the  period  of  its
 solidification.   Davy,  however,  endeavoured  to  form  a
vacuum, in a somewhat similar manner, over fused tin, with
but partial  success; he also made  many other  attempts to
 obtain  a perfect  vacuum ;  his main  object being  to ascertain
 tvhat Avould be  the effect of electricity across empty space : 
LIGHT
135
he admits  that he  could not succeed in procuring a vacuum,
but found  electricity much less  readily conducted or trans-
mitted by the best vacuum he could procure than by the ordi-
nary Boylean vacuum.
    Morgan found  no conduction by a good Torricellian vac-
uum ; and, although Davy does not seem to place much reliance
on  Morgan's experiments, there  AAras one point in Avhich they
were less liable to error than those of Davy.   Morgan, whose
experiments seem to have been carefully conducted, operated
with hermetically-sealed glass tubes and by induced electricity,
AAdiile Davy scaled a platinum wire into the extremity of the
tube in  Avhich he sought to produce a vacuum.  I have found
in very numerous  experiments which I made to exclude air
from  Avater, that platinum Avires, most carefuUy sealed into
glass, alloAV liquids to pass betAveen  them and the glass; and
this gives every reason to believe that gases may equally pass
through ; I have observed such effect in the gas battery Avhen
it has been in action for a long period.  Davy supposed that
the particles of bodies maybe detached,  and so produce elec-
trical effects in a vacumm ; and such effects Avould more read-
ily  take place  in his experiments, Avhere a Avire  projected
into the exhausted space, than in Morgan's, where the  in-
duced electricity was  diffused  over the surface of the glass.
    M.  Masson found that the barometric vacuum  does not
conduct a current of  electricity,  or even a discharge,  unless
the  tension is considerable and  sufficient to detach particles
from the electrodes;  and by adopting  a plan of Dr. An-
drews,  viz. absorbing carbonic acid by potash,  M. Gassiot
has  recently succeeded   in  forming  vacua across  Avhich
the  powerful discharge  from the Rhumkorf coil  will not
pass.
    The  odour  which many  metals, such  as iron,  tin,  and
einc emit,  and the so-caUed thermographic  radiations, we
can hardly explain upon any other theory than the evapora-
tion of an infinitesimally small portion of the metal itself. 
136        correlation of physical  forces.

    So universal  is the tendency of matter to diffuse itself
into space,  that  it gave  rise to the old saying that nature
abhors a vacuum ; an aphorism which, though cavilled at and
ridiculed by the self-sufficiency of some modern philosophers,
contains in  a terse, though somewhat metaphorical, form of
expression a comprehensive truth, and evinces a large extent
of observation in those who, Avith few of the advantages which
we possess, first generalised by this sentence  the  facts of
Avhich they had become cognisant.
    It has been argued that, if matter were capable of infinite
divisibility, the earth's atmosphere would haA*e no hmit, and
that consequently portions of it would exist at points of space
where the attraction of the sun and planets would be greater
than that of the  earth, and Avhence  it would fly off to those
bodies and  form  atmospheres around them.   This Avas sup-
posed to be negatived  by the argument of the well-known
paper of Dr. Wollaston ; in Avhich, from the absence of nota-
ble refraction near the margin of the sun and of the planet
Jupiter, he  considered  himself entitled to conclude  that the
expansion of the  earth's atmosphere had a definite hmit, and
was balanced  at  a certain point by gravitation : this deduc-
tion has been shown to be inconclusive by Dr.  Whewell, and
has also been impugned upon others grounds by Dr. Wilson.
There is a point not ad\~erted to in these papers, and which
Wollaston does not seem to have considered,  viz. that there
is no evidence that the apparent discs  of the sun and of Jupi-
ter show us their real discs  or bodies.  Sir. W. Herschel
regards  the  margin of the visible discs as that of clouds or a
pccuhar state of atmosphere, and the rapidly changing char-
acter of the apparent surfaces render some such conclusion
necessary.   If this be so, refraction of an occulted star could
not be detected—at all events,  in  the denser portion of the
atmosphere.
    Sir W.  Herschel's  observations  go  to  prove  that  the
sun and Jupiter have dense atmospheres, while Wollaston's 
LIGHT.
137
were  believed to prove that they have no appreciable atmoa
pheren.
    If  it be admitted, or considered proved, that the sun and
planets ha\-e atmospheres—and little doubt now exists on this
point—then the grounds upon which  WoUaston founded his
arguments are untenable ; and there appears no reason why
the atmosphere  of the  different planets should not be, with
reference to each other, in a state of equihbrium.   Ether, or
the highly-attenuated  matter existing  in the interplanetary
spaces, being an expansion of some  or all of these  atmos-
pheres, or of the more Aolatile portions of them, would thus
furnish matter for the transmission of the modes of  motion
which  avc call light, heat, &c.; and possibly minute portions
of these atmospheres may, by gradual changes, pass from
planet to planet, forming a hnk of material communication
between the distant monads of the universe.
    The  vieAV given above Avould approximate the  theory of
the transmission of light by the undulations of  ordinary mat-
ter to the other two theories, which equally suppose the non-
existence of a vacuum;  for, according to the emissive of
corpuscular theory, the vacuum is filled by the matter itself,
of light, heat, &c.; according to the  ethereal, it is filled by
the all-penetrating ether.   Of the  existence of matter in the
interplanetary spaces we have some evidence  in the diminish-
ing periods of comets ;  and where, from its highly attenuated
state,  the character of the medium  by Avhich  the forces are
conveyed cannot be tested, the term ether is a most appropri-
ate generic name for such medium.
    NcAvton has some curious passages on the subject matter
of hght.   Iu the ' Queries to the Optics ' he says :—
    ' Are  not gross bodies and light  convertible  into  one
another, and may not bodies receive  much of their activity
from the particles  of  hght which enter  their composition?
   *   *  *   The changing of bodies into hght and light into
bodies  is very conformable to  the  course of nature,  which 
138
correlation of physical forces.
seems delighted with  transmutations.   Water, which is a
very fluid,  tasteless  salt,  she  changes by heat into vapour,
which is a  sort of air, and by cold into  ice, which is a hard,
pellucid, brittle, fusible stone,  and this s^one  returns into
water by heat, and vapour returns into water by cold.  *   *
And, among such various and strange  transmutations, Avhy
may not nature  change  bodies  into  light,  and  hght into
bodies ?'
   NeAvton has here  seemingly  in his mind the emissive
theory of light; but the passages might be apphed to either
theory; the analogy he saAv in the change of state  of matter,
as in ice, water, and vapour, with the hypothetic change into
light, is very striking, and would seem to show that he regard-
ed the change or  transmutation of which he speaks as one
analogous to the  knoAvn changes of state, or consistence, in
ordinary matter.
   The difference between the view which 1 am advocating
and that of the ethereal  theory as  generaUy enunciated is,
that the  matter which in the interplanetary spaces serves as
the means of transmitting by its undulations light and heat, I
should regard  as possessing the quahties of ordinary, or as it
has sometimes been caUed gross, matter, and particularly
Aveight; though, from its extreme rarefaction, it would mani-
fest these properties in an indefinitely smaU degree ;  whilst, on
the surface  of the earth, that matter attains a density cognisa-
ble by our  means of experiment, and the dense  matter  is
itself, in great part, the conveyer of the undulations in which
these agents consist.  Doubtless, in very many of  the  forms
which  matter  assumes  it is porous, and pervaded by more
volatile essences, which may differ as much in kind as matter
does.   In these cases a composite  medium, such as that indi-
cated by Dr. Young, would result; but even on such a suppo-
sition, the  denser matter  Avould probably exercise  the more
important influence on  the undulations.   Returning to  the
somewhat strained  hypothesis,  that the  particles of  dense 
LIGHT.
139
matter in a so-caUed sohd are as distant as the stars in heaven,
still a certain depth or thickness of such sohd would present
at every point of space a particle  or rock  in the successive
progress of a wave, which particles, to carry on the move*
mcnt, must vibrate in unison with  it.
    At the  utmost,  our assumption, on the one hand, is that
Avherever light, heat, &c, exist, ordinary matter exists, though
it may be so attenuated that we cannot recognise it  by the
tests of other forces, such as gravitation, and that to the ex-
pansibility of matter no limit can be assigned.  On the other
hand, a specific matter without weight must be assumed, of
the existence of which there is no eA'idcnce, but in the  phe-
nomena for the explanation of Avhich its existence is supposed.
To account for the phenomena the ether is assumed,  and to
prove the  existence  of the ether  the phenomena are cited.
For these reasons,  and others above given, I think that the
assumption of the universality of ordinary matter is the least
gratuitous.
           OySej' ti ran irayros Kevov irePVe: ouSe irepiaaov.

    A question has  often occurred to me  and possibly to oth-
ers : Is  the continuance of a luminous impulse in the inter-
planetary spaces perpetual, or does it after a certain distance
dissipate itself and become lost as light—I do not  mean by
mere divergence directly as  the squares of the distances  it
travels, but does the physical impulse itself lose  force as  it
proceeds?   Upon  the  view I have advocated, and indeed
upon  any undulatory hypothesis, there  must  be some  resist-
ance to its progress ; and  unless  the matter or ether in the
interplanetary spaces  be  infinitely  elastic,  and there  be no
lateral action of a  ray of light, there  must be  some loss.
That it is exceedingly  minute is proved by the distance light
travels.   Stars whose  parallax is  ascertained are at such a
distance from the earth that their hght, traveUing at the  rate
of 192,500 miles in a second, takes more than ten years to 
140       CORRELATION of  physical  forces.

reach the earth; so that we  see them  as they existed ten
years ago.   The distance of most A'isible stars is probably far
greater than this, and  yet  their brilliance is great, and in-
creases Avhen their rays are coUected by the telescope in pro-
portion ceteris paribus to the area of the object-glass or spec-
ulum.   There is, however, an argument  of a someAvhat spec-
ulative  character, by which light Avould  seem to  be lost,  or
transformed into some other force in the interplanetary spaces.
    Every increase of  space-penetrating power in  the  tele-
scope gives us a new field of visible stars.  If this expansion
of the stellar universe go on indefinitely  and no hght be  lost,
then, assuming the  fixed stars to  be of an  average equal
brightness with  our sun, and no light lost  other than by diver-
gence, the night ought to be equally luminous with the day ;
for though the light from each point diminishes in  intensity
as the square of the distance, the number of luminous points
would fiU up the whole  space around us ; and if every point
of space is occupied by an equally briUiant point of light, the
distance of the points becomes immaterial.  The loss of  light
intercepted by steUar bodies would make no difference in the
total quantity of light, for each of these would yield from its
own self-luminosity at least as much light as it intercepted.
Light may, howeATer, be intercepted by  opaque bodies,  such
as planets ; but, making every  allowance for these, it is  diffi-
cult to understand why we get so little light at night from the
stellar universe, without assuming that some light is lost in its
progress through space—not lost absolutely, for that would be
an annihilation  of force—but converted into some other mode
of motion.
    It may be objected that this hypothesis assumes the  stel-
lar uniA-erse to be  illimitable :  if pushed to its extreme so as
to make the light  of  night equal  that  of day, provided no
stellar light be lost, it does make this  assumption;  but  even
this is a far more rational assumption to  make than  that tho
stellar universe is limited.  Our experience gives no indica 
LIGHT.
141
tion of a limit; each improvement in telescopic power gives
us new realms of stars or of nebulae, which,  if not steUar
clusters, arc at all events self-luminous matter ; and if we as-
sume a hmit, what is it?  We cannot conceive a physical
boundary, for then immediately comes  the  question, Avhat
bounds the boundary ?  and to suppose the steUar universe to
be bounded  by infinite  space or by infinite chaos, that is to
say,  to suppose a spot—for it would then become so—of mat-
tor in definite forms, with definite forces, and probably teem-
ing with  definite organic beings, plunged  in  a universe  of
nothing, is to my mind at least far more unphilosophical than
to suppose a boundless universe of matter existing in forms
and actions analogous to those which, as far as our examina-
tion  goes, pervade space.   But without speculating on topics
in which the  mind loses  itself, it may not  unreasonably be
expected that a greater amount of light would reach us from
the surrounding  self-luminous spheres were not some portion
lost as light, by its action on the medium which conveys  the
impulses.   What force this  becomes, or what it effects, it
would be idle to speculate upon. 
VI.—MAGNETISM.
      MAGNETISM, as was proved by the important discov-
       ery of Faraday, avUI produce electricity, but with this
pecuharity—that in itself it is static ; and, therefore, to pro-
duce a dynamic force, motion must be superadded to it: it is,
in fact, directive, not  motive, altering the direction of other
forces, but not, in strictness, initiating them.  It is difficult
to convey a definite notion of the force of magnetism, and of
the mode in which it affects other forces.  The following il-
lustration may give a rude idea of magnetic polarity.   Sup-
pose a number  of wind-vanes,  say of the shape of arrows,
with the spindles on which they revolve arranged in a row,
but the vanes pointing in various directions :  a wind blowing
from  the  same  point with an uniform velocity wiU instantly
arrange these vanes in a definite direction, the  arrow-heads
or narrow parts  pointing one way, the swaUow-taUs or broad
parts  another.  If they be dehcately suspended on their spin-
dles, a very gentle  breeze avUI so arrange them, and a very
gentle breeze will again deflect them ; or, if the Avind  cease,
and they have been originaUy subject to other forces, such as
gravity from unequal suspension, they wiU  return to irregu-
lar positions, themselves creating a slight breeze by their re-
turn.   Such a state of things will represent the state of the
molecules of soft iron ; electricity acting  on them—not indeed
in straight lines, but in a definite direction—produces  a polar 
MAGNETISM.
143
arrangement, which they wiU lose as soon as the dynamic in-
ducing force  is removed.
    Let us now suppose the vanes, instead of turning easily,
to be more stiffly fixed to the axles, so as to be turned with
difficulty: it avUI require a stronger wind to move  them  and
arrange them definitely ;  but  when so arranged, they wiU re-
tain their position ; and should a gentle breeze spring up in
another direction, it will not alter their position, but will it-
self be definitely deflected.   Should the conditions of force
and stability be intermediate,  both the breeze and  the  vanes
will be slightly deflected; or,  if there be no breeze, and the
spindles be aU moved in any direction, preserving their linear
relation, they AviU  themselves create  a breeze.   Thus it is
with the molecules of hard iron or steel in permanent mag-
nets ; they are polarised with  greater difficulty, but, when so
polarised, they cannot be  affected by a feeble current of elec-
tricity.   Again,  if the  magnets be moAed, they themselves
originate a current of electricity; and, lastly, the magnetic
polarity  and the electric current may be both mutually af-
fected, if the degrees of motion and stability be intermediate.
    The above  instance will, of course, be taken only as an
approximation, and not as binding  me to any closer analogy
than is generally expected of a mechanical illustration.   It
is difficult to convey by Avords a definite idea of the  dual or
antithetic character of force involved in the term polarity.
The illustration I have employed may, I hope, somewhat aid
in elucidating the  manner in which  magnetism acts on  the
other dynamic forces ;  i. e., definitely directing them, but not
initiating them, except while in motion.
    Magnets  being  moved in  the  direction  of hnes, joining
their poles, produce electrical currents in such neighbouring
bodies  as are conductors of  electricity, in directions  trans-
verse to  the  line of motion;  and if the  direction  of motion
or the position of the magnetic poles be reversed, the current
of electricity flows  in a reverse direction.  So if the  magnet 
144        CORRELATION  OF PHYSICAL FORCES.

be stationary, conducting bodies  moved  across any  of the
lines of magnetic force, i. e. hnes in the  direction of which
the mutual  action of the poles of the  magnet would place
minute  portions of iron, haA-e currents of electricity devel-
oped in them, the direction  of which is dependent upon  that
of the motion of the substance with reference to the magnetic
poles.   Thus, as bodies affected by an electrical current are
definitely moved by a magnet in  proximity to  them, so  con-
versely bodies moved near a magnet have an electrical  cur-
rent developed in them.   Magnetism can, then, through the
medium of electricity, produce heat, light,  and  chemical affin-
ity.  Motion it can directly produce  under the  above  condi-
tions ;  i. e. a magnet being  itself moved will moAre other fer-
reous bodies : these avUI acquire a static condition of equilib-
rium, and be again moved when the magnet is also moved.
By motion or arrested motion only, could  the  phenomena of
magnetism ever have become knoAvn to us.  A magnet, hoAV-
ever poAverful, might  rest for ever unnoticed and unknoAvn,
unless  it were moved near to iron, or iron moved near to it,
so as to come Avithin the sphere of its attraction.
   But even with other than either magnetic or electrified
substances, all  bodies wiU be moA'ed when placed near the
poles of very powerful magnets—some  taking a position ax-
ially, or in the  line from pole to pole of the  magnet;  others
equatorially, or in a  direction transverse to that line—the
former being attracted, the  latter  apparently repelled, by tho
poles of the magnet.   These effects, according to the views
of Faraday, show a  generic difference  between  the  two
classes of bodies, magnetics and diamagnetics ; according  to
others, a difference of degree or a resultant of magnetic ac-
tion ; the less magnetic substance being  forced into a trans-
verse  position  by the magnetisation of  the  more magnetic
medium Avhich surrounds it.
    According to the view  given above,  magnetism may bo
produced by the other forces, just as the vanes in the. instance 
MAGNETISM.
145
given are definitely deflected, but cannot produce them except
Avheu in motion : motion, therefore, is to be regarded in this
case as  the  initiative force.   Magnetism  wiU,  however, di-
rectly affect the other forces—light, heat, and chemical  affin-
ity, and change their direction or mode of action, or, at aU
events, wiU  so  affect matter subjected to  these forces, that
their direction is changed.  Since these  lectures were deliv-
ered, Faraday has discovered a remarkable effect of the mag-
netic *force in occasioning the deflection of  a ray of polarised
light.
    If a ray  of polarised light pass through  water, or through
any transparent liquid or solid Avhich does not  alter or turn
aside the plane of polarisation, and the column, say of Avater,
tlirough which it passes be  subjected to the action of a pow-
erful magnet, the hne of magnetic force, or that  which would
unite the poles of  the magnet, being in the  same  direction as
the ray of polarised hght, the water acquires, with  reference
to the light,  simUar, though not quite  identical, properties to
oil of turpentine—the  plane  of polarisation is rotated, and
the  direction of this  rotation is changed by changing the di-
rection of the magnetic  force: thus, if we suppose a polar-
ised ray to pass first in its course the north  pole  of the  mag-
net, then between that and the south pole it wiU be deflected,
or curved to  the right;  while if it meets the south  pole first
in its course, it wiU, in its journey between that and the north
pole, be turned to  the left.  If the substance through which
the ray is transmitted  be of itself capable of deflecting  the
plane of polarisation, as, for instance, oU of turpentine, then
the magnetic influence wiU increase  or diminish this rotation,
according to its direction.   A similar effect  to this is observed
with polarised heat when  the medium  through which it is
transmitted is subjected to magnetic influence.
    Whether this effect of magnetism is rightly termed an ef-
fect upon hght and heat, or is a molecular change of the mat-
ter transmitting the light and heat, is a question the resolu-
              7 
146        CORRELATION  OF PHYSICAL FORCES.

tion of which must be left to the future ; at present, the  an-
swer to it would depend upon the  theory we adopt.  If  the
view of hght and  heat which I have stated be adopted, then
we may fairly say that magnetism, in these experiments, di-
rectly affects the other forces;  for  light and heat  being, ac-
cording to that view, motions of ordinary matter, magnetism,
in affecting these movements, affects the forces which occa-
sion them.   If, however, the other theories be adhered to, it
would be more  consistent with the facts to view these results
as exhibiting an action upon the matter itself, and the heat
and light as secondarUy affected.
   When substances are undergoing chemical changes, and a
magnet is brought  near them, the direction or hnes of action
of the chemical force will be changed.  There are  many  old
experiments which probably depended on this effect, but
which were erroneously considered to prove that permanent
magnetism could produce or increase chemical  action :  these
have recently been extended and explained by Mr. Hunt and
Mr. Wartmann, and are now better understood.
   The above cases are apphcable to the subject of the pres-
ent Essay, inasmuch as they show a relation to exist between
magnetic and the other forces, which relation is, in  all proba-
bility, reciprocal; but in these cases there is not a production
of light, heat, or chemical affinity, by magnetism, but a change
in their direction or mode  of action.
   There is, however, that  which may be vieAved as a  dy-
namic condition of magnetism ;  i. e. its condition at the com-
mencement and the termination, or during  the increment or
decrement of its development.  While iron or steel is  being
rendered magnetic, and as  it progresses from its non-magnetic
to its  maximum magnetic state, or recedes  from its maximum
to zero, it  exhibits a dynamic force ; the molecules are, it
may be inferred, in motion.   Similar effects can then be pro-
duced to those which are produced by a magnet whhst in mo-
tion. 
MAGNETISM.
147
    An experiment which I published in 1845 tends, I think
to illustrate this,  and in some  degree to show the character
of the  motion impressed upon the molecules of a magnetic
metal at the period of magnetisation.  A tube filled with the
liquid  in which magnetic oxide of iron had been prepared,
and terminated at each end by plates of glass, is surrounded
by a coil of coated wire.   To a spectator looking through this
tube a flash of light is perceptible whenever the coil is elec-
trised, and less light is transmitted when the electrical current
ceases, shoAving a symmetrical arrangement of  the  minute
particles of magnetic oxide whUe  under the magnetic in-
fluence.
    In  this  experiment it should  be borne in mind, that the
particles of oxide of iron arc not shaped by the hand of man,
as would be the case  with iron filings, or similar minute  por-
tions of magnetic  matter, but being chemically precipitated,
are of the form given to them by nature.
    While magnetism is in the state of change above described,
it AviU  produce the other forces ;  but it may be  said, whUe
magnetism is thus progressive, some other force is acting on
it, and therefore  it does not initiate : this  is true, but the
same may be said of  aU the other  forces ;  they have no com-
mencement that Ave can trace.  We must  ever  refer them
back to some antecedent  force equal in amount  to that  pro-
duced,  and  therefore  the  word initiation cannot in strictness
apply,  but must only be taken as signifying the force selected
as the  first: this is another reason why the idea of abstract
causation is inapplicable to physical  production.   To  this
point I shall again advert.
   Electricity may thus be  produced directly by magnetism,
either  when the magnet as a mass is in motion, or when its
magnetism is commencing, increasing, decreasing, or ceasing ;
and heat may sinularly be directly produced by magnetism.
I have,  since  the first edition of  this Essay was pubhshed,
communicated to the Royal Society a paper by which I think 
148       CORRELATION OF  PHYSICAL  FORCES.

I have satisfactorily proved, that whenever any metal suscepti-
ble of magnetism is magnetised or demagnetised, its tempera-
ture is raised.  This was shown, first, by subjecting a bar of
iron, nickel, or cobalt to the influence of a poAverful electro-
magnet,  which was rapidly magnetised and demagnetised in
reverse directions, the electro-magnet itself being kept cool by
cisterns of water, so that the magnetic metal subjected to the
influence  of magnetism  was  raised to a higher temperature
than the  electro-magnet itself, and could not, therefore, have
acquired its increased temperature by conduction or radiation
of heat from the electro-magnet; and secondly, by rotating
a  permanent  steel  magnet with its pole opposite to a  bar
of  iron,  a thermo-electric pile  being placed  opposite  the
latter.
    Dr. Maggi covered a plate of homogeneous soft iron with
a thin coating of wax mixed Avith oil, a tube  traversed  the
centre through which the Arapour of boiling water was passed.
The plate was made to rest on the poles of an electro-magnet,
with card interposed.  When the iron is not magnetised, the
melted wax assumes a circular form, the tube occupying the
centre, but when the electro-magnet is put in action, the curve
marking the boundary of the melted substance changes its form
and becomes elongated in a direction transverse to the line
joining the poles, showing that the conducting power of the
iron for heat is changed by magnetisation.
    Thus we get heat produced by magnetism and the conduc-
tion of heat altered by it in a direction having a definite rela-
tion to the direction of the  magnetism.   Is  it necessary to
call in aid ether or the substance ' caloric' to explain these
results ?  is it not more rational to regard the  calorific effects
as changes in the molecular arrangements of the matter sub-
jected to  magnetism?
    There is every probability that magnetism, in  the dyna-
mic state, either when the magnet is in motion, or when the
magnetic intensity is varying, TriU also directly produce chemi- 
MAGNETISM.                    149
 cal affinity and light, though, up to the present time, such has
 not been proved to be the case ; the reciprocal effect, also, of
 the direct production of magnetism by light and heat has not
 yet been experimentally estabhshed.
    I have used, in contradistinction, the terms dynamic and
 static to represent the different states of magnetism.  The
 applications I have made of these terms may be open to some
 exception, but I know of no other words Avhich wiU so nearly
 express my meaning.
    The static condition of  magnetism resembles the  static
 condition of other forces : such as the state of tension exist-
 ing  in  the  beam and  a  cord of a balance, or in a  charged
 Leyden phial.   The old  definition of force was, that which
 caused  change in  motion; and yet  even this definition pre-
 sents a difficulty: in a case of static equilibrium, such, for
 instance, as  that Avhich obtains in the two arms of a balance,
 Ave get the idea of force without any palpable apparent motion :
 Avhether there be really an absence of motion may be a doubt-
 ful question, as such absence would  involve in this case per-
 fect  elasticity, and, in all other cases, a stabUity which, in a
 long course of time, nature  generally negatives, showing, as
 I believe, an inseparable connection of motion with matter,
 and an  impossibility of  a perfectly immobile or durable state.
 So  with magnetism: I believe no  magnet can exist  in an
absolutely stable state,  though  the duration  of  its stability
will  be proportionate to its original  resistance to assuming
a polarised condition.  This, hoAvever, must be taken merely
as a matter of opinion :  we have, in support of it, the general
facts that magnets do deteriorate in the course of years ; and
we have the further general fact of the instabihty, or fluxional
state, of all  nature,  Avhen Ave  have  an opportunity of  fairly
investigating it at different and remote periods: in many
cases, hoAvever,  the action is so  slow  that the  changes escape
human  observation,  and,  until this  can be brought to bear
over a proportionate period of time, the proposition cannot be 
150        CCRRELATION OF PHYSICAL  FORCES.
said to be experimentally or inductively proved, but must be
left to the mental conviction of those who examine it by the
hght of already acknoAvledged facts.
   AU cases of static force present the same difficulty : thu3,
tAvo springs pressing against each other would be said to be
exercising force ; and yet there is no resulting action, no heat,
no light, &c.
   So if gas be compressed by a piston, at the time of com-
pression  heat is  given  off; but when  this  is  abstracted,
although the pressure continues, no further heat is ehminated.
Thus,  by an equihbrium produced by opposing forces,  motion
is locked up, or in abeyance, as it were, and may be again
developed Avhen the forces are  reheved from the tension.
But in the  first instance,  in producing the state of tension,
force has to be employed ; and as we have said in treating of
mechanical force, so with the other forces the original  change
which  disturbs equihbrium produces other changes which go
on Avithout  end.   Thus,  by the  act  of  charging  a Leyden
phial, the cyhnder, the rubber, and the adjoining portions of
the electrical machine have each and aU their states changed,
and thence produce  changes in surrounding bodies ad infini-
tum ;  when  the jar is discharged, converse changes are again
produced.
   As Avith heat, light, and electricity, the daUy accumulating
observations tend to show that each change in the phenomena
to Avhich these names  are given is accompanied by a change
either temporary or permanent in the matter affected by them;
so many recent  experiments on magnetism have  connected
magnetic phenomena Avith a molecular change in the  subject
matter.  Thus M. Wertheim has shown that the elasticity of
iron and steel is altered by magnetisation ;  the co-efficient of
elasticity in  iron  being temporarily, in steel permanently
diminished.
   He has also examined the effects of torsion upon magnet-
ised iron, and concludes, from his experiments, that in a bar 
MAGNETISM.
151
of iron arrived at a state of magnetic equihbrium, temporary
torsion diminishes the magnetism, and that the untwisting or
return to its primitive  state restores  the original degree of
magnetisation.
   M. Guillemin observed that a bar slightly curved by its
own weight is straightened by being magnetised.   Mr. Page
and  Mr. Marrion discovered that a sound is emitted when
iron or steel is rapidly magnetised or demagnetised; and Mr.
Joule found that a bar  of iron is shghtly elongated by mag-
netisation.
   Again, with  regard  to diamagnetic  bodies, M.  Matteucci
found that the  mechanical  compression of glass  altered the
rotatory power  upon a ray of polarised hght which it trans-
mitted.   He further considered that a change took place in
the  temper of portions of glass  which he submitted to the in-
fluence of powerful magnets.
   The  same  arguments  which  have been submitted to
the  reader  as to the other affections of matter being modes
of molecular motion, are therefore equaUy apphcable to mag-
netism. 
           VII.—CHEMICAL  AFFINITY.

    CHEMICAL AFFINITY, or the force by which dissimi-
     lar bodies tend to unite and  form compounds differing
generaUy in character from their constituents, is that mode of
force of which the human mind has hitherto formed the least
definite  idea.  The  Avord itself—affinity—is iU chosen, its
meaning, in this  instance, bearing no analogy to its ordinary
sense ; and the mode of its action is conveyed by certain con-
ventional  expressions,  no dynamic .theory of it  worthy of
attention having  been adopted.  Its  action so modifies and
alters the  character  of matter,  that  the changes it  in-
duces have  acquired, not perhaps  very logically, a  generic
contradistinction  from  other  material  changes, and  wre
thus use,  as contradistinguished,  the  terms physical and
chemical.
    The main distinction between chemical  affinity and physi-
cal attraction or aggregation, is the  difference of character of
the chemical compound from its components.  This is, how-
ever, but a vague line of demarcation ; in many cases, Avhich
would  be classed by aU  as  chemical  actions, the  change of
character is but slight; in others, as in the  effects of neutrali-
sation, the difference of  character  would be a result which
would  equaUy foUow from  physical attraction of dissimilar
substances, the preArious characters of the constituents depend-
ing upon this very attraction or affinity:  thus an acid corrodes 
CHEMICAL  AFFINITY.
153
because it tends to unite with another body;  Avhen  united,
its corrosive power, i. e. its tendency to unite, being satiated,
it cannot,  so to speak, be further attracted, and it necessarily
loses its corrosive  poAver.   But there are other cases where
no such result could a  priori be anticipated, as where  the
attraction or combining tendency of the compound is higher
than that of its constituents: thus, who could, by physical
reasoning, anticipate a  substance  like  nitric  acid from the
combination of nitrogen and oxygen?
   The nearest approach,  perhaps, that we can form to a
comprehension of chemical action, is by regarding  it (vaguely
perhaps)  as  a  molecular  attraction  or  motion.   It whl
directly produce motion of definite masses, by the resultant
of the molecular changes  it  induces:  thus, the  projectile
effects of  gunpowder may be cited as famihar instances of
motion produced by chemical action.   It may be a question
whether, in this  case, the  force which occasions  the motion
of the mass  is a conversion of the force of chemical  affinity,
or Avhether it is not, rather, a liberation of other forces exist-
ing in  a state of static equilibrium, and having been brought
into  such state by previous  chemical  actions;  but, at aU
events, through the medium of electricity chemical affinity
may be directly and quantitatively converted into the other
modes  of force.   By chemical affinity, then, we can  directly
produce electricity; this latter  force  was,  indeed,  said by
Davy to be chemical  affinity acting on masses:  it appears,
rather, to  be chemical  affinity acting in a definite direction
through a chain of .particles; but by no definition  can the
exact relation of chemical affinity and electricity be expressed ;
for the latter, however closely related to the former, yet exists
where  the former does not, as in a metallic wire, which when
electrified, or  conducting   electricity,  is, nevertheless,  not
chemicaUy altered,  or,  at least, not known to be chemieaUy
ul'.eied.
   Volta, the  antitype of Prometheus, first enabled us de 
154        CORRELATION OF  PHYSICAL FORCES.

finitely  to  relate  the  forces  of  chemistry  and  electricity.
When two  dissimilar  metals  in  contact are  immersed in a
liquid belonging to a certain class, and  capable  of acting
chemically on one of them, what is termed  a voltaic circuit is
formed, and, by the chemical action, that pecuhar mode of
force called  an electric current is generated, which circulates
from metal to metal, across the liquid, and  through the points
of contact.
   Let us take,  as an instance of the conversion of chemical
force into electrical, the foUowing, which I  made known some
years ago.  If gold be immersed in hydrochloric acid, no
chemical action  takes  place.  If gold be immersed in nitric
acid, no chemical action takes place  ; but mix the two acids,
and the  immersed gold is  chemicaUy attacked and dissolved :
this an is ordinary chemical action, the result of a double chemi-
cal affinity.   In hydrochloric acid, which is composed of
chlorine and hydrogen, the affinity of chlorine for gold being
less than its affinity for hydrogen, no  change takes place ; but
when the  nitric  acid is added, this latter  containing a great
quantity of  oxygen  in a state of feeble  combination, the
affinity of oxygen  for hydrogen opposes that of hydrogen for
chlorine, and then the affinity of the latter for gold is enabled
to act, the gold combines  with the chlorine,  and chloride of
gold remains in solution in the hquid.   Now, in  order to
exhibit this chemical  force in the  form of  electrical force,
instead of mixing the  liquids, place  them in  separate vessels
or compartments, but  so  that they may be in contact, which
may be  effected  by having a  porous material,  such as un-
glazed porcelain, amianthus, &c, between them.  Immerse  in
each of these liquids a  strip or wire of gold :  as long as these
pieces of gold remain  separated,  no chemical  or electrical
effect takes  place;  but the instant they  are brought into
metallic contact, either immediately or by connecting  each
with the same metallic Avire,  chemical  action takes  place—
the gold in the hydrochloric acid is dissolved, electrical action 
CnEMICAL  AFFINITY.
155
also takes place,  the  nitric  acid is deoxidised by the trans-
ferred hydrogen, and a current of electricity may be detected
in the metals o» connecting metal by the apphcation of a gal
vanometer or any instrument appropriate for detecting such
effect.
    There  are few, if  any, chemical actions which cannot be
experimentally made to produce electricity:  the oxidation of
metals; the burning of combustibles, the combination of oxy
gen and  hydrogen, &c, may all be made  sources of elec
tricity.  The  common mode in which the electricity of the
voltaic battery is generated is by the chemical action of water
upon zinc ; this  action is increased by adding certain acids to
the wratcr, which  enable  it to act more poAverfuUy upon the
zinc, or in some cases  act themselves upon it; and one of the
most poAverful  chemical actions  known—that of nitric acid
upon oxidable metals—is that Avhich produces the most pow-
erful voltaic battery, a combination which I made known in
the year  1839 : indeed, we may safely say, that when the
chemical force is utilised, or not wasted,  but all converted  into
electrical  force,  the  more powerful the chemical action, the
more poAverful is the electrical action which results.
    If, instead of employing manufactured products or educts,
such  as zinc and acids,  we could realise as electricity the
whole of the chemical force which is active in the combustion
of cheap and abundant raw materials, such as coal, wood, fat,
&c, with  air or water, we should obtain one of the greatest
practical desiderata, and have at our command a mechanical
poAver in   every respect superior in its applicability to  the
steam engine.
    I have shown that the flame of the common blowpipe gives
rise to a very marked  electrical  current, capable  not only of
affecting the galvanometer, but of producing chemical decom-
position :  two plates or coUs  of platinum  are placed, the one
in the portion  of the  flame  near the orifice of the jet, or at
the points where combustion  commences, the other in the full 
156       CORRELATION OF PHYSICAL  FORCES.

yeUow flame where combustion is at its maximum ;  this latter
should be kept cool, to enable a thermo-electric current, Avhich
is produced by the different  temperature of the  platinum
plates, to co-operate with the flame current; wires attached
to the plates of platinum form the terminals or poles.   By a
row of jets a flame battery may be formed, yielding increased
effects ; but in these experiments, though theoretically inter-
esting, so smaU a fraction of the poAver, actually at Avork in
the  combustion, has been throAvn into an electrical form, that
there is no immediate promise of a practical result.
    The quantity of the electrical current, as measured by the
quantity of matter it acts upon  in  its  different phenomenal
effects,  is proportionate  to the quantity of  chemical action
which generated it; and its intensity, or power of overcoming
resistance, is also  proportionate to  the  intensity of chemical
affinity Avhen a single^ voltaic pair is employed, or to the num-
ber of reduplications  when the well-knoAvn instrument  caUed
the  voltaic battery is used.
    The mode in which the voltaic current is  increased in in-
tensity by these reduplications, is in itself a striking instance
of the mutual  relations  and dynamic analogies of different
forces.  Let a plate of zinc or other metal possessing a strong
affinity for oxygen, and  another of platinum or other  metal
possessing little or no affinity for  oxygen, be  partially im-
mersed  in a vessel, A, containing  dUute nitric acid, but not
in contact Avith each other ; let platinum  wires touching each
of these plates have their extremities immersed in another
vessel, B, containing also dilute nitric  acid: as the acid in
vessel A is decomposed, by the chemical affinity of the zinc
for  the oxygen of the  acid,  the acid  in vessel B is also decom-
posed, oxygen  appearing at the extremity of  the wire Avhich
is connected with  the platinum: the chemical power is con-
veyed or transferred through the wires,  and,  abstracting cer-
tain local effects,  for every unit of  oxygen which combines
with the zinc in  the one vessel, a unit  of oxygen is evolved 
CHEMICAL AFFINITY.               157
from  the platinum wire in the other.  The platinum wire in
thus thrown into a condition analogous to zinc, or has a poav
er given to it of determining the oxygen  of the hquid to ita
surface, though it  cannot, as  is the  case- with  zinc, com
bine with it under similar circumstances.  If Ave now substi
tute for the platinum wire  which was connected with the
platinum plate, a zinc wire, we have in addition to the deter-
mining tendency by which the platinum was affected,  tho
chemical affinity  of the oxygen in vessel B for the zinc wire
thus we have, added to the force which was originaUy pro-
duced by the" zinc of the combination in  vessel A, a second
force, produced by the zinc in vessel B, co-operating with the
first;  two pairs of zinc and platinum thus connected produce,
therefore, a more intense effect  than one pair; and if we go
on adding to these alternations of zinc, platinum, and hquid,
Ave obtain an indefinite exaltation of chemical power, just as
in mechanics we obtain accelerated motion by adding fresh
impulses to motion  already generated.
    The same rule of proportion which holds good in chemi-
cal combinations  also obtains in electrical effects, when these
are produced by chemical actions.  Dalton and others proved
that the constituents of a vast number of compound substances
always  bore a definite  quantitative relation to each other:
thus, water, which  consists of one part by weight of hydro-
gen united  to eight parts of oxygen, cannot be formed by the
same elements in any other than these proportions ; you  can
neither  add to nor subtract  from the normal ratio  of  the
elements, Avithout entirely altering the nature of the com-
pound.   Further, if  any element  be selected as unity,  the
combining  ratios of other elements  wUl bear an invariable
quantitative relation to that and  to each other : thus if hydro-
gen be chosen as  1, oxygen wiU be 8, chlorine wiU be 36 ;
that is, oxygen wUl unite Avith hydrogen in the proportion of
8 parts by  weight to 1, while chlorine  wUl unite with hydro-
gen in the proportion of 36 to 1, or with oxygen in the pro- 
158
CORRELATION OF PHYSICAL FORCES.
portion of 36 to 8.  Numbers expressing  their combining
weights, which are thus relative, not absolute, may by a con-
ventional assent as to the point of unity, be fixed for aU chemi-
cal reagents ; and, Avhen so fixed, it avUI be found that bodies,
at least in inorganic compounds, generally unite in those pro-
portions, or in simple multiples of them: these proportions
are termed Equivalents.
    Now a voltaic battery, which consists usually of alterna-
tions of two' metals, and a hquid capable of acting chemicaUy
upon  one of them,  has, as we have  seen,  the power of pro-
ducing chemical action in a hquid connected with it by metals
upon which this hquid is incapable of acting:  in such case the
constituents of the hquid AviU be eliminated at the surfaces of
the immersed metals, and at a distance one from the other.
For example, if the  two platinum terminals of a \-oltaic
battery be immersed in water, oxygen wiU be evolved at one
and hydrogen at the other  terminal, exactly in the propor-
tions  in  which they form water; whUe, to  the most minute
examination, no  action is perceptible in  the stratum of
hquid.  It was known before Faraday's time that, whUe this
chemical action was going on in the subjected liquid, a chemi-
cal action  was going on in the ceUs of the voltaic battery;
but it was scarcely if at all known that the amount of chemi-
cal action in the one bore a constant relation to the amount
of action in the other.   Faraday proved that it bore a direct
equivalent  relation:  that is,  supposing the  battery to  be
formed of zinc, platinum, and  water, the amount of oxygen
which  united with the  zinc in each cell of  the battery was
exactly equal to the amount evolved at the one platinum ter-
minal, whUe the hydrogen evolved from each platinum plate
of the battery was  equal  to the hydrogen evolved from the
other platinum terminal.
    Supposing the battery to be  charged  with hydrochloric
ftcid, instead of water, whUe the terminals are separated by
water, then for every 36 parts  by weight of chlorine which 
CHEMICAL AFFINITY.
159
united with each plate of zinc, eight parts of  oxygen  would
be evolved from one of  the platinum terminals :  that  is, the
weights would be precisely in the same relation which Dalton
proved to exist in their  chemical combining weights.   This
may be extended to aU hquids capable  of being  decomposed
by the voltaic force, thence caUed Electrolytes : and as no vol-
taic effect is produced by liquids incapable of being thus de-
composed, it foUows that voltaic action is chemical action tak-
ing place at a distance, or  transferred through  a chain of
media, and that the chemical equivalent numbers are the ex-
ponents of the amount of  voltaic  action for corresponding
chemical substances.
   As heat, light, magnetism, or motion, can be produced by
the requisite  application of the electric current, and as  this is
definitely produced by chemical  action,  we  get these  forces
very definitely, though not immediately, produced by chemi-
cal action.  Let us,  hoAvever, here enquire, as  we have al-
ready done Avith respect to the other forces,  how far other
forces may directly emanate from chemical affinity.
   Heat is an immediate product  of  chemical  affinity.  I
know of no exception to the general proposition that aU bod-
ies  in chemically combining produce heat;  i.  e. if  solu-
tion be not considered as  chemical  action, and even in  that
case, when cold results,  it is from a  change of consistence, as
from  the sohd to the hquid state, and not  from chemical
action.
   We shaU  find that the same vieAV of  the expenditure of
force which we have considered in treating  of latent heat
holds good as to the expenditure of  chemical force when re-
garded with  reference to the amount of heat or repulsive
force which it engenders, the chemical force being here ex-
hausted by chemical expansion—that is, by heat.  Thus, in
the chemical action of the  ordinary combustion of coal and
oxygen, the expenditure of  fuel wUl be in proportion to the
expansibility of the substances heated;  water passing freely 
160        CORRELATION OF PHYSICAL FORCES.
into the steam wiU consume more fuel tlan if it be confined
and kept at a temperature above its boUing point.
   Why chemical action produces heat, or what is the action
of the  molecules  of matter when chemically  uniting, is a
question upon which many theories have been  proposed and
which may possibly be  never more  than approximately  re-
solved.
   Some authors explain it by the  condensation which takes
place ;  but this will not account for the many instances where,
from the hberation of gases, a great  increase of volume  en-
sues upon chemical combustion, as in the familiar instance
of the explosion of gunpowder:  others explain it as resulting
from the union of atmospheres of positive and negative elec-
tricity which are assumed to surround the atoms of bodies ;
but this involves hypothesis upon hypothesis.  Dr. Wood has
lately thrown out a view of the heat of chemical action which
is more in accordance with a  dynamic theory  of  heat, and
as such demands some notice.   Starting with his proposition,
AArhich I have previously mentioned, '  that the nearer the par-
ticles of bodies are to each other the less they require  to
move to produce a given motion in the particles of  another
body,' his argument, if I rightly understand it, assumes some-
thing of this form.
   In the mechanical approximation of  the particles of a
homogeneous body heat results ; the particles a a of the body
A would, by their  approximation, produce expansion in  the
neighbouring body B, the more so in  proportion as they them-
selves were previously nearer to each other.   In chemicaUy
combining, a a the particles of A are brought into  very close
proximity with b b the particles of B ; heat should therefore
result, and the greater because  the proximity may  fairly be
assumed to be greater in the case of chemical combination
than in  that of mechanical compression.   In cases, then,
where  there is no  absolute diminution  of bulk ensuing  on
chemical combination, if the greater  proximity of  the com- 
CHEMICAL AFFINITY.
161
bining particles be such that the correlative expansion  ou«ht
to be greater (if there were no  chemical combination)  than
that occupied by the total volume of the new compound, an
extra expanding  power  is evolved, and heat or  expansion
ought to be produced in surrounding bodies.   In other words,
if a a could be brought  by physical attraction as  near each
other as they are by chemical attraction brought near to b 6,
they Avould, from their increased proximity, produce an ex-
pansive poAver ultra the volume occupied by the actual chem-
ical compound A  and B.   The  question, however, immedi-
ately occurs, why should the volume of the compound be lim-
ited and not occupy the fuU space equivalent to the expanding
power induced by  the contraction  or  approximation of the
particles.   As the distance of the particles is the resultant
of the  contending contracting and  expanding powers,  this
result ought to express itself in terms of the actual volume
produced by the combination, which it certainly does not.
    Though I see  some difficulties in Dr. Wood's theory, and
perhaps have not rightly conceived it, his views  have to my
mind great interest, his mode of regarding natural phenomena
being analogous to that wliich I have in this  Essay, and for
many years, advocated, viz. to divest physical science  as
much as possible of hypothetic  fluids, ethers, latent  entities,
occult qualities, &c.  My own notion of the heat produced
by chemical combination, though I scarcely dare venture  an
opinion upon a subject so controverted,  is, that it is analogous
to the heat of friction, that the particles of matter in  close
approximation and rapid motion inter se evolve heat as a con-
tinuation of the motion interrupted by the friction or intesti-
nal motion of  the  particles: heat would thus be  produced,
whether the resulting compound were of greater  or less  bulk
than the sum of the components, though of course  when the
compound is  of greater bulk less heat would be apparent in
neighbouring bodies, the expansion taking place in one of the
substances  themselves—I say in one of them, for it is stated 
162        CORRELATION  OF PHYSICAL FORCES.
in books of authority that there is no instance of two or mora
sohds or liquids, or a solid and a hquid, combining and pro-
ducing  a compound which  is  entirely gaseous  at ordinary
temperatures and pressures.  The substance gun-cotton, how-
ever, discovered by Dr. Schoenbein, very nearly realises this
proposition.
   Dr. Andrews has arrived at the  conclusion, after  careful
experiment, that in chemical  combinations  where acids and
alkalies or analogous substances are employed, the amount of
heat produced is determined by the basic ingredient, and his
experiments have received general assent; although it should
be stated that M. Hess arrived at contrary results, the  acid
constituent according to his experiments furnishing the meas-
ure of the heat developed.
   Light is directly produced by chemical action, as in the flash
of gunpowder, the burning of phosphorus in oxygen gas, and aU
rapid combustions : indeed, wherever intense heat is developed,
hght  accompanies it.  In many cases of slow combustion,
such as the phenomena of phosphorescence, the hght is apparent-
ly much more intense than the heat;  the former being obvious,
the latter so difficult of detection that for a long time it was
a question whether any heat was ehminated ; and I am  not
aware that at the present day, any thermic effects from  cer-
tain modes of  phosphorescence, such as those of phospho-
rescent wood, putrescent fish, &c, have been detected.
   Chemical  action produces magnetism whenever it is thrown
into a definite direction, as in the phenomenon of electrolysis.
I may adduce the gas voltaic battery, as presenting a simple
instance of the  direct production of magnetism by chemical
synthesis.  Oxygen and hydrogen in that combination chemi-
caUy unite ; but instead of combining by intimate molecular
admixture, as in the ordinary cases, they act upon water, i. e.
combined oxygen and hydrogen,  placed between them  so as
to produce a line of chemical action; and a magnet adjacent
to this hne of  action is  deflected, and places  itself at right 
CHEMICAL AFFINITY
163
 angles to it.  What a  chain  of molecules does here, there
 can be no doubt all the molecules entering into  combination
 would produce in ordinary chemical actions ;  but in  such
 case-, the direction of the lines of combination being  irregu-
 lar and confused, there is no general resultant by wliich the
 magnet can be affected.
    What the  exact nature of the transference of chemical
 power across an electrolyte is, we at present know not,  nor
 can we form any more  definite idea of it than that given by
 the  theory of Grotthus.  We  have  no knowledge as  to the
 exact  nature of my  mode of chemical  action,  and, for the
 present must leave it as an obscure action of force, of which
 future researches may simplify our apprehension.
    We have seen that an equivalent or proportionate electri-
 cal effect is  produced by a given amount  of chemical action ;
 if Ave, in turn,  produce  heat and magnetism and  motion by
 the electricity resulting  from chemical action, we shaU be able
 to measure  these forces far more accurately than  when they
 are directly produced, and thus to deduce their equivalent re-
 lation to the initial chemical action.   Thus M. Favre, after
 ascertaining the quantity of heat produced by the  oxidation
 of a quantity of zinc, and finding, as  have others, that the
 heat is the same Avhen evolved from  a voltaic battery by the
 same consumption of zinc forming its positive element,  makes
 the following experiment.
   A voltaic battery and electro-magnet are immersed in cal-
 orimeters, and the heat produced  when the connection with
 the magnet is effected is noted.
   The  electro-magnet is then made to raise a Aveight, and
 thus perform mechanical work,  and the heat produced is
 igain noted.  It is  found in the latter case that less heat is
evoh'ed than in  the former, a  certain quantity of heat has
therefore been replaced by the mechanical work ; and by esti-
mating tho  amount of  heat subtracted, and the  amount of
work produced, he deduces the relative equivalent of work to 
 164        CORRELATION OF  PHYSICAL  FORCES.

 heat.  These experiments give a production of mechanical
 work by chemical action, not, it is true, a direct production.
 but, as the heat and work are in inverse ratios, and each has
 its source in chemical action, they prove that they are definite
 for a definite amount of chemical action, and as each is pro-
 duced respectively by electricity and magnetism, these forces
 must also bear a definite relation to the initial chemical force.
    The doctrine of definite  combining proportions, which so
 beautifuUy serves  to relate chemistry to voltaic electricity,
 led to the atomic theory, wliich, though adopted in its univer-
 sality by a large majority of chemists, presents great difficul-
 ties when extended to aU chemical combinations.
    The equivalent ratios in which  a great number  of sub-
 stances chemicaUy combine, hold  good in so many instances,
 that the atomic doctrine is beheved by many to be universally
 applicable, and called a law; and yet, when foUowed in the
 combinations of substances whose natural chemical attractions
 are very feeble, the relation  fades away, and is sought to  be
recovered by applying a separate  and arbitrary multipher to
the different constituents.
    Thus, when it was found that a vast number of substances
 combined  in definite  volumes and weights, and in definite vol-
 umes and  weights only, it  was argued that their ultimate
molecules  or atoms  had a definite size, as  otherwise there
was no apparent reason why this equivalent ratio should hold
good: why, for instance, water should only be formed of two
volumes or one unit  by weight of hydrogen, and of one vol-
ume or eight units by weight of oxygen ; why, unless there
were some ultimate limits to the divisibility of its molecules,
should not water, or a fluid substance approximating to water
in character, be formed by a half, a third, or a tenth  part  of
hydrogen, with eight parts of  oxygen ?
   It Avas  perfectly  consistent with  the  atomic  view that a
 substance  might be formed with one part combined with eight
 parts, or with sixteen, or with tAventy-four, for in such a sub- 
CHEMICAL AFFINITY.
165
stance there would be no subdivision of the (supposed indivi-
sible) molecule ;  and this held  good with many compounds •
thus fourteen parts by weight, say grains of nitrogen, wiU
combine respectively with eight, sixteen, twenty-four, thirty-
two, and forty parts by weight, or grains, of oxygen.
    So, again, twenty-seven  grains of iron wUl  combine with
eight grains of  oxygen or with  twenty-four grains, i. e. three
proportionals of oxygen.  No compound is known in which
twenty-seven grains of iron wiU combine with  two propor-
tionals or sixteen grains of oxygen ; but this does not  much
affect the theory, as such a compound may be yet discovered,
or there may be reasons at present unknown Avhy it cannot be
formed.
    But now comes a difficulty : twenty-seven parts by weight
of iron will combine with twelve parts by Aveight of oxygen,
and twenty-seven parts  of iron AviU  also combine wit" ten
and two-third parts of oxygen.  Thus if we  retain the unit
of iron we must subdivide the unit of oxygen, or if we retain
the unit of oxygen we must subdivide the unit of iron, or Ave
must subdiAride both by a different  divisor.  What then be-
comes of the notion of an atom or  molecule  physically indi-
visible ?
    If iron were  the only substance to which this  difficulty
applied, it might be viewed as an unexplained  exception, or
as a mixture  of two oxide3;  or recourse might be had to a
more minute subdivision  to form the  units or equivalents of
other substances ; but numerous other substances faU under
a similar category ; and in organic combinations, to preserve
the atomic nomenclature we must apply a separate  multipher
or divisor to far the greater number of the elementary con-
stituents, i. e. we must divide that which is, ex hypothesis indi-
visible.
    Thus,  to take a more complex substance than any formed
bv the combination of iron and oxygen, let us select the  sub-
stance  albumen,  composed  of  carbon, hydrogen, nitrogen. 
166        CORRELATION OF  PHYSICAL  FORCES.
oxygen, phosphorus, and sulphur.   In this case Ave must ei-
ther divide the atoms of phosphorus and  sulphur so as to re-
duce them to small fractions, or multiply the atoms of the
other  substances  by extravagant numbers ; thus to preserve
the unit of one of the constituents of this substance, chemists
say it is composed of 400 atoms of carbon, 310 of  hydrogen,
120 of oxygen, 50 of nitrogen, 2 of sulphur, and  1 of phos-
phorus.   This is a somewhat extreme case, but similar diffi-
culties wUl be found in different degrees to prevail  among or-
ganic  compounds ; in very many no constituent can be taken
as a unit to which simple multiples of any of the  others wiU
give their  relative  proportions.  By  the  mode  of notation
adopted,  if any conceivable  substance be selected, it could,
Avhatever be  the  proportions of it3 constituents,  be termed
atomic.   A solution of an ounce of sugar in a pound of wa-
ter, in a pound  and a half, in a pound  and a quarter, in a
pound and a  tenth, might be expressed in an atomic form, if
we select arbitrarily a multiplier or divisor.
   It is true  that in the case of solution, different proportions
can be united up  to the point of saturation without any dif-
ference in the character of the  compound, though  the same
may be predicated to some extent of an acid and  an alkali;
but even where the  steps are sudden, and compounds  only
exist with definite proportions, they cannot, in a multitude of
cases, be reconcUed with the  true idea of an atomic combina-
tion, i. e. one to one, one to two, &c.
   Although, therefore, nature  presents us with facts which
show that there is some restrictive laAV of combination which
in numerous  cases limits the ratios in Avhich substances wiU
combine, nay, further, shows  many instances of a proportion
between the combining weights of one compound  and those
of another; although she shows also a remarkable  simplicity
in the combining volumes of  numerous gases, she  also gives
numerous cases to which the  doctrine of atomic combinations
cannot fairly be applied. 
CHEMICAL AFFLNrTV.
167
    That there must be something in the constitution of mat-
ter, or in the  forces which act on it, to account for  the per
saltum manner in which chemical  combinations take place, is
inevitable ; but the idea of atoms does not seem satisfactorUy
to account for it.
    By  selecting a  separate multipher or divisor,  chemists
may  denote  every combination in terms derived  from the
atomic  theory ; but they have passed from the original law,
Avhich contemplated only definite  multiples, and the very hy-
pothetic expressions of atoms, which the  apparently simple
relations of combining weights first  led them to adopt, they
are obliged to vary and  to contradict in terms, by dividing
that which their hypothesis and the expression of it assumed
to be  indivisible.
    WhUe, therefore, I fully recognise a great  natural truth
in the definite ratios presented by a vast number of chemical
combinations, and in the per saltum steps in which nearly aU
take place, I cannot accept as an argument  in favour of an
atomic theory, those combinations  which are made to support
it by  the application of an arbitrary notation.
    A similar straining of theory seems graduaUy  obtaining
in regard to the doctrine of compound radicals.   The discov-
ery of cyanogen by Gay-Lussac  was  probably the first in-
ducement  to  the  doctrine of compound radicals; a doctrine
Avhich is now generally,  perhaps  too  generaUy, received in
organic  chemistry.   As, in the case of cyanogen, a body ob-
viously compound  discharged in almost all its  reactions the
functions of an element, so in many other cases it was found
that compound bodies in  Avhich a  great number of elements
existed, might be regarded as binary combinations, by con-
sidering certain groups of these elements as a compound rad-
ical ;  that is, as a simple body when treated of in relation to
the other complex subslauces  of which it forms  part, and
only as  non-elementary when  referred to its  internal consti-
tution. 
168        CORRELATION OF  PHYSICAL  FORCES.

    Undoubtedly, by approximating in theory the reactions of
inorganic and of  organic  chemistry,  by keeping the mind
within the hmits of a beaten path, instead of aUowing it to
wander through  a maze of isolated facts,  the doctrine of com-
pound radicals has been of service ; but, on the other hand,
the indefinite variety of changes wliich may be rung upon the
composition of an organic substance, by different associations
of its primary elements, makes the binary constituents vary
as the minds of the authors who  treat of them, and makes
their grouping depend  entirely upon the strength of the anal-
ogies  presented to  each individual mind.  From this cause,
and from the extreme license which has been taken in theo-
retic groupings deduced from this doctrine, a serious question
arises  whether it  may not ultimately, unless carefully  re-
stricted, produce confusion  rather than simplicity, and be to
the student an embarrassment rather than an assistance.
* 
       VIII.—OTHEli MODES  OF FOECE.

  C~"ATALYSIS, or the chemical  action  induced by the
      mere presence of a foreign body, embraces a class of
facts which must considerably modify many of our notions of
chemical action: thus oxygen and hydrogen, Avhen mixed in
a gaseous state, wUl remain unaltered for  an indefinite pe-
riod ; but the introduction to them of a shp of clean plati-
num will cause more or less rapid combination, without being
in itself in any respect altered.   On the other hand, oxygen-
ated water, which is a compound of one equivalent of hydro-
gen plus tAvo  of oxygen, wUl, Avhen under a certain tempera-
ture, remain  perfectly stable ; but touch it with  platinum in
a state of minute division,  and it is instantly decomposed,
one equivalent of oxygen being set  free.  Here, again, the
platinum is unaltered, and thus we have synthesis and analy-
sis effected apparently by the mere contact of a foreign body.
It is not improbable that the increased electrolytic power of
water by the addition of some  acids, such  as the sulphuric
and phosphoric, where the acids themselves are  not decom-
posed, depends upon a catalytic  effect of these acids ; but we
know too httle of the nature and rationale of catalysis to ex-
press  any confident opinion  on its modes of action, and pos-
sibly we  may comprehend very different molecular actions
under one and the  same  name.  In no case does  catalysis
yield us new  power or force : it only determines or facilitates
             8 
 170        CORRELATION OF  PHYSICAL FORCES.

 the action of chemical force, and, therefore, is no creation of
 force by contact.
    The  force so  deAeloped by catalysis may be converted
 into a voltaic form thus:  in a single pair of the gas  battery
 above aUuded to,  one portion of a strip  of platinum is im-
 mersed in  a tube  of oxygen, the other in one of hydrogen,
 both the gases and the extremities of the platinum being con-
 nected by water or other electrolyte ;  a voltaic combination
 is thus formed, and electricity,  heat,  light, magnetism, and
 motion, produced at the wiU of the experimenter.
    In this combination we  have a striking instance  of cor
 relative expansions and conti actions, analogous, though in a
 much more refined form, to the expansions  and contractions
 by heat and cold detaUed in the early part of this essay, and
 illustrated by the alternations of  two bladders  partiaUy filled
 with  air: thus, as by the effect  of chemical combination in
 each  pair of tubes of the  gas  battery the gases oxygen and
hydrogen lose their gaseous character and shrink into Avater,
 so at the platinum terminals of the battery, when immersed
in water, water is  decomposed, and expands into oxygen and
hydrogen gases.   The correlate  of the  force which  changes
gas into  liquid at one point of space, changes  hquid into gas
at another, and the exact A-olume which disappears in the
 one place reappears in the other ; so that it  Avould appear to
 an  inexperienced  eye as  though the gases passed  through
solid wires.
    Gravitation, inertia, and aggregation, were but cursorily
 alluded to in my original lectures ; their relation to the other
modes of force seemed to  be less definitely traceable ; but the
phenomenal effects of gravitation  and  inertia, being motion
 and resistance to  motion, in  considering motion  I  have in
 some degree included their relations to the other forces.
    To my  mind gravitation would only produce  other force
 Avhen the motion  caused by it ceases.   Thus, if we  suppose
 a meteor to be a mass rotating in an orbit  round the earth, 
OTHER MODES  OF FORCE.
171
 and with no resisting medium, then, as long as that rotation
 continues,  the  motion of the  meteoric mass  itself would be
 the  exponent of the force impelling it;  if there be a resist-
 ing medium, part of this motion would be arrested and taken
 up by the medium, either as motion, heat, electricity, or some
 other mode of force ; if the meteor approach the earth suffi-
 ciently to  fall  upon it, the  perceptible motion of the  meteor
 is stopped, but  is  taken up  by the  earth  which  vibrates
 through its mass ; part also reappears as heat in both earth
 and meteor, and  part in the change  in  the  earth's position
 consequent on its increase of gravity, and so on.  Gravita-
 tion is but the  subjective idea, and its relation to other modes
 of force seems to me to be identical with that of pressure or
 motion.  Thus, when arrested motion produces heat, it mat-
 ters not whether the motion  has been produced by a faUing
 body, i.  e. by  gravitation, or a body projected by an explo-
 sive compound, &c.; the heat AArill be the same, provided the
 mass and  A'elocity at the time of arrest be the same.   In no
 other sense can I  conceive a relation between gravitation  and
 the other forces, and, Avith all  diffidence,  I cannot agree with
 those who  seek a more mysterious link.
    Mosotti has mathematicaUy treated  of  the identity  of
 gravitation Avith cohesive attraction, and Pliicker has recently
 succeeded  in showing that crystaUine bodies  are definitely af-
 fected by magnetism, and take a position in relation to  the
 lines of magnetic  force dependent upon their optical axis or
 axis of symmetry.
    What is termed  the optic axis is a fixed direction through
 crystals, in Avhich they do not doubly refract light, and which
 direction, in those crystals Avhich have one axis of figure, or
 a line around which the  figure is symmetrical, is parallel to
 the axis of symmetry.  When submitted to  magnetic influ-
 ence such crystals take up a position, so that their optic axis
points diamagnetically or  transversely to the lines of magnetic
force;  and when, as is the case  in some crystals, there is 
172        CORRELATION OF PHYSICAL FORCES.
more  than one optic axis, the resultant of these axes  points
diamagnetically.  The mineral cyanite is influenced by mag-
netism in so marked a manner that  when suspended it will
arrange itself definitely with reference to the direction of ter-
restrial magnetism, and  may, according to Plucker, be used
as a compass-needle.
    There is scarcely any doubt that the  force which is con-
cerned in aggregation is the same which  gives to matter its
crystalhne form; indeed, a vast number of inorganic bodies,
if not all, which appear  amorphous are, wdien closely exam-
ined, found to be crystalhne in their structure : we thus get a
reciprocity of action  between the force which unites the mole-
cules of matter and the magnetic force,  and through the me-
dium of the latter the  correlation of the  attraction of  aggre-
gation with the other modes of force may be established.
    I believe that the same principles  and mode of  reasoning
as have  been adopted in this  essay might be applied  to tho
organic as Avell as the inorganic world; and that muscular
force,  animal and vegetable heat, &c,  might,  and at some
time avUI, be shown to have similar definite correlations ; but 1
have purposely avoided this subject, as pertaining to a depart-
ment  of science to which I haA'e not devoted my attention.
I ought,  however, while aUuding to this subject,  shortly to
mention some experiments of Professor Matteucci, communi-
cated  to the Royal Society in the year 1850, by which it ap-
pears  that whatever  mode of force it be which is propagated
along the nervous filaments, this mode of force is definitely
affected by  currents  of electricity.   His experiments shoAV
that when a current of positive electricity traverses a portion
of the muscle of a hving animal in the same direction as that
in Avhich the nerves ramify—i. e. a direction from  the  brain
to the extremities—a muscular contraction is produced  in the
limb experimented on, showing that the nerve of motion is
affected;  while, if the current, as it is termed, be made to
traverse the muscle in the  reverse  direction, or toAvards the 
OTHER MODES OF FORCE.
173
nervous centres, the animal utters cries, and exhibits  all the
indications of suffering  pain, scarcely any  muscular move
ment being produced;  showing that in this case the nerves
of sensation are affected by the electric current, and therefore
that some definite polar  condition  exists, or is induced, in the
nerves, to  which  electricity is correlated, and that probably
this polar condition  constitutes nerA'ous agency.  There are
other analogies given in the papers of M. Matteucci, and de-
rived from the action of the electrical organs of fishes, which
tend to corroborate and devclope the  same vieAV.
    By an  application  of the  doctrine  of the  Correlation of
Forces,  Dr. Carpenter  has shoAvn Iioav  a  difficulty  arising
from the ordinary notions of the developement of an organised
being from its germ-ceU  may be  lessened.   It  has  been
thought by many physiologists that the  nisus formativus, or
organising force of an  animal or A-egetable structure, hes dor-
mant in the primordial germ-cell.   ' So that the organising
force required to build up an oak  or a palm, an elephant or a
Avhale,  is concentrated in a minute  particle only discernible
by microscopic aid.'
    Certain other views of nearly equal difficulty have been
propounded.  Dr. Carpenter suggests the probability of ex-
traneous forces, as heat, hght, and chemical affinity, contin-
uously operating upon the material germ ; so that all that ia
required in this is a structure capable of receiving, directing,
and converting these forces  into those which tend to the assim-
Uation of extraneous matter and the definite developement of
the particular  structure.  In proof of  this position he shows
how dependent the process of germ developement is upon the
presence and agency of external forces, particularly heat and
light, and how it is regulated by the measure of these forces
supplied to it.
    It certainly is  far less difficult so to conceive the supply
of force  yielded to organised beings in their gradual process
of groAVth, than to suppose  a store of dormant or latent force
pent up in a microscopic monad. 
174       CORRELATION OF PHYSICAL FORCES.

    As by the artificial structure of a A-oltaic battery, chemi-
cal actions may be made to cooperate in a definite direction,
so, by the organism of a vegetable or animal, the mode of
motion which constitutes heat, light, &c, may, without extra-
vagance, be conceived  to be  appropriated and changed into
the forces which induce the absorption, and assimUation of
nutriment, and  into nervous  agency and muscular  poAver.
Indications of similar thoughts maybe detected in the writings
of Liebig.
    Some  difficulty in studying the correlations of vital with
inorganic physical forces arises from  the effects of sensation
and consciousness, presenting a  similar confusion to that
alluded to, when, in  treating of heat, I ventured to suggest,
that observers are too apt to confound the sensations with the
phenomena.  Thus, to  apply some of the  considerations  on
force, given in the introductory portion of this essay, to cases
where  vitality or consciousness interA-encs.   When a Aveight
is  raised by the hand, there  should, according to the doctrine
of non-creation of force, have been somewhere an expenditure
equivalent to the amount of gravitation overcome in raising
the weight.  That there is expenditure we can prove, though
in  the present state of science we  cannot measure it.  Thus,
prolong the effort, raise weights for an hour or two, the vital
powers  sink, food, i.  e. fresh  chemical force, is required to
supply the  exhaustion.   If this  supply is withheld and the
exertion is continued, Ave see the consumption of force in
the supervening  weakness and emaciation of the body.
    The consciousness of effort, which has  formed a topic of
argument  by some writers when treating of force, and is by
them  believed to be that wliich  has originated the  idea of
force, may by the physical  student be regarded as feehng is *
in  the phenomena of  heat  and cold,  viz. a  sensation of the
struggle of opposing molecular motions  in  overcoming the
resistance of the masses to be moved.  When we say  we feel
hot, we feel cold, we feel that we are  exerting ourselves, our 
                 OTHER  MODES OF FORCE.             175

expressions are intelligible to beings Avho are capable of ex-
periencing  similar  sensations; but  the  physical  changes
accompanying  these sensations are not  thereby explained.
Without pretending to knoAv what probably we shaU never
knoAA*. the actual modus agendi of the brain, nerves, muscles,
&c, wre may study vital as we do inorganic phenomena, both by
observation and experiment.   Thus, Sir Benjamin Brodie has
examined the effect of respiration on animal heat by inducing
artificial respiration after the  spinal cord has been severed;
in which  case  he finds the  animal heat declines, notAvith-
standing the continuance of the chemical action of respiration,
carbonic acid being formed as usual;  but he also finds that
under such circumstances  the struggles or muscular actions
of the  animal are very great,  and sufficient probably to ac-
count for  the  force eliminated by  the chemical action in
digestion  and respiration;  and Liebig,  by measuring the
amount of chemical action  in  digestion and respiration, and
comparing it  with the labour performed, has to some extent
established their equivalent relations.
    Mr. Hehnholtz has found that the chemical changes Avhich
take place in muscles are  greater when these are made to
undergo contractions than when they are in repose ; and that,
as Avould be expected,  the consumption of the matter of the
muscles, or, in other terms, the  waste  or excrementitious
matter throAvn off, is greater in the former than in the latter
case.
   M. Matteucci has ascertained that the muscles of recently
killed frogs absorb oxygen and exhale carbonic acid, and that
when they are thrown into a  state  of contraction,  and still
more Avhen they perform mechanical Avork, the  absorption is
increased; and he even calculates the equivalents of work so
performed.
   M. Beclard finds that the  quantity of heat  produced by
voluntary muscular contraction in man is greater AArhen that
contraction is Avhat he  terms  static, that is, when it produces 
176        CORRELATION OF PHYSICAL FORCES.

no external work,  but is effort  alone, than Avhen that effort
and contraction are employed dynamically, so as to raise a
weight or produce mechanical Avork.
    Thus, though we  may see no  present promise of being
able to resolve sensations into their ultimate elements, or to
trace, physically, the link which unites volition with exertion
or  effort, in terms  of our own consciousness of it, Ave may
hope to approximate the solution of these deeply interesting
questions.
    In the same individual the chemical and physical state of
the secretions in the warm may be compared with those in
the cold parts of the body.   The changes in digestion and
respiration, when the body is in a state of rest, may be com-
pared with those which obtain when it is in a state of activity.
The relations with external matter, maintaining, by the con-
stant play of natural forces, the vital nucleus, or the organi-
sation by means  of  Avhich matter  and force  receive, for a
definite period, a definite incorporation and direction, may be
ascertained, while the more  minute structural changes are
revealed to  us by the  ever-improving powers of the micro-
scope ; and thus step by step  we may learn that which it is
given to us to learn,  boundless in its range and infinite in its
progress, and therefore never giving a response to the ultimate
—Why?
    As the first glimpse of a new star  is caught by the eye of
the astronomer while directing his vision to a different point
of space, and disappears Avhen steadfastly gazed at, only to
have its position and figure ultimately ascertained by the em-
ployment of more penetrative powers, so the first scintUlations
of new  natural phenomena  frequently present  themselves to
the eye of the observer,  dimly seen  when viewed askance,
and disappearing if  directly looked  for.  When  new powers
of thought and experiment have developed and corrected the
first notions, and given a character to the new image, proba-
bly very different from the first impression, fresh objects are 
OTHER MODES OF FORCE.
177
again glanced  at  in  the  margin of the new field of vision,
which  in  their turn  have to  be  verified, and again lead to
new extensions ; thus the effort to estabUsh one observation
leads to the  imperfect perception of new and wider fields of
research;  and, instead of  approaching finality, the  more
we discover, the more infinite appears the range of the undi>
covered 1 
     IX.—CONCLUDING  REMARKS.

I HAVE now gone  through the affections of matter  for
    which distinct names have been given in  our received
nomenclature : that other forces may be detected, differing as
much from  them  as they differ from each other, is highly
probable,  and that when  discovered, and their modes of
action fuUy traced out, they will be found to be related inter
se, and  to these forces as these are to each other, I beheve
to be as far certain as certainty can be predicted of any future
event.
   It may in many cases be a difficult question to  determine
what  constitutes  a distinct affection of matter or  mode of
force.  It is highly probable that different hnes of demarca
tion  would have  been  drawn between the  forces  already
known,  had they been  discovered  in a different manner, or
first observed at different points of the chain which connects
them.  Thus, radiant heat and hght are mainly distinguished
by the manner in which  they affect  our  senses:  were they
vieAved according to the  way in which they affect inorganic
matter,  very different  notions would possibly be entertained
of their  character  and relation.    Electricity, again,  was
named from the substance in wdiich, and magnetism from the
district Avhere, it first  happened to be observed, and a chain
of intermediate phenomena have so connected electricity Avith
galvanism that they are  now regarded  as the same force, 
CONCLUDING REMARKS.
179
differing only in the degree  of its  intensity  and  quantity.
though for a long time they were regarded as distinct.
   The phenomenon of attraction and repulsion by amber,
Avhich originated the term electricity, is as unhke that of the
decomposition of water by the voltaic pile, as any two natural
phenomena can well  be.   It is only because the historical
sequence  of scientific discoveries has  associated them  by a
number of intermediate hnks, that they are classed under the
same category.   What  is  caUed voltaic  electricity might
equally, perhaps more appropriately, be caUed voltaic chemis-
try.   I mention these facts to show that the distinction in the
name may frequently be much greater than the distinction of
the subject which it represents, and vice versa,  not as at aU
objecting  to the received nomenclature on these  points;  nor
do I say it would be advisable to depart from it:  were Ave to
do  so,  inevitable  confusion  would  result, and objections
equally forcible might be found to apply to our new termi-
nology.
    Words, AA-hen estabhshed  to a  certain point, become a
part of the social mind; its  powers and very existence de-
pend upon  the adoption of conventional symbols; and were
these suddenly departed from, or varied, according to indivi-
dual apprehensions, the acquisition and transmission of knowl-
edge would cease.   Undoubtedly, neology is more permissi-
ble in physical science than in any other branch of know ledge,
because it is more progressive; new facts or new relations
require new names, but even here it should be used with great
caution.
                  Si forte necesse est
       Indiciis monstrare recentibus abdita rerum,
       Fingere cinctutis non exaudita Cethegis,
       Continget; dabiturquo licentia, sumpta pudenter.

   Even should the mind ever be led  to dismiss the idea of
various forces, and regard them as the exertion of one force, 
ISO        CORRELATION  OF PHYSICAL FORCES.
 or resolve them definitely into motion; stUl we could never
 avoid the use of different conventional terms for the different
 modes of action of this one pervading force.
    Reviewing the  series  of relations between the A'arious
 forces  which we have been considering, it would appear that
 in many case3 where one of these is excited or exists, aU the
 others  are also set in action :  thus, when a substance, such as
 sulphuret of antimony, is electrified, at the instant of electri-
 sation  it becomes magnetic in directions at right angles to the
 hnes of electric  force ; at the same time it becomes heated to
 an  extent greater or less  according to  the intensity of the
 electric force.  Bf this intensity be exalted to a certain  point
 the sulphuret becomes luminous, or light is produced:  it ex-
pands, consequently motion is  produced; and it is decomposed,
 therefore chemical action is  produced.   If Ave take anothei
 substance, say a metal, all these forces except the last are
 developed;  and although  we  can  scarcely apply the  term
mechanical action to a substance  hitherto undecomposed, and
which,  under  the circumstances  we  are  considering,  enters
into no  new combination,  yet it undergoes that  species of
polarisation  which, as far  as we can judge, is the first step
towards  chemical  action,  and  which, if the substance  were
decomposable, would resolve it into  its elements.   Perhaps,
indeed, some hitherto undiscovered chemical action is pro-
duced  in substances which we regard as undecomposable  :
there  are experiments to  show that metals which have been
electrised are permanently changed in their molecular consti-
tution.   Oxygen, we have seen, is changed by the electric
spark  into ozone, and phosphorus into ^Uotropic phosphorus,
both Avhich changes were for  a long  time  unknown to those
familiar with electrical science.
    Thus, with some  substances, when one mode of force is
produced all the  others are  simultaneously developed.  With
other substances, probably with aU matter, some of the other
 forces are developed, whenever one is excited, and all may bo 
CONCLUDING  REMARKS.
181
 so were the matter in a suitable condition for their develope-
 ment, or our means of detecting them sufficiently delicate.
    This simultaneous production of several different forces
 seems at first sight to be irreconcileable with their mutual and
 necessary dependence, and it certainly presents a formidable
 experimental difficulty in the way of estabhshing  their equiv-
alent relations ; but  when examined closely, it is not in fact
 inconsistent with  the views we have been considering, but is
 indeed a strong argument in favour of the  theory which re
 gards them as modes of motion.
    Let us select one  or two  cases in which  this  form of ob
 jection may be prominently put  forward.  A voltaic battery
 decomposing water in a voltameter, whUe the same current
 is employed  at the same time to make an electro-magnet,
 gives nevertheless in the voltameter an equivalent of  gas, or
 decomposes an equivalent of  an  electrolyte for  each equiva-
 lent of  chemical decomposition in the battery ceUs, and wUl
 give the same ratios if the electro-magnet be removed.   Here,
 at first sight, it would appear that the magnetism was an ex-
 tra force  produced, and that thus more than the equivalent
 power was obtained from the  battery.  In answer to this
 objection  it may be  said, that  in  the  circumstances  under
 which  this experiment is ordinarUy performed, several cells
 of the  battery are used, and  so there is a far greater amount
 of force generated in the cells than is indicated by the effect
 in the   voltameter.  If, moreover, the  magnet be not inter-
 posed,  stiU the magnetic  force is equaUy existent throughout
 the whole current; for instance, the wires joining the plates
 will attract iron filings, deflect magnetic needles, &c, and
 produce diamagnetic effects  on surrounding  matter.   By the
 iron core a small  portion of the  force is, indeed, absorbed
 while it is being  made a magnet, but this  ceases to be ab-
 sorbed  when the  magnet is  made ; this has been proved by
 the observation of Mr. Latimer Clarke, Avho has found that
 alonf the  wires of  the electric telegraph  the magnetic needles 
 182        CORRELATION OF  PHYSICAL  FORCES.

 placed at different stations remained fixed after the connection
 with the battery was made, and  whUe  the  electric current
 acted by induction on surrounding conducting matter, separa-
 ted from the wires by their gutta percha coating, so that a
 sort of Leyden phial Avas formed; but as soon as this  induc-
 tion had produced its effect between each station, or, so to
 speak, the  phial  was charged, the needles successively were
 deflected : it is like the case of a puUey and weight, which lat-
 ter exhausts force while it is being raised ; but  when raised,
 the force is free, and may be used  for other purposes.
    If a battery of one ceU, just capable of decomposing water
 and no more, be employed, this wiU cease to decompose while
 making a magnet.  There  must, in every case, be prepon-
 derating chemical affinity in the battery ceUs,  either by the
 nature of its elements or by the reduphcation of series, to
 effect decomposition in the  voltameter; and if the point is
just reached at which this is  effected, and the power is then
 reduced by any  resistance, decomposition  ceases:  were it
 otherwise,  were  the decomposition  in  the  voltameter the
 exponent of the entire force  of the generating ceUs, and these
 could  independently produce  magnetic  force,  this  latter
 force  would  be got  from nothing, and perpetual  motion be
 obtained.
    To take  another and different example: A  piece of zinc
 dissolved in dilute sulphuric acid giA-es somewhat less heat than
 when the zinc has a wire of  platinum attached to it,  and is
 dissolved by the  same  quantity of acid.   The  argument is
 deduced  that, as  there is more electricity in the second than
 in the first case, there  should  be less heat; but as, according
 to our received theories, the heat is a product of the electric
 current, and in consequence of the impurity of zinc electrici-
 ty is generated in the first case molecularly, in what is called
 local  action,  though not  thrown into  a  general direction,
 there should be more of both  heat and electricity in the sec-
 ond than in the first case, as the  heat and electricity due to 
CONCLUDING REMARKS.
183
the voltaic  combination of zinc and  platinum are added to
that excited on the surface of the zinc, and the zinc should be,
as in fact it is, more rapidly dissolved; so that the extra heat
and electricity is  produced by extra  chemical force.   Many
additional cases of a similar description  might be suggested.
But although it is difficult, and perhaps impossible, to restrict
the action of  any one force to the production of one other
force,  and of  one only—yet if the whole of one force, say
chemical  action, be supposed to be employed in producing its
fuU equivalent of another force, say heat, then as this heat is
capable in its  turn of reproducing chemical action, and in the
hmit, a quantity equal or at least only infinitely short  of the
initial  force: if this could at the same time produce indepen-
dently another force, say  magnetism, Ave  could,  by adding
the magnetism to the total heat, get more than the original
chemical  action, and thus  create force  or obtain perpetual
motion.
    The term  Correlation, which I selected as the title  of my
Lectures  in 1843,  strictly interpreted,  means a necessary
mutual or reciprocal dependence of two ideas, inseparable
c\ren in mental conception: thus, the idea of height cannot
exist A\uthout  involving the idea of its correlate, depth; the
idea of parent cannot exist without involving  the  idea of off-
spring.  It has been scarcely,  if at aU, used by writers on
physics, but there are a vast variety of  physical relations to
which, if  it does not in  its strictest original sense  apply,
cannot certainly be  so weU expressed by any other  term.
There  are, for example, many facts, one of which cannot take
place without  involving the other; one  arm of a lever can-
not be depressed without the other being elevated—the finger
cannot press  the  table without the table pressing the finger.
A body cannot be heated  without  another being cooled, or
some other force  being exhausted in an equivalent ratio to
the production of heat;  a body cannot be positively elec-
trified  without some other body being  negatively electri-
fied, &c. 
184       CORRELATION OF PHYSICAL  FORCES.

    The probabUity is, that, if not aU, the greater number of
physical  phenomena  are  correlative,  and that,  without a
duahty of conception, the mind cannot form an idea of them:
thus motion  cannot be perceived or probably imagined with-
out parallax or relative change of position.  The  world was
believed fixed, until by comparison with the celestial bodies,
it  was found  to change its place with  regard to them:  had
there been no perceptible matter external to the world, we
should never have  discovered its motion.  In sailing along a
river, the stationary vessels and objects on  the banks seem
to  move past  the observer : if at last he  arrives at the convic-
tion that he is moving, and not these objects, it is by correct-
ing his senses by reflection derived from a more extensive
previous use of them:  even then he can only form a notion
of the motion of the vessel he is in, by  its change of position
with regard  to the objects it  passes—that is,  provided his
body partakes of the motion of the vessel,  which it only  does
when its  course is perfectly smooth, otherwise the relative
change of position of  the different parts of the body and the
vessel inform him  of its alternating, though  not of its pro-
gressive movement.  So in all physical phenomena, the effecta
produced  by  motion are aU in proportion to the relative mo-
tion : thus, whether the rubber  of an  electrical machine be
stationary, and the cyhnder mobUe, or the  rubber mobUe and
the cylinder stationary, or both mobUe in different directions,
or in the same direction with different degrees of  velocity,
the electrical effects are, cceteris paribus, precisely the same,
provided the relative motion is the same, and so, without ex-
ception, of aU  other phenomena. The  question of whether
there can  be absolute motion, or, indeed, any absolute isolated
force, is purely the metaphysical question of ideahsm or  real-
ism—a question for our purpose of little import;  sufficient
for the purely phyjical inquirer, the maxim ' de non apparently
bus et non existentibus eadem est ratio.'
    The sense  I have  attached to the word correlation, in 
CONCLUDING REMARKS.
185
treating of physical phenomena, wUl, I think, be evident from
the previous  parts  of this  essay, to be that of a necessary
reciprocal production : in other Avords, that any force capable
of producing  another may,  in it3 turn, be produced by it—•
nay, more, can be itself resisted by the force it produces, in
proportion to the energy of such production, as action is ever
accompanied and resisted by reaction : thus, the action  cf an
electro-magnetic  machine  is  reacted  upon by the magneto-
electricity developed by its action.
    To many, however, of the cases we have  been consider-
ing, the term correlation may be  applied  in a more  strict
accordance with its original  sense: thus, Avith regard to the
forces  of  electricity and  magnetism in a dynamic state, we
cannot electrise a substance Avithout magnetising it—Ave  can-
not magnetise it Avithout  electrising it:—each molecule, the
instant it is affected by one of these forces, is  affected by the
other; but, in transverse  directions, the forces are insepara-
ble and mutually dependent—correlative, but not identical.
    The evolution of one force or mode of force into  another
has induced many to regard  all the different natural agencies
as reducible to unity, and as resulting from one force wliich
is the efficient cause of all the others :  thus, one author Avrites
to  prove  that electricity is the  cause of every  change in
matter; another, that chemical action  is the  cause of every-
thing ; another, that heat  is  the  universal cause,  and so on.
If, as I have stated it, the true expression of the fact is, that
each mode of force is capable of producing the others, and
that none of them  can be  produced but by some other  as an
anterior force, then any view which regards either of them as
abstractedly the efficient cause of all  the rest, is erroneous;
the vieAV has,  I believe, arisen from a  confusion between the
abstract  or generalised  meaning of the term cause, and ita
concrete  or special sense ; the Avord itself being indiscrimi-
nately used in both these senses.
    Another confusion of terms has arisen, and has, indeed. 
186        CORRELATION OF PHYSICAL FORCES.
 much embarrassed  me  in  enunciating  the  propositions put
 forth in these pages, on account of the imperfection of scien-
 tific language ; an imperfection in great measure unavoidable,
■ it is true, but not the less embarrassing.   Thus, the  words
 light, heat, electricity, and magnetism, are constantly used in
 two senses—viz. that of the force producing, or the subject-
 ive idea of force or  poAver, and of the effect  produced, or the
 objective  phenomenon.  The  word  motion, indeed, is  only
 applied to the effect, and not to the force, and the term chem-
 ical affinity is generally applied to the force, and not  to the
 effect;  but the  other four  terms are, for want of a distinct
 terminology, applied indiscriminately to both.
    I may have  occasionally used the same Avord at one time
 in a subjective, at  another in  an objective sense;  aU I can
 say  is, that this cannot be avoided Avithout  a neology, Avhich
 I have not the presumption to introduce, or the authority to
 enforce.  Again, the use of the term  forces  in  the  plural
 might be  objected to by those who do not attach to the term
 force the notion of a specific agency, but  of  one universal
 poAver associated with matter, of which its  various  phenom-
 ena are but diversely modified effects.
    Whether the  imponderable agents, vieAved as force, and
 not  as matter, ought to be regarded as distinct forces or aa
 distinct modes of force, is probably not very material,  for, as
 far as I am aware, the same result Avould follow either view ;
 I have therefore used the  terms indiscriminately, as  either
 happened to be the more expressive for the occasion.
    Throughout this essay I have placed motion in the same
 category  as the other affections of matter.   The course of
 reasoning adopted in it,  hoAvever, appears to me to lead inev-
 itably to  the  conclusion that  these affections  of matter are
 themselves modes of motion ;  that, as in the case of friction,
 the  gross or palpable  motion, Avhich is arrested  by the  con-
 tact of  another body, is subchvided into molecular  motions or
 vibrations, which vibrations  are heat  or electricity,  as the 
CONCLUDING REMARKS.
187
case may be ; so the other affections are only matter moved
or  molecularly agitated in certain definite directions.   We
haA-e already considered the  hypothesis that the  passage of
electricity and  magnetism causes vibrations in an ether  per-
meating the  bodies through which the  current is transmitted,
or  the  apphcation of the  same  ethereal hypothesis to these
imponderables  which had previously been apphed to light;
many, in speaking of some of the  effects, admit that electri-
city and magnetism cause or produce by their passage vibra-
tions in the particles  of matter, but  regard the vibrations
produced as an  occasional, though not always a necessary,
effect of the passage of electricity,  or of the increment or
decrement of magnetism.   The view which I have taken is,
that such vibrations, molecular  polarisations, or motions of
some sort from particle to particle, are  themselves electricity
or magnetism ; or, to express  it in the converse, that dynamic
electricity and  magnetism are themselves  motion, and  that
permanent magnetism, and Franklinic electricity, are static
conditions of force bearing a similar relation to motion which
tension  or gravitation do.
    This theory  might  Avell  be  discussed  in  greater detail
than has been used in this work ; but to do this and to anti-
cipate  objections Avould lead  into  specialities foreign to my
present object, in the  course  of this essay my principal  aim
having  been rather to show the relation of forces as evinced
by acknowledged facts, than to enter upon  any detailed ex-
planation of their specific modes of action.
    Probably man will never know the  ultimate structure of
matter  or the  minutiaj of molecular  actions;  indeed  it is
scarcely conceivable that the mind  can ever attain  to  this
knoAvledge; the  monad irresolvable  by a given  microscope
may be resolved by an  increase  in poAver.  Much harm has
already  been done by  attempting hypotheticaUy to  dissect
matter  and  to  discuss the shapes, sizes, and numbers of at-
oms, and their atmospheres of heat, ether, or electricity. 
188        CORRELATION OF PHYSICAL FORCES.
   Whether the regarding electricity, hght, magnetism, &c.,
as simply motions of ordinary matter, be or be not admissi-
ble, certain it is, that aU past theories have resolved, and  aU
existing theories do resolve, the actions of these  forces into
motion.  Whether it be that, on  account of our familiarity
Avith motion, we refer other  affections to it, as to a language
AA-hich is most  easUy construed and  most capable of explain-
ing them ; whether it be that it is in reahty the only mode in
wliich our minds, as contradistinguished from our senses, are
able  to conceive material  agencies; certain it is, that since
the period at which the mystic notions of spiritual or  preter-
natural powers were applied to account for physical phenom-
ena,  all hypotheses  framed to  explain  them  have resolved
them into motion.  Take, for example, the theories of hght
to Avhich I have before aUuded: one of these  supposes hght
to be a highly rare matter, emitted  from—i. e. put in motion
by—luminous  bodies; a second supposes that the matter is
not emitted from luminous  bodies, but  that it is put into a
state of vibration or undulation,  i.  e. motion,  by them; and
thirdly, light may be regarded as an undulation or motion of
ordinary matter, and propagated  by undulation of air, glass,
&c,  as I have before stated.  In aU these hypotheses,  matter
and  motion are the only  conceptions.   Nor,  if we  accept
terms derived from our own sensations, the which  sensations
themselves may be but modes of motion in the nervous fila-
ments, can we find words to describe  phenomena other than
those expressive of matter and motion.  We in vain struggle
to escape  from these ideas; if we ever  do so, our  mental
powers must  undergo a change of wliich at present  we see
no prospect.
   If we  apply to  any other  force the mode of reasoning
which we  have applied to heat, we shaU arrive at the same
conclusion, and see that a given  source of power can, sup-
posing it to be  fully utilised in each case, yield no more  by
employing it as an exciter of one force than of another.  Lei 
CONCLUDING  REMARKS.
189
as take electricity as an example.  Suppose a pound of mer-
cury at 400° be  employed to produce a thermo-electric cur
rent, and  the  latter be in its turn employed to produce me-
chanical force ; if this latter force be greater than that a\ hich
the direct effect of heat would produce, then it could by com-
pression raise the temperature of the mercury itself, or of a
simUar quantity equally heated, to  a higher point than  its
original temperature, the 400° to 401°, for example, which
is obviously impossible; nor, if we  admit  force to be inde-
structible, can it produce less than  400°, or cool the second
body except  by some portion of  it being  converted into
another form or mode of force.
    But as the mechanical effect here is produced through the
medium of electricity, and the mechanical  effect is definite,
so  the  quantity of electricity producing it  must  be definite
also, for unequal quantities of electricity could only produce
an equal mechanical effect by a loss  or gain  of their oavo
force into or out of nothing.   The same reasoning will apply
to the  other  forces, and wUl lead, it appears to me, necessa-
rhy and inevitably to the conclusion, that each force is defi-
nitely and equivalently convertible into  any other, and that
where  experiment does not give the  fuU equivalent, it is be-
cause the  initial force has been dissipated, not lost, by con-
version into other unrecognised forces.  The equivalent is the
Hmit never practicaUy reached.
    The great problem which remains to be solved, in regard
to the correlation of physical forces,  is this  establishment  of
their equivalents of power, or their measurable relation to a
given standard.   The progress made in some of the branches
of this  inquiry has  been already noticed.  Viewed in their
static relations, or in the conditions  requisite for  producing
equilibrium  or quantitative equality of force,  a remarkable
relation betAveen chemical affinity and heat is that discovered
in many simple bodies by Dulong and Petit, and  extended to
compounds by Neumann and AArogadro.  Their  researehea 
190       CORRELATION  OF PHYSICAL FORCK?.

have  shoAvn  that  the  specific  heats  of  certain  substances,,
when multiplied by their chemical equivalents, give a con-
stant quantity as producti—or, in other Avords, that the com*
bining weights of such substances are those weights which
require  equal accessions  or  abstractions  of heat, equally to
raise  or loAver  their temperature.   To put the  proposition
more in accordance with the view we have  taken of the na-
ture of heat: each body has a power of communicating or
receiving  molecular  repulsiA-e  power, exactly equal, weight
for weight, to  its chemical  or combining  power.   For in-
stance, the equivalent of lead is 104,  of zinc 33, or, in round
numbers,  as  3 to 1 : these numbers  are therefore inversely
the exponents of their chemical power, three times as much
lead as  zinc being required to saturate the same  quan-
tity of an acid  or substance  combining  with  it; but their
power  of communicating or abstracting  heat or repulsive
power is precisely the same, for three times as much  lead as
zinc is required to produce the same amount of expansion or
contraction in a given quantity of a third  substance, such as
water.
    Again, a  great number of bodies chemically  combine in
equal volumes, i. e. in the ratios of their specific gravities;
but the specific  gravities represent the attractive powers of
the substance, or are the  numerical  exponents of the forces
tending to produce motion in masses of matter  towards each
other; while  the chemical equivalents are the  exponents of
the affinities or tendencies of the molecules of dissimilar sub-
stances to combine, and saturate each other;  consequently,
here we have to some extent an cquiA-alent relation between
these two modes of  force—gravitation and  chemical attrac
tion.
    Were the above relations extended into an universal laAV,
Ave should have the same numerical  expression for the three
forces of heat, gravity, and  affinity; and as  electricity and
magnetism are quantitatively related to them, Ave should have 
                 CONCLUDING REMARKS.               191

a simUar expression for these forces :  but at present the bod-
ies in which this parity of force has  been discovered, though
in themselves numerous, are small compared with the excep-
tions, and, therefore, this point can only be indicated as prom-
ising a generalisation,  should subsequent researches alter our
knoAvledge as to^the elements and combining  equivalents of
matter.
   With regard to what may be caUed dynamic equivalents,
i. e.  the definite relation to time of the action of these varied
forces upon equivalents of matter, the difficulty of establish-
ing them is  stiU greater.  K the proposition which I stated
at the commencement  of this paper be  correct, that motion
may be subdivided or  changed in  character, so as to become
heat, electricity, &c, it ought to foUow that Avhen we collect
the  dissipated  and changed  forces, and reconvert them, the
initial motion,  minus  an infinitesimal quantity affecting the
same amount of matter with  the same velocity, should be re-
produced, and so of the  changes in  matter produced by the
other forces ; but the difficulties of proving the truth of this
by experiment avUI, in  many cases, be  aU but insuperable;
Ave cannot imprison motion as Ave can matter, though we may
to some extent  restrain its. direction.
   The term perpetual motion, which I haATe not unfrequent-
ly employed in these pages, is  itself  equivocal.  If the doc-
trines here advanced be founded, aU motion is, in one sense,
perpetual.  In  masses whose motion is stopped by  mutual
concussion, heat or motion of the particles is generated ;  and
thus the motion continues, so that if Ave could venture to extend
such  thoughts to the  universe, Ave should assume the same
amount of motion affecting the same amount of matter forever.
Where force  opposes force, as in cases of static equilibrium,
the balance of pre-existing equilibrium is  affected, and fresh
motion is started equivalent  to that Avhich  is withdraAvn  into
a state of abeyance.
   But the term perpetual motion is  applied, in ordinary par- 
192        CORRELATION OF PHYSICAL FORCES.
lance (and in such sense I have used it), to a perpetual recur-
rent motion, e.g.  a weight which by  its faU would  turn  a
wheel, which Avheel would, in its turn, raise the initial weight,
and so on forever, or until the material of which the machine
is made be Avorn out.   It is strange that to common appre-
hension the impossibility of this is not self-evident: if the in-
itial weight is to be raised by the force it has itself generated,
it must necessarUy generate a force  greater  than  that of its
own weight or centripetal attraction ; in other words,  it must
be capable of raising a weight heavier than  itself:  so that,
setting aside the resistance of friction,  &c, a weight, to pro-
duce perpetual  recurrent motion, must  be heavier  than an
equal weight of matter, in short,  heavier than itself.
    Suppose two equal weights  at each end of an equi-armed
lever, there is no motion ; cut off a fraction of one of them,
and it rises wdiile the  other faUs.    How, now,  is the lesser
weight to bring back the greater without any extraneous ap-
plication of force?  If, as is obvious, it cannot do  so in this
simple form of experiment, it is a fortiori more impossible if
machinery be added, for increased resistances have then to
be overcome.   Can we again  mend this by employing any
other  force?   Suppose  we employ electricity,  the  initial
weight in descending turns a cyhnder against a  cushion, and
so generates  electricity; to make this  force recurrent, the
electricity so generated  must, in its  turn, raise  the initial
weight, or one heavier than it, i. e.  the  initial  weight must,
through the medium of electricity, raise a weight heavier than
itself.  The same problem, applied to any other forces, will
involve the same  absurdity:  and  yet simple as the  matter
seems, the world is hardly yet disabused of an idea little re-
moved from superstition.
    But the importance of the deductions to be  derived from
the negation of perpetual motion  seems scarcely to have im-
pressed philosophers, and we only find here and  there a scat-
tered hint of  the consequences  necessarily  resulting from that 
CONCLUDING REMARKS.
193
which to the thinking mind is  a conviction.   Some of these
I have ventured  to  put forward in  the  present  essay,  but
many remain, and wiU crowd upon the  mind  of  those  who
pursue the subject.  Does not, for instance, the impossibility
of perpetual motion, when  thought out, involve the demon-
stration of the impossibility, to which I have  previously aUud-
ed, of any event identicaUy recurring?
    The pendulum in vacuo, at each beat leaA-es a  portion of
the force wliich started it in the form of heat at its point of
suspension :  this  force, though ever existent, can never be re-
stored in its integrity to the baU of the pendulum, for in the
process of restoration it must  affect  other matter, and  alter
the condition of the universe.  To restore the initial force to its
integrity, everything as it existed at the moment  of the first
beat of the pendulum must be restored in its  integrity:  but
how can this be—for while the force was escaping from the
pendulum  by radiating heat from the point of  suspension,
surrounding  matter has not stood stiU;  the very attraction
which caused the beat of the pendulum has changed in degree,
for the  pendulum is nearer to or  further from the sun, or
from some planet or fixed star.
    It might be an interesting and  not profitless  speculation
to foUow out these and other consequences ;  it would, I be-
lieve, lead us  to  the   conviction that the universe  is  ever
changing, and that notwithstanding secular recurrences which
would prima, facie seem to replace matter in its original posi-
tion, nothing in fact ever returns or can return to a state of
existence identical with a previous state.  But the field is too
illimitable for me to venture further.
    The inevitable dissipation or throwing off  a  portion of
the initial force presents a great experimental difficulty in the
way of estabhshing the equivalents  of the  various natural
forces.  In the steam-engine, for instance,  the heat  of  the
furnace not only expands the water and thereby produces the
motion of the piston, but it also expands the  iron of the boil-
              9 
 194        CORRELATION OF PHYSICAL FORCES.

 er, of the cylinder and all surrounding bodies.   The force ex-
 pended in expanding this iron to a very small extent is equal
 to that which expands the vapour to a very large extent: this
 expansion of the iron is capable, in its  turn, of  producing a
 great mechanical force, Avhich is practically lost.  Could aU
 the force be applied to the vapour, an enormous  addition of
 power Avould be gained for the  same expenditure :  and per-
haps even with our present  means more  might  be  done  in
utilising the expansion of the iron.
   Another great difficulty in experimentally ascertaining the
dynamic equivalents of different forces arises from the effects
of disruption, or the overcoming  an existing  force.    Thus,
Avhen a part of the initial force employed is engaged  in tAvist-
ing or tearing  asunder  matter previously held together by
cohesive attraction, or in overcoming gravitation or  inertia,
the same amount of heat or  electricity would not be  CA*olved
 as if such obstacle  were non-existent,  and the initial  force
were wholly employed in producing, not in opposing.  There
is  a difficulty  apparently extreme in devising experiments
 in which some portion of the force is not so employed.
   The initial  force, however, that has been employed for such
disruption is not lost, as at the  moment  of  disruption the
bodies producing it fly off, and  carry with  them their force.
Thus, let two weights be attached to a  cord placed across a
bar; when their force is sufficient to break the cord or the
bar, the weights fall down and  strike  the earth,  making it
vibrate, and so conveying away or  continuing the force ex-
pressed by the cohesion  of the  bar or  cord.   If, instead of
 breaking a cord, the Aveiglits be employed to bend a bar, their
 gravitating force, instead of making the  earth  vibrate, pro-
 duces heat in the  bar, and so Avith Avhatever  other  force be
 employed to produce effects of  disruption, torsion,  &c,  so
 that, though difficult  in  practice, the numerical  problem of
 the equivalent of the  force is not theoreticaUy irresolvable
    The voltaic battery affords us the best means of ascertain- 
CONCLUDING REMARKS.
195
ing the dynamic equivalents of different forces, and it is probable
that by its aid the best theoretical and practical results AviUbe
ultimately attained.
    In investigating the relation of the different forces,! have
in turn taken each one as the  initial force or starting-point,
and endeavoured to shoAV hoAv the force thus  arbitrarily se-
lected could mediately or immediately produce and be merged
into the others : but it AviU be  obvious to those who  have at-
tentively considered the subject, and brought their minds into
a general accordance with the views I have submitted to them,
that no force can, strictly speaking, be initial, as  there  must
be some anterior force Avhich produced it: Ave cannot create
force  or motion any more than we can create matter.
    Thus, to take an example previously noticed,  and recede
backwards;  the  spark  of  light is produced by electricity,
electricity by motion, and motion is  produced by something
else, say a steam-engine—that is, by heat.  This  heat is pro-
duced by chemical affinity, i.e. the affinity  of the carbon of
the coal for the oxygen of the air: this carbon and this oxy-
gen haAre been  previously eliminated by  actions  difficult to
trace, but  of the pre-existence of Avhich  we cannot doubt.
and in which  actions  we  should  find  the conjoint  and al-
ternating effects of heat, light, chemical affinity, &c.    Thus,
tracing any force  backAvards to its antecedents, Ave  are merged
in an  infinity of changing forms of force ;  at  some point we
lose it, not because it has been in fact created at any definite
point, but because it resolves itself into so  many contributing
forces, that the evidence of it is lost to our senses or powers
of detection ; just as in foUowing it forAvard into the  effect it
produces, it becomes, as I have before  stated, so  subdivided
and dissipated as to be equally lost to our means of detection.
   Can avc, indeed, suggest a  proposition, definitely conceiv-
able by the mind, of force without antecedent force?   I can-
not, without calling for the interposition  of  created poAver,
any more than  I  can conceive the sudden appearance  of a 
196        CORRELATION OF PHYSICAL FORCES.

mass of matter come from nowhere, and  formed from noth-
ing.   The  impossibility, humanly speaking, of creating or
annihilating matter, has long been admitted, though, perhaps,
its distinct reception in philosophy may be  set  down to the
overthroAV of the doctrine of Phlogiston,  and the reformation
of chemistry at the time of Lavoisier.  The reasons for the
admission of a similar doctrine as to force appear to be equally
strong.   With regard to  matter, there  are  many cases in
Avhich  we never practically prove  its  cessation  of  existence,
yet we do not the  less believe in it:  who, for instance, can
trace,  so  as to  rc-wTeigh,  the particles  of  iron  Avorn off
the tire of a carriage wheel? Avho can re-combine the  parti-
cles of wax dissipated and chemically changed in the burning
of  a candle?   By  placing matter undergoing physical or
chemical  changes under special limiting circumstances, we
may, indeed, acquire  evidence  of  its continued  existence,
weight for weight—and so Ave may in some instances of force,
as in definite electrolysis : indeed the evidence we acquire of the
continued existence of  matter is by the continued exertion of
the force it  exercises,  as, when Ave weigh it,  our evidence is
the force of attraction; so, again, our  evidence of force is
the matter it acts upon.  Thus, matter and  force  are corre-
lates, in the strictest sense of the word;  the conception  of
the existence of the one involves the conception  of  the exis-
tence of the other: the quantity of matter again, and the de-
gree of force, involve conceptions  of  space and time.   But
to foUoAV out these abstract relations would lead me too  far
into the aUuring paths of metaphysical  speculation.
    That the theoretical portions of this essay are open to ob-
jection I am fully conscious.  I cannot,  hoAvever,  but think
that the fair way to test a theory  is to compare it with other
theories, and to see whether upon the whole  the balance of
probability is in its favour.   Were a theory  open  to no  ob-
jection it would  cease to be a theory, and  becc me  a law;
and were  we not to theorise, or to take  generalised views of 
CONCLUDING  REMARKS.
197
natural phenomena untU those generalizations Avere sure and
unobjectionable—in other Avords, were  laAvs—science  would
be  lost in  a complex mass of  unconnected  observations,
which Avould probably never disentangle themselves.  Excess
on  either side is to be avoided;  although Ave may often err on
the side of hasty generahsation, we may equaUy err on  the
side  of mere  elaborate  collection of  observations, which,
though sometimes leading to a valuable result, yet, when  cu-
mulated without a connecting link, frequently occasion a cost-
ly waste of time, and leave the subject to which they refer in
greater obscurity than that in which it Avas  involved at their
commencement.
    Collections of facts differ in  importance, as  do theories:
the former, in many instances, derive their  value  from their
capability of generalisation ; Avhile, conversely, theories are
valuable as methods of co-ordinating given series of facts,
and more valuable in proportion as they require feAver excep-
tions  and fewer postulates.  Facts  may  sometimes  be as
well  explained by one view  as by another, but without a
theory they are  unintelligible and incommunicable.  Let us
use our utmost effort to communicate a fact without using the
language of theory, and we faU;  theory is involved  in  all
our expressions ;  the knoAvledge of bygone times is imported
into succeeding times by terms involving theoretic conceptions.
As  the knowledge of any particular  science  developes itself
our views of it become  more simple ; hypotheses,  or the  in-
troduction of supposititious views, are  more and more dis-
pensed  with ; Avords become apphcable more  directly to the
phenomena, and, losing the hypothetic meaning which they
necessarily  possessed at their reception, acquire a secondary
sense, which brings more immediately to our minds the facts
of Avhich they are  indices.   The scaffolding has  served its
purpose.  The hypothesis fades  aAA-ay, and a theory, or gen-
eralised view of phenomena, more independent of supposition,
but stiU fuU of gaps and difficulties, takes its place.  This in 
198        CORRELATION  OF PHYSICAL FORCES.
its turn, should the science continue to progress, either gives place
toamore simple and wider generalisation, or becomes, by the re-
moval of objections,  estabhshed as a law.   Even in this move
advanced stage, words  importing theory must  be used,  but
phenomena are now intelligible and connected, though express-
ed by \-aried forms of speech.
   To think on nature is to theorise ; and  difficult it is  not
to be led on by the continuities of natural phenomena to  the-
ories Avhich appear  forced and uninteUigible to those who
have not pursued the same path  of  thought:  Avhich, more-
over, if allowed to gain an undue  influence, seduce us from
that truth wliich is the  sole object of  our pursuit.
   Where to draw the  hne—where to say thus  far  we may
go, and no farther, in any particular class of analogies or re-
lations which Nature presents to us ;  how far to foUow  the
progressive indications  of thought, and where to resist its  al-
lurements—is a question of degree which must  depend upon
the judgment of each individual or of each class of thinkers;
yet it is consolatory that thought is seldom expended in vain.
   I have throughout endeavoured to discard the hypotheses
of subtle or occult entities; if in this endeavour some of my
vieAvs have been adopted upon insufficient data,  I stUl hope
that this essay wUl not prove valueless.
   The conviction that the so-called imponderables are modes
of motion,  wUl, at aU events, lead  the observer of natural
phenomena to look for changes in these  affections, wherever
the intimate structure of matter is changed; and, conversely,
to seek for changes in matter, either temporary or permanent,
whenever it is affected by these forces.   I beheve he will
seldom do this in vain.  It was not until I had long reflected
on the subject, that I ventured to publish my  vieAArs: their
pubheation may induce others to think on their  subject-mat-
ter.  They are  not put forward with the same objects, nor do
they aim at the same  elaboration of detail, as memoirs on
aeAvly-discovered physical facts : they purport to be a method 
                  CONCLUDING REMARKS.              199

of mentally regarding known facts, some few of which I have
myself made known on other occasions, but the great  ma3s
of which  have been  accumulated by the labours of others,
and are admitted as estabhshed truth.-.  Every one has a  right
to view these facts through any medium he thinks fit to em-
ploy, but some theory must exist in the minds  of those Avho
reflect upon the many new phenomena Avhich have recently,
and  more particularly during the present century, been dis-
covered.  It is by a  generalised or connected  view of past
acquisitions in natural knoAvledge that deductions can best be
drawn as  to the probable character of the results to be antici-
pated.   It is a great  assistance in such investigations to  be
intimately convinced that no  physical phenomena can stand
alone: each is inc\itably connected with anterior changes,
and as ineA'itably productive of consequential changes,  each
Avith the other, and all with time and space; and, cither  in
tracing back these antecedents or folloAving up their conse-
quents,   many  new  phenomena AviU  be  discovered,  and
many existing phenomena, hitherto believed  distinct, Avill
be connected and explained: explanation is, indeed, only re-
lation to  something more  familiar,  not more   known—i.e.
known as  to causative or  creative agencies.   In aU pheno-
mena the more closely they are investigated the more are we
convinced that, humanly  speaking, neither  matter nor force
can be created or annihUated, and that an essential cause  is
unattainable.—Causation  is the will,  Creation the act,  of
God. 
           NOTES  AND  REFERENCES.

                         -------»♦•-------
PAGE
 13. The reader who is curious as to the views of the ancients, regarding
      the objects of science, will find clues to them in the second book of
      Aristotle's Physics, and in the first  three books of the Metaphy-
      sics.  See also the Timaeus of Plato, and Ritter's History of
      Ancient Philosophy, where a sketch of the Philosophy of Leucipfus
      and Democritus will be found.
 14. Bacon's Novum Organum, book ii. aph. 5 and 6.
 16  Hume's Enquiry concerning Human Understanding, S.  7, London,
      1768.
     Brown's  Enquiry into the Eelations of Cause and Effect, London,
      1835.
     The illustration I have used of floodgate has been objected to, as
      being one to which the term cause would scarcely be applied, but
      after some consideration I have retained it:  if cause be  viewed
      only as sequence, it must be limited to sequence under given condi-
      tions or circumstances, and here, given the conditions, the sequence
      is invariable.   I see no  difference quoad the  argument, between
      this illustration and that of Brown  of a lighted  match and gun-
      powder (4th edit. p. 27), to which my reasoning would equally well
      apply.
     Herschel's Discourse  on the Study of Natural Philosophy, pp. 88
      and 149.
 17. Quarterly Review, vol. lxviii. p. 212.
     Whewell,  On the Question ' Are  Cause and Effect Successive or
      Simultaneous?  (Cambridge Philosophical Transactions, vol. vii. p.
      319.)
 L8. Herschel's Discourse, p. 93.
    Ampere,  Theorie  des Phenomenes Electro-dynamiques,  Memoirs in 
NOTES  AND  REFERENCES.
201
PAGE
      the Ann. de Chimic et de Physique, and works from 1820 to 1826
      Paris.
 23.  Lamarck, ' Sur la Matiere du Son' (Journal de Physique, vol. xlix.
      p. 397).
 25.  D'Alembert, Traite de Dynamique, pp. 3 and 4, Paris, 1796.
 28.  Babbage, On the Permanent Impression of our Words and Actions ok
      the Globe we inhabit,  9th Bridgewater Treatise, ch. ix.
 30.  Mater, Annalen der Pharmacie Leibig und Wohler, May 1852.
 33.  Joule  on  the Mechanical Equivalent of Heat (Phil. Trans. 1850,
      p. 61.)
 33.  Erman, Influence of Friction upon  Thermo-electricity (Reports of the
      British Association, 1845.)
 85.  Becquerel, Tegagement de l'Elcctricite* par Frottement, Traite*  de
      l'Electricit6, torn. ii. p. 113 etseq.
 36.  Sullivan, Currents produced by the vibration of metals (Archiv.  de
      rElectricite1, t. 10, p. 480).  Leroux, Vibrations arrested produce
      heat (Cosmos, March 30, 1860).
 87.  Wheatstone on  the  Prismatic  Decomposition of Electrical Light
      (Notices  of Communications  to the British  Association,  p. 11.
      1835).
 89  Bacon, De Forma Calidi, Nov. Org. book 2,  aph. 20.
     Rumford, An Enquiry concerning the Source of Heat which is excited
      by Friction (Phil. Trans, p. 80, 1798).
     Davt, On  the  Conversion of Ice  into Water by Friction (West  of
      England Contributions, p. 16).
     Of Heat or Calorific  Repulsion (Elements of Chemical Philosophy,
      p. 69).
 41  Baden Powell on the Repulsive Power of Heat (Phil. Trans. 1834,
      p. 485).
     Fresnel, Annales de Chimie, torn. xxix. pp. 57 and 107.
 42  Moser on Invisible Light (Taylor's Scientific Memoirs,  vol.  iii. pp.
      461 and 465).
 43  Black  on  Latent neat (Elements of Chemistry, p.  144 et passim,
      1803).
 45  The experiments of Henry and Donnt have  shown that the cohesion
      of liquids, as far as their antagonism  to  rupture goes,  is much
      greater than has been generally believed.  These experiments,
      however, make no difference in the A-iew I have put forth,  as, what-
      ever be the character of the attraction, there is a molecular  attrac-
      tion to be overcome  in changing bodies from the solid to the liquid
      state, which must require and exhaust force. 
202
NOTES  AND  REFERENCES.
    Doxny, Sur la Cohdsion des Liquidcs (Memoires de l'Acadeinie Roy-
     ale de Bruxelles, 1843).
    Henry, Proceedings of the American Philosophical Society, April
     1844 (Silliman's Journal, vol. xlviiii. p. 215).
48. Thilorier,  Solidification de l'Acide carboniquc (Ann.  de Ch. et de
     Phys. torn. Ix. p. 432).
60. I. Wedgwood, Thermometer for measuring the  Higher Degrees of
     Heat (Phil. Trans. 1782, p. 305 ; and 1785, p. 390.
    Tyndall, on the  physical  properties of  Ice (Phil.  Trans. 1858,
     p. 211).
    Despretz, Recherches  sur le Maximum de Densit6 de l'Eau pure ct
     des Dissolutions aqueuses  (Ann. de. Ch. et de Ph. torn. Ixx. p. 45,
     and torn. Ixxiii. p. 295).
51. Biot (Comptes rendus de l'Academic des Sciences,  Paris 1850, p.
     281).   The experiments on circular polarisation by water were, I
     believe, by Dr. Leeson.
52. I. Thompson, Trans. R. S. Edin. vol. xvi. p. 575.
    W. Thompson, Phil. Mag. August 1850, p. 123.
    Bunsen, Pogg. Ann.  vol. Ixxxi.  p. 562; Ann. de Ch.  ct de Phys. vol.
     xxxv. p. 383.  Effects of Pressure on the Freezing Point.
53. Joule, Phil. Trans. 1852, p. 99.
    Although, taking  the  phenomena as  they are known to exist, the
     mechanical laws may be deduced, yet in  any physical conception
     of the nature of heat the expansion  by cold has  always been a
     great stumbling-block to me, and I believe to many others.
    Dulong  and Petit, and  Regnault.  See  their Memoirs abstracted
     and referred to in Gmelin's Handbook of Chemistry, translated by
     Watts for  the Cavendish Society, vol. i. p. 242 et seq.
54. Wood, Phil. Mag. 1851, 1852.
66. Senarmont, Conduction of Heat by Crystals (Gmelin's Handbook vol.
     i. p. 222).
56. Knoblauch, Ann. de Ch. et de Ph. vol. xxxvi. p.  124.
    Tyndall, Transmission of Heat through  Organic Structures (Phil.
     Trans, vol. cxliii. p. 217).
58. Grove, Electricity produced  by approximating Metals:  Report of
     a  Lecture  at the  London  Institution  (Literary Gazette, 1843,
     p. 39).
    Gassiot, Phil. Mag. October 1844.
    Roget, On the Improbability of the Contact exciting Force:  Trcatiss
     on Galvanism (Library of Useful Knowledge, S.  113).
    Faraday, Phil. Trans.  1840, p.  126. 
NOTES AND REFERENCES.
203
PAGB
 60. Melloni, Sur la Polarisation de la Chaleur: Recherches sur plusieurs
      Ph6nomenes  calorifiques (Annales  de Chimie et de Ph. torn, xlv
      pp. 5—68 ; torn. xli. pp. 375-410; torn, xlviii. pp. 198, 218).
    Forbes,  On the Refraction and Polarisation of Heat (Transactions of
      the Royal Society of Edinburgh, vol. xiii. pp. 131, 168).
 61. Kirchoff Trans. Belin Acad. 1861.
    Balfour Stewart on the theory of Exchanges (Report British Asso-
      ciation, 1861).
 63. T.  Wedgwood, On  the Production of Light and Heat by different
      Bodies (Phil. Trans, vol. lxxxii. p. 272).
 65. Grove, On the Decomposition of Water into its  Constituent Gases bj
      Heat (Phil. Trans.  1847, p. 1).
    Robinson, On  the Effect of Heat in lessening the Affinities of the
      Elements of Water (Transactions of  it e Royal Irish Academy, vol
      xxi. p. 2).
 07. Grove, Water decomposed by Chlorine find Heat (Phil. Trans. 1847,
      p. 20).
 70. Carnot, Reflexions sur la Puissance motrice du Feu, Paris, 182-1.
 76 Seguin, Influence des Chemins de Fer, p. 378  et seq.
 77 Rogers, Consumption of Coal for Man power (Cosmos, vol. ii. p. 56).
 80 Mr. Waterston has suggested that  solar heat may arise from the
      mechanical action  of meteoric stones falling into the sun, and Mr.
      Thompson has written  an elaborate paper  on the  subject (Trans.
      Brit. Assoc. 1853).  If a number of gravitating, bodies exist in the
      neighbourhood of the sun,  and form, as is conjectured, the zodia-
      cal  light,  it is difficult to conceive how  comets as they approach
      this region steer clear of such bodies, and are not  even deflected
      from their orbits.
    For Mr. Thompson's various and valuable papers, see Phil. Mag. 1851
      to 1854 inclusive.
 dl  Poisson, Comptes rendus, Paris, January 30, 1837.
 63  Dufaye, Symmer, Watson, and Franklin, Theories of Electric Fluid
      and Electric Fluids (Priestley's History of Electricity, pp. 429—
      441).
 83  Grotthus, Sur  la Decomposition de l'Eau et des Corps qu'elle tient
      en dissolution a aide de l'Electricitd galvanique (Ann. de Chimie,
      torn, lviii. p. 54).
    Faraday, On the  Question whether  Electrolytes  conduct without
      Decomposition (Proceedings of the Weekly Meetings of the  Royal
      Institution, 1855).
    Grove (Comptes rendus, Paris, 1839). 
204
NOTES AND REFERENCES.
 84. Faraday, On Induction  as  an Action of contiguous Particles (Phil.
       Trans. 1838, p. 30).
 85. Matteucci,  Plates of  Mica  polarised by Electricity (De la Rive's
       Electricity, p. 140).
     Grove, Electrolysis across Glass (Phil. Mag. Aug. 1860).
 85. Karsten on Electrical Figures (Archiv. de l'Elec. vols. ii. iii.  and iv).
 87. Grove, Etching Electrical Figures and transferring them to Collo-
       dion (Phil. Mag. January 1857).
 88. Fusinieri,  Du  Transport des Matieres ponderable qui s'opere dans
       les Decharges electriques (Archives de l'Electricite ; Supplement k
       la Bibliotheque universelle  de Geneve, torn. iii. p.  597).
 88. Grove, On the Voltaic  Arc (Report of Lecture at the Royal  Insti-
       tution,  Lit. Gaz. and Athenaeum, Feb. 7, 1845; Phil. Trans.  1847,
       p. 16).
 90 to 94.  Grove, On the Electro-chemical Polarity of Gases (Phil. Trans.
       1852, p. 87).
 94. Fremy and E. Becquerel, Oxygen changed to Ozone by the  Electric
       Spark (Ann. de  Ch. et  de  Phys. 1852).  This subject and the na-
       ture of  Ozone was  first investigated by Dr. Schonbein.  See also a
       paper by Mr. Brodie On the Conditions of certain Elements at the
       Moment of Chemical Change (Phil.  Trans. 1850).
  95, 96. Molecular Changes  in Electrised  Metals (Nairne,  Phil. Trans.
       1780, p. 334,  and 1793, p.  223; Grove, Electrical  Mag. vol. i. p.
       120; Peltier, Archives de l'Electricite, vol. v. p.  182 ; Fusinieri,
       id. p. 516).
 96. Wertheim, Change in Elasticity of Metals by Electrisation (Ann. de
       Ch. et de Phys. voL xii. p. 623 ;  Arch. Elec. vol. iv. p. 490).
     Dufour, Alteration in Tenacity of Metals by Electrisation (Bibl. univ.
       de Geneve, Fev.  1855, p. 156).
 97. Matteucci, Conduction of Electricity by Crystals (Comptes rendus de
       l'Acad., Paris, March, 5, 1855, p. 541).
 98. E. Becquerel, Transmission  of Electricity by heated Gases (Ann. de.
       Ch. et de Phys. vol. xxxix.  p. 355).
     Grove, Proceedings of the Royal Inst. (1854, p.  361).
     Becquerel, Divergence of Gold-Leaves in Vacuo (Traite d'Electricite,
       vol. v.; part ii. p. 53).
     Newton,  Thirty-first Query to the Optics.
 99. Grove, Particles of Metals and Metallic Oxids detached in Liquids by
       Electricity (Elec. Mag. vol.  i. p. 119).
100. Matteucci, Relations of Electricity and Nervous Force (Phil. Trans, 
NOTES AND REFERENCES.
205
       1845, p. 285, 1846, p. 497; Phenomenes  physiques des Corp*
       vivants, p. 305 ; Lezioni di Fisica, p. 360).
     Galvani Volta Marianini  et Xobili on Physiological Effects  of
       Electricity (Ann. de Ch. et de Phys. vols. 23, 25, 29, 38, 40, 43,
       44, 66).
102. Becquerel, Chemical Changes by Friction (Traite de l'Elec. vol. v.
       part  1, p. 16).
106. De la  Rive, Heat of the Voltaic Pile (Bibl. univ., vol. xiii. p. 389).
     Davy,  On the Properties of  Electrified  Bodies in their relations to
       Conducting Powers and Temperature (Phil. Trans. 1821, p. 428).
106. Grove, On the Effects of surrounding Media on Voltaic Ignition (Phil.
       Trans. 1849, p. 49).
107. Oersted, Experience sur 1'Effet du Conflict 61ectrique sur l'Aiguille
       aimant6e (Ann. de Ch. et de Phys., torn. xiv. p. 417).
108. Coleridge, Table Talk, vol. i. p. 65.
109. Lenz and Jacobi, Pogg. Ann. vol. xvlii. p. 403 ; Bulletin de l'Acad.
       St. Petersburg, 1839 ; Harris, Magnetism, part 2, p. 63.
     Davy,  Decomposition of the fixed Alkalies (Phil. Trans. 1808, p. 1).
     Becquerel Des Composes electro-chimiques (Trait6 de l'Electricite,
       vol. iii. c. 13).
     Crosse, Transactions of the British Association, vol. v. p. 47 ; Pro-
       ceedings of the Electrical Society, p. 320.
110. Malus, Polarisation of Light by. Reflection (Memoires d'Arcueil, torn.
       ii. p.  143).
     Arago, Circular Polarisation by Solids (Memoires de l'Institut, 1811).
111. Biot, Circular Polarisation by Liquids (Memoires de l'Institut, 1817).
111. Niepce and Daguerre,  Historique  et Description  des Proc6des du
       Daguerrdotype, Paris, 1839.
     Talbot, Photogenic  Drawing and Calotype (Phil. Mag. March. 1839,
       and August 1841).
113. Herschel, Chemical Action of the  Solar  Spectrum on various  Sub-
       stances (Phil. Trans. 1840, p. i. and 1842, p. 181).
     Hunt, Researches on Light, London, 1844.
116. Grove, Other Forces produced  by Light (Lit. Gaz. January 1844).
117. Grove, Influence of Light on the  Polarised Electrode (Phil. Mag.
       December 1858).
     Somerville (Mrs.), On the Magnetising Power of the more Refrangi-
       ble Solar Rays (Phil. Trans. 1862,  p. 132).
     MohiCHiNi's experiments are given in Mrs. Somerville's paper.
118. Herschel,  On the  Absorption of Light  in Coloured Media viewed 
206
NOTES  AND  REFERENCES.
       in  connection with  the  Undulatory Theory (Phil.  Mag.  Decern
       ber 1863).
     Seebeck, Heat of Coloured Rays (Brewster's Optics, p. 90).
 118. Knoblauch (Ann.  de Ch.  vol. xxxvi. p. 124, and Pogg. Ann. there
       referred to).
 119. Herschel, Epipolised Light (Phil. Trans, vol. exxxv. pp. 143, 147).
     Stokes, Change in Refrangibility of Light (Phil. Trans, vols, cxlii.
       cxliii.)
 123. For the first enunciations of the Corpuscular and Undulatory Theories,
       see Inewton's Optics, Hooke's  Micographia, and  Huyghens' Trac-
       tatus de Lumine.  See also Brewster's Optics, p. 138.
 124.  Young, Lectures  edited by Kelland, p.  358, et seq.; Phil.  Trans.
       1800,  p.  126; Herschel, Encyc. Metro, art. Light, pp. 450 and
       738 ; Newton's Optics, p. 322; Whewell's Hist. Indue. Sc. vol.
       ii. p. 449 ; Foucault, Comptes rendus, Paris, 1850, p. 65 ;  Harri-
       son, Phil.  Mag. November 1856 ; Camb. Phil. Trans.
 126. Sondhauss,  Refraction  of  Sound (Ann.  de Ch.  et de Phys.  vol.
       xxxv. p. 505); Dov£, Polarisation of Sound  (Cosmos, May 13,
       1859).
 132. Pasteur, Rotation  of Plane  of Polarised Light  by Solutions of
       Hemihedral Crystals (Ann. de Ch. et de Phys. vol. xxiv. p. 442).
134 to 135. Wollaston, Phil. Trans.  1822, p. 89; Whewell, Phil, of
       the Induct. Sc. vol. i. p. 419 ; Wilson, Trans, of the Roy. Soc. of
       Edin. vol.  xvi. p.  79 ;  Sir W. Herschel, Phil. Trans. 1793, p. 201,
       and 1801, p.  300; Morgan,  Phil.  Trans, vol. lxxv. p. 272 ; Davy,
       Phil. Trans. 1822, p. 64; Elements of Chemical Philosophy, p. 97 ;
       Gassiot, Phil. Trans. 1859, p. 157.
137. Diminishing Periods of Comets (Herschel's Outlines of Astronomy,
      p. 357).
140. Since  writing the passage in the text, I find that  Struve has been
      led,  from  his astronomical researches, to the conclusion that some
      light is lost in the interplanetary spaces.  He gives as an approxi-
      mation one per cent, as lost by the passage of light from a star of
      the first magnitude, assuming a mean or average distance (Etudes
      d'Astronomie Stellaire, 1847).
    Newton, Thirtieth Query to the Optics.
142. Faraday, Evolution of  Electricity from  Magnetism (Phil. Trans.
       1832, p. 125).
144. Faraday, Magnetic Condition of all Matter (Phil. Trans. 1846, p. 21;
      PhiL Mag. 1846, p. 249).
    Becquerel,  Ann. de  Ch. et de Ph. 'torn,  xxxvi. p. 337; Comptes
       rendus, Paris, 1846, p. 147;  and 1850, p.  201. 
NOTES  AND REFERENCES.
207
PAGE
145. Faraday, On the Magnetism of Light (Phil. Trans. 1846, p. 1).
145. Wartmann, Rotation of the Plane of Polarisation of Heat by Magnet-
       ism (Journal de l'lnstltute, No. 644).
     Provostaye and Dessaines, Ann. de Ch. et de Phys. October 1849.
146. Hunt, Influence of Magnetism on Molecular Arrangement (Phil. Mag
       1846,  vol. xxviii. p. 1;  Memoirs of the Geological Society, vol. i
       p.  433).
     Wartmann, Phil. Mag. 1847, vol. xxx. p. 263.
147, Grove,  Experiment on Molecular Motion of a Magnetic Substance
       (Electrical Mag. 1845, vol. i. p. 601).
147. On the direct Production of Heat by Magnetism (Proceedings of the
       Royal Society, 1849, p. 826).
       After this paper was communicated  and ordered to be printed in the
       Philosophical Transactions, I found that I had been anticipated by
       Mr. Van Breda, who communicated, in 1845, a paper to the Insti-
       tut on the subject:  his paper appears in the Comptes rendus under
       an erroneous title, which accounts for its having been overlooked :
       he does not give thermometric measures of the heat he obtained,
       nor did he produce heating effects by a permanent steel magnet, or
       with other metals than iron.  (Comptes rendus,  October 27, 1845).
       See also an  earlier experiment by Mr. Joule (Phil. Mag. 1843), to
       which he  called my attention after my paper was read.
148, 151. The Experiments on  the  effects of Magnetism on the Matter
       magnetised, are collected by Mr.  De  la Rive in his recently-pub-
       lished  Treatise on Electricity, vol. i.
1C3. Davy, Electricity defined as Chemical affinity acting on Masses (Phil.
       Trans. 1826,  p. 389).
     Yolta, Electricity excited  by the mere Contact of conducting Sub-
       stances (Phil. Trans.  1800, p. 403).
154. Grove, Gold-Leaf Experiment (Comptes rendus, Paris,  1839, p. 567).
155. Grove, Voltaic Action of  Sulphur,  Phosphorus, and Hydrocarbons
       (Phil. Trans.  1845, p. 351).
     Grove, New Voltaic Combination (Phil. Mag. vol. xiv. p. 388 ;  vcj.
       xv. p. 287).
lo5. Grove,  Electricity of  Blowpipe Flame (Proceedings  of the Royal
       Institution, February 1854), Phil. Mag.
157  Dalton, New System of Chemistry, London, 1810.
158. I  have here and elsewhere used whole numbers, a3 sufficiently approxi-
       mate  for the  argument, but without intending to express any opin-
       ion as to the law of P,rout.
158. Faraday, Definite Electrolysis (Phil. Trans. 1834,  p. 77). 
208
NOTES  A1TD  REFERENCES.
 PAGE
 160. Wood, Heat disengaged in Chemical Combinations (Phil. Mag. 1852)
 162. Andrews, Phil. Trans. 1844, p. 21.
     Hess, Poggendoff's Annalen, Bd. Iii. p. 197.
 163. Favre, Ann. de Ch. et de Phys. vols. 39, 40 ;  Comptes rendus, Paris,
       vol. 45, p. 66, and vol. 46, p. 337.
 169. Catalysis  by Platinum  (Dobereimer, Ann. de Ch. et de Phys. torn
       xxiv. p. 93 ; Dulong and  Thenard, Ann. de Ch. et de Phys. torn.
       xxiii. p. 440).
 170. Grove, Gas Voltaic Battery (Phil. Mag. February 1839, and Decem-
       ber 1842; Phil. Trans. 1843, p. 91).
 171. Mosotti, Forces which regulate the Internal Constitution of Bodies
       (Taylor's Scientific Memoirs, vol. i. p. 448).
 172. Plucker, Repulsion of the  Optic Axes of Crystals by the Poles of a
       Magnet (Taylor's Scientific Memoirs, vol. v. p. 353).
     Magnetic Action of Cyanite (Lit. Gaz. 1849, p. 431).
 172. Matteucci, Correlation of Electric Current and Nervous Force (Phil.
       Trans. 1850, p. 287).
 173. Carpenter, On the Mutual Relations of the Vital and Physical Forces
       (Phil. Trans. 1850, p. 751).
174. On Effort.  See Brown, Cause and Effect; Herschel's Discourse ;
       and Quarterly Review, June 1841.
175. Helmholtz, Muller's Archives, 1845 ; Matteucci, Comptes rendus,
     Paris, 1856 ; Beclard, Archives de Medicine, 1861.
189. Dulong and Petit, Relation between Specific Heat and Chemical
       Equivalents (Ann.  de Ch. et de Phys. torn. x. p. 395).
189. Neumann, Poggendorff's Annalen, Bd. xxiii. p.  1.
     Avogadro, Ann. de  Ch. et de Phys. torn. Iv. p.  80. 
                 ON THE





INTERACTION  OF. NATURAL  FORCES.





        By Peof. IT. L. F. HELMHOLTZ.





      Translated by JOHN  TYNDALL, F.R.S. 
    Herman Ludwig Ferdinand Helmholtz was bom  at Pottsdam, August
31, 1821.  He was first military physician, and afterwards assistant of the
Astronomical Museum in  Berlin (1848), and  subsequently Professor Extra-
ordinary of Physiology at the University of Konigsberg (1849 to 1852).  He
Decame Professor of Physiology at the University of Bonn in 1855, and in
1858 accepted the physiological chair in the University of Heidelberg.  Tho
lecture which follows was delivered at Konigsberg in 1854.  He is an emi-
nent investigator, and an able promoter of the recent philosophy of forces;
but of his life we have fewer particulars than of his accomplished translator.
    The ancestors of John Tyndall emigrated from England to the eastern
or Saxon border of Ireland about the middle  of the last century.  He was
born at the village of  Leighlin Bridge in 1820, where he received his early
education and acquired a taste for mathematics.  In 1839 he left school
and joined the Ordnance Survey as  a civil assistant, where he became in
turn draughtsman, computer, surveyor, and trigometrical observer.  He was
five years connected with the survey, and  for  three years  occupied as rail-
road engineer.  In 1847 he became teacher in Queenswood College in Hamp-
shire,  a school for agriculturists and engineers, where  he was distinguished
for his mild but efficient discipline.  Professor Frankland, the chemist, was
here joined with him in the work of instruction, and in 1848 the two friends
left the institution and went  to the University of Marburg in Hesse Cassel,
to study with the eminent chemist, Bunsen.   In  1851 Professor Tyndall
went to Berlin and worked at the subject of diamagnetism in the laboratory
of Professor Magnus.  He returned  to London the  same year, and was
elected Fellow of the Royal Society in 1852.
    Through the influence of Dr. Bence Jones,  General Sabine, and Professor
Faraday, he was  appointed Professor of Natural  Philosophy in the Royal
Institution in 1853, an appointment which he  now holds.  In company with
his friend, Professor Huxley,  he visited the Alps in 1856 ; and returning each
succeeding year, he accumulated the observations and adventures which are
so graphically described in his "Glaciers of the Alps," published in 1860.
Professor Tyndall has worked with eminent success  at  various scientific
questions, but he is chiefly distinguished for his  original  and elaborate re-
searches on  the relations of  radiant heat to gaseous and vaporous matter.
These researches are given in his able work on " Heat as a mode of Motion,"
issued in 1863.  As an experimenter, Professor Tyndall is marked for his
caution, accuracy, and tireless perseverance  under difficulties ; as  a writer,
for his clear, vivid, and vigorous style. 
[NTERACTION OF NATURAL FORCES.
     ANEW conquest of very general interest has been recently
      made by natural philosophy.  In the following pages, I
will endeavour to give a notion of the nature of this conquest.
It has reference to  a new  and universal natural law, which
rules the action of  natural forces in their mutual relations
towards each  other, and is as  influential  on our theoretic
views of natural processes as it is important in their technical
applications.
   Among the practical arts wliich owe their progress to the
development of the natural  sciences, from the conclusion of
the middle  ages downwards, practical mechanics, aided by
the mathematical  science which bears the same name, was
one of the most prominent.  The character of the art was, at
the time referred to, naturally very different from its present
one.  Surprised and stimulated by its own success, it thought
no problem beyond its power, and immediately attached some
of the most difficult and complicated.  Thus it was attempted
to build automaton figures which should perform the functions
of men and animals.  The wonder of the last century was
Vaucanson's duck, which  fed and digested its food; the flute-
player of the  same  artist, which moved  all its  fingers cor- 
212         INTERACTION OF NATURAL FORCES.

rectly ;  the writing boy of the older, and the piano-forte play-
er of the  younger Droz :  which latter, when performing, fol-
lowed its hands with  his eyes, and at the conclusion of the
piece bowed courteously  to  the  audience.   That men like
those mentioned,  whose  talent might bear comparison with
the most inventive heads  of the present  age, should spend so
much time in the construction of these  figures, which we at
present  regard as the merest trifles, would be incomprehensi-
ble, if they had not hoped in solemn  earnest to solve a great
problem.  The writing boy of the elder Droz was publicly
exhibited in Germany  some years ago.   Its wheel-work is so
complicated,  that no  ordinary head  would  be sufficient to
decipher its manner of action.   When, however,  we are in-
formed that this boy and its constructor, being suspected of the
black art, lay for a time in the  Spanish Inquisition, and with
difficulty obtained  their freedom,  we may infer that in those
days even such a toy appeared great enough  to excite doubts
as to its natural  origin.  And though these  artists  may not
have hoped to breathe  into the creature  of their ingenuity a
soul gifted with moral completeness, still there were many
who would be willing to dispense  with the moral qualities of
their servants, if,  at the  same time,  their immoral  qualities
could also be got rid of; and accept, instead of the mutability
of flesh  and  bones, services which should combine the regu-
larity of a machine  with the durability of brass  and steel.
The object,  therefore,  which the inventive genius of the past
century  placed before it with  the  fullest earnestness, and not
as a piece of amusement merely, was boldly chosen,  and was
followed up Avith an expenditure of sagacity which  has contri-
buted not a little to enrich the mechanical experience which a
later time knew how  to  take advantage of.   We no  longer
seek to build  machines  which  shall fulfil the thousand services
required of one man, but  desire, on the  contrary,  that a ma-
chine shall perform one service,  but shall occupy in doing it
the place of a thousand men. 
        4T   TnE OLD MECHANICAL  PROBLEM.         213

    From these efforts to imitate living creatures, another idea,
also by a misunderstanding,  seems to have developed itself,
which, as it were, formed the new philosopher's stone of the
seventeenth and eighteenth centuries.  It was now the endeav-
our to construct a perpetual motion.   Under this term was un-
derstood a machine, wliich, without being wound up, without
consuming in the working of it, falling water, wind, or any
other natural force, should still continue in motion, the motive
power being perpetually supplied by the machine itself.  Beasts
and human beings seemed to  correspond to the  idea of such an
apparatus, for they moved themselves energetically and inces-
santly as long as they lived, were never wound  up, and nobody
set them in motion.  A  connection between the taking-in of
nourishment and the development of force did not make itself
apparent.  The nourishment  seemed only necessary to grease,
as it were, the wheel work of  the animal  machine, to replace
what  was used up, and to renew the old.    The development
of force out of itself seemed to be the essential  peculiarity, the
real quintessence of organic life.   If, therefore, men were to
be constructed, a perpetual motion must first be found.
   Another hope also seemed to take up incidentally the sec-
ond  place, which,  in our wiser age, would  certainly have
claimed the first rank in the thoughts of men.  The perpetual
motion  was to produce  work  inexhaustibly  without  corre-
sponding consumption, that is to say, out of nothing.   Work,
however, is money.  Here, therefore,  the  practical problem
which the cunning heads of all centuries have  followed in the
most diverse ways, namely, to fabricate money out of nothing,
invited solution.  The  similarity with the philosopher's stone
sought by the  ancient chemists was complete.  That also
was thought to contain the quintessence of organic life, and to
be capable of producing gold.
   The spur wliich drove men to inquiry was sharp, and the
talent of some of the seekers must not be estimated as small.
The nature of the problem was quite calculated to entice poi> 
214        INTERACTION OF NATURAL FORCES.   <«»

ing brains,  to lead them round a circle  for years, deceiving
ever with new expectations, wliich vanished upon nearer ap-
proach, and finally reducing these dupes of hope to open  in-
sanity.  The phantom could not  be grasped.  It would be
impossible to  give a history of these  efforts, as the clearer
heads, among whom the elder Droz must be ranked, convinced
themselves of the  futility of their experiments, and  were
naturally not inclined to speak much about them.   Bewildered
intellects,  however, proclaimed  often enough that they had
discovered the grand secret; and as the incorrectness of their
proceedings was always speedily manifest, the matter fell into
bad repute, and the opinion strengthened itself more and more
that the problem wa3 not capable of solution; one difficulty
after another was brought under the dominion  of  mathemati-
cal mechanics, and finally a point was reached  where it could
be proved, that, at least by the use of pure mechanical forces,
no perpetual motion could be generated.
   We have here  arrived at the idea of the driving force or
power of a  machine, and shall  have much to do  with it in
future.  I must, therefore,  give an explanation of it.  The
idea of work is evidently transferred to machines  by compar-
ing their  arrangements  with those of men and  animals to
replace which they were applied.   We still reckon the work
of steam engines according to  horse-power.   The value  of
manual labor is determined partly by the force which is ex-
pended in it (a strong laborer is valued  more highly than a
weak one), partly however, by the skill which is brought into
action.  A  machine, on the contrary, which  executes work
skilfully, can always be multiplied to  any extent; hence its
skill has not the high value of human skill in domains where
the latter cannot be supplied by machines.  Thus the idea of
the quantity of work in the case  of machines has been limited
to the consideration of the expenditure of force;  this was the
more important, as indeed most machines are constructed for
the cypress purpose of exceeding, by the magnitude of their 
         MEASUREMENT OF MECHANICAL FOV/ER.      215

effects, the powers of men and animals.  Hence, in a mechani-
cal sense, the  idea of work is become identical with that of
the expenditure of force, and in this way I will apply it.
   How, then, can we measure this expenditure, and compare
it in the  case of different machines ?
   I must here conduct you a portion of the way—as short a
portion as possible—over the uninviting field of mathematico-
mechanical ideas, in order to bring you to a point of view from
wliich a more rewarding prospect will open.  And though the
example  which I shall here choose, namely, that  of  a water-
mill  with iron hammer,  appears to be tolerably romantic, still,
alas, I must leave the dark forest valley, the  spark-emitting
anvil,  and the black Cyclops wholly out of sight, and beg a
moment's attention to the  less poetic  side  of the  question,
namely, the machinery.  This is driven by a water-wheel which
in its turn is set in motion by the falling water.   The axle of the
water-wheel has at certain  places small  projections, thumbs,
which, during the rotation,  lift the heavy hammer and permit
it to  fall  again.   The foiling hammer  belabors the  mass of
metal, which  is introduced beneath it.   The  work therefore
done by the machine consists, in this case, in the lifting of the
hammer, to do wliich the gravity of the latter must be over-
come.  The expenditure of force will, in  the first place, other
circumstances  being  equal,  be proportioned to the weight of
the hammer ; it will, for example, be double when the weight
of the hammer is doubled.    But the action of the hammer
depends  not upon its weight alone, but also upon the height
from  which it falls.  If it falls through two feet, it will pro-
duce a greater effect  than if it falls through only one foot.  It
is, however, clear that if the machine, with a certain expendi-
ture  of force,  lifts the  hammer  a  foot  in height,  the same
amount of  force must be expended to raise it a second foot in
height.   The  work  is therefore  not only doubled when the
weight of the hammer is increased twofold, but also when the
space through which it falls is doubled.   From this it is cacA 
216         INTERACTION OFNATURAL FORCES.

to see that the work must be measured by the product of tha
weight into the space  through which it ascends.   And in this
way, indeed, do we measure in mechanics.
    The unit of work is a foot-pound, that is, a pound weight
raised to the height of one foot.
    While the work in this case consists in the raising of  the
heavy hammer-head, the driving force which sets the latter in
motion, is generated  by falling water.  It is not necessary
that the water should  fall vertically, it  can also flow in a
moderately inclined bed;  but  it must always, where it has
water-mills to set in motion, move from a higher to a lower
position.  Experiment and theory coincide in teaching, that
when a hammer of a hundred weight is to be raised one foot,
to accomplish this at least a hundred  weight of water must
fall through the space of one foot;  or what is equivalent to
this, two hundred weight must fall full half a foot, or four hun-
dred weight a quarter  of a foot, etc.  In short, if we multiply
the weight of the falling water by the height through which it
falls, and regard, as before, the product as the measure of the
work, then the work performed by the  machine in raising the •
hammer, can, in the most favourable case, be only equal to the
number of foot-pounds of water which have fallen in the same
time.   In practice, indeed, this ratio  is by no means attained  ;
a great portion of the work of the falling water escapes unused,
inasmuch  as  part of the force  is willingly sacrificed for the
sake of obtaining greater speed.
    I will further remark, that this relation remains unchanged
whether the hammer is driven immediately by the axle of  the
wheel, or  whether—by the intervention of wheel-work, end-
less screws, pulleys, ropes—the motion is transferred to  the
hammer.  We may,  indeed, by such arrangements,  succeed
in raising a hammer of ten hundred weight, when by the first
simple arrangement, the elevation of a hammer of one hundred
weight  might alone be  possible ; but either this heavier ham-
mer is  raised to only one tenth of the height,  or tenfold tho 
              TRUE FUNCTION OF MACHINES.          O.J 7

lime is required to raise it to the same height; so that, how-
ever we may'alter, by the interposition of machinery, the in-
tensity of the acting force, still in a certain time, during which
the mill-stream furnishes us with a definite quantity of water,
a certain definite quantity of work, and no more, can be per-
formed.
    Our  machinery, therefore, has, in the first place, done
nothing more than make use of the gravity of the falling wa-
ter in order to overpower the gravity of the hammer, and to
raise the latter.   W hen it has lifted the hammer to the neces-
sary height, it again liberates it, and  the  hammer falls upon
the metal mass which is pushed beneath it.  But why does
the falling hammer here exercise a greater force than when it
is- permitted simply to press with its own  weight on the mass
of metal?  Why is its power greater as the height from wliich
it falls  is increased?  We  find, in fact, that the work per-
formed  by the hammer  is  determined by its velocity.   In
other cases, also, the velocity of moving masses is a means of
producing great effects.  I only remind you of the destructive
effects of musket-bullets, which, in a state of rest, are the most
harmless things in the world.  I remind you of the wind-mill,
which derives its force from the moving air.  It may appear
surprising that motion, which we are accustomed to regard as
a non-essential  and transitory endowment of bodies, can pro-
duce such great effects.  But the fact is, that motion appears
to us, under ordinary circumstances, transitory, because the
movement of all  terrestrial  bodies  is  resisted perpetually by
other forces, friction, resistance of the air,  etc., so that motion
is incessantly weakened  and finally neutralized.   A body,
however,  which  is opposed by no resisting force, when once
Bet in  motion,  moves onward  eternally with undiminished
velocity.   Thus we  know that the  planetary bodies have
moved without change, through space, for thousands of years.
Onl\ by resisting forces can motion be diminished or destroyed.
A moving body, such as the hammer or the musket-ball, when
              10 
 218        INTERACTION OF NATURAL FORCES.

 it strikes against another, presses the latter together, or pene-
 trates it, until the sum of the resisting forces which the body
 struck presents to its pressure, or to the separation of its par-
 ticles, is sufficiently great to destroy the motion of the ham-
 mer or of the bullet.  The motion of a mass regarded as
 taking the place of working force is called the living force (via
 viva) of the  mass.   The word  " living " has of  course  here
 no reference whatever to living beings, but is intended to rep-
 resent solely the force of the motion as distinguished from the
 state of unchanged rest—from  the gravity of a motionless
 body, for example,  which  produces an incessant pressure
 against the surface which supports it, but does not produce
 any motion.
   In the case before us, therefore, we had first power in the
 form of a falling mass of water, then in the form of a lifted
 hammer, and, thirdly, in the form of the living  force of the
 fallen hammer.  We should transform the third form into the
 second,  if we, for example, permitted the hammer to fall upon
 a highly elastic steel beam strong enough to resist the shock.
 The hammer would rebound, and in the most favourable  case
 would  reach  a height equal to  that from  which it fell, but
would never rise higher.   In this way its mass would ascend :
 and at the moment when its highest point has been attained,
it would represent the same number of raised foot-pounds as
before  it fell,  never a greater  number ; that is to say, living
force  can generate  the same  amount of work as that ex-
pended  in its  production.  It  is therefore  equivalent to this
 quantity of work.
   Our clocks are driven by means of sinking weights, and
 our watches by means of the  tension of springs.   A weight
which lies  on the  ground, an  elastic spring which is without
 tension, can produce no effects ;  to obtain such we must first
raise the weight or  impart tension to the spring, which ia
 accomplished when we  wind  up  our clocks and watches.
 The  man who winds the clock or watch communicates to the 
RESERVOIR OF ACCUMULATED POWER.       219
weight  or  to  the spring a certain  amount of power, and ex-
actly so much as is thus communicated is gradually given out
again during  the  following twenty-four hours,  the  original
force being thus slowly consumed to overcome the friction of
the wheels and the resistance which the pendulum encounters
from the air.  The wheel-work of the clock therefore exhibits
no working force which was not previously communicated to
it, but simply  distributes the force given to it uniformly over
a longer time.
    Into the chamber of an  air-gun we squeeze, by means of
a condensing  air-pump, a  great quantity of air.  When we
afterwards open the cock of a gun and admit the compressed
air  into the barrel, the ball is driven out of the latter with a
force similar to that exerted  by ignited powder.  Now we
may determine the work consumed in the pumping-in of the
air, and the living force which, upon firing, is communicated
to the ball, but we shall never find the latter greater than the
former.  The  compressed air has generated no working force,
but simply gives to the bullet that which has been previously
communicated to it.  And while we have pumped for perhaps
a quarter of an hour to charge the gun,  the force is expended
in a few seconds when the bullet is discharged ;  but because
the  action is compressed into so short a time,  a much greater
velocity is imparted to the ball than would be possible to com-
municate to it by the  unaided effort of the  arm in throw-
ing  it.
  •From these  examples you observe, and the mathematical
theory has corroborated this for all purely mechanical, that is
to say, for moving forces, that all our machinery  and appara-
tus  generate  no force, but  simply yield up the power com-
municated  to  them by natural forces,—falling water, moving
wind, or by the muscles of men and animals.   After this law
Lad been estabhshed by the great mathematicians of the last
century, a perpetual motion, which should make only use of
pure mechanical forces, such as gravity, elasticity, pressure of 
 220        INTERACTION OF NATURAL FORCES.

 liquids and gases, could only be sought after by bewildered
 and iU-instructed people.  But  there are still other natural
 forces  which  are  not reckoned among  the purely moving
 forces,—heat, electricity, magnetism, hght,  chemical  forces,
 all of which nevertheless stand  in manifold relation  to me-
 chanical  processes.   There is hardly a" natural process to be
 found which is not  accompanied by mechanical  actions, or
 from which mechanical work may  not be derived.  Here the
 question of a perpetual motion remained open; the decision
 of this question marks the progress of modern physics.
    In the case of the air-gun, the work to be accomplished in
 the propulsion of the ball was given by the  arm of the man
 who pumped in the air.  In ordinary firearms, the condensed
 mass of air which propels the bullet is obtained in a  totally
 different  manner, namely, by the combustion of the powder.
 Gunpowder is transformed by combustion for the most part
 into gaseous products, which endeavor  to  occupy a much
 larger space than that previously taken up by the volume of
 the powder.  Thus, you see, that,  by the use of gunpowder,
 the work which the  human arm  must accomplish  in the case
 of the air-gun is spared.
   In the mightiest of our machines, the steam engine, it is a
 strongly compressed aeriform body, water vapour, which, by
its effort to expand, sets the machine in motion.   Here also,
we  do not condense  the  steam by means  of an  external
mechanical  force, but by communicating  heat  to a mass of
water in  a closed  boiler, wo  change this water into  steam,
which, in consequence of the limits  of the space, is developed
 under strong pressure.   In this case, therefore, it is the heat
 communicated which generates the mechanical force.  The
heat thus necessary for the machine we might obtain in many
ways ; the ordinary method is to procure it from the combus-
tion of coal.
    Combustion is a chemical process.  A particular constitu-
 ent of our  atmosphere, oxygen,  possesses a strong force of 
         PRODUCTION OF FORCE BY COMBUSTION.      221

attraction, or, as  it is named in  chemistry, a strong affinity
for the  constituents of the combustible body, which affinity,
however, in most cases, can only  exert itself at high tempera-
tures.   As soon as a  portion of the combustible body, for ex-
ample the coal, is sufficiently heated, the carbon unites itself
with great violence to the oxygen  of the atmosphere and forms
a peculiar gas, carbonic acid, the  same which we see foaming
from beer and champagne.  By this combination, light and heat
are generated ; heat is generally developed by any combination
of two bodies of strong affinity for each other ; and when the
heat is  intense enough, light appears.  Hence, in the steam
engine, it is chemical processes and chemical forces which pro-
duce the astonishing work of these machines.   In like manner
the combustion of gunpowder is  a chemical process, which,
in the barrel of  the  gun, communicates living force to the
bullet.
    While now the steam engine  develops for us  mechanical
work out of heat,  we can conversely generate heat by mechani-
cal forces.   A skilful blacksmith can render an iron wedge red
hot by hammering.   The axles of our carriages must be pro-
tected by careful greasing,  from ignition through friction.
Even lately this property has been  applied on a large scale.   In
some factories, where  a surplus of water power is at hand, this
surplus is applied to cause a strong iron plate to rotate swiftly
upon another, so that  they become strongly heated by the fric-
tion.  The heat so obtained warms the room, and thus a stove
without fuel is provided.  Now, could not the  heat generated
by the plates be applied to a small steam engine, which, in its
turn,  should be  able to keep the rubbing plates in motion ?
The perpetual motion would thus be at length found.  This
question might be asked,  and could not be  decided by the
older mathematico-mechanieal investigations.   I will remark,
beforehand, that  the  general law which I will lay before you
answers the question  in the negative.
    By a similar  plan, however,  a speculative American set 
 222        INTERACTION OF NATURAL FORCES.

 some time ago the industrial world of Europe in excitement.
 The magneto-electric machines often made use of in the case
 of rheumatic  disorders are well known  to  the public.   By
 imparting a swift rotation  to the magnet  of  such a machine,
 we obtain powerful currents of electricity.  If those  be con-
 ducted through  water, the latter will be reduced into its twj
 components, oxygen and hydrogen.   By the combustion of
 hydrogen, water is again generated.  If this combustion takes
 place, not in  atmospheric  air, of which oxygen only consti-
 tutes a fifth part, but in pure oxygen, and  if a bit of chalk be
 placed in the flame, the chalk will be raised to a white heat,
 and  give us the sun-like Drummond's light.-  At  the same
 time, the flame develops  a  considerable quantity of heat.
 Our American  proposed to  utilize in this  way the gases
 obtained from electrolytic decomposition, and asserted that by
 the combustion a sufficient amount of heat was generated to
 keep a small steam engine  in  action,  which  again drove his
 magneto-electric machine, decomposed  the water, and thus
 continually prepared its own fuel.   This would certainly have
 been the most splendid of all discoveries ; a perpetual  motion
which, besides the force which kept it going, generated hght
like the sun, and warmed all around it.  The matter was by
no means badly cogitated.  Each practical step  in the affair
was known to be possible ; but  those Avho at that time were
acquainted  with the physical investigations which bear upon
this subject  could  have  affirmed, on  the  first hearing the
report, that the matter was to be numbered among the numer-
ous stories of the fable-rich America;  and indeed, a fable it
remained.
   It is  not  necessary to multiply examples- further.   You
will  infer from  those  given, in v/hat immediate connection
 heat, electricity,  magnetism, light, and chemical affinity, stand
 with mechanical forces.
   Starting from  each of these  different manifestations  of
 natural forces, we can set every other in motion, for the most 
            STATEMENT OF  DYNAMIC PROBLEM.        223

part not in one way merely,  but in many ways.   It is here as
with the weaver's web,—

        Where a step stirs a thousand threads,
        The shuttles shoot from side to side,
        The fibres flow unseen,
        And one shock-strikes a thousand combinations.

    Now it is clear  that if by any means we could succeed, as
the above American professed to have done, by mechanical
forces, to excite  chemical,  electrical, or  other  natural pro-
cesses, which, by any circuit whatever, and without altering
permanently the active masses in the machine, could produce
mechanical force in greater quantity than that at first applied,
a portion  of the work thus gained might be made use of to
keep the machine in motion, while the rest of the work might
be  applied to any other purpose whatever.   The problem
was,  to find in the complicated net of reciprocal actions, a
track through  chemical, electrical, magnetical, and thermic
processes, back to mechanical actions, which might be foUowed
with a final gain of mechanical work ; thus would the perpet-
ual motion be found.
    But, warned  by the futility of former experiments, the
public had "become wiser.  On the whole, people did not seek
much after combinations which promised to furnish a perpetual
motion, but the  question was inverted.   It was  no more
asked, How can I make use of the known and unknown rela-
tions of natural forces so as to construct a perpetual motion ?
but it was asked, If a perpetual motion be impossible, what
are the relations Avhich must subsist between natural forces ?
Everything  was  gained by this inversion of  the  question.
The relations of natural forces  rendered necessary by the
above assumption, might be easily and completely stated.  It
was found that all known  relations of force harmonize with
the consequences  of that assumption, and a series of unknown
relations were discovered at the same time, the correctness of 
224        INTERACTION  OF NATURAL FORCES.

which remained to be proved.   If a single one of them could
be proved false, then a perpetual motion wotdd be possible.
    The first who endeavoured to travel this way was a French-
man, named Carnot, in the year 1824.   In spite  of a too
limited conception of his subject, and an incorrect view as to
the nature of heat,  which led him to some erroneous conclu-
sions, his experiment was not quite unsuccessful.   He dis-
covered a law which now bears his name,  and to which I will
return further on.
    Hi3 labors remained for a long time without notice, and it
was not  till eighteen years  afterwards, that is, in 1842, that
different  investigators in different countries, and independent
of Carnot, laid hold of the same thought.
    The first who saw truly  the general law here referred to,
and expressed it  correctly," was a German physician, J. It.
Mayer, of Heilbronn, in the year  1842.  A little  later, in
1843, a  Dane, named Colding, presented a memoir to the
Academy of Copenhagen, in  which the same law found utter-
ance, and some  experiments were described for its further
corroboration.  In England, Joule began about the same time
to make  experiments having reference to  the same  subject.
We  often find, in the case  of questions  to  the  solution of
which the development of science points, that several heads,
quite independent of  each other, generate exactly the  same
series of reflections.
    I myself,  without being  acquainted with either Mayer or
Colding,  and having first made the  acquaintance of Joule's
experiments at the end of my investigation, followed the same
path. I endeavoured to ascertain all the relations between the
different natural processes, which followed from our regarding
them from the above point of view.   My inquiry was  made
public in  1847,  in a small pamphlet  bearing the title, " Ou
the Conservation of Force."
    Since that time the interest of the scientific public for this
subject has  gradually augmented.   A great  number of the 
            PROGRESS  OF THE INVESTIGATION.         225

 essential  consequences  of the  above manner of viewing the
 subject,  the proof of  which was  wanting when the  first
 theoretic  notions were  published, have since been confirmed
 by experiment, particularly by those of  Joule ;  and during
 the last year the most eminent physicist of France, Regnault,
 has  adopted the new mode regarding the question,  and by
 fresh investigations on the specific heat of gases has contri-
 buted much to its support.  For some important consequences
 the  experimental proof is still  wanting, but the  number of
 confirmations  is so predominant, that I have not deemed it
 too  early to bring the subject before even a non-scientific
 audience.
   How tne question has  been decided you may already infer
 from what has been stated.  In the series of natural processes
 there is no circuit to be  found, by which mechanical force can
 be gained without  a  corresponding  consumption.  The  per-
 petual motion remains impossible.  Our reflections, however,
 gain thereby a higher interest.
   We have thus  far  regarded the development of force by
 natural processes, only in  its relation to its usefulness to man,
 as mechanical  force.  You now see that we have arrived at a
general law, which holds good  wholly  independent  of the
application which  man  makes  of natural  forces; we must
therefore make the  expression of our new  law correspond to
this more general  significance.   It is in the first place  clear,
that the work which, by any natural process whatever, is per-
formed under favourable conditions by a machine,  and which
may be measured in the way already indicated, may be used
as a  measure of  force common to all.  Further,  the impor-
tant  question arises, " If the quantity of force cannot be aug-
 mented except  by corresponding  consumption,   can  it be
diminished or lost?   For the purpose of our machines it cer-
tainly can, if  we neglect the opportunity to convert natural
processes  to use, but as  investigation haS proved, not for a
nature as a whole." 
 226        INTERACTION OF NATURAL FORCES.

    In the collision and friction of bodies agaiust each other,
 the mechanics  of former years assumed simply that living
 force  was lost.   But I have already stated that each collision
 and each act of friction generates heat;  and, moreover, Joule
 has estabhshed  by experiment  the important  law,  that for
 every foot-pound of force which is lost,  a definite quantity cf
 heat is always generated, and that when work is performed
 by the consumption of heat, for  each foot-pound thus gained a
 definite  quantity of heat disappears.   The quantity of heat
 necessary to raise the temperature of a  pound of water a de-
 gree of the centigrade thermometer, corresponds to a mechani-
 cal  force by which a pound weight would be raised  to the
 height of 1350  feet; we  name  this quantity the mechanical
 equivalent of heat.  I may mention here that these facts con-
 duct of necessity to the conclusion, that the  heat  is not, as
 was formerly imagined,  a fine  imponderable  substance,  but
 that,  hke  light,  it is a peculiar  shivering  motion of the ulti-
 mate  particles of bodies.   In collision and friction, according
 to this manner of viewing the subject, the motion of the mass
 of a body which is apparently lost is converted into a motion
 of the ultimate  particles of the body;  and conversely, when
mechanical force is generated by heat, the  motion of the ulti-
mate particles is converted into a motion of the mass.
    Chemical combinations generate heat, and the quantity of
this heat is totally independent of the time and  steps through
which the combination has been effected, provided that other
actions are not at the same time brought into play.  If, however,
mechanical work is at the same time accomphshed, as in the
 case of the steam  engine, we obtain as much less heat as is
 equivalent to this work.  The quantity of work produced by
 chemical force   is  in  general very great.   A pound of the
purest coal gives, when burnt, sufficient  heat to raise the tem-
perature  of 8086 pounds  of water one degree of the centi-
 grade thermometer ;  from this we can calculate that the mag-
 nitude of the chemical force of attraction between the parti- 
   AMOUNT OF FORCE IN THE UNIVERSE UNALTERABLE.  227

cles of a pound of coal and the quantity of oxygen that corre-
sponds  to it, is  capable  of  lifting a weight  of one hundred
pounds  to  a height of twenty miles.  Unfortunately,  in our
steam engines, we have hitherto been able  to gain only the
smaUest portion of this work; the greater part is lost in the
shape of heat.   The  best  expansive  engines give back as
mechanical work only eighteen per cent, of the heat generated
by the fuel.
   From a similar -investigation of all the other known physi-
cal and  chemical  processes, we arrive at the  conclusion that
Nature  as a whole possesses a store of force  which cannot in
any way be either increased  or diminished.  And that, there-
fore, the quantity of force in nature is  just as  eternal and
unalterable as the quantity of matter.  Expressed in this form,
I have named the general law " The Principle of the Conser
vation of Force."
   We  cannot create mechanical force, but we may help our-
selves from the general  store-house of Nature.  The brook
and the wind, wliich drive our mills, the forest and the coal-
bed,  which supply our steam engines and warm our rooms,
are to us the bearers of a small portion of the great natural
supply which we draw upon for our purposes, and the actions
of which we can  apply as we think fit.   The possessor of a
mill claims the gravity of the descending rivulet, or the living
force  of the moving wind,  as his possession.   These por-
tions of the store of Nature are what  give his property its
chief value.
   Further, from the  fact that  no portion of force can be
absolutely lost, it does  not follow that a portion may not be
inapplicable to  human purposes.  In  this respect the infer-
ences drawn by William Thomson from, the  law of Carnot
are of importance.   This law, which was discovered by Car-
not during  his endeavours to ascertain  the relations between
heat  and mechanical  force, which, however, by no means
belongs to the necessary consequences of the conservation of 
228        INTERACTION  OF NATURAL FORCES.

force, and which Clausius was the first to modify in such a
manner that it no longer contradicted the above general law,
expresses  a  certain relation between the compressibility, the
capacity for  heat, and the  expansion by heat of all bodies.  It
is not yet considered as  actually proved, but some remarkable
deductions having been drawn from it,  and afterwards proved
to  be facts  by experiment,  it has  attained thereby a great
degree of probability.  Besides  the mathematical  form in
which the law was first expressed by  Carnot, we can give it
the foUowing more general expression:—" Only when heat
passes  from a warmer to a colder body, and even then only
partially, can it be converted into mechanical work."
    The heat of  a body  which we cannot cool further, cannot
be changed  into  another form of force; into the electric or
chemical force, for example.  Thus, in our steam  engines,
we convert  a portion of  the heat of the glowing coal into
work, by permitting it to pass to the  less warm  water of the
boiler.  If,  however,  all the bodies in nature had the same
temperature, it would be impossible to convert any portion of
their heat into mechanical work.  According to this, we can
divide the total force store of the universe into two parts, one
of which is heat, and must continue to be such ;  the other, to
which a portion  of the  heat of the warmer bodies, and the
total supply  of chemical, mechanical, electrical, and magneti-
cal forces belong, is  capable of the  most varied changes of
form, and constitutes the whole wealth of change which takes
place in nature.
    But the  heat of the warmer bodies strives perpetually to
pas3 to bodies less warm by radition and conduction,  and thus
to establish  an equilibrium of temperature.  At each motion
of a terrestrial body,  a  portion of mechanical force passes by
friction or  collision  into  heat, of which only a .part can be
converted back  again  into mechanical force.   This is  also
generally the case in every electrical  and chemical process.
From this, it follows that the first portion of the store of force, 
       THE FORCES OF NATURE DISSIPATED IN HEAT.    229

the unchangeable heat, is augmented by every natural pro-
cess,  while the second portion, mechanical, electrical, and
chemical force, must be diminished;  so that if the universe
be delivered over to the undisturbed action of its physical pro-
cesses, all force will finally pas3 into the form of heat, and all
heat come  into a state of equilibrium.  Then all possibility of
a further change -would be at an end, and the complete  cessa-
tion of all  natural processes  must  set in.  The life of men,
animals, and plants,  could not of course continue if the sun
had lost its high temperature, and with it his light,—if all the
components of the earth's surface had closed those combina-
tions  which  their affinities  demand.  In short, the universe
from  that  time forward would be  condemned to a state of
eternal rest.
    These  consequences of the law of Carnot are, of course,
only valid, provided  that the law, when  sufficiently tested,
proves to be universally correct.  In  the mean time there is
little  prospect  of the law being  proved incorrect.  At all
events we must admire the sagacity of Thomson, Avho,  in the
letters of a long known little mathematical formula, which
only speaks of  the  heat,  volume,  and pressure  of bodies,
was able to discern  consequences wliich threatened the uni-
verse, though certainly after an infinite period of  time, with
eternal death.
    I have already given you notice that our path lay through
a thorny and unrefreshing field of mathematico-mechanical
developments.  We have now left  this portion of our road
behind us.   The general principle which I have sought to lay
before you has conducted us to a point from which our view
is  a wide  one, and,  aided by this principle, we  can now at
pleasure  regard this  or the  other side  of the surrounding
world, according as  our interest in the matter leads us.   A
glav.ee into the narrow laboratory of the  physicist, with its
small apphances and  comphcated abstractions, will not be  so
attractive as  a glance at tho wide heaven above us, the cloudsj 
230        INTERACTION OF  NATURAL  FORCES.

the rivers, the woods, and the living beings around us.  While
regarding  the laws which have been deduced from the physi-
cal processes of terrestrial  bodies, as applicable also to the
heavenly bodies, let me remind you that the same force which,
acting at the earth's surface, we call gravity  (Schwere), acts
as gravitation in the celestial spaces, and also manifests its
power in the motion of the immeasurably distant double stars
which are governed by exactly the same laws  as those sub-
sisting  between the earth  and moon;  that, therefore,  the
light and heat of terrestrial bodies do not in any way differ
essentially from those of the sun, or of the most distant fixed
star;  that the meteoric  stones which sometimes fall from ex-
ternal space upon the earth  arc composed of exactly the same
simple  chemical substances  as  those with  which we  are
acquainted.  We need, therefore, feel no scruple in granting
that general laws to  which all terrestrial natural processes
are subject,  are also valid for other  bodies  than the earth.
We will, therefore, make use  of our law to glance  over  the
household of the universe with respect to  the store of force,
capable of action, which it possesses.
   A number of singular pecuharities in the structure of our
planetary system indicate that it was  once a  connected mass
with a uniform motion of rotation.  Without such an assump-
tion, it is impossible to explain why all the planets move in the
same direction round the sun, why they all rotate in  the same
direction round their axes, why the planes of their orbits, and
those  of their satellites  and  rings ah nearly coincide, why all
their orbits differ but little from  circles; and much besides.
From these remaining indications of a former state, astrono-
mers  have shaped an hypothesis regarding the formation of
our planetary system, which, although from the  nature of the
case it must ever remain an hypothesis, still  in its  special
traits is so well supported  by analogy,  that  it certainly de- ■
serves our attention.  It was Kant, who,'feeling great inter-
est in the physical description of the earth and  the planetary 
ORIGIN OF THE  NEBULAR HYPOTHESIS.      231
system, undertook the labour of studying the works of New-
ton, and as an evidence of the depth to which he had pene-
trated into the fundamental ideas of Newton, seized the notior.
that the same  attractive force of all ponderable matter which
now  supports the motion of the planets, must also aforetime
have been able to form from matter loosely scattered in space
the planetary system.  Afterwards, and independent of Kant,
Laplace, the great author of the Mecanique Celeste, laid hold
of the same thought, and introduced it among astronomers.
    The  commencement of our planetary  system, including
the  sun, must, according to this, be regarded as an immense
nebulous mass which filled the portion of space which is now
occupied by our  system, far beyond the limits of Neptune,
our most  distant planet.  Even now we perhaps see similar
masses in the distant regions of the firmament, as patches of
nebulap, and nebulous stars ; within our system also, comets,
the zodiacal hght, the corona of the sun during a total echpse,
exhibit  remnants of a nebulous substance, which is  so thin
that the hght of  the stars passes through it unenfeebled and
unrefracted.  If we calculate the density of the mass of our
planetary system, according to the above assumption,  for the
time  when it  was  a nebulous  sphere, which reached to the
path  of the outmost  planet, we should find that it  would
require  several cubic miles of such matter to weigh a single
grain.
   The general attractive force of all matter must, however,
impel these masses to approach each other, and to condense,
so that the- nebulous sphere became  incessantly smaller, by
which, according to mechanical laws, a motion of rotation
originally slow, and the existence of which  must be assumed,
would gradually become quicker and  quicker.  By the cen-
trifugal force wliich must act most energetically in the neigh-
bourhood of the equator  of  the nebulous  sphere,  masses
could from time to time be torn away, which afterwards would
continue their  courses separate from the main mass, forming 
232        INTERACTION OF NATURAL FORCE'.

themselves into single planets, or, similar to the great ongl*
nal sphere, into planets with satellites and rings, until finally
the  principal   mass condensed  itself into the sun.   With
regard  to the  origin of heat and  light, this view gives us no
information.
    When the nebulous chaos first separated itself from other
fixed star masses, it must not only have contained all kinds
of matter which was  to  constitute the future planetary sys-
tem, but also,  in accordance with our new law, the whole
store of force which at one time must unfold therein its wealth
of actions.   Indeed  in this respect an immense dower was
bestowed in the shape of the  general attraction of ah the par-
ticles for each other.   This force, which  on the earth exerts
itself as gravity, acts in the heavenly spaces as gravitation.
As terrestrial  gravity when  it draws a weight  downwards
performs work and generates vis  vie a, so  also the heavenly
bodies do  the  same when they draw two  portions of matter
from distant regions of space  towards each  other.
   The chemical forces  must have been also present, ready
to act; but as these forces  can  only come  into  operation
by the most intimate contact of the different masses,  con-
densation must have taken place before the play of chemical
forces began.
   Whether a  still  further  supply of force  in the shape of
heat was present at the commencement we do not know.   At
all events, by aid of the law of the equivalence of heat and
work, we find in  the mechanical forces, existing at the time
to which we refer, such a rich source of heat and hght, that
there is no necessity whatever to take refuge in the idea of a
store of these forces originally existing.  When through con-
densation of the masses  their particles came  into  collision,
and clung to each other, the vis viva of their motion would be
thereby annihilated, and must reappear as heat.  Already in
old theories, it has been calculated, that cosmical masses must
generate heat by their collision, but it was far from any body's 
        HEAT DEVELOPED  IN THE  SOLAR  SYSTEM.     233

thought, to make even a guess  at the amount of heat to be
generated  in this way.  At  present  we  can give  definite
numerical values with certainty.
    Let us  make this addition  to our assumption;  that, at the
commencement,  the density  of the nebulous matter was a van-
ishing' quantity, as compared  with the  present density of tho
sun  and planets ;  we can then calculate how much work has
been performed by the condensation;  we can further calcu-
late  how much of this work  rtill exists in the form  of mechani-
cal force, as attraction of the  planets towards the  sun, and as
vis viva of their motion, and  find, by this, how much of the
force has been converted into heat.
    The result of this calculation is, that only about the 454th
part of the original mechanical force  remains as such, and
that the remainder, converted  into heat, would be  sufficient to
raise a mass of water equal to the sun  and  planets taken to-
gether, not less  than twenty-eight millions of degrees of the
centigrade  scale.   For the sake of comparison*, I will mention
that the highest temperature  wliich we can  produce by the
oxyhydrogen blowpipe, which is sufficient to fuse  and vapor-
ize even platina,  and which  but few  bodies  can endure, ia
estimated at about two thousand centigrade degrees.   Of the
action of a temperature of  twenty-eight millions  of such de-
grees we can form no notion.  If the mass of  our entire sys-
tem were pure coal, by the combustion  of the whole of it only
the 3500th part of the  above quantity would be generated.
This is also clear, that such  a  development of heat must have
presented  the  greatest  obstacle to  the speedy union of the
masses, that the larger part  of the heat must  have  been
diffused by radiation into space, before  the masses could form
bodies possessing the present  density of the sun and planets,
end that these bodies must once have been in a state of fiery
fluidity.  This  notion is corroborated by the  geological phe-
nomena of our planet; and  with regard to the other planetary
bodies, the flattened form of the sphere, which i>. the form of 
234
INTERACTION OF NATURAL FORCES.
equilibrium of a fluid mass, is indicative of a former state of
fluidity.   If  I  thus  permit an  immense quantity of heat
to disappear without compensation from our  system,  the
principle of the  conservation of force is not thereby invaded.
Certainly for  our planet it is lost, but not for the universe.
It has proceeded outwards, and daily proceeds outwards into
infinite space ; and  we know not whether the medium which
transmits the undulations of light and heat possesses an end
where the rays must return, or whether they  eternally pursue
their way through infinitude.
   The  store of force at present  possessed by our system, is
also  equivalent to immense quantities of heat.   If our earth
were by a sudden shock  brought  to rest on her orbit—which
is not to  be feared in the existing  arrangements of our system
—by such  a  shock a quantity of heat Avould be  generated
equal to that produced by the combustion of fourteen  such
earths of solid coal.  Making the  most unfavourable assump-
tion as to its  capacity for heat, that is, placing it equal to that
of water, the mass of the earth would thereby be heated 11,200
degrees; it would therefore be quite fused and for the most
part reduced  to vapour.   If, then, the earth, after having been
thus brought  to rest, should faU into the sun, which of course
would be the  case, the quantity of heat developed by the shock
would be four hundred times greater.
   Even now, from time to time, such a process is repeated
on a small  scale.  There can hardly be a doubt that meteors,
(ire-balls, and meteoric stones, are masses which belong to
the universe,  and before coming into the domain of our earth,
moved like the planets round the sun.  Only when they enter
our atmosphere do they become visible and fall  sometimes to
the' earth.    In  order to explain the emission of light by
these bodies, and  the  fact that for some time after their
descent they are very hot, the friction was long ago thought
of which they experience in passing through  the air.   We
can  now calculate  that a velocity  of  3000 feet a  second, 
           THE LIGHT AND HEAT OF METEORS.        235

supposing the whole of the friction to be expended in heating
the solid mass, would raise a piece of meteoric iron 1000° C.
in temperature, or, in other words, to a vivid red heat.   Now
the average velocity of the meteors seems to be thirty or forty
times the above amount.  To compensate this, however, the
greater portion of the heat is, doubtless, carried away by the
condensed mass of air which the meteor drives before it.  It
is known that bright meteors generally leave a luminous trail
behind them, which probably consists of several portions of
the red-hot surfaces.  Meteoric masses which fall to the earth
often burst  with a violent explosion, which may be regarded
as  a result of the quick  heating.  The newly-faUen  pieces
have been for the most part found hot, but not red-hot,  which
is easily explainable by the circumstance,  that during the
short time occupied by the meteor in  passing through the
atmosphere, only a thin, superficial layer is heated to redness,
while but a small quantity of heat has been able to penetrate
to the interior of the mass.  For this reason the red heat can
speedily disappear.
    Thus has the falling  of the  meteoric  stone, the minute
remnant of processes which seems to have played an impor-
tant part in the formation of the heavenly bodies, conducted
us to the present time, where we pass  from the darkness of
hypothetical views to the brightness of knowledge.   In what
we have said, however, all that is hypothetical is the assump-
tion of Kant and Laplace,  that the masses of our system were
once distributed as nebula; in space.
    On  account of the rarity of the case, we will still further
remark, in what close coincidence the results of science here
stand with the  earlier legends of the human family, and the
forebodings of poetic fancy.  The cosmogony of ancient na-
tions generally commences with chaos and darkness.
    Neither  is  the Mosaic tradition very divergent, particu-
larly when we remember that that which Moses names heaven
is different from the blue dome above us, and  is synonymous 
236
INTERACTION OF NATURAL FORCES.
 with  space, and that the unformed earth, and the Avaters of
 the great deep, which were  afterwards  divided into waters
 above the firmament, and waters below the firmament, resem-
 bled the chaotic components of the world.
    Our earth  bears still the unmistakable traces of its old
 fiery fluid condition.  The granite formations of  her moun-
 tains  exhibit a structure, wliich can only  be produced by the
 crystallization  of fused  masses.   Investigation still  shows
 that the temperature in mines, and borings, increases as we
 descend;  and if this increase is uniform, at the depth of fifty
 miles, a heat exists sufficient to fuse all our minerals.  Even
 now our volcanoes  project, from time to time,  mighty masses
 of fused rocks  from their interior, as a testimony of the heat
 which exists there.  But the cooled crust of the earth has
 already become so  thick, that, as may be shown by calcula-
 tions  of its conductive  power, the heat coming to the surface
 from  within, in comparison with that reaching  the earth from
 the sun, is exceedingly small, and increases the temperature
 of the surface only about one thirtieth of a degree centigrade ;
 so that the remnant of the old store of force which is enclosed
 as heat within the bowels of the earth, has a sensible influence
 upon  the  processes at the earth's  surface, only through the
 instrumentality  of volcanic phenomena.   These processes owe
 their power almost wholly  to  the action of other heavenly bodies,
particularly to the light  and heat of the sun, and partly also,
 in the case of the tides, to  the attraction of the sun and moon.
    Most varied and numerous are the changes which we owe
 to the light and heat of the sun.  The sun heats our atmos-
 phere irregularly, the warm rarefied air ascends, while fresh
 cool air flows from the sides to supply its place : in this way
 winds are generated.  This action is most powerful at the
 equator, the warm air of which incessantly flows in the upper
 regions  of the  atmosphere  towards the poles: while  just as
 persistently, at  the earth's surface, the trade wind carries new
 and cool air to the  equator.  Without the heat of the sun aU 
    BOLAR FORCE PRODUCES THE WATER CIRCULATIONS. 237

winds  must, of necessity, cease.   Similar  currents are pro-
duced by the same cause in the waters of the sea.  Their pow-
er may be  inferred from the influence which  in  some cases
they exert  upon climate   By them the Avarm water of the
Antilles is  carried to the British Isles, and confers upon them
a mild, uniform Avarmth and rich  moisture;  Avhile, through
Bimilar causes, the floating ice of the North Pole is carried to
the coast of Newfoundland, and produces cold.  Further, by
the heat of the sun, a portion of the  water is  converted into
vapour which  rises in the atmosphere, is condensed to clouds,
or falls in rain and snoAV upon the  earth, collects  in the form
of springs, brooks, and rivers, and finally reaches the sea
again, after having gnawed the rocks, carried  away the light
earth,  and  thus performed  its part in the geologic changes of
the earth; perhaps, besides all this it has  driven our water-
mill upon  its  way.   If the heat of the  sun were with drawn, i
there Avould remain only a single  motion of water,  namelv,
the tides, Avhich are produced by the attraction of the  sun and
moon.
    How is it,  now, with the motions and the work of organic
beings. To the builders of the automata of the last  century,
men and animals  appeared as clockwork  which was never
wound up, and created the force which they exerted out of
nothing.  They did not  know how to establish a connection
between the nutriment consumed  and  the work generated.
Since, however, we have learned to discern in the steam-en-
gine this origin of mechanical force, we must inquire whether
something similar does not hold good with regard to men.  In-
deed, the continuation of hfe is dependent on the consumption
of nutritive materials : these are combustible substances, which,
after digestion and being passed into the blood, actually under-
go a slow  combustion, and finally enter into almost the same
combinations with the oxygen of the atmosphere that are pro-
duced in an open fire.   As the  quantity of  heat generated by
combustion is independent of the duration of the combustion and 
238        INTERACTION  OF NATURAL FORCES.
the steps in Avhich it occurs, we can calculate from the mass of
the consumed material how much heat, or its equivalent Avork
is thereby generated in an  animal body.  Unfortunately, the
difficulty of the  experiments  is  still very great; but within
those limits of accuracy Avhich have been as yet attainable, the
experiments show that the heat generated in the animal body
corresponds to the amount which would be generated by the
chemical processes.  The animal body therefore does not differ
from the steam-engine, as regards  the  manner in  which it
obtains heat  and force, but  does differ  from it in the  man-
ner  in which the force  gained is to be  made use of.   The
body is, besides, more limited than the machine in the choice
of its fuel; the latter could be heated with sugar, with starch-
flour, and butter, just as well as with coal or wood ; the ani-
mal body must dissolve its materials artificially, and distribute
them through its system ;  it must, further, perpetually renew
the used-up materials  of  its organs, and as it cannot itself
create  the matter necessary for  this, the matter must come
from without.  Liebig Avas the first to point out these various
uses of the consumed nutriment.  As material for the perpet-
ual renewal of the body, it seems that certain definite albumi-
nous substances which appear in plants, and form the chief
mass of the animal body, can alone be used.  They form only
a portion of the mass of nutriment taken daily; the remain-
der,  sugar, starch, fat, are really only materials for Avarming,
and are perhaps  not to be superseded by coal, simply because
the latter does not permit itself to be  dissolved.
   If,  then, the  processes in  the  animal  body are not in this
respect to be  distinguished from inorganic processes, the ques-
tion  arises, whence  comes the  nutriment which  constitutes
the source of the body's force?  The answer is, from  the
vegetable kingdom;  for  only the  material of plants, or  the
flesh of plant-eating  animals, can be made use of for food.
The  animals which  live on  plants)  occupy a mean position
between  carnivorous animals, in a* hich Ave  reckon man, and 
            SOLAR  ORIGIN OF  ORGANIC FORCE.         239

vegetables, Avhich the former could not make use of immedi-
ately as nutriment.   In hay and grass the same nutritive sub-
stances  are present as in meal and flour, but in less quantity.
As, however, the digestive organs of man are not in a condi-
tion to extract the small quantity of the useful from the great
excess of the insoluble,  we  submit, in the first place, these
substances to the powerful  digestion  of the  ox, permit the
nourishment to store  itself in the animal's  body, in order in
the end to gain it for  ourselves in a more agreeable and use-
ful form.   In answer to  our question, therefore, we are re-
ferred to the vegetable world.   Now when what plants take
in and Avhat they give out are made the subjects of investiga-
tion, we find that the  principal part of the former consists in
the products of  combustion which  are  generated by the ani-
mal.  They take the consumed carbon given off in respira-
tion, as carbonic acid, from  the ah, the consumed hydrogen
as water, the nitrogen in its simplest and  closest combination
as ammonia; and from  these  materials, with  the assistance
of small ingredients  which they take from the soil, they gen-
erate anew the compound combustible substances, albumen,
sugar, oil, on Avhich the animal subsists.  Here, therefore, is
a circuit Avhich appears  to  be a perpetual store  of force.
Plants prepare fuel and nutriment, animals consume these,
burn them  slowly in  their lungs, and  from the products of
combustion  the  plants again derive their nutriment.  The
latter is an eternal source  of chemical, the former of  mechan-
ical forces.  Would not the combination of both organic king-
doms produce the perpetual motion ?  We must not conclude
hastily : further inquiry shoAvs,  that plants are capable of pro-
ducing combustible substances  only when they are under the
influence of the  sun.   A portion of the sun's rays exhibits a
remarkable relation to chemical forces,—it can  produce and
destroy chemical combinations ;  and these rays, which for the
most part  are  blue or violet,  are  called therefore chemical
rays.   We make use  of their action in the production of pho« 
240         INTERACTION OF NATURAL FORCES,

tographs.   Here compounds of silver are decomposed at the
place where the sun's rays strike them.  The same rays over-
power in the green leaves of plants the strong chemical affinity
of the carbon of the carbonic acid for oxygen, give back the
latter free to the  atmosphere, and  accumulate the other, in
combination with other bodies, as woody fibre, starch, oil, or
resin.   These chemically active  rays  of the  sun disappear
completely as soon as they encounter the green portions of the
plants, and hence it is that in daguerrotype  images the green
leaves of  plants  appear uniformly black.    Inasmuch  as the
hght coming from them does not contain the chemical rays, it
is unable to act upon the silver compounds.
   Hence a certain portion of force disappears from the sun-
light, while combustible substances are generated and accumu-
lated in plants ; and  v,re can assume it  as very probable, that
the former is the cause of the latter.  I must indeed remark,
that  we are in possession of no experiments from which wre
might determine  whether the vis viva of the sun's rays which
have disappeared, corresponds to the chemical forces accumu-
lated during the same time ; and as long as these experiments
are wanting, Ave  cannot regard the stated relation as a cer-
tainty.   If this view should prove correct, we derive 'from it
the flattering result, that all force, by means of which our bodies
live and move, finds its source in the  purest  sunlight; and
hence Ave are all, in point of nobility, not behind the race of the
great monarch of China, A\rko heretofore alone called himself
Son of the Sun.  But it must also be conceded that our lower
felloAv-beings, the  frog  and leech, share  the  same ethereal
origin, as  also the whole  vegetable world, and even the fuel
which comes to us from the ages past, as well as the youngest
offspring of the forest with which we heat our stoves and set
our machines in motion.
   You see, then, that the immense Avealth of ever-changing
meteorological, chmatic, geological, and organic processes of
our earth are almost Avholly preserved in action by the ligh* 
DYNAMICS  OF SUNLIGHT.
241
and heat-giving rays of the sun;  and you see in this a re-
markable example,  how  Proteus-like the effects of a single
cause, under altered external conditions, may exhibit itself in
nature.   Besides these,  the  earth  experiences an action of
another  kind from its central luminary, as Avell as from its
satellite  the  moon, AA-hich exhibits itself in the  remarkable
phenomenon of the ebb and flow of the tide.
   Each of these bodies excites, by its attraction upon the
Avaters of the sea, tAVO gigantic waves, which flow in the same
direction round the Avorld, as the attracting bodies themselves
apparently do.  The two waves of the moon, on account of
her greater nearness, are about three and a half times as large
as those  excited by the sun.   One of these Avaves has its crest
on the quarter of the earth's surface which is turned towards
the moon, the other is at the opposite  side.  Both these quar-
ters possess the flow of the tide, Avhile the regions which lie
between  have  the ebb.   Although in the  open sea the height
of the tide amounts  to only about three feet, and  only in cer-
tain  narrow channels, where  the  moving Avater  is squeezed
together, rises  to thirty feet, the might of the  phenomena is
neA-ertheless manifest from the calculation of Bessel, accord-
ing to which a quarter of the  earth covered by the sea pos-
sesses, during the flow of  the  tide, about  25,000 cubic miles
of water more than during the ebb, and that therefore such a
mass of  water must, in  six  and a quarter hours, Aoav from
one quarter of the earth to the other.
   The phenomena of the ebb and Aoav, as already recognized
by Mayer, combined with the law of the conservation of force,
stand in  remarkable  connection with the question of the sta-
bility of  our planetary system.  The mechanical theory of the
planetary motions discovered by Newton  teaches, that if a
solid  body in  absolute vacuo, attracted  by the   sun, move
around him  in the  same manner as  the planets, this motion
will endure unchanged through all eternity.
   Now  we have  actually not only one, but several such
              11 
242        INTERACTION OF NATURAL FORCES.

planets, Avhich move around  the  sun, and by their mutual
attraction create little changes and disturbances in each other's
paths.   Nevertheless Laplace, in his great work, the Mece.n-
ique Celeste, has proved that in our planetary system all these
disturbances increase and diminish periodically, and can never
exceed certain hmits, so that by this cause the eternal exist-
ence of the planetary system is unendangered.
    But I have already named two assumptions which must be
made : first that the celestial spaces must be absolutely empty;
and secondly, that the sun and  planets  must be solid bodies.
The first is  at least the case as  far  as astronomical observa-
tions reach, for they have never been able to detect any retar-
dation of the planets, such as would occur if they moved in a
resisting medium.  But on a body of less mass, the comet of
Encke, changes are observed of such a nature : this comet de-
scribes ellipses  round the sun which  are becoming gradually
smaller.   If this kind of motion, which certainly  corresponds
to that through a resisting medium, be actually due to the ex-
istence of such a medium, a time will come when the comet
Avill strike the sun ; and a similar end threatens aU the planets,
although after  a time, the length of which baffles our imagina-
tion to conceive of it.  But even should the existence of a re-
sisting medium appear doubtful to us, there is no doubt that
the  planets are  not wholly composed  of sohd materials which
are  inseparably bound together.  Signs of the  existence of an
atmosphere  are observed on the Sun, on Venus,  Mars, Jupi-
ter, and  Saturn.  Signs of water and ice  upon Mars; and
our earth has  undoubtedly  a fluid  portion  on  its surface,
and perhaps a  still greater portion of fluid within it.   The
motions  of the tides, however, produce friction, all friction
destroys vis viva, and the loss in this case can only affect the
vis  viva of the planetary system.   We come thereby to the
unavoidable conclusion, that every tide, although  with infinite
slowness, still with certainty, diminishes the store of mechani-
cal force of the system ; and as a consequence of this, the ro- 
     INFLUENCE OF TIDES UPON THE EARTIl's ROTATION.  243

 taticn of the planets in question round their axes must become
 more slow;  they must therefore approach the sun, or  their
 satellites must approach them. What length of time  must
 pass before the length of our day is diminished one second by
 the  action of the tide  cannot be calculated, until  the height
 and time of  the tide in aU portions of the ocean are knoAA-n.
 This alteration, however, takes place with extreme  slowness,
 as is known  by the  consequences which Laplace has deduced
 from the observations of Hipparchus,  according  to which,
 during a period of  2000 years, the duration of the day has
 not  been shortened by the one three hundredth part of a sec-
 ond.  The final consequence would be, but after millions of
 years, if in  the mean time the ocean did not become frozen,
 that one side of the earth would be constantly turned toAvards
 the sun, and enjoy a perpetual day, whereas the opposite side
 would  be  involved  in eternal  night.   Such  a position we
 observe in our moon Avith regard to the earth, and also in the
 case of the satellites as regards their  planets ; it is, perhaps,
 due  to the  action of the mighty ebb  and flow to Avhich these
 bodies, in  the time of their fiery fluid  condition, were  sub-
 jected.
   I would not have brought forward these conclusions, which
again plunge us in  the most distant future,  if they  were not
unavoidable.   Physico-mechanical  laws  are, as it  were, the
telescopes of  our spiritual eye, which can penetrate into the
deepest night of time, past and to come.
   Another  essential question  as regards the future of our
planetary system has reference  to its future  temperature and
illumination.   As  the internal heat of the earth has  but little
influence on  the temperature of the  surface, the heat of the
sun  is the  only thing which  essentially affects the  question.
The  quantity of heat falling from the sun during a given time
upon a given portion of the earth's surface may be measured,
and from this it can be calculated how much heat in a given
lime  is  sent  out from the entire sun.   Such  measurements 
244        INTERACTION  OF NATURAL FORCES.

have been  made by the French physicist Pauiilet, and it has
been found that the sun gives out a quantity of heat per hour
equaV to that which a layer of the densest coal ten feet thick
would give out by its combustion;  and  hence in a year a
quantity equal to the combustion of a layer of seventeen mile3.
K this heat Avere drawm uniformly from the entire mass of the
sun, its temperature would only be diminished thereby one and
one third of a degree  centigrade per year, assuming its capa-
city for heat to be equal to that of Avater.   These results can
give us an  idea of the* magnitude of  the emission, in relation
to the surface and mass of the  sun;  but they cannot inform
U3 whether the sun radiates heat as a glowing  body, which
since its formation has its heat accumulated within  it, or
whether  a new generation of heat hj  chemical processes
takes place at the sun's surface.  At aU e\-ents the law of the
conservation of force teaches us that no process  analogous to
those known at the surface of the earth, can supply for eternity
an  inexhaustible amount  of light and heat to the sun.   But
the same law  also teaches that the store of force at present
existing, as heat, or as what may become heat, is sufficient for
an immeasurable time.  With regard to the store of chemical
force in the sun, we can form no conjecture, and the  store of
heat there  existing can only be determined by very uncertain
estimations.  If, however, we adopt the very probable view,
that the remarkably small density of so large a body is caused
by its high temperature, and may become  greater in time, it
may be calculated that if the diameter of the sun were dimin-
ished  only the ten-thousandth  part  of its present length, by
this act  a sufficient quantity of heat would be generated to
coA-er the total emission for 2100 years.  Such a small change
besides it would be difficult to detect even by the finest  astro-
nomical observations.
    Indeed, from  the  commencement of the period  during
which we  possess historic accounts, that  is, for a period of
about 4000 years, the temperature of the earth has not sensi- 
       CONSTANCY  OF TUE EARTH'S TEMPERATURE.   245

bly diminished.   From these old ages Ave have certainly no
thermometric observations, but we have information regard-
ing the distribution of certain cultivated plants, the vine, the
ohve tree, which are very sensitive to changes of the mean
annual temperature, and we find that these plants at the pres-
ent moment have the same limits of distribution that they had
in the times of Abraham and Homer ; from which we may in-
fer backAvards the constancy of the climate.
    In opposition to this it has been urged, that here in Prussia
the  German knights in former times cultivated the  vine,
cellared their own wine and drank it, which is no longer pos-
sible.  From this the conclusion has been  drawn,  that the
heat of our climate has diminished since the time  teferred to.
Against this, hoAvever, Dove has cited the reports of ancient
chroniclers, according to which, in some peculiarly hot years,
the Prussian grape  possessed  somewhat less than its usual
quantity of acid.  The fact  also speaks not so much for the
climate of the country as for the throats of the German
drinkers.
    But even though the force  store of our planetary system
is so  immensely great, that  by the  incessant  emission which
has occurred during  the period of human history it has not
been sensibly diminished, even  though the length  of the time
Avhich must Aoav by, before a sensible  change in the  state of
our planetary system  occurs, is totally incapable of measure-
ment, still the inexorable laws of mechanics indicate that this
store of force, Avhich can only suffer loss and not gain, must
be  finally exhausted.   ShaU Ave terrify ourselves  by this
thought?   Men  are  in the  habit of measuring the greatness
and the wisdom of the universe by the duration and the profit
Avhich it promises to their own race ;  but the past history of
the earth already shows Avhat an insignificant moment the
duration of the existence of our race upon  it constitutes.   A
NineAreh  vessel,  a Roman sword awakes in us the conception
of grey antiquity.  What the museums of Europe show us o 
246       INI ER ACTION  OF NATURAL FORCES.

the remains of Egypt and Assyria we gaze upon Avith silent
astonishment, and despair of being able to carry our thoughts
back to a period so remote.   Still must the human race have
existed for ages, and multiplied itself before the pyramids of
Nineveh could have been erected.  We estimate  the duration
of human history at 6000 years ; but immeasurable as this time
may appear to us, what is it in comparison with the time dur-
ing which the earth carried successiA'e series of rank plants
and mighty animals, and no men ; during which in our neigh-
bourhood the amber-tree bloomed, and dropped its costly gum
on  the earth and in  the  sea; when in Siberia,  Europe  and
North America groves of tropical  palm's flourished; where
gigantic  lizards, and after them elephants, A\rhose mighty re-
mains  we still find buried in the earth, found a home ?   Dif-
ferent  geologists, proceeding from different premises, have
sought to estimate the  duration of the above creative period,
and vary from a million to nine million years.  And the time
during which  the earth generated  organic beings  is  again
small when we  compare  it with the ages during which the
world was a ball of fused rocks.  For the duration of its cool-
ing from 2000° to 200° centigrade, the experiments of Bishop
upon  basalt show that about 350 millions of years would be
necessary.  And with regard to the time during which the first
nebulous mass condensed into our planetary system, our most
daring conjectures must cease.  The history of man, there
fore, is but a short ripple in  the ocean of time.   For a much
longer series of years than that during which man has already
occupied this Avorld, the existence of the present state of in-
organic nature favourable to the duration of man seems to be
secured, so that for ourselves  and for  long generations after
us, we have nothing to fear.  But the same forces of air and
Avater, and of the volcanic  interior, which produced former
geological revolutions,  and  buried one series of  hving forms
after another,  act still  upon the earth's  crust.   They more
probably will bring about the last day of the human race than 
            CULMINATION OF  THE ARGUMENT.         241

those  distant cosmical alterations of which we have spoken,
and perhaps  force us  to make way for new and more com-
plete  hving forms, as  the  lizards and the  mammoth have
given place to us and our feUoAV-creatures which now exist.
   Thus the thread which was spun in  darkness  by those
who sought a perpetual motion has conducted us to a univer-
sal laAv of nature, which radiates light into the distant nights
of the beginning and of the end of the history of the universe.
To  our OAvn race it permits a long  but not an endless exist-
ence ;  it  threatens it  with a day of judgment, the  dawn of
which is stiU happUy obscured.   As each of us  singly must
endure the thought of his  death, the race must endure the
same.  But above the forms of life gone by, the human race
has higher moral problems before  it, the bearer of which it is,
and in the completion  of which it fulfils its destiny. 
 
I.
                   REMARKS ON

  THE FORCES OF INOKGANIC NATUKE.

                Br Dn. J. R. MAYER.

            Translated by J. C. FOSTER, B.A.





                      n


        ON CELESTIAL DYNAMICS.

                By Dr. J. R. MAYER.

            Translated bt De. H. DEBUS, F.E.S.



*
                      in.

                   REMARKS ON


THE MECHANICAL EQUIVALENT OF HEAT,

                Bt Dr. J. R. MAYER.

            Translated by J. C. FOSTEE, B.A. 
    Julius Robert Mayer was born at Heilbronn, November 23, 1814.  He
received a medical education, and became first, county wound-physician and
afterwards city physician of Heilbronn.  But few particulars of his life have
been obtained.   In 1840 he made a voyage on a Dutch freighter to Java,
and it was the accident of bleeding  a feverish patient in this country, and
observing that the venous blood in the tropics was of a much brighter red
than in colder latitudes, that  led him to those investigations of natural
forces, the chief results of which are given  in  the following essays.   Two
years  after bis attention was drawn to the subject—in 18413, he published
his first paper on the " Forces  of Inorganic  Nature."  It was  put together
briefly, and published in Liebig's journal to secure the public recognition of
his claims.  His second publication, " On Organic Motion and Nutrition"
(1845), an able essay of one hundred and  twelve pages, is  not yet translated.
His third paper, on " Celestial Dynamics," was published  in  1848 ; and hia
fourth, on the " Mechanical Equivalent of Heat," appeared in 1851.
    These  vast and rapid labors were too much for his  strength.  His over-
tasked mind gave way, and he was taken  to an insane asylum.  He, how-
ever, fortunately recovered, and is now reported as occupied with the culti-
vation of the vine in Heilbronn. 
I.
THE  FORCES  OF  INORGANIC  NATURE.
    THE folloAving pages are designed as an attempt to an
     swcr the questions, What are we to understand by
" Forces" ? and hoAv are different forces related to each other?
Whereas the term m,atter implies the possession, by the object
to which  it is  apphed, of  very definite properties, such as
weight and extension;  the  term force conveys for the most
part the idea of something unknown, unsearchable, and hypo-
thetical.   An attempt to render the  notion of force equaUy
exact with that of matter, and so to denote by it only objects
of actual  investigation, is one which, with the consequences
that floAv from it, ought not to be  unwelcome  to those who
desire that their Ariews of nature may be clear and unencum-
bered by hypotheses.
   Forces are  causes: accordingly,  we may in relation to
them make fuU apphcation  of the  principle—causa cequat ef-
fectum.  If the cause  c has the effect e, then c= e; if, in its
turn, e is the  cause of a second effect/, we have e=f, and so
on:  c=e=/... = c.  In a chain  of causes  and effects,  a
term or a part of  a term can never, as plainly appears from
the nature of an  equation, become equal to nothing.  This
first property of aU causes we call their indestructibility.
   If the given cause  c has produced an effect e equal to it-
self, it  has in that very  act ceased to be : c has  become e ; if,
after the production of  e, c still remained in whole 01 in part, 
252       THE FORCES OF ESORGAXIC XATUKE.

there must  be stiU further effects  corresponding to this  re
maining cause : the total effect of c would thus be > e, which
would be contrary to  the supposition  c=e.   Accordingly,
since cbecomes e, and e becomes/, &c, Ave must regard these
various magnitudes as  different forms  under Avhich one  and
the same object  makes its appearance. This capability of
assuming various forms is the second essential property of aU
causes.   Taking both properties together, we  may say, causes
are (quantitatively) indestructible and (qualitatively) convert-
ible objects.
   Two  classes of causes occur in nature, which, so far as
experience goes, never pass one into another.  The first class
consists of such  causes  as possess the  properties of  Aveight
and  impenetrability;  these are  kinds of Matter: the other
class is made up of causes  which are  Avanting in the proper-
ties just mentioned, -namely Forces,  called  also Impondera-
bles, from  the negative property that  has been  indicated.
Forces are  therefore indestructible,  convertible, imponderable
objects.
   We AviU  in the first  instance take  matter,  to afford us  an
example  of  causes and  effects.   Explosive gas, H+O, and
Avater, HO,  are related to each  other  as cause  and effect,
therefore H+0=HO.  But if H+O becomes HO, heat, cal.,
makes its appearance as avcU' as water;  this heat must like-
wise have a cause, x, and we  have therefore H+0+o;=HO
■\-cal.   It might, however, be asked whether H+O is really
=HO, and x=cal., and not perhaps H+0=caZ., and sc=HO,
whence the  above equation could equaUy be deduced ; and so
in many  other cases.  The phlogistic chemists recognized the
equation between cal. and  x, or  Phlogiston  as they caUed it,
and  in so doing made a great step in advance; but they in-
volved themselves again in a system of mistakes by putting—x
in place of 0 ; thus, for instance, they obtained H=HO+x.
   Chemistry, whose problem it is to  set forth in equations
the causal connection existir.g between the different kinds of 
              MATTER AND  FORCE AS CAUSES.         253

matter, teaches us that matter, as a cause, has matter for its
effect;  but Ave are equally justified in saying that to force  as
cause, corresponds force as effect.  Since c=e, and e—c, it
is unnatural to caU one term of an equation a force, and the
other an  effect of force or phenomenon, and to attach differ-
ent notions to the expressions Force and Phenomenon.  In
brief, then, if the cause is matter, the effect  is matter; if the
cause is a force, the effect is also a force.
    A cause which brings  about  the raising of a Aveight is a
force; its effect (the raised weight) is, accordingly, equaUy a
force;  or, expressing this relation in a more general form,
separation in space of ponderable objects is a force ;  since this
force causes the faU of bodies, we call it falling force.   FaU-
ing force  and  faU, or, more generally stiU,  falhng  force and
motion, are forces which  are related to each  other as cause
and effect—forces which are convertible one into  the other—
two different forms of one and the  same  object.  For  exam-
ple, a weight resting on the ground is not a force : it is neither
the cause of motion, nor of the lifting of another weight;  it
becomes so, hoAvever, in  proportion as it is  raised above the
ground: the cause—the  distance between a weight and the
earth—and the effect—the quantity of motion produced—beai
j) each other, as Ave learn from mechanics, a constant rela-
tion.
    Gravity being regarded as the cause of the faUing of bod-
ies, a gravitating force is spoken  of, and so the notions of
property and  of force are confounded with  each other:  pre-
cisely that Avhich is  the  essential  attribute of every force—
the union of  indestructibility with  convertibility—is wanting
in every property: betAveen a property and  a force, between
gravity and motion, it is therefore  impossible to estabhsh the
equation required for a rightly-conceived causal relation.  If
gravity be caUed a force, a cause is supposed which produces
effects without itself diminishing,  and incorrect conceptions
of the causal connections of things arc thereby fostered.  In 
254       THE FORCES OF INORGANIC NATURE.

order that a body may faU, it  is no  less necessary that it
should be lifted up, than  that it should be  heavy or possess
gravity;  the faU of bodies ought not therefore to be ascribed
to their gravity alone.
    It is the problem of Mechanics  to  develop the  equations
which subsist  between falhng force and  motion, motion and
faUing force, and between  different motions : here we wUl caU
to mind only one  point.   The magnitude of the faUing force
v is directly proportional (the earth's radius being assumed=
oo ) to the magnitude  of  the mass m, and the height d to
which it  is raised; that is, v~md.   If the  height d=l, to
which the mass jn is raised, is transformed into  the final  A'e-
locity c=l of this mass, we  have  also v=mc; but from  the
known relations existing between d and c, it results  that,  for
other values of d or of c,  the measure of the force v is mc1;
accordingly v=md=mc>:  the law of the conservation of  vis
viva is thus found to be based on the general law of the inde
structibility of causes.
    In numberless cases we see motion cease without having
caused another motion or  the lifting of a Aveight; but a force
once in existence cannot be annihilated, it can only change its
form ; and the question therefore arises, What other forms is
force, which we have become acquainted with as falling force
and motion, capable of assuming?   Experience alone  can
lead us to a conclusion on this  point.  In  order to experi-
ment with advantage, we  must  select  implements which,  be-
sides causing a real cessation of  motion, are as little as possi-
ble  altered by the objects to be  examined.  If, for example,
we  rub together two metal plates, we  see motion disappear,
and heat, on the other hand, make its  appearance, and we
have now only to  ask whether  motion is the cause of heat.
In order  to come to a decision on this point, we  must discuss
the  question.whether, in the numberless cases  in which  the
expenditure of motion  is accompanied  by the appearance of
heat, the motion  has not some other effect than  the pro- 
             EFFECTS OF DESTROYED MOTION.          255

duction of  heat, and the heat  some  other  cause than  the
motion.
   An attempt to ascertain the effects of ceasing motion  has
never yet been seriously made ; Avithout, therefore, wishing to
exclude d priori the  hypothesis which it may be  possible to
set up, we observe only that, as a rule, this effect cannot be
supposed to be an alteration in the state of aggregation of the
moved (that is, rubbing, &c.) bodies.   If  we assume that a
certain quantity of motion v is expended in the conversion of
a rubbing substance m into n, we must  then have w+v=n,
and «=wi+v; and when n is reconverted into m, v must ap-
pear  again  in some form or other.  By the friction  of  two
metallic plates continued for  a very long time, we can grad-
ually cause  the cessation of an immense  quantity of move-
ment ; but would it  ever occur to us to  look  for even the
smaUest trace of the  force which has disappeared  in the  me-
tallic dust that we could coUect, and to try to regain it thence?
We  repeat, the motion  cannot have been annihilated;  and
contrary, or positive and negative, motions cannot be regarded
as =0, any more than contrary motions  can  come  out of
nothing, or a Aveight  can raise itself.
   Without  the recognition  of a causal connection betAveen
motion and heat, it is just as difficult to explain the produc-
tion of heat  as  it is  to give  any account of the motion that
disappears.   The heat cannot be derived from the diminution
of the volume of the  rubbing substances.  It is Avell  known
that  two  pieces of ice may be melted  by rubbing them to-
gether in  vacuo ; but let any one try to convert ice into water
by pressure,* however enormous.   Water undergoes,  as Avas

   *  Since the original publication of this paper, Prof. W. Thomson has
shown that pressure has a sensible effect in liquefying ice ( Conf. PhiL Mag.
S. 3, vol. xxxvii. p. 123); but the experiments of Bunsen  and of  Hopkins
have  shown that the melting-points of bodies which expand on becoming
liquid are raised by pressure, which  is all that Mayer's argument requires.—
G.  C. F. 
256       THE  FORCES OF INORGANIC NATURE.

found  by the  author, a rise of temperature Avhen violently
shaken.  The water so heated (from 12° to 13° C.) has a
greater bulk after  being  shaken than it had before ;  Avhence
now comes this quantity of heat, Avhich by repeated shaking
may be caUed into  existence in the  same apparatus as often
as we  please ?   The vibratory hypothesis  of heat is an ap-
proach  toward the doctrine of heat being the effect of mo-
tion, but it does not favour the admission of this causal rela*
tion in its fuU generahty;  it rather lays  the chief stress on
uneasy oscillations (unbehagliche Schwingungen).
    If it be now considered as estabhshed that in  many cases
(exceptio confirmat regulam) no other effect of motion can be
traced except heat, and that no  other cause than motion can
be found for the heat that  is produced, Ave prefer the assump-
tion that heat proceeds from motion, to the assumption of a
cause without effect and of an effect without a cause—just as
the chemist, instead of aUowing oxygen and hydrogen to dis-
appear without further investigation, and water  to  be pro-
duced  in some  inexplicable manner, establishes a connection
between oxygen and hydrogen on the one hand and Avater on
the other.
    The natural connection existing between faUing force, mo-
tion, and heat may be conceived of as foUoAvs : We know that
heat makes its appearance when the  separate  particles of a
body approach nearer to  each other; condensation produces
heat.   And what applies to the  smallest particles of matter,
and the smaUest intervals  between them, must also apply to
large masses and to measurable distances.   The falling of a
weight  is a diminution of the bulk of the earth, and must
therefore without doubt be related  to  the  quantity  of heat
thereby developed; this quantity of heat must be proportional
to the  greatness of the  weight  and  its  distance from the
ground.  From  this point of vieAV we are very easily bd to
the equations between falhng  force, motion, and heat, that
have already been discussed. 
           EQUIVALENCE OF  HEAT AND MOTION.       257

   But just as little as  the  connection  between falling force
and motion authorizes the conclusion that the essence of fall-
ing force is motion, can  such a conclusion be adopted in the
case  of heat.   We  are, on  the  contrary, rather inclined to
infer  that, before it can  become  heat, motion—whether sim-
ple, or vibratory as in the case of light and radiant heat, &c,
—must cease to exist as motion.
   If falling force  and  motion are equivalent to heat, heat
must also naturaUy be equivalent to motion and falling force.
Just as heat appears as an effect of the diminution of bulk and
of the cessation of motion, so also does heat disappear as a
cause when its effects are produced in the shape of motion,
expansion, or raising of  Aveight.
   In water-mill.-, the continual diminution in bulk which the
earth undergoes, OAving to the faU of the water, gives rise to
motion, Avhich afterwards disappears again, calling forth un-
ceasingly a great quantity of  heat; and  inversely, the steam-
engine serves to decompose  heat again into motion or the
raising of Aveiglits.  A locomotive engine with its  train may
be compared to a distiUing apparatus ; the heat applied under
the boiler passes off as motion, and this  is deposited again as
heat at the axles of the wheels.
   We avUI close our disquisition, the propositions of which
have resulted as necessary consequences from the principle
" causa oequat  effectum,"  and which are in accordance with
all the phenomena  of Nature, with  a practical  deduction.
The solution of  the equations subsisting  between faUing force
and  motion requires that the space faUen through in a given
time, e. g. the  first second, should be  experimentaUy deter-
mined ; in like manner, the solution of the equations  subsist-
ing betAveen falling force and motion on the one hand  and
heat on the other, requires an ansAver to  the question, How
great is  the quantity of heat Avhich corresponds  to  a given
quantity of motion or faUing force ?  For instance, we must
ascertain how high a given weight requires to be  raised above 
25S       THE FORCES OF INORGANIC  NATURE.

the ground in order that its falhng force  may be equivalent to
the raising  of  the temperature of an equal weight of water
from 0° to 1° C.   The attempt to  show that such  an equa-
tion is the expression of a physical truth may be regarded as
the substance of the foregoing remarks.
    By applying the principles  that have been set forth to the
relations subsisting  between the temperature and the volume
of gases, we find that the sinking of a mercury column by
which a gas  is compressed is  equivalent to the quantity of
heat set free by  the  compression; and  hence it folloAvs, the
ratio between the capacity for heat of air under constant pres-
sure and its capacity under constant volume being  taken as
= 1*421, that the warming of a given weight of water from
0° to  1° C. corresponds  to the faU of an equal weight from
the  height Of about 365  metres.*   If we compare with this
result  the working of our best steam-engines, we  see hoAv
small a part only of the heat apphed under the boUer is really
transformed  into motion or the raising of weights ;  and this
may serve  as justification for the  attempts at  the  profitable
production of motion by some other method than the expendi-
ture of the chemical difference between carbon  and oxygen—
more particularly by the transformation  into motion of elec-
tricity obtained by chemical means.

  * When the corrected specific heat of air is introduced into the calcu-
lation this number is  increased, and agrees then with the experimental de-
terminations of Mr. Joule. 
II
CELESTIAL  DYNAMICS.
                I.—INTRODUCTION.  ■

     EVERY  incandescent and  luminous body diminishes in
      temperature and luminosity in the  same  degree  as it
radiates  hght and heat, and at last, provided its loss  be not
repaired  from some  other source of these  agencies, becomes
cold and  non-luminous.
    For light, like  sound,  consists  of vibrations Avhich are
communicated by the luminous or sounding body to a sur-
rounding medium.   It is perfectly clear that  a body can only
excite such vibrations in another substance when its own par-
ticles undergo a sinhlar movement; for there is  no  cause for
undulatory motion when a body is in a state  of rest, or in a
state of  equilibrium with the  medium by which it  is sur-
rounded.   If a beU or a string is to be sounded, an external
force must be apphed;  and this is the cause of the sound.
    If the vibratory motion of a string could  take place with-
out any resistance, it would vibrate for aU time ; but in this
case no sound could  be produced, because sound is essentially
the  propagation of motion;  and  in the same degree as the 
200
CELESTIAL DYNAMICS.
string communicates its vibrations to the  surrounding and re«
sisting medium its own motion becomes weaker and weaker,
untU at last it sinks into a state of rest.
   The sun has often and appropriately been compared to an
iucessantly sounding beU.   But by what  means is the power
of this body  kept up in  undiminished force so as  to enable
him to send forth his rays into the universe in such a grand
and magnificent manner?   What are the causes which coun-
teract or prevent his exhaustion, and thus save the planetary
system from darkness and deadly cold ?
   Some endeavoured to approach  "  the grand secret," as
Sir Wm. Herschel caUs this question, by  the assumption that
the rays  of the sun, being themselves  perfectly cold, merely
cause the " substance" of heat, supposed to be contained in
bodies, to pass from a state of rest into  a  state of motion,  and
that in order to send forth such cold rays  the sun need not be
a hot body, so  that, in spite of the  infinite development of
light, the coohng of the sun was a matter  not to be thought of.
   It is plain that nothing is gained by such an explanation ;
for, not to speak of the  hypothetical  " substance"  of heat,
assumed to be at one time at rest and at another time in mo-
tion, now cold and then hot, it is a weU-founded fact that  the
sun does not  radiate a cold phosphorescent  light, but a hght
capable of warming bodies intensely; and to ascribe such
rays to a cold body is at  once at variance  Avith reason  and
experience.
   Of course such and similar hypotheses could  not satisfy
the demands of exact science, and I avUI therefore try to ex-
plain in a more satisfactory manner than has been  done up
to this time the connexion between the  sun's radiation and its
effects.   In doing so, I have to claim the indulgence of scien-
tific men, who are acquainted with the  difficulties of my task. 
SOURCES  OF HEAT.
261
             II.—SOURCES  OF  HEAT.

    Before we  turn  our attention to the special subject of
this paper, it will be necessary to  consider the means by
which light and heat are produced.   Heat may be obtained
from very different sources.   Combustion, fermentation, pu-
trefaction, slaking  of hme, the decomposition of chloride of
nitrogen and of gun-cotton, &c. &c, are all of them sources
of heat.  The electric spark, the voltaic current, friction, per-
cussion, and the vital processes are also accompanied by the
evolution of this agent.
    A general law of nature, which knows of no exception,
is the foUoAving:—In order to obtain heat, something must
be expended; this something, however different it may be in
other respects, can always be referred to one of tAvo catego-
ries : either it consists of some material expended in a chem-
ical process, or of  some sort of mechanical Avork.
    When substances endoAved with considerable chemical af-
finity for each other combine chemically, much heat is devel-
oped during the process.   We  shaU estimate the quantity of
heat thus set free by the  number of kUogrammcs  of water
which it would heat 1° C.   The  quantity of  heat necessary
to raise  one kilogramme of water one degree is called a unit
of heat.
    It has been established by numerous experiments that tho
combustion of one  kilogramme of dry charcoal in oxygen, so
as to form carbonic acid, yields 7200 units of heat, which fact
may be  briefly expressed by saying that charcoal furnishes
7200 ' degrees of heat.
    Superior coal yields 6000°, perfectly dry wood from 3300°
to  3900% sulphur 2700,  and hydrogen 34,600° of heat.
    According to experience, the number of units of heat only
depends on the  quantity of matter Avhich is consumed,  and 
202
CELESTIAL DYNAMICS.
not on the conditions under Avhich the  burning takes place.
The same amount of heat is given out Avhether the combus-
tion proceeds slowly or quickly, in atmospheric air or in pure
oxygen gas.  If in one case a metal be burnt in air and the
amount of heat directly measured, and in another instance
the same quantity of metal be oxidized in a galvanic battery,
the heat being developed in some  other place—say, the wire
which  conducts  the  current,—in both of these experiments
the same quantity of heat avUI be  observed.
    The same law also holds good for the production of heat
by mechanical means.  The amount of heat obtained is only
dependent  on the quantity of poAver consumed, and is  quite
independent of the manner in Avhich this power has been ex-
pended.  If, therefore, the amount of heat which is produced
by certain  mechanical work is knoAvn, the quantity which
AviU be obtained by any other amount of mechanical work
can easily be found by calculation.  It  is of no  consequence
whether this Avork consists in the compression, percussion, or
friction of bodies.
    The amount of mechanical work done by a force may be
expressed  by a Aveight, and the height to Avhich this weight
would be raised  by the same  force.  The mathematical ex-
pression for " work done,"  that is to say, a measure for  this
Avork, is obtained by multiplying the height expressed in  feet
or o'.hcr units by the number of pounds  or kilogrammes hfted
to this  height.
    We shall take one kilogramme as the unit of weight, and
one metre  as the unit  of  height, and we thus  obtain the
weight of one kilogramme raised to the height of one  metre
as a unit measure of mechanical work  performed.   This
measure we shaU call a kUogrammetre, and adopt for it the
symbol Km.
    Mechanical work may likewise be measured by the  vcio
city obtained by a given weight in passing from a state of rest
into that of motion.   The  work  done is then expressed by 
SOURCES OF  HEAT.
263
the product obtained by the  multiplication of the Aveight by
the square of its velocity.   The  first  method, however, be-
cause it is the more convenient, is  the  one usuaUy adopted;
and the numbers obtained therefrom may easUy be expressed
in other units.
    The product resulting frcm the  multiplication of the num-
ber of units of weight  and  measures  of  height, or, as it  is
called, the  product  of mass  and height, as AveU as the  pro-
duct of the mass and the square of its velocity, are called " vis
viva  of motion,"  u mechanical effect,"  dynamical effect,"
" work done," " quantite de travail," &c. &c.
    The amount of mechanical work necessary for the heating
of  1 kilogramme of water 1° C has been  determined by ex-
periment  to be = 367  Km; therefore Km = 0*00273 units
of heat.*
    A mass which has faUen  through a height of 367 metres
possesses a velocity of 84-8 metres in  one second; a mass,
therefore, moving with  this velocity originates 1° C. of heat
when its  motion  is  lost by percussion, friction,  &c.  If the
velocity be two or three times as great,  4° or 9°  of  heat  will
be  developed.  Generally  speaking, Avhen the velocity  is c
metres, the corresponding  development of heat  wiU be  ex-
pressed by the formula
                      0-000139° Xc\
   * This essay was  published in  1845.   At that  time de la Roche and
Berard's determination of the specific heat of air was generally accepted.
If the physical constants used by Mayer be corrected according to the re-
sults of more recent investigation, the mechanical equivalent of heat is
found to be 771*4 foot-pounds.  Mr. Joule finds it  = 772  foot-pounds,—
Tb. 
264
CELESTIAL DYNAMICS
       III.—MEASURE OF  THE  SUN'S HEAT.

    The actinometer is an instrument invented by Sir John
Herschel for the  purpose of measuring  the heating  efffeci
produced by the sun's rays.   It is essentially a thermometer
with a large cylindrical bulb  filled with a blue liquid, which
is acted  upon by the sun's rays, and the expansion of which
is measured by a graduated scale.
    From observations made  with this  instrument, Sir Jolin
Herschel calculates the amount of heat received from the sun
to be sufficient to melt annuaUy at the surface of the globe a
crust of ice 29*2 metres in thickness.
    PouUlet has recently shown by some careful experiments
with the lens pyrhehometer, an instrument invented by him-
self, that every square centimetre of  the surface of our globe
receives, on an average, in one minute an amount of solar
heat which would  raise  the temperature of one gramme of
water 0*4408°.   Not much more  than one-half of this quan-
tity of heat, however, reaches the  sohd  surface of  our  globe,
since  a considerable portion  of it is  absorbed by  our  atmo-
sphere.  The layer of ice which, according to Pouillet, could
be melted by the solar heat which yearly  reaches  our globe
would have a thickness of 30*89 metres.
    A square metre of our earth's surface receives, therefore,
according to PouiUet's results, which we shaU adopt in the
following pages, on an average in one minute 4*408  units of
heat.   The whole  surface of the  earth is = 9,260,500 geo-
graphical square mUes* ;  consequently the earth receives in
one minute 2247 billions of units  of heat from the sun.
    In  order to obtain  smaUer numbers,  we shaU caU the
quantity of heat necessary to  raise a cubic  mile of water 1°
  * The geographical mile = 7420 metres,  and one English  mile —1608
metres. 
              MEASURE OF THE Sun's HEAT.          205

 C. in temperature, a cubic mUe of heat.   Since one cubic
 uhle of water weighs 408*54 biUions of kilogrammes, a cubic
 mUe of heat contains  408*54 biUions of units of heat.  The
 effect produced by the  rays of the sun on the surface of the
 earth in one minute is therefore 5*5 cubic mhes of heat.
    Let us  imagine the sun to be surrounded  by a hoUow
 sphere  whose radius is equal to the  mean distance of the
 earth from the sun, or 20,589,000 geographical miles; the
 surface  of this  sphere  would  be equal to 5326  biUions of
 square  miles.   The surface  obtained by the intersection  of
 this hoUoAv sphere and our globe, or the base of the  cone  of
 solar hght which reaches our earth, stands to the whole sur-
 face of  this hoUow sphere as '  4' : 5326 bilhons, or as 1 to
 2300 mUlions.  This  is the ratio  of the  heat received by
 our  globe to the whole amount of heat sent forth  from the
 sun, which  latter in one minute amounts to 12,650  mUlions
 of cubic miles of heat.
    This amazing radiation  ought, unless the loss is by some
 means made good, to cool  considerably even a body of the
 magnitude of the sun.
    If we assume the sun to be endoAved with the same capa-
 city for  heat as a mass of Avater of the same A-olume, and its
 loss of heat by radiation to  affect uniformly its Avhole  mass,
 the  temperature of the sun ought to decrease 1°*S C. yearly,
 and for the historic time of 5000 years this  loss Avould conse-
 quently amount to  9000° C.
   A uniform cooling of the whole of the  sun's huge mass
 cannot, however, take place ; on the contrary, if the radiation
 were to occur  at the expense of a given store of heat or ra-
 diant power, the sun would become  covered in a short space
 of time with a cold crust, Avhereby radiation  would be brought
 to an end.  Considering the  continued activity of  the sun
through countless centuries,  we may assume with mathemati-
cal certainty the existence of some compensating influence to
 make good its  enormous loss.
           12 
266
CELESTIAL DYNAMICS.
   Is this restoring agency a chemical process ?
   If such were the case, the  most favourable  assumption
would  be to suppose the whole mass of the sun to be  one
lump of coal, the combustion of every kilogramme of which
produces 6000 units of heat.   Then the sun would only bo
able  to sustain for forty-six centuries  its present expenditure
of hght and  heat, not  to mention the  oxygen necessary to
keep up such an immense combustion, and other unfavourable
circumstances.
   The revolution of the sun on his axis has  been suggested
as the cause of his  radiating energy.  A closer examination
proves this hypothesis also to be untenable.
   Rapid rotation, without  friction or resistance, cannot in
itself alone be  regarded as a cause of light and  heat, espe-
ciaUy as  the  sun is in no way to be distinguished  from  the
other bodies of our system by velocity of axial rotation.   The
sun turns on his axis in about twenty-five days, and his diam-
eter  is nearly 112  times as great as that of the earth, from
which it foUows that a point on the solar equator  travels  but
a httle more than  four times as quickly as a  point on  the
earth's equator.   The  largest  planet of the solar system,
whose diameter is about f0th that of the sun, turns on its axis
in less than ten hours ;  a point on its equator  revolves about
six times quicker than one on the solar  equator.  The outer
rino" of Saturn exceeds the sun's equator more than ten times
in velocity of rotation.  Nevertheless no generation of light
or heat is observed  on our globe, on  Jupiter, or on the  ring
of Saturn.
   It might be thought that  friction, though  undeveloped in
the case of the other celestial bodies,  might be engende  ed by
the sun's rotation, and that such friction might generate enor-
mous quantities of heat.  But for  the  production of friction
two bodies, at least, are always  necessary which are in imme-
diate contact Avith one  another, and which  move with differ-
ent velocities or in  different  directions.   Friction, moreover 
MEASURE OF THE SUN's HEAT.
267
has a tendency to produce equal motion of the two rubbing
bodies;  and when  this is attained, the generation of heat
ceases.  If now the sun be  the  one moving body, where  is
the other? and if the second body exist, what poAver prevents
it from assuming the same rotary motion as the sun?
    But could  even these  difficulties be disregarded, a weight-
ier and more formidable obstacle cpposes this  hypothesis.
The known volume and mass of the sun aUoAv us to calculate
the vis viva which he possesses in consequence of his rotation.
Assumjng his  density to be uniform throughout his mass, and
his period of rotation twenty-five days, it is equal to 182,300
quintiUions of kilogrammetres  (Km).  But  for  one unit of
heat generated,  367  Km are  consumed;  consequently the
whole rotation-effect of the sun could only cpArer the expendi-
ture of heat for the space  of 183 years.
    The space of our solar system is fiUed with a great  num-
ber  of ponderable  objects, which  have  a tendency to  move
towards  the  centre of gravity of  the  sun; and in so doing,
their rate of motion is more and more accelerated.
    A mass, without motion, placed within the sphere of the
sun's attraction, wiU obey this  attraction, and, if there be no
disturbing influences, AviU fall in a straight hne into the  sun.
In reahty, however, such a rectihnear path can scarcely occur,
as may be shown by experiment.
    Let a weight be suspended by a string so that it can  only
touch the floor in one  point.  Lift the weight up to a certain
height, and at the same time stretch the string out to its full
length; if the Aveight be  now aUoAved to faU, it  will be ob-
served,  almost in every case, not to reach at once the point on
the floor toAvards Avhich it tends to move, but to move  round
this point for some  time in a curved hne.
    The reason of this phenomenon is that the slightest devia-
tion of the weight from its shortest route towards  the  point
on the floor, caused by some disturbing  influence such as the
resistance of the air against a not perfectly uniform surface, 
2G8
CELESTIAL DYNAMICS.
wiU  maintain itself as long as motion lasts.  It is neverthe-
less  possible for the weight to move at once to the point;  the
probability of its doing so, however, becomes the less  as  the
height from which it is aUowed to drop increases, or the string,
by means of which it is suspended, is lengthened.
   SimUar  laAvs influence the  movements of bodies  in  the
space of  the  solar system.   The.  height  of the  faU is here
represented by the original distance from the sun at which the
body begins to move ; the length  of the string by the sun's
attraction, which increases when the distance decreases ; and
the smaU surface of contact on  the  floor by the area of  the
section of the sun's sphere.   If now a cosmical mass within
the physical limits  of the sun's sphere of attraction begins its
faU  toAvards that  heavenly body,  it AviU be disturbed in  its
long path for many centuries, at  first  by the  nearest fixed
stars, and afterwards  by the  bodies  of  the  solar  system.
Motion of such a mass in a straight line, or its  perpendicular
faU into the sun, would, therefore, under  such  conditions, be
impossible.   The  observed movement of aU planetary bodies
in closed curves  agrees with this.
   We  shaU  now return to the example  of the  weight sus-
pended by a  string and  oscillating round a point towards
which it  is attracted.  The diameters of the orbits described
by this weight are  observed to be nearly equal; continued  ob-
servation, however, shows that these diameters gradually di-
minish in length, so that the weight wiU by degrees approach
the point in which  it can touch the floor.  The weight, how-
ever, touches  the floor not in a mathematical point, but in  a
smaU surface ; as soon, therefore, as the diameter of the curve-
in which the weight moves is equal to  the diameter of this
surface, the weight wUl touch the floor.  This final contact is
no accidental or improbable  event, but a necessary phenome-
non  caused by the  resistance which the osciUating mass con-
stantly suffers from the air and  friction.  If aU resistance
could be annihUated, the motion of the weight would of course
continue in equal oscillations. 
              MEASURE OF THE SCx's I1EAT.           209

   The same laAv holds good for celestial bodies.
   The movements of celestial bodies in an absolute vacuum
would be as uniform  as those of a mathematical  pendulum,
Avhereas a resisting medium pervading all space would cause
the planets to move in shorter and shorter  orbits, and at last
to fall into the sun.
   Assuming such a resisting medium, these Avaudering ce-
lestial bodies must have on the periphery of the solar system
their  cradle, and in its centre their grave ;  and however  long
the duration, and however great the number of their revolu-
tions  may be, as many masses  Avill on the average in a cer-
tain  time arrive at the sun  as  formerly in a like period of
time came  within his sphere of attraction.
   All these bodies plunge with a violent impetus into their
common grave.  Since no cause exists Avithout an effect, each
of these cosmical masses wUl,  hke a Aveight  faUing  to the
earth, produce  by its percussion an amount  of heat propor-
tional to its vis viva.
   From the idea of a sun whose attraction acts throughout
space, of ponderable bodies scattered throughout the universe,
and  of  a resisting aether, another idea necessarhy follows—
that, namely, of a continual and inexhaustible  generation of
heat  on the central body of this  cosmical system.
   "Whether such a conception be reahzed in our solar system
—Avhether, in other words, the wonderful and permanent evo-
lution of hght and heat be caused by the  uninterrupted fall
of cosmical matter into the  sun—Avill now be more closely
examined.
   The existence of matter in a primordial condition ( Urma-
terie), moAdng about  in the universe, and assumed to foUow
the attraction of the nearest stellar system, will scarcely be
denied by  astronomers and  physicists;  for  the richness of
surrounding nature, as Avell as the aspect of  the starry heav-
ens, pre\ents the belief that the wide space which separates
our solar system from the regions governed by the other fixed 
270
CELESTIAL DYNAMICS
stars  is  a vacant solitude destitute of  matter.    We shaU
leave, however, aU suppositions concerning subjects so distant
from us both in time and space, and confine our attention ex-
clusively to what may be learnt from the observation of the
existing state of things.
   Besides the  fourteen known planets  with their eighteen
satelhtes, a great many other cosmical masses move within
the space of  the  planetary system, of Avhich the comets de-
serve to be mentioned first.
   Kepler's celebrated statement that " there are more com-
ets in the heavens than fish in the ocean," is founded on the
fact  that, of  aU the  comets belonging to our  solar system,
comparatively few can be seen by the inhabitants of the earth,
and therefore the not inconsiderable number of actuaUy ob-
served comets obhges us, according to the rules of the  calcu-
lus of probabUities, to assume the existence of a great many
more beyond the sphere of our vision.
   Besides planets,  sateUites, and comets, another class of
celestial  bodies exists within  our solar  system.   These are
masses which, on account of their smaUness, may be consid-
ered as cosmical atoms, and  which Arago has  appropriately
caUed asteroids.   They, hke the planets and  the  comets, are
governed  by gravity, and move in elliptical orbits round the
sun.   When  accident brings them into the immediate neigh- •
bourhood of the earth, they produce the phenomena of shoot-
ing-stars and fireballs.
   It has been shoAvn by repeated observation, that on a
bright night twenty minutes seldom elapse without a shooting-
star being visible to an observer in any situation.   At certain
times these meteors are observed in astonishingly great  num-
bers ; during the meteoric shower at Boston, which lasted
nine hours, when they were  said to fall  " crowded together
like  snoAv-flakes," they were  estimated as at least 240,000.
On the whole, the number of asteroids Avhich come near the
earth in the space of a year must be computed to be  many 
              MEASURE OF THE  SUx'fi HEAT.          ^71

thousands of miUions.  This, without doubt, is only a smaU
fraction of the number of asteroids that move round the sun,
Avhich number, according to the rules of the calculus of prob-
abilities, approaches the infinite.
   As has been already stated, on the existence of a resisting
asther it depends whether the celestial bodies, the planets, the
comets, and the asteroids, move  at  constant mean  distances
round  the sun, or  whether they are constantly approaching
that central body.
   Scientific men do not doubt the existence of such an aether.
Littrow, amongst others, expresses himself on  this point as
follows :—" The assumption that the planets and the  comets
move in an absolute vacuum can in no way  be  admitted.
Even if the  space between  celestial bodies contained no other
matter than that necessary for the existence of light (whether
light be considered as emission of matter or the undulations
of a uniArersal aether), this alone  is sufficient to alter the mo-
tion of the planets in  the course of time and the arrangement
of the whole system itself; the faU of all the planets and the
comets into  the sun and  the destruction of the present  state
of the solar system must be the final results of this  action."
   A direct proof of the existence of such a resisting medium
has been furnished by the academician Encke.   He found
that the  comet named after him, which revolves  round the
sun in the short space of 1207 days, shows a regular acceler-
ation of its motion, in consequence of which the time  of each
revolution is shortened by about six hours.
   From the great density and magnitude of the planets, the
shortening of the diameters of their orbits proceeds, as might
be expected, very slowly, and is up to the present time inap-
preciable.   The smaUer the cosmical masses are, on the con-
trary, other circumstances remaining the same, the faster they
move towards the sun; it may therefore  happen  that in a
space of time wherein the mean distance of the  earth  from
the sun would  diminish  one metre, a smaU asteroid would 
272
CELESTIAL. DYNAMICS.
travel  more than  one thousand  mUes toAvards the  central
body.
   As cosmical masses  stream from  aU sides in immense
numbers towards the sun, it follows that they must become
more and more croAvded together as they approach thereto.
The  conjecture at once suggests itself that the zodiacal light,
the nebulous light  of vast dimensions which surrounds the
sun,  owes its origin to such closely-packed asteroids.   Hoav-
ever it may be, this much is certain, that this phenomenon is
caused by matter Arhich moves according to the same laws as
the planets  round the sun, and  it consequently foUows that
the whole mass which originates the zodiacal light is contin-
uaUy approaching the sun and faUing into it.
   This hght does not  surround the  sun  uniformly on aU
sides ;  that is to say, it has not the form of a sphere, but that
of a thin convex lens, the greater diameter of which is in the
plane of the solar equator, and  accordingly it has to  an ob-
server on our globe a pyramidal form.   Such lenticular  dis-
tribution of the masses  in the  universe is repeated in a re-
markable  manner  in- the disposition of the  planets and the
fixed stars.

   From the great number of cometary masses and asteroids
and the zodiacal light on  the one hand,  and the existence of a
resisting aether on the other, it necessarily foUows that pon-
derable matter must continually be arriving  on the solar sur-
face.   The effect produced by these masses evidently depends
on their final velocity ; and, in order to determine the latter, we
shall discuss some of the elements of the theory of gravitation.
   The final velocity of a weight attracted by and moving
towards a celestial  body AviU become  greater as  the  height
through which the weight faUs increases.   This velocity, how-
ever, if it be only produced by the fall, cannot exceed a cer-
tain  magnitude ; it has a maximum, the value of which de-
pends on the volume and mass of the attracting celostial body 
MEASURE OF THE SUN's  HEAT.
273
    Let r be the radius of a spherical and sohd celestial body.
and g the velocity at the end of the first second of a weighi
faUing on the surface of this body ; then the greatest velocity
which this weight can obtain by its faU toAvards  the  celestial
body, or the velocity with wliich it will arrive at its surface
after a faU from an  infinite height, is \/2gr in  one second.
This  number,  wherein  g and r are  expressed in metres, we
Bhall caU G.
    For our  globe the  Aralue of g is 9*8164 . . and that of f
6,369,800 ; and consequently on our earth
        G =  {/(2x 9*8164x6,369,800) = 11,183.
    The solar radius is 112'05 times that of the earth, and the
velocity produced by gravity on  the sun's surface is  28*36
times  greater  than  the same  velocity on the surface of our
globe *, the greatest velocity therefore which a body could ob-
tain in consequence of the solar attraction, or
       G=  t/(28*36X 112*05) X 11,183 = 630,400;
that is, this maximum velocity is equal to 630,400  metres, or
85 geographical mUes in one second.
    By tlie help of this constant number, Avhich may be called
the characteristic of the  solar system, the velocity of a body
in central motion may easily be determined at any point of its
orbit.  Let a be the mean distance of the planetary body from
the centre of gravity of the sun, or the greater semidiameter
of its orbit (the radius of the sun being taken as unity) ; and
let h be the distance  of the same body at any point of its orbit
from  the  centre of gravity  of  the sun;  then the velocity,
expressed in  metres, of  the planet at the distance h is
                            /2a -h
                       GXV~2aXh-
At the moment the planet comes in contact with the solar sur
face, h is equal to 1, and its velocity is therefore
                            /2a-1 
274
CELESTIAL DYNAMICS.
    It follows from this formula that the smaUer 2a (or th«
major axis of the orbit  of a planetary body) becomes, the
less will be its velocity when it reaches the sun.  This velo-
city, like  the  major axis, has a minimum ; for so long as the
planet moves outside the sun, its major axis cannot be shorter
than the diameter of the sun, or, taking the solar  radius as a
unit, the quantity 2a can never be less than 2.  The smallest
velocity with which Ave can imagine a cosmical body to arrive
on the surface of the sun is consequently

                       GrX|/|=445,750,

or a velocity of 60 geographical miles in one second.
    For this  smaUest value the orbit of the asteroid is circu«
lar ; for a larger value it becomes eUiptical, untU finally, with
increasing excentricity, when the value of 2a  approaches in-
finity, the  orbit becomes a parabola.  In  the last case tho
velocity is
or, 85 geographical miles in one second.
   BT the value of the major axis become negative, or the
orbit  assume  the  form of a hyperbola, the velocity may in-
crease without end.  But this could only happen when cosmi-
cal masses enter the  space of the  solar system with a pro-
jected velocity, or when masses, having missed the sun's sur-
face, move into the universe and never  return; hence a Are-
locity greater  than G can only be regarded as a rare excep-
tion, and we shaU therefore only consider velocities comprised
within the limits of 60 and 80 mUes.*
   The  final velocity with  which a weight moving  in  a

   *  The relative velocity also with which an asteroid reaches  the solar
surface depends in some degree on the velocity of the sun's rotation.  This,
however,  as well as the rotatory effect of the asteroid, is without moment,
rmd may be neglected. 
MEASURE OF THE SUN's HEAT.
275
straight hne towards the centre of the sun arrives at the solar
surface is expressed by the formula

                    C-GX4/EI,

wherein  c expresses the  final velocity in metres, and  h the
original distance from the centre of the sun in terms of  solar
radius.  If this formula be compared with  the  foregoing, it
avUI be seen that a mass which, after moving in central mo-
tion, arrives at the sun's surface  has the same velocity as it
would possess had it fallen perpendicularly into the sun  from
a distance* equal to the major axis of its orbit; whence it is
apparent that a planet, on arriving at the sun, moves at least
as  quickly as a Aveight which falls freely  towards the sun
from a distance as great as the solar radius, or 96,000  geo-
graphical nines.
    What  thermal effect corresponds to such velocities ?  Is
the  effect sufficiently great to play an important part in the
immense development of heat on the sun ?
    This crucial question may be easily answered by help of
the preceding considerations.  According to the formula given
at the end of Chapter II., the degree of heat  generated by
percussion is
                     = 0*000139° Xc2,
where c denotes the velocity of the striking body expressed in
metres.  The velocity of an asteroid when it strikes the sun
measures from 445,750 to 630,400 metres ;  the  caloric effect
of the  percussion is consequently equal to from 27| to 55 mil-
lions of degrees of heatf.
    An asteroid, therefore, by  its faU  into the sun developes
   * This distance is to be counted from the centre of the sun.
   f Throughout this memoir the degrees of heat are expressed in the
Centigrade  scale.  Unless stated to the contrary, the measures of length
are given in geographical miles.  A geographical mile = 7420 metres, and
an English mile = 1608 metres.—Ta. 
276'
CELESTIAL DYNAMICS.
from 4600 to 9200 times as much heat as would be generated
by the combustion of an equal mass of coal.
        IT.—ORIGIN  OF THE SUN'S  HEAT.

The  question why the planets move in curved orbits, ont
of the grandest of problems, was solved by Newton in con-
sequence, it is beheved, of his  reflecting on the faU of an ap-
ple.   This story is not improbable, for we are  on  the right
track for the discovery of truth when once we clearly recog-
nize that between great and smaU no qualitative but  only a
quantitative difference exists—when Ave resist the suggestions
of an ever active imagination, and look for the same laws in
the greatest as weU as in the smallest processes of nature.
   This universal range  is the  essence of a law of nature,
and the touchstone of the correctness of human theories.  We
observe the fall of an apple, and investigate the law which
governs this phenomenon;  for the  earth we substitute the
sun, and for the apple a planet, and thus  possess ourselves of
the key to the mechanics of  the hea\Tens.
   As the same laAvs  prevail in the greater as well as in the
smaller processes of nature,  Newton's method may be used in
solving the  problem  of the origin of the sun's heat.  We
know the connexion between the space through which a body
falls, the velocity,  the vis viva, and the generation of heat on
the surface of this globe; if Ave again substitute for the earth
the sun, with a mass 350,000  greater, and for a height of a
f^AV metres celestial distances, we obtain a generation of heat
exceeding aU terrestrial measures.  And since we have suffi-
cient reason to assume the actual existence of such mechani-
cal processes in  the heavens, we find  therein the only tenable
explanation of the origin of the heat of the sun. 
ORIGIN OF TNE  SEN S  HEAT.
277
   The fact that the  development  of  heat by mechanical
means on the surface of our globe is, as a  rule, not so great,
and  cannot be so great as the generation of the same agent
by chemical means, as  by combustion, foUows from the laws
already discussed; and this  fact cannot be used as an argu-
ment against the assumption of a  greater development of
heat by a greater  expenditure of mechanical work.   It has
been  shown that the heat generated by a weight faUing from
a height of 367  metres is only ^th part  of  the heat pro-
duced by the combustion of the same weight of coal; just  as
smaU is the amount of heat developed by a weight moving
with the not inconsiderable velocity of 85  metres in one sec-
ond.  But, according to the  laws of mechanics, the effect is
proportional to the square of the velocity; if therefore the
Aveight  move  100 times faster,  or with  a  \-elocity of 8500
metres in one second, it wiU produce a greater effect than the
combustion of an equal quantity of coal.
    It is true that so great a velocity cannot be obtained by
human means ; everyday experience, however, shoAvs the de-
velopment  of high  degrees  of  temperature by mechanical
processes.
    In the common flint and steel, the particles of steel which
are struck  off are sufficiently heated to  burn in air.   A few
blows directed by a skUful blacksmith with a sledge-hammer
against a piece of cold metal may raise the temperature of
the metal at the points  of collision to redness.
    The new crank of a  steamer, whUst  being polished by
friction, becomes red-hot, several buckets of water being re-
quired to cool it down to its ordinary temperature.
    When a rahway train  passes with even less than its ordi-
nary velocity along a very sharp curve of the hne, sparks are
observed in consequence of the friction against the rails.
    One of the grandest constructions for the  production of
motion by human art is the channel  in which the wood was
allowed to glide down from the steep and lofty sides of Mount 
278
CELESTIAL DYNAMICS.
PUatus into the plain below.  This wooden channel which
was  built about thirty years ago by the engineer Rupp, was
9 Enghsh mUes in length ; the largest trees were shot down
it from the top to the bottom of the mountain in about two
minutes and a half.   The momentum possessed by the  trees
on their escaping at their journey's end from the channel was
sufficiently great to bury their thicker ends in the ground to
the depth of from 6 to 8 metres.  To prevent the wood get-
ting too hot and taking fire, water was conducted  in  many
places into the channel.
   This stupendous mechanical process, Avhen compared with
cosmical processes on the sun, appears infinitely small.   In
the latter case it is the  mass of the  sun which attracts, and
in lieu of the height of Mount PUatus we lurve distances of a
hundred thousand and more miles ; the amount of heat gene-
rated by cosmical faUs  is therefore  at  least 9 million  times
greater than in our terrestrial example.

   Rays of heat on passing through glass and other transpa-
rent bodies undergo partial  absorption, which differs in de-
gree, however, according to the  temperature of the source
from which the heat is derived.  Heat radiated from sources
less warm than boiling water is almost completely stopped  by
thin plates of glass.  As the temperature of a source of heat
increases, its rays pass more copiously through diathermic
bodies.   A plate of glass, for example, weakens the rays  of
a red-hot substance, even when the latter is placed very  close
to it, much  more than  it does those  emanating at a much
greater  distance from a white-hot body.  If the quahty of
the sun's rays be examined in this respect, their diathermic
energy is  found to  be  far superior  to that of aU artificial
sources of heat.  The temperature of the focus of a concave
metallic reflector in which the sun's light  has been collected
is only diminished from one-seventh to one-eighth by the  in-
terposition of a screen of glass.  If the same experiment be 
ORIGIN OF THE  SUN'S HEAT.
270
made with an  artificial and luminous source of heat, it is
found that, though  the focus be very hot when the screen is
away, the interposition of the  latter cuts off nearly all the
heat; moreover, the focus wUl not recover its former temper-
ature Avhen reflector and screen are placed sufficiently near to
the source of heat to make the focus appear brighter  than it
did in the former position Avithout the glass screen.
    The empirical law, that the diathermic energy of heat in«
creases Avith the  temperature of the source from  which the
heat is radiated, teaches us that the sun's  surface must be
much hotter than the most powerful  process of combustion
could render it.
    Other methods  furnish the same conclusion.  If we ima-
gine the  sun to be surrounded by a hollow sphere, it is  clear
that the inner surface of this sphere must receive aU the heat
radiated from the sun.  At the distance of our globe from the
Bun, such a sphere would  have a radius  215 times as great,
and an area 46,000 times as large as the  sun  himself; those
luminous and calorific rays, therefore, Avhich meet this spheri-
cal surface  at  right angles  retain only jg-oooth part of their
original  intensity.   If it be further considered that our at-
mosphere absorbs a part of the solar rays, it is clear that the
rays which reach  the  tropics of our  earth  at noonday can
only possess from j^bth to wjwoth of the poAver with which
they started.   These rays, when  gathered from a surface of
from 5 to 6 square  metres, and concentrated  in an area of
one square centimetre, would produce about the temperature
which exists on the sun, a temperature more than sufficient
to vaporize platinum, rhodium, and similar metals.
    The  radiation calculated in Chapter HI. likewise proves
the enormous temperature of the solar surface.  From the
determination mentioned therein, it follows that each square
centimetre of the sun's surface  loses  by radiation about 80
units of  heat per minute—an immense quantity in compari-
son with terrestrial radiations. 
250
CELESTIAL  DYNAMICS.
    A correct theory of the origin of the sun's heat must ex-
plain the cause of such enormous temperatures.  This expla-
nation can be deduced from the foregoing statements.  Ac-
cording to PouUlct,  the temperature  at which bodies appear
intensely white-hot is about 1500° C.  The heat generated by
the combustion of one kilogramme of hydrogen is, as deter-
mined by Dulong, 34,500, and according to  the more recent
experiments of Grassi, 34,666  units  of heat.  One part  of
hydrogen combines with eight parts of oxygen to form water ;
hence one kUogramme of these two gases mixed in this ratio
would produce 3850°.
    Let us now compare  this heat with  the amount of the
same agent generated by the fall of an asteroid into the sun.
Without taking into account the  low specific heat of such
masses when compared with that of Avater, Ave find the heat
developed by the asteroid to be from  7000  to 15,000 times
greater  than that of the oxyhydrogen mixture.  From data
like these, the  extraordinary diathermic energy of the sun's
rays, the immense radiation from  his surface, and the high
temperature in the focus of the reflector are  easily accounted
for.
    The facts above mentioned  show that, unless Ave assume
on the sun the existence of matter Avith unheard of chemical
properties as a deus  ex machine}, no chemical process could
maintain the  present high radiation of the sun; it also fol-
Ioavs from the above results, that the  chemical nature of bo-
dies which fall into the sun does  not  in  the  least  affect our
conclusions;  the effect  produced by  the  most inflammable
substance would not differ by one-thousandth part  from  that
resulting from the fall of matter possessing but feeble chemi-
cal affinities.   As the brightest artificial hght appears dark in
comparison Avith the sun's light, so the mechanical processes
of the heavens throw into the shade the most powerful chem-
ical actions.
    The quality of the sun's rays, as dependent on his temper 
ORIGIN  OF THE SUN S HEAT.
281
ature, is of the greatest importance to mankind.  If the solai
heat  Avere originated  by a chemical process, and  amounted
near  its source to a temperature of a few thousand degrees.
it Avould be possible  for  the  light to reach  us, whUst  the
greater part of the more important calorific rays would be ab-
sorbed by the higher strata of our  atmosphere and then re-
turned to the universe.
    In consequence of  the high temperature of the  sun, how-
ever, our atmosphere is highly diathermic to his rays, so that
the latter  reach  the surface of our earth and warm it.   The
comparatively low  temperature of the terrestrial  surface is
the cause why the heat cannot easUy radiate back through the
atmosphere into the universe.   The atmosphere acts, there-
fore, like an envelope, which  is easily pierced by the  solar
rays, but which offers  considerable resistance to the radiant
heal, escaping from our earth ;  its action resembles that of a
vah-e which aUows liquid to pass freely in one, but stops  the
Aoav in the opposite direction.
    The action of the  atmosphere is of the greatest impor-
tance as regards  climate and  meteorological processes.   It
must raise the mean temperature of the earth's surface.  Af-
ter the setting of the  sun—in  fact, in aU places Avherc  his
rays do not reach the  surface, the  temperature of  the earth
would soon be as low as that  of the universe, if the  atmos-
phere were removed, or if it did not exist.   Even the power-
ful solar rays in the tropics would be unable to preserve wa-
ter in its hquid state.
   Between  the  great cold which Avould reign  at all times
and in all places, and the moderate warmth which  in reality
exists on our globe, intermediate temperatures may be ima-
gined ;  and it is easUy  seen that the mean temperature would
decrease if the  atmosphere  were to become more and  more
rare.   Such a rarefaction of a valve-like acting atmosphere
actuaUy takes place as we  ascend higher and higher  above 
282
CELESTIAL DYNAMICS.
 the level of the sea, and it is accordingly and necessarily ao
 companied by a corresponding diminution of temperature.
    This weU-known fact of the  lower mean temperature of
 places of greater altitude has led to the strangest hypotheses.
 The sun's rays were not supposed to contain aU the condition?
 for warming a body, but to set  in  motion  the "substance'
 of heat contained in the earth.   This "substance" of heat,
 cold when at rest, was attracted by the earth, and Avas there-
 fore found in greater abundance near  the centre of the globe.
 This vieAV, it Avas thought,  explained why the warming power
 of the sun was so much weaker  at the top of a mountain than
 at the bottom, and why, in spite of his immense radiation, he
 retained his fuU powers.
    This belief, which especiaUy  prevails amongst imperfectly
 informed people,  and which will scarcely succumb to correct
 views, is  directly  contradicted by the excellent experiments
 made by PouiUet at different altitudes  with the pyrheliometer.
 These  experiments show that, everything else being  equal,
 the generation of  heat by the solar rays is more powerful in
 higher altitudes than near the surface  of our globe, and that
 consequently a portion of these rays is absorbed on their pas-
sage through the atmosphere.  Why,  in  spite of this partial
absorption, the  mean temperature of  low  altitudes is never-
theless higher than it  is in more elevated positions,  is ex-
plained by the fact that the  atmosphere stops to a far greater
degree the calorific rays emanating from the earth than it
does those from the sun.
      V.—CONSTANCY OF  THE  SUN'S  MASS.

   Newton, as  is weU  known, considered light  to  be the
amission of luminous particles from the sun.   In the  contin-
ued emission of light this great phUosopher saw a cause tend- 
             CONSTANCY OF  THE  SUn's MASS.          233

ing to diminish the solar mass ; and he assumed, in order to
make good this loss, comets and other  cosmical  masses to be
continually falhng into the central body.
    If Ave express this vieAV of Newton's in the  language  of
the undulatory theory, which is now universally  accepted, we
obtain the results  developed in the preceding pages.  It is
true that our theory does not accept a pecuhar  " substance "
of light or of heat; nevertheless, according to it, the radia-
tion of hght and heat consists also in purely material pro-
cesses, in a sort of motion, in the vibrations of ponderable
resisting substances.  Quiescence is darkness and death ; mo-
tion is light and life.
    An undulating motion  proceeding from a point or a plane
and excited in an unlimited medium, cannot be imagined apart
from another simultaneous motion,  a translation of the parti-
cles themselves ;* it therefore follows, not only from the emis-
sion, but also from the undulatory theory, that radiation con-
tinually diminishes the mass of the  sun.  Why,  nevertheless,
the mass of the sun does not really diminish has  already been
stated.
    The radiation of the sun is a centrifugal action equivalent
to a centripetal motion.
    The caloric effect of the centrifugal action of the sun can
be  found  by direct observation;  it amounts, according  to
Chapter III., in one minute to 12,650 millions of cubic miles
of heat, or 5*17 quadrillions of units  of heat.  In Chapter
PV. it has been shown that one kilogramme of the mass of an
asteroid originates  from 27*5 to 55 millions of units of heat;
the quantity of cosmical masses, therefore, which falls every
minute into the sun amounts to from 94,000 to  188,000 bil-
lions of kilogrammes.
    To obtain this remarkable result, we made use of a method
   * This centrifugal motion is perhaps the cause of the repulsion of the
tails on comets when  in the neighbourhood of the sun, as  observed  by
Bcssel 
284              CELESTIAL DYNAMICS.

which is common in physical inquiries.  Observation of the
moon's  motion reveals to us the external form of the earth.
The physicist determines with the torsion-balance the weight
of a planet, just as the merchant finds the Aveight of a parcel
of goods, whUst the pendulum has become a magic  power in
the hands  of the geologist, enabhng him to discover cavities
in the bowels of the earth.  Our case is similar to these.  By
obsenration and calculation of the  velocity of sound in  our
atmosphere, we obtain the ratio of the specific heat of air un-
der constant pressure and under constant volume, and by the
help of  this number Ave determine the quantity of heat  gene-
rated by mechanical work.  The heat Avhich arrives from the
sun in a given time on a smaU surface of our globe  serves as
a basis for the calculation of the whole radiating effect of the
sun; and  the  result of a  series of observations and  weU-
founded conclusions is the quantitative determination of those
cosmical  masses which, the  sun receives  from the  space
through which he sends forth his rays.
    Measured by terrestrial  standards, the ascertained number
of so many biUions of kUogrammes per minute appears in-
credible.  This quantity, however, may be brought  nearer to
our comprehension by comparison with other cosmical  mag-
nitudes.  The nearest  celestial  body to us (the moon) has a
mass of about 90,000  trillions of kilogrammes, and  it would
therefore cover  the expenditure of  the  sun for from one to
two years.   The mass  of the earth would afford nourishment
to the sun for a period of from 60 to 120 years.
    To facilitate the appreciation of the masses and the  dis-
tances occurring in the planetary system, Herschel draws the
foUowing picture.  Let the sun be  represented by  a globe 1
metre in  diameter.  The  nearest planet (Mercury) wiU be
about as large as a pepper-corn, 3£ millimetres in thickness,
at a distance of 40  metres.  78 and 107 metres  distant from
the sun will move Venus and the Earth, each 9 miUimetres in
diameter,  or a little larger than a pea.   Not much more than 
             CONSTANCY OF THE  SUNS MASS.         285

a quarter of a metre from  the Earth wiU be  the  Moon, th.
size of a mustard seed, 21  millimetres in  diameter.   Mars,
at a distance of 160 metres, wiU have  about half the diame-
ter of the Earth ; and the smaller planets (Vesta, Hebe, As
trea, Juno, PaUas, Ceres, &c), at a distance of from 250 to
300  metres from the sun,  will resemble particles of sand.
Jupiter and Saturn, 560 and 1000 metres distant from the cen-
tre, AviU  be represented by  oranges, 10 and 9 centimetres in
diameter.  Uranus, of the size of  a nut 4 centimetres across,
AviU  be 2000 metres; and  Neptune, as large as an apple 6
centimetres in  diameter, Avill be nearly twice as  distant, or
about half a  geographical mile aAvay  from  the sun.   From
Neptune to the nearest fixed star AviU be more  than 2000 geo-
graphical miles.
   To complete this picture, it is necessary to  imagine finely
divided matter grouped in a diversified manner, moving sIoaa'Tv
and graduaUy towards the large central globe, and on its ar-
rival  attaching itself thereto; this matter, when  favourably
illuminated by the sun, represents  itself to us  as the  zodiacal
light.  This nebulous substance forms also an important part
of a creation in which nothing is by chance, but Avherein  aU
Is arranged Avith Divine foresight and wisdom.

   The  surface of the sun measures 115,000 millions  of
square mUes, or 61 trilhons of square metres; the mass of
matter which in the shape of asteroids falls into the sun every.
minute is from 94,000  to 188,000 billions of kilogrammes;
one square metre of solar  surface, therefore,  receives on an
average from 15 to 30 grammes of matter per minute.
   To compare this process Avith a terrestrial  phenomenon, a
gentle rain may be considered which sends down in one hour
a layer of water 1 millimetre in thickness (during a thunder-
storm the rainfall is often from ten to fifteen times  this quan-
tity) ; this amounts on a square metre to 17 grammes per
minute. 
286
CELESTIAL DYNAMICS.
   The continual bombardment of the sun by these cosmical
masses  ought to  increase its volume as weU as its mass, if
centripetal action  only existed.   The  increase of  volume,
could scarcely be appreciated by man ; for if the specific grav-
ity of these  cosmical  masses be assumed to  be the same as
that of the sun, the enlargement of his apparent diameter to
the extent of one second, the smaUest appreciable magnitude,
would require from 33,000 to 66,000 years.
   Not quite so inappreciable  would  be the  -increase  of the
mass  of the  sun.   If this mass, or the weight of the sun,
were augmented, an acceleration of the motion of the planets
in their orbits Avould be the consequence, whereby their times
of revolution  round the  central body would be  shortened.
The mass of the sun is 2*1 quintillions of kilogrammes; and
the mass of  the cosmical  matter annually arriving at the sun
stands to the above as 1 to from 21 ^42 mUlions.   Such  an
augmentation of the weight of the  sun ought to shorten the
sidereal year  from i^oobth to sT.ooo^ooti1 of its  length, or from
|ths to ^ths  of a second.
   The observations  of  astronomers  do not  agree with this
conclusion ;  we must  therefore faU back on the theory men-
tioned at the beginning of this chapter, which assumes that
the sun, like  the  ocean, is constantly losing and receiving
equal quantities of matter.   This harmonizes with the suppo-
sition that the vis viva of the universe is a constant quantity.
       VI—THE  SPOTS ON  THE SUN'S  DISC.

   The solar disc presents, according to Sir John Herschel,
the following appearance.    " When the  sun is  observed
through a powerful telescope provided with coloured glasses
in order to lessen  the  heat  and brightness  which would be 
             THE SPOTS ON THE SUN's DISC.           287

hurtful to the eyes, large dark spots are often seen surrounded
by edges which are not quite so dark as the spots themselves,
and which are called  penumbras.   These spots, however, are
neither permanent nor unchangeable.  When  observed from
day to day,  or even from hour to hour, their form is seen to
change ;  they expand or contract,  and  finaUy disappear; on
other parts of the solar surface  new spots  spring  into exists
ence Avhere none could be discovered before.  When  they dis-
appear, the darker part in the middle of the spot contracts to
a point and  vanishes sooner than the edge.  Sometimes  they
break up into two or more parts that show aU the  signs of
mobUity characteristic  of a liquid,  and  the extraordinary
commotion Avhich it seems only possible for gaseous matter to
possess.  The magnitude of their motion is very great.  An
arc of 1 second, as seen from our globe, corresponds to 465
English  miles on the sun's  disc;  a circle of this diameter,
which measures nearly 220,000 English square mUes, is tho
smallest  area that  can be seen on the solar surface.   Spots,
hoAvever, more than 45,000  English miles in diameter,  and,
if Ave may trust some statements, of even greater dimensions,
have  been  observed.  For  such a spot to disappear in the
course of six Aveeks (and they rarely last longer), the  edges,
whilst approaching each other, must move through a  space of
more than 1000 miles per diem.
   " That portion of the solar disc Avhich is free from  spots
is by no means uniformly bright.   Over it are scattered small
dark spots or pores, which are found by careful observation
to be  in a state of continual change.  The slow sinking of
some  chemical precipitates  in  a transparent  liquid, Avhen
vieAved  from the upper surface and in a direction perpendicu-
lar  thereto,  resembles  more  accurately than any other  phe-
nomenon the changes Avhich the pores undergo.  The similar-
ity is  so striking,  in fact, that one can scarcely resist the idea
tliat the appearances above described are owing to a luminous
medium moving about  in a non-luminous atmosphere, either 
288              CELESTIAL DYNAMICS.

hke the clouds in our air, or in wide-spread planes and flame-
like columns, or in rays hke the aurora borealis.
    " Near large spots, or extensive groups  of them, large
spaces are observed to be covered with pecuharly marked
lines much brighter than the other parts of the surface ; these
lines are curved, or deviate in branches, and are caUed facuh.?.
Spots are  often seen betAveen these lines, or to  originate there.
These  are in aU probabihty the  crests of immense waves in
the luminous regions of the solar  atmosphere, and bear wit-
ness to violent action in their immediate neighbourhood."
    The changes on the solar surface  evidently point to the
action of some external disturbing force; for eATery moving
power resident in the sun itself ought to exhaust itself by its
own action.   These changes, therefore, are no unimportant
confirmation of the theory explained in these pages.
    At the same time it must be observed that our knowledge
of physical hehography is, from  the nature  of the subject.
very limited; even the meteorological processes and other phe-
nomena of our own planet are stiU in many respects enigmat-
ical.  For this reason no special  information  could be giAren
about the manner in which  the  solar surface is affected by
cosmical masses.  However, I may be aUowed  to mention
some probable conjectures which offer themselves.
    The extraordinarily high temperature which exists  on the
sun almost precludes the possibility of its surface being solid ;
it doubtless consists  of an  uninterrupted ocean of fiery fluid
matter.   This gaseous envelope  becomes more  rarefied in
those parts most distant from the  sun's centre.
    As most substances are able to assume the gaseous state
of aggregation at high temperatures, the height of the sun's
atmosphere cannot be inconsiderable.  There are, however,
sound reasons for believing that the relative  height of  the so-
/ar atmosphere is not very great.
    Since the gravity is 28 times greater on the sun's surface
;har it is on our earth, a column  of air on the former must 
              THE SPOTS ON THE  SUN's DISC.          289

 cause a pressure 28  times greater  than it would on  our
 globe.  This great pressure compresses air as much as a tem-
 perature of 8000° would expand it.
    In a stUl greater degree than this increased gravity do the
 qualities peculiar  to gases affect the height of the solar atmo-
 sphere.  In  consequence of these  properties, the  density of
 our atmosphere rapidly diminishes as we ascend, and increases
 as wc descend.  Generally speaking,  rarefaction increases in
 a geometrical progression  when the  heights are in an arith-
 metical progression.   If we  ascend  or descend 2\, 5, or 30
 miles, Ave find our atmosphere 10, 100, or a billion times more
 rarefied or more dense.
    This law, although modified by the unequal temperatures
 of the different  layers of the  photosphere, and the unknown
 chemical nature of the substances of which it is composed,
 must also hold good in some measure for the sun.   As, how-
 ever, the mean temperature  of the  solar atmosphere  must
 considerably exceed that of our atmosphere, the density of the
 former wiU not vary so rapidly Avith the height as  the latter
 does.  If we assume this increase and decrease on the sun to
 be ten times  sloAver than it is on our earth, it follows that at
 the heights of 25, 50, and 300  miles, a rarefaction of 10,
 100, and a billion times respectively would be observed.  The
solar  atmosphere, therefore, does not attain  a height of 400
geographical  mhes, or it cannot be as much as 240th of the
sun's radius.   For if we take  the density of the loAvest strata
of the sun's atmosphere to be  1000  times greater that that of
our OAvn near the level of the sea, a density greater than that
of Avater, and necessarily too high, then at  a height of 400
miles this  atmosphere would be 10 billion times  less dense
than the  earth's atmosphere; that  is  to  say,  to human  com-
prehension it has ceased to  exist.
    This discussion shows that the solar atmosphere, in  com-
parison with the  body of the sun, has  only an insignificant
height; at  the same  time it  may be remarked that on the
           13 
290
CELESTIAL DYNAMICS.
sun's  surface, in spite of the  great  heat, such  substances aa
water may possibly exist in the hquid state under a pressure
thousands of times greater than that of our atmosphere.
   Since gases, when free from any solid particles, emit, even
at very high temperatures, a pale transparent  hght—the  so-
caUed lumen philosophicum—it is probable that the intense
Avhite light of the sun has its  origin in the denser parts of his
surface.  If such be assumed to be  the  case, the sun's spots
and faculaj  seem to be the disturbances of the fiery liquid
ocean, caused by most powerful meteoric processes, for which
all necessary materials are present,  and  partly to be caused
by the direct influence of streams of asteroids.   The deeper
and less heated parts of this fiery ocean become thus  exposed,
and perhaps appear to us as spots, whereas  the elevations
form the so-called faculas.
   According to the experiments  made by Henry, an Ameri-
can physicist, the rays sent forth from the spots do  not pro-
duce the same heating effect as those emitted by the  brighter
parts.
   We ha\*e to mention one more remarkable  circumstance.
The spots appear to be confined to a zone which extends  30°
on each  side of the sun's equator.   The  thought naturally
suggests itself that some connexion exists between those solar
processes which produce the spots and faculae, the velocity of
rotation of the sun, and the swarms of asteroids, and to  de-
duce  therefrom the limitation of the spots to the zone men-
tioned.   It  stiU remains  enigmatical by what  means nature
contrives to bring about the uniform radiation which pertains
alike  to the polar and equatorial regions of the sun. 
THE TIDAL WAVE.                291
             VII—THE  TIDAL   WAVE.

    In  almost every case the forces and motions on the sur
 face of the  earth  may be traced back to the rays of the  sun.
 Some processes, however, form  a remarkable exception.
    One of these  is the tides.  Beautiful,  and in some re-
 spects  exhaustive researches on this phenomenon  have been
 made by NeAvton, Laplace, and others.  The tides are caused
 by the  attraction  exercised by the sun and the moon on the
 moveable parts of the earth's surface,  and by the  axial rota-
 tion of  our globe.
    The alternate rising and falling of the level  of the  sea
 may be compared to the ascent and  descent of a pendulum
 oscillating under the influence of the earth's  attraction.
    The continual  resistance, however weak it may be, which
 an instrument of this nature (a physical pendulum) suffers,
 constantly shortens the amplitude of the osciUations  which it
 performs ; and if the pendulum be required  to continue in
 uniform motion, it must  receive a constant supply  of vis viva
 corresponding to the resistance it has to overcome.
    Clocks regulated by a pendulum obtain such a supply,
 either from a raised weight or a bent spring.  The power
 consumed in  raising the  weight or in bending the  sprint,
 which power is represented by the raised  weight or the bent
 spring,  overcomes for a time the resistance, and thus secures
 the uniform motion of the pendulum and clock.  In doing so,
 the Aveight sinks  doAvn or the spring  uncoUs, and therefore
 force must be expended in winding the clock up again, or it
 would stop moving.
   Essentially the same holds good for the tidal wave.   The
 moving waters rub against each other, against the  shore, and
against  the atmosphere, and thus, meeting constantly Avith re*
sistance, would soon  come to rest if a vis viva  did not  exist
competent to overcome these  obstacles.  This vis viva is tho 
292               CELESTIAL DYNAMICS.
 rotation of the earth on its axis, and the diminution and final
 exhaustion thereof wiU be a consequence of such an action.
    The tidal wave causes a diminution of the velocity of tht
 rotation of the earth.
    This important conclusion can be proved in different Avays.
    The attraction of the sun and the moon disturbs the equi-
 librium of the moveable parts of the earth's surface, so as to
 move the waters of the sea towards  the  point or meridian
 above and below which the moon culminates.  If the waters
 could move without resistance, the elevated parts of the tidal
 wave would exactly coincide  with the moon's meridian, and
 under such conditions no  consumption of vis viva  could take
 place.   In reality, however, the moving Avaters  experience
 resistance, in consequence  of which  the  flow of  the tidal
 wave is delayed, and high water occurs  in the  open  sea on
 the average  about 2\ hours  after  the  transit of the moon
 through the meridian of the place.
    The waters of the ocean move from west and east toAvards
 the meridian  of the moon, and the more elevated wave is, for
 the reason above stated, always to the east of the moon's me-
 ridian ;  hence the sea must press and flow more  powerfully
from east to west than from west to east.  The ebb and flow
 of the  tidal wave therefore consists not only in an alternate
 rising and faUing of the waters, but also in a slow progressive
motion from east to west.  The tidal wave  produces a gen-
eral western current in the ocean.
    This current is opposite in direction to the earth's rota-
tion, and therefore its friction  against  and  collision with  the
 bed and shores of the oceart must offer everywhere resistance
 to the axial rotation of the earth, and diminish the vis viva of
 its motion.  The  earth here plays the part of a fly-wheel.
 The moveable parts of its surface adhere,  so to speak, to the
 relatively  fixed moon, and are dragged in a direction opposite
 to that of the earth's rotation, in consequence of Avhich, ac-
 tion takes place between the solid and liquid parts of this fly- 
THE TIDAL WAVE.
293
wheel, resistance is  overcome, and the given rotatory effect
diminished.
    Water-mill3 have been turned by the action of the tides ;
the effects produced by such an arrangement are distinguished
in a remarkable manner from those of a miU turned by a
mountain-stream.  The one obtains the vis viva  with Avhich
it works from the earth's rotation, the  other from the sun's
radiation.
    Various causes combine to incessantly maintain, partly in
an  undulatory, partly in a progressive  motion, the waters of
the ocean.   Besides the influence of the sun and the moon on
the rotating earth, mention must be made of the influence of
the movement of the lower strata of the  atmosphere on the
surface of the ocean, and  of the different temperatures of the
sea in  \Tarious climates; the configuration of the shores and
the bed of the ocean likewise exercise a manifold influence on
the velocity, direction, and extent of the oceanic currents.
    The motions in  our atmosphere, as well as those of the
ocean, presuppose  the  existence and consumption of  vis viva
to overcome the continual resistances, and to prevent a state
of rest or equilibrium.   GeneraUy speaking, the poAver neces-
sary for the production of aerial currents may be of threefold
origin.' Either  the  radiation  of the sun, the heat  derived
from a store in the interior of the earth, or, lastly, the rota-
tory effect of the earth may be the source.
    As far as quantity is concerned the sun is by far the most
important of the above.  According to PouUlet's measure-
ments, a square metre of the earth's surface receives on the
average 4*408 units of heat from the sun per minute.  Since
one unit of  heat is equivalent to 367 Km, it folloAvs that one
square  metre  of the surface of our globe receives per minute
an addition  of vis viva equal to 1620 Km, or the whole of the
earth's surface in the same time 825,000 biUions of Km.  A
power  of 75 Km per second is called a horse-power.  Ac-
cording to this, the effect of the solar radiation in mechanical 
294
CELESTIAL DYNAMICS.
work on one square  metre of the  earth's surface would be
equal to 0*36, and the total effect for the whole globe 180 bil-
lions of horse-powers.  A not inconsiderable portion of this
enormous quantity of vis viva is consumed in the production
of atmospheric  stations,  in consequence of which numerous
motions are set up in the earth's atmosphere.
    In spite of their  great \Tariety, the atmospheric  currents
may be reduced to a single type.   In consequence of the une-
qual heating of the earth in different degrees of latitude, the
colder and heavier air of the polar regions passes in an under
current towards the equator ;  Avhereas the heated  air of the
tropics  ascends  to  the higher parts of the atmosphere, and
flows from thence towards the poles.  In this  manner the air
of each hemisphere performs a circuitous motion.
    It is known that these currents are essentiaUy modified by
the motion of the earth on its axis.   The polar currents, with
their smaUer rotatory velocity, receive a motion from east to
west contrary to the earth's rotation, and the  equatorial  cur-
rents  one from west to east in advance of the axial  rotation
of the earth.   The former of  these  currents,  the  easterly
Avinds, must diminish the rotatory effect of the globe, the lat-
ter, the westerly Avinds, must increase the same poAver.   The
final result of the action of these opposed influences is, as re-
gards the rotation of the earth, according to weU-known  me-
chanical principles, =0 ; for these  currents counteract each
other, and therefore cannot exert the least influence on  the
axial  rotation of the earth.  This important conclusion  Avas
proved by Laplace.
    The same  law  holds  good for  every imaginable action
which is caused either by the radiant heat of the  sun, or by
the heat which  reaches the surface from the earth's interior,
whether the action be in the air, in the water, or on the land.
The effect of every single motion produced by these means on
the rotation  of the globe, is exactly compensated by the effect
of another motion in an opposite direction; so that the result 
THE TIDAL AVAVE.
295
 ant of all these motions is, as far as the axial rotation of the
 globe is concerned, = 0.
    In those actions known as the tides, such compensation,
 however, does not  take place;  for the pressure or pull  by
 Avhich they are produced is always stronger from east to west
 than  from  west to  east.  The currents caused by this pull
 may ebb and flow in different directions, but their motion pre-
 dominates in that which is opposed to the earth's rotation.
    The velocity of the currents caused by the tide of the at-
 mosphere amounts, according to  Laplace's calculation, to not
 more than 75  millimetres in a second, or nearly a geographi-
 cal mUe in twenty-four hours;  it is  clear that much more
 powerful effects produced by the sun's  heat  would hide this
 action from observation.   The influence of these air-currents,
 however, on the rotatory effect of the  earth is, according to
 the laws of mechanics, exactly the same as it would  be were
 the atmosphere undisturbed by the sun's radiant heat.
    The combined motions of ah and water are to be regarded
 from  the same point of vieAV.   If we imagine  the influence
 of the sun and that of the interior of our globe  not to exist,
 the motion of the air and ocean from east to  west is still left
 as an obstacle to the axial rotation of the earth.
    The motion of the waters of the ocean from east to west
 Avas long ago  verified  by observation,  and it is certain  that
the tides are  the most  effectual of the  causes to which this
great westerly current is to be referred.
    Besides the tidal  waAre, the lower air-currents moving in
the same direction, the trade-winds of the tropics especiaUy,
may be  assigned as causes of this general movement of the
waters.   The Avesterly direction of the latter, however, is not
confined to the  region of easterly winds  ; it is met with in the
region of perpetual  calms, where it possesses a velocity of
several mUes a day ; it is observed far aAvay from the tropics
both north  and  south, in regions where westerly winds pre- 
296
CELESTIAL DYNAMICS.
vail, near the Cape of Good Hope, the Straits of Magellan,
the arctic regions, &c.
    A third  cause for the production of a general motion of
translation of the waters of  the ocean is the unequal heating
of the sea in different zones.  According to the laAvs of hy-
drostatics, the colder Avater of the  higher  degrees of latitude
is compeUed to flow towards the  equator, and  the warmer
water of the tropics  towards the poles,  in  consequence of
which, similar movements are produced in the ocean to those
in the atmosphere.  This is  the cause of the cold under cur-
rent from the poles to the equator, and of the warm surface-
current from the equator to the poles.  The waters of the lat-
ter, by virtue of the greater velocity of rotation  at the equa-
tor, assume in their onward  progress a direction from west to
east.  It is a striking proof of the preponderating influence
of the tidal wave that, in  spite  of this,  the  motion of the
ocean is on the whole in an opposite direction.
    Theory and experience thus agree in the result that the
influence of the moon on the rotating  earth causes a motion
of  translation from east to west in  both atmosphere  and
ocean.  This motion must continuaUy diminish  the rotatory
effect of the earth, for want of an  opposite and compensating
influence.
    The continual pressure of the tidal  wave against the axial
rotation of the earth may also be deduced from statical laws.
    The gravitation of the moon affects without  exception aU
parts of the globe.   Let the earth  be divided by the plane of
the meridian in which the moon happens to be into two hemi-
spheres,  one to the  east, the  other to the west of this merid-
ian.  It is clear that the moon, by its attraction of the east-
ern hemisphere, tends to retard the  motion of the  earth, and
by its attraction of the western  hemisphere, to accelerate the
same rotation.
    Under certain conditions both these tendencies compensate
each other, and  then the action  of the moon on the earth's 
THE TIDAL WAVE.
297
rotation becomes zero.  This happens when both hemispheres
are arranged in a certain manner symmetrically, or when no
parts of the earth can change their relative position;  in  the
Latter case a sort of symmetry is produced by the rotation.
    The form of the earth  deviates from a perfectly symmet-
rical sphere on account of the  three following causes :—(1)
the flattening of the poles,  (2) the mountains on the surface,
and (3) the tidal Avave.   The first two causes do not change
the velocity of the  earth's  axial  rotation.  In  order to com-
prehend clearly the effect of the tidal wave, we shaU imagine
the earth to be a perfectly symmetrical sphere uniformly sur-
rounded by water.   The attraction of the  sun and the moon
disturbs the equilibrium of this mass, and two flat mountains
of water are  formed.  The top of one  of these is directed
towards  the  moon, and the summit of the  other  is  turned
away from it.  A straight  line passing through the tops of
these tAvo  mountains is called  the major  axis  of this  earth-
spheroid.
    In this  state the earth may be  imagined^ to be divided
into three  parts—a smaller  sphere, and two spherical  seg-
ments attached to the opposite sides of the latter, and  repre-
senting the elevations of the tidal wave.   The attraction of
the moon on the smaU central sphere does  not change the ro-
tation, and we have therefore  only to  consider the influence
of this attraction on the two tidal elevations.  The upper ele-
vation or  mountain, the  one nearest the moon, is attracted
towards the west because its mass is principally situated to the
east of the moon, and the opposite mountain, which is to the
west of the moon, is attracted towards the east.  The upper
tidal elevation is not only more powerfuUy attracted because
it is nearer to  the  moon, but also because the angle  under
which it is puUed aside is more "favourable for  lateral  deflec-
tion than in the case of the  opposite protuberance.  The pres-
sure from  east to west of the  upper elevation  preponderates
therefore over the pressure from west to east of the opposite 
298
CELESTIAL DYNAMICS.
mountain ;  according to calculation, these quantities stand t4
each other nearly as 14 to 13.  From the relative position of
these two tidal protuberances and the moon, or the unchange*
able position of the major axis of the earth-spheroid towards
the centre of gravity of the  moon, a pressure results, which
preponderates from east to west, and offers an obstacle to the
earth's rotation.
    If gravitation were to be compared with magnetic attrac-
tion, the earth might be considered to be a large  magnet, one
pole of which, being more powerfully attracted, would  repre-
sent the upper, and the other pole the  lower tidal elevation.
As the upper tidal wave tends to move towards the moon, the
earth would act hke a galvanometer, Avhose needle  has been
deflected from the magnetic meridian, and which, whUe tend-
ing to return thereto, exerts  a constant lateral pressure.
    The foregoing discussion may suffice to demonstrate the
influence of  the moon on the earth's rotation.  The  retarding
pressure of the tidal wave may quantitatively be determined
in the same manner as that employed in computing the pre-
cession of the equinoxes and the nutation of the earth's axis.
The varied distribution of land  and water, the unequal and
unknoAvn depth of the ocean, and the as yet imperfectly ascer-
tained  mean difference between the time of the moon's cul-
mination and that of high water in the  open sea, enter, how-
ever, as elements into such a calculation, and render the de-
sired result an uncertain quantity.
    In the mean time this retarding pressure, if imagined to
act at the equator, cannot be assumed  to  be less than 1000
miUions of kilogrammes.  In order to start with a definite
conception, we may be allowed to use this round number as a
basis for the following  calculations.
    The rotatory velocity of the earth at the equator is 464
metres, and the consumption of mechanical work,  therefore,
for the maintenance of the tides 464,000  miUions of Km, or
600C millions of horse-powers pes. second.  The effect of tha 
THE TIDAL WAVE.
299
tides may consequently be estimated at js^th of the effect re-
ceived by the earth from the sun.
   The rotatory effect which the earth at present possesses,
may be calculated from its mass, volume, and velocity of rota-
tion.  The volume  of the earth is 2,650,686,000 cubic mUes,
and its specific gravity, according to Reich, = 5*44.   If, for
the sake  of simphcity, we assume the density of the  earth to
be uniform throughout  its mass, we  obtain from  the above
premises, and the known velocity of rotation, 25,840 quadril-
lions  of  kUogrammetres as the rotatory effect of the  earth.
If, during every second  in 2500 years,  464,000  miUions of
Km of this effect were consumed by the  ebb  and  flow of the
tidal wave, it would suffer a diminution of 36,600  trillions of
Km, or about foo^th of its quantity.
   The velocities of rotation of a sphere stand to each other
in the same  ratio as the  square roots of  the  rotatory effects,
when the volume of the sphere remains constant.   From this
it foUows that, in the assumed time of 2500 years, the  length
of a  day has  increased f^both;  or if a  day be taken equal
to 86,400 seconds, it has lengthened  ^fh of a second, if the
volume of the earth has not changed.   Whether this supposi-
tion be  correct  or  not, depends  on the  temperature of our
planet, and avUI be discussed in the next chapter.
   The tides  also  react on  the motion  of the moon.   The
stronger attraction of the elevation nearest to, and  to the east
of the moon, increases with the tangential velocity  of our sat-
ellite ; the mean distance of the earth and the  moon, and the
time of revolution of the latter, are consequently augmented.
The  effect of this action, however, is insignificant,  and, ac-
cording to calculation, does not  amount to more than a frac-
tion of a second in the course of centuries. 
300
CELESTIAL  DYNAMICS.
      VIII.—THE EARTH'S INTERIOR HEAT.

    Without doubt there  was once a time when our globe
had not assumed its present magnitude.  According to this,
by aid of this simple assumption, the origin of our planet may
be reduced to the union of  once separated masses.
    To the mechanical  combinations of masses of the second
order, with masses of the  second and  third order, &c, the
same laws as those enunciated for the sun apply.  The collis-
ion of such masses must always generate an amount of heat
proportional to the squares  of their velocities, or to their me-
chanical effect.
    Although we are not in a position to affirm anything cer-
tain respecting the primordial conditions under which the
constituent parts of the earth existed, it is nevertheless of the
greatest interest to estimate the quantities of heat generated by
the collision and  combination  of these parts by a standard
based on the simplest assumptions.
    Accordingly we shall consider for the, present the earth to
have been  formed by the union of two parts, which obtained
their relative motions by their mutual  attraction  only.  Let
the whole mass  of the present earth, expressed  in kilo-
grammes, be T, and the masses of the two portions T—x and
x.  The ratio of these two  quantities  may be imagined to
assume various Aralues.  The two extreme cases are, when x
is considered infinitely smaU in comparison with T, and when
a* == T— x = % T.  These  form the limits of all imaginable
ratios of the parts T — x and x, and will noAV be more closely
examined.
    Terrestrial  heights are of course excluded from the fol-
lowing consideration.   In the first place, let x, in comparison
with  T — x,  be  infinitely  smaU.   The  final  velocity Avith
which x arrives on the surface of the large mass, after having 
THE EAETIl's INTEKIOS  HEAT.
301
passed through a great space in a straight line, or after pre-
vious central motion round it, is, according to the laws devel-
oped in relation to the sun  in Chapter IH., confined within
the limits of 7908 and 11,183 metres.   The  heat  generated
by this process  may amount  to from 8685Xx to 17,370X%
units, according to the value  of the major  axis of the orbit
of x.   Tliis heat, however, vanishes by its distribution through
the greater mass, because x is, according to supposition, infi-
nitely smaU in comparison with T.
    The  quantity  of heat generated increases with x, and
amounts in the second case,'when x — IT, to from 6000XT
to 8685XT units.
    If Ave assume  the earth to possess a very great capacity
for  heat, equal in fact to that of its volume of water, which
when calculated for equal weights = 0*184, the above discus-
sion leads to the conclusion that the difference of temperature
of the constituent parts, and of the earth after their union, or,
in other words, the heat generated  by the collision of these
parts, may range, according to their relative magnitude, from
0° to 32,000°, or even to 47,000° !
    With the number of parts which thus mechanically com
bine, the quantity of  heat developed increases.  Far greatei
stUl would have been the generation of heat if the constituent
parts had moved in separate orbits round the sun before their
union,  and had accidentaUy approached  and met each other.
For various reasons, however, this latter  supposition is  not
very probable.
    Several  facts indicate  that our earth was once a fiery
liquid mass, which has since cooled graduaUy, down to a com-
paratively inconsiderable depth from the  surface, to its pres-
ent temperature.  The first proof  of this is the form of the
earth.   " The form of the earth is its history."  According
to the most  careful measurements, the flattening at the poles
is exactly such as a liquid mass rotating on its axis with  the
velocity of the earth would  possess ; from this we may con- 
302
CELESTIAL DYNAMICS.
elude that the earth at the time it received its rotatory motion
was in a liquid state ; and, after much controversy, it may be
considered as settled that this liquid condition was not that of
an aqueous solution, but of a mass melted by a high tempera-
ture.
    The  temperature of the crust of  the globe  likewise fur-
nishes proof of the existence of a store of heat in its interior.
Many exact experiments and measurements show that the
temperature of the earth  increases with the depth to which
we  penetrate.   In boring the artesian weU at Grenelle, which
is 546 metres deep, it Avas observed that the temperature aug-
mented at the rate of 1° for every 30  metres.  The same re-
sult was  obtained by observations in the artesian weU at Mon-
dorf in  Luxembourg: this Avell is 671 metres in  depth, and
its Avater 34° warm.
    Thermal springs  furnish a striking proof of the high tem-
perature  existing in the interior of the earth.  Scientific  men
are agreed that  the  aqueous deposits from the atmosphere,
rain, hail, dew, and snow, are the sole causes of the forma-
tion of springs.  The water obeying the laws of gravity, per-
colates through  the  earth wherever it can, and  reappears  at
the  surface in places  of a lower situation.  When water sinks
to considerable depths through vertical crevices in the rocks,
it acquires the temperature of the surrounding strata, and
returns as a thermal  spring to the surface.
    Such waters are  frequently distinguished from the water
of ordinary springs merely by their possessing a higher tem-
perature.  If, however, the  water in  its course meets with
mineral or organic substances which  it can dissolve  and re-
tain, it then reappears  as  a mineral spring.   Examples  of
Buch are  met with at Aachen, Carlsbad, &c.
    In a far more decided manner than by the high tempera-
ture of the water of  certain springs, the  interior heat of our
globe is  made manifest by those  fiery fluid masses which
sometimes rise from  considerable depths.  The temperature 
THE EARTH'S INTERIOR HEAT.
303
of the earth's crust increases at the  rate of 1° for  every 30
metres we descend from the surface towards the centre.   Al-
though it is incredible that this augmentation can continue at
the same rate till the centre be reached, we  may nevertheless
assume Avith certainty that it does  continue to a considerable
depth.  Calculation based on this  assumption shows that at
a depth of a  few miles a temperature must  exist  sufficiently
poAverful to fuse most substances.   Such molten masses pene-
trate  the cold  crust of the  globe in  many places, and  make
their appearance as lava.
    A distinguished scientific man  has  lately expressed him-
self on the origin of the interior heat of the earth as follows :
—" No one of  course can explain the final  causes of things.
This  much,  however, is clear to   every thinking  man,  that
there  is just as  much reason that a body, like the  earth, for
example, should be warm, warmer  than ice or human blood,
as there is that it should be  cold or  colder than the latter.   A
particular cause for this absolute heat is as little necessary as
a cause for motion or  rest.  Change—that is to say, transi-
tion from one state of things to another—alone  requires and
admits of explanation."
    It is evident that this reflection is not fitted to suppress the
desire for an  explanation of the phenomenon in question.  As
all matter has the tendency to assume the same temperature
as that possessed by the substances  by which it happens to be
surrounded, and  to remain in a quiescent  state as soon as
equilibrium has been established, we  must conclude that,
whenever we meet with a body warmer than its neighbours,
such  body must ha\Te received at a (relatively speaking) not
far distant time, a certain degree of heat,—a process which
certainly aUows of, and requires explanation.
    Newton's theory of gravitation, whUst it enables us to de-
^rrr&ine, from its present  form,  the earth's  state of aggrega-
tion in ages past, at the same time points  out to us a source
of heat powerful enough to produce such a state of aggrega- 
304
CELESTIAL DYNAMICS.
 tion, powerful  enough to melt Avorlds;  it teache3 us to coil«
 sider the molten state of a planet as the result of the mechan-
 ical union of cosmical masses, and thus derive the radiation
 of the sun and the heat in the  boAvels of the  earth  from a
 common origin.
    The rotatory effect of the  earth also  may be  readily ex-
 plained by the collision of its constituent parts ;  and we must
 accordingly subtract the vis viva of the axial rotation from
 the whole effect of the collision and mechanical  combination,
 in order to obtain the quantity of heat generated.  The rota-
 tory effect, hoAvever, is only a small quantity in comparison
 Avith the interior  heat  of the  earth.   It amounts to about
 4400XT kUogrammetres, T being the weight of the earth in
 kilogrammes, which  is equivalent to 12XT units  of heat, if
 Ave assume the density of the earth to be uniform throughout.
    If we imagine the moon in the course of time, either in
 consequence of the  action  of a resisting medium  or from
 some other cause, to unite herself with our earth, two  princi-
 pal effects  are to be discerned.  A result  of the  coUision
 would be, that the whole  mass of the moon and the cold crust
 of the  earth would be raised  some  thousands of  degrees in
temperature, and consequently the surface of the earth would
be converted into a fiery  ocean.  At the same time the velo-
city of the earth's axial rotation would be somewhat acceler-
ated, and the position of  its axis with regard to the heavens,
and to its  own surface; slightly altered.   If the  earth had
been a cold body without  axial  rotation, the process of its
combining with the  moon Avould have imparted  to  it both
heat and rotation.
    It is probable that such processes of  combination between
 different  parts  of our globe may have repeatedly happened
before the earth attained its present magnitude, and that lux-
 uriant vegetation may have at different times been buried un-
 der the. fiery debris resulting from the conflict of these masses. 
THE EARTH S  INTERIOR  HEAT.
305
    As long as the surface of our  globe was in an incandes-
cent state, it must have lost heat at a very rapid  rate ; grad-
ually this process became slower ; and although it has not yet
entirely ceased, the rate of cooling must have diminished to a
comparatively smaU magnitude.
    Two phenomena are caused by the  cooling of the earth,
Avhich, on account of their common origin, are  intimately re-
lated.   The decrease of temperature, and consequent contrac-
tion of the earth's crust, must have caused  frequent distur-
bances  and revolutions  on its surface, accompanied by the
ejection of molten masses and the formation of protuberances ;
on  the  other  hand, according to the laws of mechanics, the
velocity of rotation must have increased with the diminution
of the volume of the sphere, or, in other words, the  cooling
of the earth must have shortened the length of the day.
    As the intensity of such disturbances and the velocity of
rotation are closely connected, it is clear that the youth of our
planet  must have  been  distinguished  by  continual Aiolent
transformations of its crust, and a perceptible acceleration of
the A-elocity of its axial rotation; whilst in the present timo
the metamorphoses of  its surface  are much slower, and the
acceleration of its axial revolution diminished to a very smaU
amount.
    If we imagine the times Avhen the Alps, the chain of the
Andes, and  the  Peak of Teneriffe  were upheaved from the
deep, and compare with  such  changes the earthquakes and
volcanic eruptions  of  historic times, we perceive in  these
modern transformations but weak images of the  analogous
processes of bygone ages.
    Whilst  Ave  are surrounded  on every side  by the monu-
ments of violent volcanic convulsions, we  possess no record
of the  velocity of the  axial rotation of our planet in antedi-
luvian times.  It is of the greatest importance that we should
have an exact knowledge of a  change in this velocity, or in
tho length of the day during historic  times.  The  investiga 
306
CELESTIAL DYNAMICS.
 tion of this subject by the great Laplace.forms a bright  mon-
 ument in the department of exact science.
    These calculations are essentially conducted in the foUow-
 ing manner :—In the first place, the time betAveen two echpses
 of the  sun, widely apart  from each  other, is  as  accurately
 as possible expressed in days, and from this the ratio of the
 time of the earth's rotation to the mean  time of the moon's
 revolution determined.  If, now, the observations of ancient
 astronomers be compared AA'ith those of our present time, the
 least  alteration in  the absolute  length of a day may be de-
 tected by a change in  this ratio, or in a disturbance in the
 lunar re\rolution.  The most perfect agreement of ancient rec-
 ords on the movements of the moon and  the planets, on the
 eclipses of the  sun, &c, revealed to Laplace  the remarkable
 fact that in the course of  25 centuries, the time in which our
 earth revolves on its axis has not altered ^fh part of a sexa-
 gesimal second;  and  the  length of a day therefore may be
 considered to have been constant during historic times.
    This result, as important as it was  convenient for astron-
 omy, wa3 nevertheless of a nature to create some difficulties
 for the physicist.   With apparently good  reason it was  con-
 cluded that, if the velocity of rotation had  remained constant,
the volume of the earth could haA*e undergone no change.
 The earth completes  one  revolution on its axis in 86,400 si-
 dereal seconds ; it consequently appears, if this time has not
 altered  during  2500 years to the extent of j00th of  a second,
or ^wiu.w^h P&rt °f a day, that during this  long space of time
the radius of the  earth  also cannot  have  altered more than
this fraction  of its length.  The  earth's radius  measures
 6,369,800 metres, and therefore its length ought not to have
diminished more than 15 centimetres in 25 centuries.
    The diminution  in volume, as a result  of the  cooling-pro-
cess, is, however, closely connected Avith the  changes on the
earth's  surface.   When  we  consider that  scarcely a  day
passes without the occurrence of an earthquake or shock in 
THE EARTH'S  INTERIOR  HEAT.
307
one  place  or another, and that of the 300 active volcanos
some are always in action, it would appear that such a lively
reaction of the interior of the earth against the crust is in-
compatible with the constancy of its volume.
    This apparent discrepancy between Cordier's theory of the
connexion  betAveen the cooling of the earth and the  reaction
of the interior on the  exterior parts, and Laplace's calcula-
tion showing the constancy of the  length of the day, a calcu-
lation which  is undoubtedly correct,  has induced most scien-
tific men to abandon Cordier's  theory, and thus to depriA'e
themselves of any tenable explanation of volcanic activity.
    The continued cooling of the earth cannot be denied, for
it takes place according to the laws of nature ; in this respect
the  earth cannot  comport  itself differently from any other
mass, however small it may be.  In spite of the heat which
it  receives from  the sun, the earth will haA-e a tendency to
cool so long as the temperature of its interior is higher than
the mean temperature of its surface.   Between the tropics the
mean temperature produced by the sun is about 28°, and  the
sun  therefore is as httle able to stop the coohng-tendency of
the earth as the moderate warmth of the air can prevent  the
coohng of a red-hot ball suspended in a room.
   Many phenomena, for instance the melting of the glaciers
near the bed on  which  they rest,  show the  uninterrupted
emission of heat from the  interior towards the exterior of the
earth; and the question  is, Has the earth in 25 centuries
actually lost  no more heat than that which  is requisite to
shorten a  radius  of  more than 6 mUlions of metres only 15
centimetres ?
    In  answering  this question, three points  enter into our
calculation;—(1)  the  absolute amount of  heat  lost  by  the
earth in a certain time, say  one day; (2) the earth's capacity
for heat; and (3) the coefficient of expansion of the muss of
the  earth.
   As none of these quantities can  be determined by direct 
308
CELESTIAL  DYNAMICS.
measurements, we are obliged to content ourselves with prob-
able estimates;  these estimates wUl carry the more weight
the less they are  formed in favour of some preconceived opin-
ion.
    Considering what is known about the expansion and con-
traction of solids and.liquids by heat and cold, we  arrive  at
the conclusion that for a  diminution of 1° in temperature,
the linear contraction of the earth  cannot weU be  less than
ioo^oth part, a number Avhich Ave aU the more  readily adopt
because it has been used by Laplace, Arago, and others.
    If we compare the capacity for heat of aU sohd and hquid
bodies which haAre been  examined, we find  that, both  as  re-
gards volume and weight, the capacity of water is the great-
est.   Even the gases  come  under  this rule ; hydrogen, how-
ever, forms an exception, it having the greatest capacity for
heat of all  bodies \vhen  compared Avith an equal weight of
Avater.   In order not to take the capacity for heat of the mass
of the earth too small, we shall  consider it to be equal to that
of its  volume of water,  which,  when calculated for  equal
weights, amounts to 0*184.*
    K we accept Laplace's result, that the length of a day has
remained constant  during the last 2500 years, and conclude

   * The capacity for heat, as well as the coefficient of expansion of mat-
ter, as a  rule, increases at higher temperatures.  As, however, these two
quantities act in opposite ways in our calculations, we may be  allowed to
dispense with the influence which the high temperature of the interior of
the earth must  exercise on these numbers. Even if, in consequence  of
the high temperature of the interior, the earth's mass could have a capa-
city two or three times as great as that which it has from 0° to 100°, it
is to be considered,  on the other  hand, that the coefficient of expansion,
TTiff.V n <T> on*y holds good for solids, and is even small for them, whilst in
the case of hquids we have to assume a much greater coefficient: for mer-
cury between 0° and 100°, it is about six times as great.  Especially great
is the contraction and expansion of bodies when  they change their state
of aggregation; and this should be taken into  account  when  considering
the formation of the earth's crust. 
THE EARTH'S  INTERIOR HEAT.
309
that the earth's radius has  not  diminished 1£ decimetre in
consequence of cooling, we arc obhged to assume, according
to the  premises  stated, that the  mean temperature of our
planet cannot have decreased 4-35° in the same period of time.
    The volume of the earth  amounts to 2650  millions of cu-
bic miles.   A  loss of heat sufficient to cool this mass ^°
would be equal to the heat given  off Avhen the temperature
of 6,150,000 cubic mUes of water decreases  1° ; hence the
loss for one day would be equal to 6*74  cubic miles of heat.
    Fourier has investigated the loss of heat sustained by the
earth.  Taking the observation that the temperature  of the
earth increases at the rate of 1 ° for every 30 metres as the
basis  of his calculations, this  celebrated mathematician finds
the heat which the globe loses by conduction through its crust
in the space of  100 years to be capable of melting a layer of
ice 3  metres in  thickness and covering the  whole surface  of
the globe ; this corresponds in one day  to 7*7 cubic miles ot
heat,  and in 2500  years to  a decrease  of 17 centimetres in
the length of the  radius.
    According to this, the cooling of the globe Avould be suffi-
ciently great to require  attention Avhen the earth's velocity of
rotation is considered.
    At the same time  it is clear that the  method employed  by
Fourier can only bring  to our knowledge one part of the heat
which is annually lost  by the earth; for simple conduction
through terra firma is not the only Avay by which heat escapes
from our globe.
    In the first  place, we  may make mention  of the aqueous
deposits of our atmosphere, which, as  far  as  they penetrate
our earth, Avash away, so to speak, a portion of the  heat, and
thus accelerate  the cooling of the globe.   The  whole quantity
of Avater which faUs from the atmosphere  upon the land in
one day, however, cannot be  assumed to be much more than
half a cubic mile in volume, hence the cooling  effect produced
by this water may be  neglected in our calculation.   The heat 
310
CELESTIAL DYNAMICS.
carried  off by aU the  thermal springs  in the  world is very
smaU in comparison with  the quantities Avhich we have to
consider here.
   Much more important is the effect produced by active vol-
canos.  As the heat Avhich accompanies the molten  matter to
the surface  is  derived from the store  in the interior of the
earth, their action must influence considerably the diminution
of the earth's heat.  And  we have not  only to consider here
actual eruptions  which take  place in succession or simulta-
neously at different parts of the earth's  surface, but also vol-
canos in a  quiescent  state, Avhich continually radiate large
quantities of heat abstracted from the interior of the globe.
If we compare the earth to an  animal body,  wre may regard
each volcano as a place where  the  epidermis has  been torn
off, leaving the interior exposed, and thus opening a door for
the escape of heat.
   Of the whole of the heat which passes  away through
these numerous outlets,  too low  an estimate must  not be
made.  To  have some basis  for the  estimation of this loss,
Ave have to recollect that in 1783 Skaptar-Jokul, a volcano in
Iceland, emitted sufficient  lava in the space of six weeks to
cover 60 square miles of country to an average depth of 200
metres,  or, in  other words, about 1|  cubic miles of laATa.
The  amount of heat lost by this one eruption of one volcano
must, when the high temperature of the lava is considered,
be estimated to be more than 1000 cubic mUes of heat;  and
the whole loss resulting from the action of  all the volcanos
amounts, therefore, in  all probability, to thousands of cubic
mUes of heat per annum.   This latter  number, Avhen added
to Fourier's result, produces a sum Avhich evidently does not
agree with the assumption  that the volume of our earth has
remained unchanged.
   In the investigation of the cooling of our  globe, the influ-
ence of the water of the  ocean has to be taken into account.
Fourier's calculations are based on the observations of the in- 
THE EARTH'S INTERIOR  HEAT.
311
crease of the temperature of the crust of our  earth, from the
surface toAvards the centre.   But two-thirda of the surface of
our  globe are  covered with water, and we cannot  assume d
priori that this large area loses heat at the  same  rate  as  the
solid parts; on the  contrary, various  circumstances indicate
that the cooling of our globe proceeds more quickly through
the waters of the ocean resting on it than from the solid parts
merely in contact Avith the atmosphere.
    In the first place, Ave have to* remark that the bottom of
the  ocean is, generaUy speaking, nearer to the store of heat
in the interior of the  earth  than  the dry land is, and hence
that the  temperature  increases most  probably in  a greater
ratio from the bottom of the sea  towards the interior of  the
globe, than  it does in our  observations on  the  land.  Sec-
ondly, we have to consider that the whole  bottom of the  sea
is covered by a layer of ice-cold water, which  moves con-
stantly  from the poles to the equator,  and  which, in its pas-
sage over sand-banks, causes, as Humboldt  aptly remarks,
the low temperatures Avhich are generally observed in shaUow
places.   That  the water near the bottom of the sea, on  ac-
count of its great specific heat and its Ioav  temperature, is
better fitted than the atmosphere to withdraAv the heat from
the earth, is a point which requires no  further discussion.
   We have plenty of  observations  which  prove  that  the
earth suffers a great loss of heat  through  the waters  of  the
ocean.  Many investigations have demonstrated the  existence
of a large expanse of  sea, much  visited by whalers, situated
between Iceland, Greenland, Norway, and Spitzbergen, and
extending from lat.  76°  to 80° N., and  from  long.  15° E. to
15° W. of Greenwich, where  the  temperature was  observed
to be higher in the deeper Avater  than near the surface—an
experience Avhich neither  accords with the general rule, nor
agrees with the  laws of hydrostatics.   Frankhn observed, in
lat. 77° N. and long. 12° E., that the temperature of the  sea
near  the  surface was — £°, and  at a  depth  of 700 fathoms 
312
CELESTIAL DYNAMICS.
+6°.  Fisher, in lat. 80° N. and long. 11° E., noticed that
the surface-water had a temperature of 0°, whilst at a depth
of 140 fathoms it stood at-f-8°.
   As sea-water, unlike pure water, does not possess a point
of greatest density at some distance above the freezing-point,
and as the water in lat. 80° N. is found at some depth to  be
warmer than water at the same depth 10° southward, we can
only explain  this remarkable phenomenon of  an increase  of
temperature with an  increase- of depth by the  existence of a
source of heat at the bottom of the sea.  The  heat, however,
which is required to warm the Avater at the bottom of an ex-
panse of ocean more than 1000 square  miles in extent to a
sensible degree, must amount, according to the lowest esti-
mate, to some cubic mUes of heat a day.
   The same  phenomenon has  been  observed in other .parts
of the world, such as the west  coast of Australia, the Adri-
atic, the Lago Maggiore, &c.  Especial mention should here
be made of an observation by Horner, according to whom the
lead, when hauled up from a depth varying  from 80 to 100
fathoms in the  mighty Gulf-stream off the coast of America,
used to be hotter than boUing water.
   The facts above mentioned, and some others Avhich might
be added, clearly show that the  loss of heat suffered by our
globe during the last 2500 years  is far too great to  have been
without sensible effect on the velocity of the earth's rotation.
The reason why, in spite of this accelerating cause, the length
of a day has nevertheless  remained constant since the most
ancient times, must be attributed to an opposite retarding ac-
tion.   This consists in the attraction of the sun and moon on
the liquid  parts of the  earth's  surface, as explained in the
last chapter.
   According to the calculations of the last chapter, the re-
tarding pressure of the  tides  against the earth's  rotation
would cause, during the  lapse of 2500 years, a sidereal day
to be lengthened to the extent of r&th of a second; as the 
               the earth's interior beat.          313

length of a day, hoAvever, has remained constant, the cooling
effect of the earth during the same period of time must have
shortened  the  day ^th  of a  second.   A  diminution  of the
earth's radius to the amount of  4£ metres in 2500 years, and
a daily I0.-53 of 200 cubic mUes of heat, correspond to this
effect.  Hence, in  the  course  of the  last 25 centuric?,  the
temperature of the whole mass of the earth must  have de-
creased ii°.
    The not inconsiderable contraction of the earth  resulting
from such a loss of heat, agrees with the continual  transfor-
mations of the earth's  surface  by earthquakes  and volcanic
eruptions ;  and Ave agree with Cordicr, the  industrious  ob-
server of volcanic processes, in  considering these  phenomena
a necessary consequence of the  continual cooling of an earth
which i3 stiU in a molten state in its interior.
    When our earth was in its  youth, its velocity of rotation
must have increased to a very sensible degree, on account of
the rapid cooling of its then very hot mass.   This  accelera-
ting cause gradually diminished, and as the retarding pressure
of the tidal wave  remains nearly constant, the latter must
finally preponderate,  and  the A^elocity  of rotation therefore
continually decrease.  Between  these two states Ave have a
period of  equilibrium,  a period Avhen the influence  of  the
cooling and that of the tidal  pressure  counterbalance each
other ; the whole life of the earth  therefore  may be divided
into three  periods—youth with increasing, middle age with
uniform, and old age with decreasing velocity  of rotation.
    The time during which the tAvo opposed  influences on the
rotation of the earth are in equihbrium can, strictly speak-
ing, only be very short, inasmuch as in one moment the cool-
ing, and in the next moment the pressure of  the  tldos must
prevail.  In a physical  sense,  however, when measured by
human standards, the influence of the cooling, and still  more
so that of the  tidal Avave, may for ages be  considered con-
stant, and  there must consequently exist a period  of many
          11 
314
CELESTIAL DYNAMICS.
thousand years' duration during  which  these  counteracting
influences wiU appear to be equal.  Within this period a si-
dereal day attains its  shortest length, and the velocity of the
earth's rotation its maximum—circumstances wliich, accord-
ing to mathematical  analysis, would tend to lengthen the du-
ration of this period of the earth's existence.
    The historical times of mankind are, according to La-
place's calculation, to be placed in this period.   Whether we
are at the present moment  stiU  near its commencement, its
middle, or are approaching its conclusion, is a question which
cannot be solved by our present data, and  must be left to fu-
ture generations.
    The continual cooling of the earth cannot be Avithout  an
influence on the temperature of its surface, and  consequently
on  the chmate ; scientific men, led by Buffon, in fact, have
advanced the supposition that the loss of heat  sustained  by
our globe must at some time render it an unfit habitation for
organic life.  Such an apprehension has  evidently no founda-
tion, for the warmth of the earth's surface is even now much
more  dependent on the rays of the sun than on the heat which
reaches us from the  interior.  According to Pouillet's meas-
urements, mentioned in Chapter III., the earth receives 8000
cubic  miles of heat a day from  the  sun,  Avhereas  the heat
which reaches the  surface from the earth's interior may be
estimated at 200 cubic miles  per  diem.   The  heat therefore
obtained from the latter source every day is but smaU in com-
parison to the diurnal heat received from the sun.
    If we imagine the solar  radiation to  be constant, and the
heat we receive from the store in  the interior of the  earth to
be cut off, we should have as a consequence various changes
in the physical constitution of the surface of our globe.  The
temperature of hot springs would gradually sink down to the
mean temperature  of the earth's crust, volcanic eruptions
would cease, earthquakes would no longer be  felt, and the
temperature of the water of the  ocean would be sensibly aU 
THE EARTH'S  INTERIOR  HEAT.          315
tered in many places—circumstances  Avhich would doubtless
affect the  chmate in many parts of the world.   Especially it
may be presumed that Western Europe, Avith its present fa-
vourable climate, Avould become colder, and thus perhaps the
seat of the poAver and  culture of  our race transferred to  the
milder parts of North  America.
    Be this as it may, for  thousands of years to come we can
predict  no diminution of  the  temperature of the surface of
our globe as a consequence of the coohng of its interior mass ;
and, as far as historic  records teach, the chmates, the tempe-
ratures of thermal  springs, and the  intensity and frequency
of volcanic eruptions are  now the same as they  were in  the
far past.
    It was different in prehistoric times, when  for centuries
the earth's surface  was heated by internal fire,  when mam-
moths lived in the now uninhabitable polar regions, and when
the tree-ferns and the tropical sheU-fish whose fossil remains
are  now  especially preserved in  the coal-formation Avere at
home in aU parts of the world. 
III.
THE MECHANICAL EQUIVALENT OF HEAT
F]P\HE vast and magnificent structure of the experimental
 JL  sciences has been  erected on only a few pillars.  His-
tory teaches us that the searching spirit of  man required
thousands of years for the discovery of the fundamental prin-
ciples of the sciences, on Avliich the superstructure was then
raised in a comparatively short  time.  But these very funda-
mental propositions are nevertheless so clear and  simple, that
the discovery of them reminds us, in more than one respect,
of Columbus's egg.
   But if, now that Ave are at last in possession of the truth,
we speak of a method by the application of AArhich the  most
essential fundamental laAvs "might have been discovered Avith-
out waste of time, it is not that we would criticize in any light
spirit the efforts  and achievements of our forerunners : it is
merely with the object of laying before the reader in an ad-
vantageous  form one of the additions to  our knowledge which
recent times have brought forth.
   The most important—not to say the  only—rule for the
genuine investigation of nature is, to remain  firm in the con-
viction that the problem before us is to learn to know phenom-
ena, before  seeking for explanations or inquiring  after higher 
         TECE NATURE OF  SCIENTTFIC  PROBLEM.-.     317

caut-c.V.   As soon as a fact is once known in all its relations,
it is therein  explained, and  the problem of science is at  an
end.
    NotAvithstanding that some may pronounce this  a trite
assertion, and  no matter  how many arguments others may
bring to oppose it, it remains none the  less  certain that this
primary rule has  been too often disregarded even up to the
most modern times; while all the speculative operations  of
even the most highly gifted minds which,  instead of taking
firm hold of facts as such, have striven to rise above them,
have as yet borne but barren fruit.
    We shall not here discuss the modern naturalistic philoso-
phy (Naturphilosophie)  further than to say that its character
is already sufficiently apparent from the ephemeral existence
of its offspring.  But even the greatest and most meritorious
of the naturalists of antiquity, in order to explain,  for exam-
ple, the properties of the lever, took refuge in  the assertion
that a circle is such a marveUous thing that no wonder if mo-
tions, taking place in a circle, offer also in their  turn most
unusual phenomena.   If Aristotle, instead  of straining his
extraordinary poAvers in meditations upon the fixed point and
advancing  line, as he  calls  the circle, had  investigated  the
numerical relations subsisting betAveen the length of the arm
of the lever and the pressure exerted, he Avould have laid the
foundation of an important part of human knowledge.
    Such mistakes, committed as they  Avere,  in accordance
Avith the spirit of those times, even by a man Avhose many
positive  services  constitute  his everlasting memorial, may
serve to point us in the  opposite road Avhich leads us surely
to the goal.  But if, even by the most correct method of in-
vestigation, nothing can be attained Avithout toil and industry,
the  cause  is to be  sought in that  divine order of the Avorld
according to which man is made to labour.   But it is certain
that already immeasurably more means  and more toil have
been sacrificed to error than Avere  needed for the discovery of
the truth. 
318     THE  MECHANICAL EQUIVALENT OF HEAT.

    The rule which must be foUowed, in order to lay the foun-
dations of a knoAvledge of  nature in the  shortest conceivable
time, may be  comprised in a few words.  The natural phe-
nomena with which  we come into most immediate contact,
and which are of most frequent occurrence, must be subjected
to a careful examination by means of the organs of sense,
and this examination must  be  continued until it results  in
quantitative determinations which  admit of being expressed
by numbers.
    These numbers are the required foundations of an exact
investigation of nature.
    Among aU natural operations, the free fall of a weight is
the most frequent, the simplest, and—witness Newton's apple
—at the same time the most  important.   When thi3 process
is  analysed in the way that has  been  mentioned, we  imme-
diately see that the weight strikes against the ground the
harder the greater the height from Avhich it has faUen ; and
the problem now consists in the determination of the quanti-
tative relations subsisting betAveen the height from Avhich the
Aveight falls, the  time occupied by it in its descent, and its
final velocity, and in  expressing  these  relations  by definite
numbers.
    In  carrying  out  this experimental investigation, various
difficulties have  to be contended Avith;  but these must and
can be overcome;  and then the  truth is  arrived at, that for
every body a faU of sixteen feet, or a time of descent of one
second, corresponds to  a final velocity of thirty-two feet per
second.
    A  second  phenomenon of daUy occurrence, wliich is  in
apparent contradiction  to  the laws of falling  bodies, is the
ascent of liquids  in tubes  by suction.  Here, again, the rule
applies, not to aUow the maxim, velle rerum cognoscere causas,
to lead us into error through useless and therefore harmful
speculations concerning the qualities of the vacuum, and the
like ; od the contrary, we must again examine  the phenome- 
            THE PROBLEM OF  FALLING  BODII^.        319

Qon Avith attention and awakened senses; and then we find,
as soon as Ave put a tube to the mouth to raise a liquid, that
the operation is at first quite easy, but that afterwards it re-
quires an amount of exertion Avhich rapidly increases as the
column  of hquid  becomes higher.   Is  there, perchance,  an
ascertainable limit to the  action of  suction ?  As soon as we
once  begin to experiment in this  direction, it can no longer
escape us that there is a barometric height, and that it attains
to about thirty inches.  This number is a second chief pihar
in the edifice of human knoAvledge.
   Question now foUoAvs question, and answer, answer.  We
have learned that the pressure exerted by a column of fluid is
proportional to its height  and  to the specific gravity of the
fluid; we have thus determined the  specific gravity of the  at-
mosphere, and by this investigation we are led to carry up
our  measuring-instrument, the  barometer, from  the  plain to
the mountains, and to express numerically the effect produced
by eleA'ation aboA'e the sea-level upon the height of the mer-
cury-column.  Such experiments suggest the question, Whether
the laws of faUing  bodies, with  which we have become
acquainted at the surface of the earth, do not likewise un-
dergo modification at greater distances from  the  ground.
And  if, as d priori we cannot but expect, this should be really
the case, the further question  arises, In Avhat manner is the
number already found modified by distance from the earth?
We have thus come upon a problem the solution of which is
attended with  many difficulties ; for what has  now to be ac-
complished, is to make observations and carry out measure-
ments in places where no human foot can tread.  History,
however, teaches  that the same  man who put the  question
was also able to furnish the ansAver. Truly he  could do  so
only  through a rich treasure of astronomical knowledge. But
how  is this knoAvledge to be attained by us ?
   Astronomy is, Avithout question,  even in its first principles,
the most difficult of aU sciences.  We have here to deal with 
320     THE MECHANICAL EQUIVALENT OF  HEAT.

objects  and  spaces wliich forbid  all thought  of experiment,
while at the same time the motions of the innumerable heaA-
enly bodies  are  of so  complicated a kind, that astronomical
science, in its stately unfolding, is rightly considered the high-
est triumph  Avhereof human inteUect  here below is able to
boast.
    In  accordance with the natural rule that, both in particu-
lars and  in  general, man  has to begin with  that Avhich is
easiest and then to advance step by step to Avhat is more diii:-
cult, it might AveU be supposed that astronomy must have ar-
rived at a flourishing  state  of development later than any
other branch of human knowledge.  But it is well known that
in reality  the direct opposite Avas the case, inasmuch as it Avas
precisely in  astronomy, and in no other branch, that the ear-
liest peoples attained  to  really sound knoAvledge,  It may,
indeed, be asserted that the science  of the heavenly bodies
had in antiquity reached as high a degree of perfection as the
complete want of aU the auxiliary sciences rendered possible.
    This early occurrence  of a vigorous development of as-
tronomy,  which, indeed, was  a necessary forerunner  of the
other sciences, since it  alone furnished the necessary data for'
the measurement of time, is observable  among the most va-
rious races of mankind: the reason of  it, moreover, lies  in
the nature of things, and  in the constitution of the human
mind.   It furnishes a remarkable  proof that a right method
is the most important condition for the successful  prosecution
of scientific inquiry.
    The explanation of this phenomenon lies in the fact that
the need which was felt at a very early period, of a common
standard for  the computation of time, made  it necessary to
institute observations such that their results  required to  be
expressed by definite numbers.  There was a felt necessity of
determining the  time in which the  sun accomplishes  his  cir-
cuit through the heavens, as AveU as the time  in which tho
moon goes through her phases, and other  similar questions. 
           FALLING BODIES  AT GREAT HEIGHTS.       321

In order to meet  this necessity, there was no  temptation  to
take up the  Book of Nature, after the  manner of expositors
and critics, merely to cover it Avith glosses:

          " Ifit eitler Rede wird hier nichis  geschafft."
   It Avas numbers that Avere sought, and  numbers that Avere
found.  The overpowering force of circumstances constrained
the spirit of inquiry into the  right path, and  therein led it at
once from success to success.
   Noav that after  long-continued,  accurate,  and fortunate
observations the needful knoAvledge of the  courses  and dis-
tances of the nearest heaA'enly bodies, as well as of the figure
and size of the earth, has been acquired, we  are in a position
to treat the question, What is the numerical influence exerted
by increased distance from the earth upon the known laAvs of
faUing bodies ? and we thus arrive at the  pregnant discovery
that, at a height  equal  to the earth's semidiameter, the dis-
tance faUen through and the final velocity, for the first second,
is four times less  than on the surface of the earth.
   In order to pursue  our  inquiry,  let us now return to tho
objects which immediately surround  us.  From  the earliest
times, the phenomena of combustion must have claimed in an
especial  degree the  attention of  mankind.   In order to ex-
plain them, the ancients, in  accordance with the method of
their naturalistic philosophy,  put forward  a peculiar  upAvard-
striving  element,  of Fire, which in  conjunction with, and  in
opposition to,  Ah, Water, and Earth, constituted all that ex-
isted.  The necessary consequence of this theory, Avhich they
discussed Avith the most acute sagacity, Avas, that in regard to
the phenomena in question and all that related to them, they
remained in complete ignorance.
   Here, again, it  is quantitative determination?, it is  num-
bers alone, Avhich put the Ariadne's clue in our hand.  If wo
want to know Avhat goes on  during the phenomena of com-
oustion, Ave must weigh the substances before and after  they 
322     THE MECHANICAL EQUIVALENT OF
are burned;  and here  the  knowledge we have  already ac-
quired of the weight of gaseous  bodies  comes  to  our aid.
We then  find that, in every case of combustion, substances
which previously existed in a separate state enter into an inti-
mate  union with each other, and that the  total Aveight of the
substances remains the same both before and after the combi-
nation.  We  thus come to know the different  bodies in  their
separate and  in their combined states, and learn how to trans-
form  them from one of these states into the other; we learn,
for instance, that water is composed of two kinds of air which
combine with each  other  in the proportion of 1: 8.  An en-
trance into chemical science is thus opened to us,  and the nu-
merical laws which regulate the combinations of  matter (die
Stochiometrie) hang like ripe fruit before us.
   As we proceed further in our investigations, Ave find that
in aU chemical operations—combinations as weU as decompo-
sitions—changes of temperature occur, which, according to
the varying  circumstances of different cases, are of aU de-
grees of intensity, from the most violent heat  downwards.
We  have measured  quantitatively  the  heat developed, or
counted the number of heat-units, and have so come into pos-
session of the law of the  evolution of heat in chemical pro-
cesses.
   We have long known, however, that in innumerable  cases
heat makes its appearance where no chemical action is going
on; for instance, whenever there  is friction, when unelastic
bodies strike one another, and when aeriform bodies are  com-
pressed.
    What then takes place when  heat is evolved in such ways
as these ?
   We are taught by history that in this   case also the  most
sagacious hypotheses concerning the state and nature  of a
peculiar  "matter" of heat, concerning a "thermal asther,"
whether  at rest or in a state of vibration, concerning " ther-
mal  atoms,"  supposed to exercise their functions in the  inter- 
          CONVERTIBILITY OF nEAT AND MOTION.     323

Btices between the material atoms, or other hypotheses of hke
nature, have not availed to solve the problem.  It is, notwith-
standing, of no less wonderfuUy simple a nature than the laws
of the lever, about which  the founder of the  peripatetic phi
losophy cudgelled his brains in vain.
   After Avhat has gone before, the reader cannot be in any
doubt about what is the course now to be pursued.   We must
again make quantitative  determinations: we must measure
and count.
   If we proceed in this  direction and measure the quantity
of heat  developed  by mechanical agency,  as  weU  as  the
amount of force used  up  in producing it, and compare these
quantities with each  other, we at once find that they stand to
each other in the simplest  conceivable relation—that is to say,
in an invariable  direct  proportion, and that the proportion also
holds when, inversely,  mechanical force is again  produced  by
the aid of heat.
   Putting these facts  into brief and plain language, we may

   Heat and motion  are transformable one into the other.
   We cannot and ought  not, however, to let this  suffice us.
We require to know  how much mechanical force is needed for
the production of a given amount of heat, and conversely.
In other words, the law of the invariable quantitative relation
between motion and heat must be expressed numerically.
   When we  appeal hereupon to experiment, we find that
raising the temperature of a given weight of water one degree
Df the  Centigrade scale corresponds to the  elevation of  an
equal weight to the height of about 1,200 [French] feet.
   This number is the Mechanical Equivalent of Heat.

   The production of heat by friction and other mechanical
jperations is a fundamental fact of such constant occurrence,
that  the importance of its establishment on a scientific basis
wiU  be recognized  by naturalists without any preliminary 
324     THE MECHANICAL EQUIVALENT  OF HEAT.

enumeration of  its useful applications;  and, for  the same
reason, a few historical remarks touching the  circumstances
attending the  discovery of the foregoing fundamental law,
wiU not be out of place here.
    In the  summer of 1840, on the occasion of bleeding Eu-
ropeans neAvly arrived in Ja\'a, I made the observation that
the blood drawn from the A-ein of the arm possessed,  almost
without exception, a surprisingly bright red colour.
    This phenomenon riveted my earnest attention.   Starting
from  Lavoisier's  theory, according to which animal  heat is
the result of a process of combustion, I regarded the tAvofold
change of colour Avhich the blood undergoes in the capillaries
as a sensible sign—as the visible indication—of an oxidation
going on in the blood.   In order that the human  body may
be  kept at  a uniform  temperature, the development of heat
within  ft must bear a quantitative relation to the  heat which
it  loses—a relation, that is, to  the  temperature of the sur-
rounding medium; and hence both the production  of heat
and the process of oxidation,  as avcII as the difference in col-
our of the two kinds of blood,  must  be  on the whole  less in
the torrid zones than in colder regions.
    In accordance with this theory, and having regard to the
known  physiological facts which bear upon the question, the
blood  must be regarded as a fermenting  liquid undergoing
slow  combustion,  Avhose  most  important  function—that  is,
sustaining  the process of combustion—13 fulfilled Avithout tho
constituents of the blood (with the  exception, that is,  of the
products of decomposition) leaving the  cavities of the  blood-
vessels  or coming into  such relation with the organs that an
interchange  of matter can take place.  This may be thus
stated in other Avords :  by far the greater part of the  assimi-
lated  food is burned in the cavities of the blood-vessels  them-
selves, for the purpose of producing a  phyoical effect, and a
comparatively smaU quantity only  serves the  less  important
end of ultimately entering the substance of the organs  them- 
            PROBLEM  OF PHYSIOLOGICAL  HEAT.        325

selves, so as to occasion groAvth and the renewal of the worn-
out solid parts.
    If hence it follows that a general balance must be struck
in the organism between receipts  and expenditure, or betAveen
work done  and wear  and tear, it is unmistakably one of the
most important problems Avith which the physiologist has to
deal, to make himself as thoroughly acquainted as it is possi-
ble for him  to be with the budget of the object of his  exami-
nation.   The  Avear and tear consists in the amount of matter
consumed ;  the Avork  done is the evolution of heat.   This
latter effect, however, is of tAvo  kinds, inasmuch as the ani-
mal body evolves  heat on the one hand directly in  its own
interior, and distributes it  by communication  to  the  objects
immediately surrounding it; Avhile,  on  the other hand, it
possesses, through its organs of motion, the poAver of produc-
ing  heat mechanically by friction or in similar Avays, even at
distant points.  We now require to knoAv
     Whether the heat directly evolved is alone to be laid to the
account of the process  of combustion,  or whether it is  the sum
of the heat  evolced both directly  and indirectly that it is to be
taken into calculation.
    This is a question that touches the very foundations of sci-
ence ; and unless it receives a trustAvorthy answer, the healthy
development of the doctrine concerned is not possible.  For
it has been already shoAvn, by various  examples, Avhat are
the consequences of neglecting primary quantitative determi-
nations.  No  Avit  of man  is able  to furnish a substitute for
what nature offers.
    The  physiological theory of  combustion starts from the
fundamental proposition, that the quantity of heat Avhich re-
sults from the combustion of a given substance is invariable—
that is, that its amount is uninfluenced by the circumstances
which accompany  the combustion ;  AAdience avc infer, " in spe-
cie," that the  chemical effect of  combustible matter  can un-
dergo no alteration in amount even  by the  vital process, or 
326     THE  MECHANICAL  EQUIVALENT  OF HEAT.

that the living organism, with aU its riddles and marvels, can-
not create heat out of nothing.
    But if we  hold  firm to this physiological axiom, the an
swer  to  the question started  above is  already given.  For,
unless we wish to attribute again fo the organism  the  power
of creatine heat which has just been denied to it, it cannot be
assumed that the heat wliich it produces can ever  amount to
more  than the  chemical  action which takes place.  On the
combustion-theory there is,  then,  no  alternative, short  of sa-
crificing the theory itself, but to admit that the total amount
of heat evolved by the  organism, partly directly, and  partly
indirectly by mechanical  action,  corresponds quantitatively,
or is equal to the amount of combustion.
    Hence it follows, no  less inevitably, that the heat produced
mechanically by the organism  must  bear an invariable quantita-
tive relation to  the work expended in producing it.
    For if, according to the varying  construction of the me-
chanical arrangements Avhich serve for the development of
the heat, the  same amount of work, and hence  the  same
amount of organic combustion, could produce varying quanti-
ties of heat, the quantity of  heat  produced from one and the
same  expenditure of material would come out smaUer at one
time and larger at another, which is contrary to our  assump-
tion.  Further, inasmuch as there is no difference in kind be-
tween the mechanical performances of the animal body and
those  of  other  inorganic sources of work, it foUows that
    AN INVARIABLE  QUANTITATIVE RELATION BETWEEN HEAT
AND "WORK IS  A POSTULATE  OF  THE  PHYSIOLOGICAL THEORY
OF COMBUSTION.
    While following in general the direction indicated, it wa3
accordingly needful for  me  in the end to  fix my attention
chiefly on the physical connection subsisting between motion
and heat; and it was thus impossible for the existence of the
mechanical equivalent of heat to remain hidden  from me.
But, although  I have to  thank an  accident  for this  discovery, 
          RELATION BETWEEN HEAT  AND WORK.      327

 (t is none the less my own, and I do not hesitate to assert my
 right of priority.
    In order to ensure what had been thus  discovered against
 casualties, I put together the most important points in a short
 paper which I sent in the spring of 1842 to Liebig, Avith a
 request that he would insert it in the Annalen der Chemie und
 Pharmacie, in the forty-second volume of Avhich, page  233, it
 may be found under the  title " Bemerkungen iiber die  Kriifte
 der unbelebten Natur."
    It was a fortunate circumstance for me that the reception
 given  to  my unpretending work  by this man, gifted with so
 deep an insight, at once secured for it an entrance into one of
 the first scientific organs, and I seize this opportunity of pub-
 licly testifying to the great naturalist my gratitude and  my
 esteem.
    Liebig himself, hoAvever, had about the  same time already
 pointed out, in more general but still unmistakable terms,  the
 connection subsisting between heat and work.   In particular,
 he asserts  that the heat produced mechanically by a  steam-
 engine is to be attributed solely to the effect of combustion,
 Avhich can never receive  any increase through the fact of its
 producing mechanical effects, and, through  these, again devel-
 oping heat.
   From these, and from similar  expressions of other scien-
 tific men, we may infer that science has recently entered upon
 a direction in Avhich the  existence  of the mechanical equiva-
 lent of heat could not in  any case have  remained longer un-
 perceived.
   In the paper to which reference has been made, the nat-
 ural law with which we  are  now concerned is referred back
 to a few fundamental conceptions of the human mind.  The
 proposition  that a magnitude, Avhich  does not spring from
 nothing, cannot be annihilated, is  so simple and clear that no
valid argument can be urged against its truth, any more than
against an  axiom of geometry;  and until  the  contrary is 
328     THE  MECHANICAL EQUIVALENT OF nEAT.

proved by some fact established  beyond a doubt, we may ao>
cept it as true.
    Now we are taught by experience, that neither motion nor
heat ever takes its rise except at the  expense of some meas-
urable object, and  that in  innumerable  cases motion disap-
pears without  any thing  except  heat  making its appearance.
The axiom that Ave have established  leads, then, noAV to the
conclusion that the motion that disappears becomes  heat, or,
in other words, that both objects bear to each other  an inva*
riable quantitative relation.   The proof of this conclusion by
the method of experiment, the establishment of it  in  all its
details, the tracing of a complete harmony subsisting between
the laws  of thought and the objective world, is the most inter-
esting, but at the same time the most comprehensive  problem
that it is possible  to find.   What I, with feeble poAvers and
Avithout any external support or encouragement, have effected
in this direction is truly little enough ; but—ultra posse nemo
obligaius.
    In the paper referred to (the  first of  Mayer's in  the pres-
ent volume) I have thus  expressed myself with regard to the
genetic connection of heat and moving force :
    " If it  be  noAV considered as established that  in many
cases (exceptio confirmat regulam) no  other effect  of motion
can be traced except heat, and that no other cause than motion
can be found for the heat that is produced, we prefer the as«
sumption that  heat  proceeds from motion, to the assumption
of a cause without  effect and of an  effect without a cause—
just as the chemist, instead of allowing oxygen and hydrogen
to disappear Avithout further investigation, and water to be
produced in some  inexplicable manner, establishes  a connec-
tion between oxygen and hydrogen on the one hand and Avater
on the other."
    From this point there  is but one  step to be  made to the
goal.   At page  257 it i3 said:  " The solution of the equa-
tions  subsisting between faUing-force [that is, the  raising of 
        CONNECTION OF  HEAT AND MOVING  FORCE.    329

weight] and motion requires that the space fallen  through in
a given time, e. g. the first second, should be experimentaUy
determined;  in  like manner, the solution of the equations
subsisting betAveen faUing-force and motion on the one hand
and heat on the other, requires an answer to the question, How
great is the  quantity of heat Avhich corresponds  to a giveD
quantity of motion or falling-force?  For instance, we must
ascertain Iioav high a given weight requires to  be raised above
the ground in order that its falling-force may be equivalent to
the raising of the temperature of an equal weight of water
from 0° to 1° C.  The attempt to sIioav that such an equation
is the expression of a plrysical truth may be  regarded as the
substance of  the foregoing remarks.
    " By applying tho principles that have been  set forth to
the relations subsisting  betAveen the temperature and the vol-
ume of ga<cs, we find that the sinking of a mercury column
by wliich a gas  is compressed is equivalent to the  quantity of
heat set  fire by the compression;  and hence it  folloAvs, the
ratio betAA'ecn the capacity for heat of air under constant press-
ure  and its  capacity under constant volume  being taken as
—1--121, that the Avarming of a given weight of  water from
0° to 1° C. corresponds  to  the fall  of  an equal weight from
the height of about 3G5  metres."
    It is plain that the expression " equivalent" is here used
in quite a different sense from Avhat it bears in chemistry.
The difference will be shoAvn most  distinctly by an example.
When  the same weight of potash  is neutralized, first, Avith
sulphuric acid, then with nitric acid, the numbers which ex-
press the ratio Avhich the absolute Aveiglits of these three sub-
stances bear to onj another are called their equivalents; but
tlurc is no thought here either of the quantitative equality or
of the  transformation  of the bodies in question.
    This peculiar signification Avhich the Avord "equivalent'
has  acquired in chemistry, is doubtless  connected Avith the
fact that the  chemist has been able to determine the object of 
330      THE  MECHANICAL  EQUIVALENT OF HEAT.

his investigation by a common quantitative standard, their ab
solute weights.  Let us suppose, however, that we  could de-
termine  one  body, for instance water, only by weight, and
another, Avater-forming or explosive gas,  only by volume, and
that we had agreed to choose one pound as the unit of weight,
and one cubic foot as the unit of volume ;  we should then have
to ascertain how many cubic feet of explosive gas could be ob-
tained from one pound of Avater, and conversely.  This num
ber, Avithout which neither the formation nor the decomposi-
tion of water could be made the subject of calculation, might
then be suitably caUed " the explosive-gas equivalent of Ava-
ter."
   In this  latter sense a raised Aveight might, in accordance
with the  known laAvs of mechanics, be caUed  the  " equiva-
lent "  of  the motion resulting from its fall.   Now, in order to
compare  these two objects, the raised and the moving Aveight,
which  admit of no common measure, we require  that  con-
stant number Avhich is generally denoted by g.   This number,
hoAvever, and the mechanical equivalent of heat, whereby the
relation subsisting betAveen heat and motion is defined, belong
both of them to one and the same category of ideas.
   In  the  paper that I have  mentioned it is further shown
hoAv we may arrive  at such a conception of force as admits
of being  consistently followed to its consequences and is sci-
entifically tenable ; and the importance of this subject induces
me to return to it again here.
   The word " force" (Kraft) is used in the higher or scien-
tific mechanics in two distinct senses.
   I. On the one hand, it denotes every push or pull, every
effort of  an inert  body to '.'hange its state of rest or of mo-
tion ;  and  this effort, when it is considered alone and  apart
from the result produced, is  called •'• pushing force,"  " pulling
force," or  shortly " force,"  and  also, in  order to distinguish
betAveen this and the foUowing conception, " dead force " (vis
mortua). 
             MEANING  OF THE TERM " FORCE."        33]

    II.  On the other hand, the product of the pressure into
 the  space through Avhich it acts, or, again, the product—or
 half-product—of the mass into the square of the velocity, is
 named  " force."   In order that motion  may actually occur, it
 is in fact necessary that the mass, whatever it may be, should
 under the influence of a pressure,  and, in the  direction of that
 pressure, traverse a  certaiu  space,  "the  effective  space"
 ( Wirkungsraum) : and in this  case a magnitude Avhich is pro-
 portional to the " pushing force " and to the effective space,
 likeAvise  receives the  name  " force;"  but  to distinguish it
 from the mere pushing  force, by which alone motion is never
 actuaUy brought about, it is also called  the " vis viva of mo-
 tion," or " moving force."
    With the generic conception of " force,"  the higher me-
 chanics, as an essentially analytic science, is not concerned.
 In  order to arrive  at it, we  must, according to the  general
 rule, coUect together the  characters possessed in common  by
 the several  species.   As is weU known,  the definition  so ob-
 tained runs  thus—" Force is every thing which brings about
 or tends to bring about, alters or tends to alter motion."
    This definition, hoAA'ever, it is  easy to see, is tautological;
 for the   last fourteen words of it  might be omitted, and the
sense Avould be still the  same.
    This erroneous solution is occasioned by the nature of the
problem,  Avhich requires  an impossibility.   Mere pressure
 (dead force) and the product of the pressure into the effective
 space (living force) are  magnitudes too thoroughly unhke  to
be by possibUity combined into a  generic conception.   Press-
 ure or attraction is, in  the theory of motion, what  affinity is
in chemistry—an abstract conception : living  force,  like mat-
ter, is concrete ; and these two  kinds of force,  hoAvever closely
connecte4 in  the  region of the  association  of ideas, are  in
reality so AAidely separated that a frame which should take
them both in must be able to include the whole  world.
    There are several conceivable ways  of escaping from the 
332     THE  MECHANICAL EQUIVALENT OF nEAT.

difficulty.  For instance, just as Ave fpeak of absolute av eight,
specific weight, and combining weight, Avithout its ever enter
ing any one's head to want to construct a generic idea out of
these distinct  notions, so two or more meanings may be at-
tached to the Avord force.  This is what is actuaUy done in
the higher mechanics, and hence in this branch of science Ave
meet Avith no mention of a generic conception of  " force."
    There has  been no lack of recommendations to  carry, in
like manner, the notions of " dead " and  "hving force" as
distinct and separate through  the  other departments of sci-
ence ;  it has, hoAvever, been found impossible to put  in prac
tice such recommendations; for the use  of ambiguous  ex
pressions, wliich can in no case contribute any thing to clear-
ness, is altogether inadmissible if confusion  can possibly arise.
It is true that the mathematician is  in no danger of confound-
ing in  his calculations a product with one of its factors ; but
in other departments of knowledge a systematic confusion of
ideas exists on  this point; and if any thing  is  to  be  done
toward clearing it up, the source of the error must be  stopped ;
for if Ave once recognize two meanings of the word  " force,"
it would be the labour of  Sisyphus to try  to distinguish  be-
tween  them in each separate case.   In order, then,  to arrive
at any result, Ave must make up our minds  to do Avithout  any
common denomination of the magnitudes  mentioned above,
as I. and II., and either  to  give  up  the use of the word
" force " altogether, or to employ it for one only of these tAvo
categories.
    The  notion of force was consistently employed in the lat-
ter sense by NeAvton.  In  solving his problems, he decom-
poses  the product of the attract'on into the effective space
into its tAvo factors, and caUs the former by  the name "force."
    As an objection to this  mode of proceeding, it must, how-
ever, be remarked that in many cases it is not possible  thus
to decompose  the  product in question.   Let us  take, for in-
stance, the foUowing very simple case : a mass M, originally 
MEANING OF THE TEEM  " FORCE.
333
at rest, is caused to move with the (uniform final) velocity c;
from the knowledge of the magnitudes M and c it is certainly
possible to  deduce the value  of the  product of the force (in
NeAvton's sense) into its effective space, but Ave are not thereby
enabled to conclude as to the magnitude of this force itself.
    As a matter of fact, the necessity soon made itself felt of
treating and naming this  product as a whole.  It also  has
been called  " force," and the expressions " vis viva of motion,"
"moving force," " working force," "horse-power" (or force),
" muscular force," &c, have been long naturalized in science.
    HoAvever happy Ave may, in many respects,  think  the
choice  of this word, there is  still the objection that a new
meaning has been fixed  upon an already existing  technical
expression,  Avithout the old one having been  caUed in from
circulation at the same time.  This formal error  has become
a Pandora's box, Avhence has  sprung a Babylonian confusion
of tongues.
    Under existing circumstances no  choice is left us but to
Avithdraw the term " force" cither from NeAvton's dead force
or from Leibnitz's hving force; but in either  case Ave come
into conflict with prevailing  usage.   But  if once  we have
made up our minds to introduce into  our science a logically
accurate use of terms, even at the cost of existing expressions
Avhich have  become easy and pleasant to us by long usage, Ave
cannot  long hesitate in  the choice avc  have to make between
the conceptions I. and II.
    Let us consider the  elementary case of a mass, originaUv
at rest, a\ hich receives motion :  this happens, as has been al-
ready said, by the mass being subjected to a certain push or
puU under the influence of which it traverses a certain space,
the effective space.  Noav, however, both the velocity  and
also the intensity of the push (Newton's force)  always vary
at every point of the effective space; and in  order to mul-
tiply these variable magnitudes into  effective  space, that is,
to deduce the  quantity of motion from the intensity of the 
334     THE MECHANICAL EQUIVALENT OF HEAT.

pushing force, we must caU in the  aid of the higher mathe-
matics.
    But hence it foUows  that, except in statics, where the ef-
fective space is  nought and the  pressure  constant, the  Ncav-
tonian conception of force is available  only in  the higher
branches of mechanics ;  and it is plainly not  advisable so to
choose  our conception of  " force" that it cannot be  consist
ently employed in that branch (namely, the elementary parts
of the theory of motion) which of aU others  is chiefly con-
cerned with fundamental notions.
    It is, however, a totally mistaken method to try to adapt
the idea of a forte, such as gravity, conceived in NeAvton's
sense, to the elementary parts of science, by leaving out of
consideration one of its most important properties, namely its
dependence on distance, and to make a " force " out of Gali-
leo's gravity thus inexactly and in some relations most incor-
rectly conceived.   Some such ideal force (No. III.) seems
to hover before the minds of most writers on natural science
as the original type of a "force of nature."
    Such quantitative determinations as hold  good only ap-
proximately and under certain conditions ought never  to be
employed to estabhsh definitions.   In a calculation, it is true,
we may correctly enough take an  arc, which  is sufficiently
small in comparison with  the  radius, as equal  in size to  the
sine or to the tangent; but if we  attempted to use such a rela-
tion in settling first principles, we should lay a foundation for
faUacies and errors.
    The  Newtonian idea of force, however,  transplanted in
the manner that is commonly done into the region  of element-
ary science, is  no whit better than the  notion of a  straight
curve.  Newton's force, or attraction, in specie gravity, g, is
equal to the differential quotient of the velocity by the  time  ;
           dc
that is,  g=~r'   This expression is quite exact, but in order to
           OX
understand and apply it a knowledge of the higher mathemat' 
             newton's  conception of force.        335

ics is required.  On the other hand, it is quite true that, so
long  as Ave have to do  only with  cases in which the space
faUen through is so small in comparison Avith the earth's semi
diameter that it may be  disregarded, the equation just given

may be abbreviated into the very convenient form <7=-. with-

out any considerable error ; but this expression can  never  be
mathematically  exact so long as the space fallen through has
any calculable  magnitude.  But on the  strength of an equa-
tion thus  radically  inaccurate, there are planted in the recep
tive mind of youth such false notions as—that gravity is a
uniformly accelerating ( ?) force, a moving ( ?) force whose ac-
tion is proportional to  the time ( ?) ; that force is directly pro-
portional  ( ?) to the velocity produced; and  many other hke
errors.
    It would certainly  be a great merit if authors of treatises
on physics would help to remedy this state of things, and in
framing  their definitions AArould  start only from thoroughly
exact determinations of magnitudes;  for elementary physics
in its present form, instead of being a weU-grounded science,
is only a sort of half-knoAvledge, such that on passing to  the
higher and strictly scientific departments  the student must
try to forget its  principles and theorems as quickly as he can.
    If we  have once  convinced  ourselves  by unprejudiced
examination that the retention, under that name, of the con-
ception of force distinguished above by I. has nothing  but  its
origin to recommend it, but much to condemn it, the rest fol-
Ioavs  almost spontaneously.    It accords with the  laws  of
thought, as weU as with the common usage of language, tc
connect every production of motion with an expenditure  of
force. Hence " force " is—
    Something whiih is  expended  in producing motion; and
this something Avhich  is expended  is to be looked upon as a
cause equivalent to the effect, namely, to the  motion pro-
duced. 
33G     the mechanical  equivalent of neat.

   This  definition not only corresponds perfectly, with facts,
but it accords as far as possible with that which already ex-
ists ; for, as I shall show, it contains by implication the con-
ception of force a3 met with in the higher mechanics, and re-
ferred to above by n.
   If a mass M, originally at rest, Avhile traA'ersing the effect-
ive space s, under the influence and in the direction of the
pressure p, acquires the velocity c, we haveps=Mc2.  Since,
however, every production of motion implies the existence of
a pressure (or of a pull) and an effective space, and also the
exhaustion of one at least of these factors, the effective space,
it foUoAVS that motion can neATer  come  into existence except
at the cost of this product, jjs=Mc9.   And this it is which
for shortness I call " force."
   The connection between expenditure and performance (in
other words, the exhaustion of force in producing its  effect)
presents itself in the simplest form in the phenomena of grav-
itation.  The necessary condition of every falling  motion is
that the centre of gravity of the  two masses concerned in it
(that is, of the earth and  of the falling Aveight) should ap-
proach each other.   But in the case  of the faUing together of
the  two masses, the approach of their  centres of gravity
reaches its natural limit, and  hence the production of a faU-
ing movement is thus bound up with an expenditure, namely,
Avith the  exhaustion of the  given falling-space, and thereby
also of the product  of that space into  the attraction.   The
falling down of a weight upon the  earth is a process of me-
chanical combination ; and just as in combustion the capacity
of performance (that is, the condition of the development of
heat)  ceases when the act of combination comes to an end, so
also the  production of motion ceases  when the weight has
fallen  to its lowest position.   The Aveight, Avhen lying  on the
solid ground, is, like the carbonic acid  formed  in combustion,
nothing but a caput mortuum.  The affinity, whether mechan-
ical or chemical, is still there  after the  union juot as much as 
         HIGHEST VELOCITY OF A FALLING  BODY.     337

before, and opposes a certain resistance to the reduction of
the compound;  but  its power of performance (Leistungs-
fahigkcit) is at an end as soon as there is no further available
falling-space.
    Whenever the attraction  becomes  indefinitely small, or
ceases altogether, space is no longer effective space  ; and thus
it folloAvs, from the diminution which gravity undergoes with
distance, that  falling-space is limited in the centrifugal  direc-
tion also, and  hence that the cause of motion or  "  force" is,
under all circumstances, a  finite  magnitude  Avhich becomes
exhausted in producing its effect.
    This fundamental physical truth will be  most easily per-
ceived when applied to a special case and reduced  to figures.
When a pound weight is lifted one foot from the ground, the
available force is, as eArery one knows, =one foot-pound.  If
the falling-height of this Aveight amounts to n feet,  n  not be-
ing a large number, the force may be taken as approximately
= 71 foot-pounds.   But  supposing  n, or  the  original distance
of the weight  from the earth, to be very considerable, or in-
deed  infinite,  the force (that is, the number of foot-pounds)
does not by any means thereby become infinite, but, according
to  Newton's laAV of gravitation, it becomes at most =r foot-
pounds, where r is the number of feet contained in the earth's
semidiameter.   Thus hoAv great soever the  distance through
which a weight falls  against the earth, or the time occupied
by its faU may be, it can acquire no higher final velocity than
34,450 Paris feet per second.  On the other  hand, were the
mass  of the earth four times as great as it is, its bulk remain-
in"" the same,  the force would likewise become four times as
great, and the maximum Arelocity would be G8,900 feet.
    It  is one of the  essentials of  a good  terminology that it
should put fundamental facts  of this kind in a  clear  light;
exactly the opposite, hoAvever, is done by the nomenclature at
present in use. A few expressions, employed by a very meri-
            15 
338     THE  MECHANICAL EQUIVALENT OF HEAT.

torious  naturalist  in combating my vieAvs, may sera to sup.
port this assertion.
    " Although," he says, " it is quite true that in nature  no
motion  can be  annihdated, or  that, as  it is commonly ex-
pressed, the quantity of motion once  in  existence continues
unceasingly and without any lessening, and  although in this
sense the character of indestructibUity belongs to every prox-
imate  cause even, eA'ery primary cause, that is, every true
physical force, possesses the additional characteristic  of being
inexhaustible.  These characteristics will best admit  of being
unfolded by the closer consideration  of gravity, the  most
active and  widely diffused of  the  natural  forces (primary
causes), which, as it were the soul of the Avorld, indestructi-
bly and inexhaustibly upholds the life of  those  great masses
on whose motions depends the  order  of  the universe, Avhile
requiring no food from without to call forth its ever  reneAved
activity."
    If these words are intended to contain a  material contra-
diction of the  vieAvs I have put forward, they must be meant
to imply that,  by virtue of its being inexhaustible, the attract-
ive  power of the earth must be capable of imparting to a faU-
ing weight, under certain conceivable circumstances,  an infin-
ite velocity.  But  our author himself in several places lets us
see that he has a (quite weU-founded)  mistrust of any so de-
cided a  conclusion: this is  shown in the following, among
other passages: " If we follow up the chain of  causes and
effects to its first beginnings, we come at length to  the true
forces of nature, to those primary causes  whose activity does
not require that they should be preceded by any others, Avhich
ask for  no  nourishment, but which can  ever call forth neAV
motions, as it were,  out of an inexhaustible  soil,  and can
uphold and quicken those that are already in being."
    Again:  " If the  moon every moment falls, at least vir-
tuaUy, a certain distance toward the earth, what is  the force
which the next moment pulls  it  away again, as  it were, in 
OBJECTIONS CONSIDERED
339
 order to give rise to a new falhng force ?  It is precisely its
 indestructibihty and  inexhaustibUity, its  power at all times
 and under all circumstances to bring about without ceasing,
 at least virtuaUy, the same effects, that is the essence of every
 true force or primary cause."
    This '• as it were" and " at least virtually,"  which always
 slips in at the critical moment, affords room for the suspicion
 that our author is himself not  quite  confident of  the power
 of his " true natural causes" to give rise to an inexhaustible
 amount of motion (of actual exertion of force)  ; and the in-
 dcfiniteness of these expressions is quite characteristic of tho
 Protean  part which the force of gravity plays in writings  on
 natural science.  The most  arbitrary explanations are giA-en
 of this Avord, and  then, when facts no longer  admit of any
 thing else,  a retreat is sought in the NeAvtonian  conception.
    Gravity being  caUed a force, and at  the same time the
 term force being connected,  in accordance Avith the  common
 use of language, with the conception of an object capable of
 producing  motion, leads to the false assumption that a me-
 chanical effect (the production  of motion) can be produced
 without a corresponding expenditure of a measurable object;
 and here is likeAvise plainly the reason why our  author could
neither keep clear in his facts nor consistent in his reasoning.
If once the production of motion  out of nothing is granted,
the annihilation of  motion must alsc be admitted as a conse-
quence ;  and the magnitude of motion must, in accordance
Avith this assumption, be simply proportional to the velocity,
 or =Mc, and  the  "quantity of  motion once  in existence"
must be = +Mc — Jlc=0.   But notwithstanding his " inex-
haustible forces,"  the writer leferred  to  expressly  declares
that motion is indestructible ; out, instead of stating his opin-
 ion as to what becomes of motion which disappears by fric-
 tion, he says in another place  again that it remains " unde-
cided " Avhether the effect of a force (the amount of motion
produced by it) is measured by the first or by the second 
340     THE MECHANICAL EQUIVALENT OF HEAT.

power of the velocity (that  is, whether it is or is not  de-
structible) : he  even appears, from repeated  expressions, to
hold it possible that a given quantity of heat can produce mo-
tion ad infinitum !   If such were the case, it would certainly
be  useless to  consider  the  convertibility  of these  magni-
tudes : the ground Avould rather have been won for the contact
theory.
    The polemics of my respected critic, Avhom I have here
introduced as the representative and spokesman of prevailing
views, and to whom I feel that my sincere thanks are due for
his attentive examination of my first publication, appear to
me to be  necessarily Avithout result, inasmuch as  the first
problem in combating my assertions, which aU revolve about
the one point of an  invariable quantitative relation betAveen
heat and motion, must be to find out.that this  relation is va-
riable, and  in  what cases.   Formal  controversy without a
material basis is only beating  the air;  and as to Avhat relates
specially to the questions about force,  the first point to con-
sider  is, not  what sort of thing a "force" is, but  to what
thing we shall  give  the name  " force."  Backwards  and for-
wards talk about gravity is fruitless, since all who understand
the matter are agreed as to its nature ; for gravity is  and re-
mains a differential  quotient  of the velocity by the  time, di-
rectly proportional to the attracting mass, and inversely pro-
portional to the square of the distance :  on this  point a final
decision was  come to long ago   But whether it is expedient
to caU this magnitude a force is quite another question.
    Since, whenever an innovation of essential importance is
proposed, the public is so ready to misapprehend, I wUl here
state  once more, as clearly as  I  can, my reasons for saying
that " the force of gravity " is an improper expression.
    It is  an  unassaUable truth that the production of every
faUing motion is connected with a corresponding expenditure
of a measurable magnitude.  This  magnitude, if it  is to be
made an object of scientific investigation (and why should it 
APPLICATION OF THE  TEEM " FORCE."
o 11
OIL
not ?), must have a name given to it;  and in accordance Avith
the logical instinct of man, as manifested in the genius of lan-
guage, no other name  can  be here  chosen  than  the  word
" force."   But since this expression is already used  in a quite
different sense, Ave might be tempted to create for the concep-
tion which is as yet—in the fundamental parts of science at
least—unnamed an entirely new name.   But before betaking
ourselves to this extreme course, Avhich for reasons that are
not  far to seek would  be  the one whereby  we  should be
brought most into conflict Avith existing usage, it is reasonable
to inquire Avhether the Avord " force,"  which in itself ansAvers
so weU to the requirements of the  case, is in its  right place
where it Avas first put by the schools.
    According to the common custom of speech, Ave  under-
stand by " force " something mo\Ting—a cause of motion ; and
if, on  the one hand, the expression  "moving force" is for
this reason, strictly speaking,  a pleonasm, the notion of  a not
moving or " dead" force is, on the other hand, a contradictio
in  adjecto.   If  it be said,  for instance, that a  load wliich
presses Avith its AAreight on the  ground exerts thereby a force—
a force which, though never  so great, is unable  of itself to
bring about the  smaUest movement—the mode of conception
and  of expression is quite justified by scholastic usage, but it
is  so far-fetched that it becomes  the  source  of unnumbered
misapprehensions.
    Between  gravity and the  force of  gravity there  is, so far
as I know, no difference; and hence  I consider  the  second
expression unscientific, inasmuch as  it  is tautological.
    Let it not be objected that the "force" of pressure, tho
"force"  of  gravity, cohesiA-e "force," &c,  are  the  higher
causes of pressure, gravity, and the like.   The exact sciences
are  concerned Avith  phenomena  and  measurable quantities.
The first cause  of things is Deity—a Being ever inscrutable
by the inteUect of man ; whUe " higher causes,"  " supersen-
suous forces," and the  rest, with  all their consequences, be- 
 342     TOE MECHANICAL  EQUIVALENT OF HEAT.

 long to the delusive  middle region of naturahstic  philosophy
 and mysticism.
    By a laAv that is universally true, waste and Avant go hand
 in hand.  IT to the  case  before us, where this rule likewise
 meets  with confirmation, we apply an equalizing process, and
 take away the word " force " from the connection in which it
 is superfluous and hurtful, and bring it to where we are in
 Avant of it, we get rid at one time of tAvo important obstacles.
 The higher mathematics at once cease to be required in order
 to gain admittance into the theory of motion: nature presents
 herself in simple beauty before the astonished eye, and  even
 the less gifted may now behold  many things which  hitherto
 were concealed from the most learned philosophers.
    Force and matter are indestructible objects.   This laAv, to
 which  individual facts may most simply be referred,  and
 Avhich  therefore I might figuratively call the heliocentric stand-
 point, constitutes a natural basis for physics, chemistry, phys-
 iology, and philosophy.
    Among the facts which,  though knoAvn, haA-e been hith-
 erto only empirically established and have remained isolated,
 but Avhich can be easily referred to this natural law, is the one
that electric and magnetic attraction  cannot be isolated  any
more  than gravity,  or that  the  strength of this  attraction
undergoes no alteration, so long as the distance remains  the
 same, by the intervening of indifferent substances (non-con-
 ductors) .
    Among facts Avhich have remained unknown  up to the
 most recent times, I wUl refer only to the influence which the
 ebb and flow of the tide exerts, in accordance with the known
 laws of mechanics, on the motion of the earth about its axis.
 A fact of  such importance, standing, as it does, in close rela-
 tion Avith  the fundamental laAv just  stated, having  been able
 to escape the attention of naturahsts, is of itself a proof that
 the prevailing system has no exclusive title.
    For the rest, it will not have  escaped those who are ac- 
                MOTION  AND FALLING-FORCE.            343

quainted Avith the modern  literature of science that a modifi-
cation of scientific language in the sense of my views  is act-
ually beginning to take place.   But  in  matters  of  this kind
the chief part of the work must be left to time.
    According to what has been said thus far, the vis viva of
motion  must be caUed a force.   But since  the  expression vis
viva  denotes  in mechanics, not only a  magnitude  which  is
proportional to the mass and to the square of its velocity, but
also one Avhich is proportional to the mass and to the  height
from Avhich it has faUen, force  thus conceived naturaUy di-
vides itself into two very easily distinguished species, each of
Avhich requires a distinct technical name, for which the Avords
motion (Bewegung) and falling-force (Fallkraft)  seem  to me
the most appropriate.*
    Hence, according  to  this  definition,  "motion"  is always
measured by the product of the  moved mass into the  square
of the  velocity, never by  the product of the mass  into the
velocity.
    By " faUing-force " Ave  understand a  raised weight, or stiU
more generally, a distance  in  space  betAveen  tAvo ponderable

   [* The distinction here drawn between " motion " and " falling-force "
is the same as that made by Helmholtz (Die Erhaltung der Kraft, 1847)
between " vis viva " (lebendige Kraft) and " tension " (Spankraft).  The Eng-
lish expressions " dynamical energy " and " statical energy " were used by
Prof. W. Thomson (Phil Mag. S. vol. iv. p. 304, 1852) in the same sense,
but were afterwards abandoned by him in favour of the terms  " actual en-
ergy "  and " potential energy " introduced  by Prof. Rankine.   More re-
cently (" Good Words " for October, 1862) Professors Thomson and Tait
have employed the expression " kinetic energy " in place of " actual ener-
gy."  The German word Kraft in the  text has been uniformly translated
force, to which term the ambiguity of the German original has thus been
transferred. This ambiguity, however, may be avoided in English by al-
lowing the word  " force " to retain the  meaning which it bears in common
language, that is, to denote all resistances which it requires the exertion of
a power to overcome (whence the expressions gravitating force, cohesive
force, &c.), and by using the word " energy " to denote force as denned by
Mayer.—G. C. F.] 
344     THE  MECHANICAL  EQUIVALENT OF  HEAT.

bodies.   In many cases falling-force  is  measured with suffi
cient  accuracy by the product of the raised weight  into ita
height;  and  the  expressions  "foot-pound,"  " kUogramme-
metre,"  " horse-power,"  and  many others, are  conventional
units for the  measurement  of this force, which  have of late
come  into general use, especially in practical mechanics.  But
in order to find the exact quantitative expression for the mag-
nitude in question, we must  consider (at least) two  masses
existing at a determinate distance from each other, Avhich  ac-
quire motion by mutually approaching; and we must  investi-
gate the relation Avhich exists betAveen the conditions of  the
motion, namely, the magnitude of the masses  and their orig-
inal and final  distance,  and the amount of motion produced.
    It very remarkably happens that this  relation is the sim-
plest conceivable ; for,  according to NeAvton's law of gravita-
tion, the quantity of motion produced is directly proportional
to the masses and to the space through which they fall,  but
inversely proportional to the distances of the centres of grav-
ity of the masses before and after the movement.  That is,
if A and B are  the  two  masses, c and c' the velocities which
they respectively acquire, and h and h' their original and final
distances apart, we have


                 Ac +iiC   ~   h.h'

or  in words,  the falling-force  is equal to  the product of the
masses into the space fallen through divided by the two distances.
    By help of this  theorem, which, as avUI be  easily seen, is
nothing but a  more  general and  convenient expression of
Newton's law of gravitation,* the laAvs of the fall of bodies

    * Newton's formula relates to the particular case in which the two dis-
tances (the initial and the final distance) are  equal, so that their product
becomes a square.  In this case, however, both the space fallen through
ind the velocity become nought; and hence,  when this expression has to 
      CONVERSIONS OF  MOTION AND FALLING-FORCE.  345

from cosmical elevations, and also the general laws of central
motions, can be developed without its being needful to employ
equations of more than  the second degree.
    Having now become  acquainted AA-ith two species of force-
motion and falling-force—Ave can arrive at a conception of " a
force" in general, according to the Avell-knoAvn rule, by col-
lecting together the common characteristics of the  two spe-
cies.  To this  end, we  must consider the properties of these
objects somewhat more closely.   Their most important prop-
erty depends on their mutual  relation.   Whenever a given
quantity of falling force disappears, motion is produced ; and
by the expenditure of this latter, the falling-force can be re-
produced in its original  amount.
    This constant  proportion Avhich  exists  betAveen faUing-
force  and  motion, and is knoAvn in the higher mechanics un-
der the  name  of " the  principle  of the  conservation  of vis
viva," may be shortly and fitly denoted by the term " trans-
formation" (Umwandlung).  For instance, we may say that
a planet, in passing from its aphelion to its  perihelion, trans-
forms a part of its falling-force  into motion, and,  as it  moves
aAvay from the  sun again, changes a part of its  motion into
falling-force.   In using  the word " transform " in this  sense,
nothing else  can or is intended to be expressed but a constant
numerical ratio.
   But it foUows from the axiom  mentioned at page 32G, that
the production of a definite quantity of motion from a given
quantity of falling-force, and vice  versd, implies  that neither
falhng-force nor motion  can be annihilated either  totally or in
part.   We thus obtain the following definition :
    Forces  are transformable, indestructible, and (in contradis*

be taken as the starting-point for  the  calculation of real velocities, mathe-
matical artifices become necessary which are inadmissible in the elementary
branches of science. 
34:6     THE  MECHANICAL EQUIVALENT OF HEAT.

tinction from matter) imponderable objects.  (Conf. paper al ■
ready quoted,  pp. 328, 329.)
    It is easy to see that this definition embraces, among other
things, the fact that the motion which disappears in mechani-
cal processes  of different kinds bears a constant relation to
the heat thereby produced, or that motion is  convertible, as
an indestructible magnitude, into heat.   Thus heat is, like mo-
tion, a force ;  and motion, like heat, an imponderable.

    I  have  characterized  the  relation Avhich  various forces
bear to one another by saying (Phil. Mag. S. 4, vol. xxiv. p.
252) that they are " different forms under which one  and the
same  object makes  its appearance."   At the same time I
have  expressly guarded myself from making the certainly
plausible, but unproved, and, as it seems to me, hazardous de-
duction that thermal phenomena are to be regarded as merely
phenomena of motion.  The foUowing is  what I said upon
this point (loc. cit.) p. 376 :
    "But just  as little as the connection between  faUing-force
and motion authorizes the conclusion that the essence of fall-
ing»force is motion, can such a conclusion  be adopted in  the
case of heat.  We are,  on the  contrary,  rather inclined to
infer that before it can become heat, motion—whether simple,
or vibratory as in  the  case of light and  radiant  heat, &c.—
must cease to exist as motion."
    The  relation which,  as we have  seen, subsists between
heat and motion  has  regard to quantity, not to quality; for
(to borrow the Avords of Euclid)  things which are equal to
one another are not therefore similar.  Let us beAvare of leav-
in°" the sohd ground of the objective, if we Avould not entan-
gle ourselves in difficulties of our own making.
    In the mean time it at least  results  from the foregoing
considerations that  the  phenomena of heat, electricity,  and
magnetism do not owe their existence to any particular fluids ;
and the immateriality  o£ heat, asserted half a century ago by 
VARIOUS KINDS  OF HEAT.
347
Rumford, becomes, through the discovery of its mechanical
equivalent, a certainty.
   The form of force denoted by the name "heat" is plainly
not  single,  but includes  several  distinct, though mutually
equivalent, objects, three principal forms of which are distin-
guished in common language : namely, I. Radiant Heat;  II.
Free (sensible) Heat, Specific Heat; and III. Latent Heat.
   There can be no doubt that radiant heat must be regarded
as a phenomenon of motion, especially since  the recent detec-
tion  of phenomena of interference in the radiation of heat.
But  whether there really exists, as  is commonly assumed, a
peculiar aither, of which the vibratory motion is perceived by
us as radiant heat, or Avhether the seat of this motion is  the
particles of material bodies, i3 a question that is not yet made
out.
   Still greater obscurity hangs about the essential nature of
specific heat, or what goes on in the interior of a heated body.
Not only does the unansAvered question of the aether enter
again  here, but, before we  can be in a position to form  any
clear ideas on this subject, we require to have an exact knoAvl-
edge of the  internal  constitution  of matter.   We are, Iioav-
evcr, still far from having reached this point; for, in particu-
lar, we do not know whether such things as atoms exist—that
is, whether matter consists of such constituents as undergo no
further change of  form in chemical processes.
   But a span of  that  time which stretches  both backwards
and  forwards into eternity is meted out to man here on earth,
and  the space which his foot can tread is narrowly bounded
above  and below: so also his scientific knowledge finds  nat-
ural limits in the direction of the infinitely smaU as AveU as of
the infinitely great.  The question of atoms  seems to me to
lead beyond these Umits, and hence I consider it unpractical.
An atom in itself  can no more become an object of our inves-
tigation than a differential, notwithstanding  that the ratio
which   such  immensely small  auxiliary magnitudes  bear to 
348     THE  MECHANICAL EQUIVALENT OF HEAT.

one another may be  represented by concrete  numbers.  In
every case, hoAvever, the conception of an atom must be re-
garded as merely relative, and  must be considered in connec-
tion Avith  some  definite  process; for, as is AveU known, the
particles of an acid and  base may  play the part of atoms in
the formation  and decomposition of a salt, while in  another
process  these atoms may themselves undergo further division.
    But  assuming that, in a chemical sense, atoms have a real
existence—an  assumption which,  among other things,  the
laws  of isomorphism  certainly render probable—the further
question arises Avhether, by the continued division of matter,
we can  at last arrive at molecules Avhich are atoms in  relation
to the phenomena of lieat, such  that heat cannot penetrate to
their interior,  and such that, when  the whole mass is heated,
they for their  parts undergo no increase  of bulk.  But  since
we are unable  to grapple Avith  such preliminary questions as
 hese, Ave are forced to confess that, Avhether the existence of
 sn aether and  of atoms be admitted or not, we  are, so far as
 ?gards  the nature of  specific heat,  in a state of ignorance.
    The expression "latent heat" has reference to its correctly
 ecognized property of indestructibility.   In all cases in which
 iiermometrically sensible specific heat disappears, it must be
assumed that it eludes our perception only by taking on  some
other  state of  existence, and that by an  appropriate  process
of inverse transformation the free heat can be reproduced in its
original amount.  These are the facts on which the  doctrine
of latent heat rests;  and  hence, if Ave have regard  to them
only, all the connected phenomena may be claimed as so many
confirmations  of the principle of the transformation and con-
servation of force.
    The  conception of latent heat is accordingly nothing  else
than the conception of something equivalent to  free heat,  and
thus the doctrine of  free  and  specific heat  embraces pretty
aearly the whole domain of physics.  A few examples, cho-
sen from  among the  abundance of facts, may  serve to show 
         HOAV LATENT HEA"T  IS TO BE REGARDED.     349

how, according to my view, the phenomena wherein heat be«
comes latent are to be regarded.
    If heat is communicated to a gas retained under constant
pressure, the free  heat of the gas is  increased, and at the
same time a calculable quantity of heat becomes latent; the
gas is  thereby caused to expand, and ther» is  consequently
produced  an amount of vis viva proportional to the  pressure
and to the space through which expansion takes place.  There-
fore as soon as we know hoAv much of the heat  that has be-
come latent is to be attributed to the expansion of the gas, we
know also  the amount  of the  remainder of the latent heat
corresponding to the vis viva  produced.   Now Gay-Lussac
has proved by experiment that the specific heat of a gas un-
dergoes no sensible alteration in flowing from a containing ves-
sel  into a vacuum.   Hence it foUows that  a  gaseous body op-
poses no perceptible resistance to the separation of its parti-
cles, and that the rarefaction of a gas does not of itself (that
is, Avhen it occurs without any evolution of force) cause any
heat to become latent.  The total  quantity of heat Avhich be-
comes latent by the expansion of a gas is therefore to be taken
as the equivalent of  the vis viva produced.
    It results from  the  principle  of the  indestructibility of
heat—a  principle Avhich  no one  calls  in  question—that the
quantity of heat which has thus  become  latent must again
become free when heat is in any way produced at the expense
of the  acquired vis  viva of motion. . Motion is latent  heat,
and heat is latent motion.
    The celebrated laAv of Dulong, that the amount of heat
produced  by the compression  of  a gas is dependent on the
amount of force expended, and not upon the chemical nature,
tension, or temperature of the gas, is a special application of
the above  general principle.  But in  the communication so
often mentioned I have shoAvn that this laAv of nature is  capa-
ble  of a very much wider application, and that the heat Avhich
becomes latent in the expansion of a gas reappears again in 
350      ME  MECHANICAL  EQUIVALENT OF HEAT.

every case, if  the vis viva thereby produced is employed to
generate heat, Avhether by the compression of air, by friction,
or by the impact of  nonelastic bodies; and  I have  there
calculated the mechanical equivalent of heat upon  principles
of which  the  accuracy cannot be disputed.  I also  measured
at that time,  by way of control, the  heat produced  in  the
manufacture of paper  in  Holland, and compared it with  the
working force expended, and so found a sufficient degree of
concordance between the two quantities.  I have  recently,
moreover, succeeded in constructing, for  the purpose  of the
direct  determination of the  mechanical equivalent of heat, a
very simple thermal dynamometer  on a small scale, Avith
which  the truth of the principle in question can be demon-
strated ad oculos; and I have  reason to believe that the effi-
ciency of water-wheels and steam-engines might be easily and
advantageously measured by means of a  similar calorimoto-
rial apparatus.  It must, however, be left to the future judg-
ment of practical men to decide whether,  and to AArhat extent,
this method deserves to be preferred to Prony's.
   Heat further becomes latent in certain changes of the state
of aggregation of bodies.   Since it is a settled fact  that both
sohd and liquid  bodies oppose  a certain resistance to the sep-
aration of their  parts, and since in general an expenditure of
vis viva is required for the  overcoming of mechanical  resist-
ances, Ave are led to conclude d priori that whenever the cohe-
sion of a body is diminished or done away with, force or heat
must  become  latent;  and this, as is  well  known,  perfectly
accords with experience.
   Starting from  this point  of view, the  French  physicist
Person has attempted to detect a direct  quantitative relation
between the  latent heat  of  metals, on which he has made a
great number of observations, and their cohesion ; but at pres-
ent determinations of this kind are beset with almost  insur-
mountable difficulties.
   The heat Avhich becomes latent in the evaporation of water 
HEAT AND CHANGES OF  STATE.
351
has been considered from quite a similar point of view by
Holtzmann in his important memoir " On the Heat and Elas-
ticity of Gases and Vapours."   Starting from the principle
that elevation of temperature is equi\-alent to the raising of a
weight, this philosopher has likeAvise calculated the mechani-
cal equivalent of heat from the  quantity of heat Avhich be-
comes latent by the expansion of a gas ;  and he very rightly
conceives of the latent heat of steam as made up of two
parts, whereof one, the  smaller, is  expended  in  overcoming
the opposing  pressure of the  atmosphere, and can hence be
easily calculated  by means of the mechanical equivalent of
heat,  whUe the remaining part, the amount of  which can also
be calculated, is Avhat Holtzmann calls the  heat  required to
destroy the cohesion of the Avater.   In aU steam-engines this
latter portion is wasted, and Holtzmann calculates from these
data  the  superior  efficiency of high-pressure  compared with
low-pressure engines.*
    If the vieAV here  taken of the  latent  heat of fusion  and
evaporation is correct, heat must  also become latent when
hard bodies are reduced to powder ; and when such substances
pass into the liquid condition from a state of fine  division,
they must absorb a smaller quantity of heat than when they
are liquefied without previous comminution.  A feAV experi-
ments that I have instituted in this direction have not hitherto
given any decisive result.
    It is also worthy of notice that certain solid bodies which
are capable of assuming allotropic states, as, for instance, the
oxygen-compounds  of iron, evolve a considerable  quantity of
heat on passing from a less to a more  hard condition.  Such
facts, the number of Avhich wiU doubtless continually increase
with time, agree perfectly Avith the above  principle, that  dim-
inution  of cohesion involves an expenditure of heat, and, on
the other hand, increase of cohesion a production of heat.
   * The engines which give the greatest  useful effect must be those ir.
which the steam receives an aidition of heat during its expansion. 
 352     THE  MECHANICAL EQUIVALENT OF HEAT.

    Customary language, according to which  gravity is called
 a moving force and  heat  a substance, occasions, on the one
 hand, the significance of an important natural object, falling-
 space, or the space through which a  body falls, to be kept  as
 much as possible out of sight, and, on the other hand, heat to
 be removed to the greatest possible distance from the vis viva
 of motion.  The sciences  are thus reduced to an artificial sys-
 tem, over whose fissured  surface Ave can  advance in  safety
 only by the poAverful aid of the higher analysis.
    Without doubt the fact that so simple and obvious a mat-
 ter as the connection between heat and motion could remain
 unperceived up to the most recent times  must also be attrib-
 uted to the  same defect.  Nevertheless, as has been already
 pointed out, the quantitative determination of chemical heat-
 ing-effects and of galvanic actions, as weU as researches into
 vital phenomena, instituted  in the spirit of those of Liebig,
 must soon have led to the  law, not difficult to  discover, of the
 equivalence of heat and motion.
    In reality this law and its  numerical  expression, the me-
 chanical  equivalent of heat, Avere published  almost simulta-
neously in Germany  and in England.
    Starting from the fact that the amount of chemical as AveU
as of  galvanic  effect is  dependent  only and solely on  the
amount of material expenditure, the celebrated Enghsh phys-
icist Joule was led to the principle  that the phenomena  of
motion and of heat  rest essentiaUy upon one and  the same
foundation, or, as he expressed himself, in the same way as I
have done, heat and motion are transformable one into the
other.
    Not only did this phUosopher indisputably make an inde-
pendent  discovery of the natural law in question, but to him
belongs the credit of having made numerous and important
contributions towards its further establishment and develop-
ment.  Joule  has shoAvn  that. Avhen motion  is produced  by
means of electro-magnetism, the  heating effect of the galvanic 
DISCOVERIES OF JOULE.
353
current is diminished in a corresponding and fixed proportion.
He has further ascertained that by reversing the  poles of a
magnetic  bar a quantity of heat is produced proportional to
the square  of the magnetic  tension—a fact which was  also
discovered by myself, though at a later date.   In  particular,
Joule has likewise demonstrated, by means of numerous ex-
periments, that the heat evolved by friction under various cir-
cumstances  stands in an unvarying proportion to the  amount
of force expended.  According to his most recent experiments
of this kind, he has fixed the mechanical  equivalent of heat
at 423.*
   Joule has likeAvise investigated experimentally, in  relation
to this question, the thermal behaviour of elastic fluids Avhen
expanded, and has thereby confirmed the earlier results of
other physicists.
   The  new subject soon began  to  excite the attention of
learned men ; but inasmuch as both at home and  abroad the
subject has been exclusively treated as a foreign discovery, I
find myself compelled to make the claims to Avhich  priority en-
titles me ; for although the few inA'estigations wliich I have
given to the public, and which have almost disappeared in the
flood of communications which every day sends forth  without
leaving a trace behind, prove, by the A*ery form of their pub-
lication, that I am not one Avho hankers after effect, it is not
therefore to be assumed that I am wilhng to be deprived of
intellectual  property which  documentary evidence proves to
be mine.

   By help of the mechanical equivalent of heat many prob-
lems can be solved Avhich, without it, could not be  attacked at
all:  among them, the calculation of the thermal efiect of the
faUing together of cosmical masses  may be especiaUy men-
tioned.  It  avUI not be out of place to indicate here briefly a
feAv results of such calculations.
          * That is, 1 thermal unit=423 kilogramroetres. 
354     THE  MECHANICAL EQUIVALENT OF  HEAT.

    The foUowing is one problem of this kind.  It is assumed
that a cosmical body enters the atmosphere of our earth Avith
a velocity of four geographical miles per second, and that, in
consequence of the resistance which it  here encounters,  it
loses so much  of its vis viva of motion  that its remaining ve-
locity when it again quits the atmosphere  amounts to three
mUes: the question now  arises, How great  is the  thermal
effect which accompanies this  process ?
    A simple calculation,  based upon the  mechanical equiva-
lent of heat, shows  that the quantity of heat required is about
eight times as great as the heat of combustion of a mass of
coal of  equal weight with th^tpdy in  question, one kilo-
gramme  of coal being taken as yielding 6,000 thermal  units.
Hence  it foUoAvs that the  velocity of the motion of shooting-
stars and fire-balls, Avhich, as is well-knoAvn,  attains, accord-
ing to astronomical observations, to from four to eight miles,
is a cause fully sufficient to produce the  most violent evolution
of heat, and an insight into the nature of  these remarkable
phenomena is thereby afforded to us.*
    The foUoAving is a problem of a similar kind: if two cos-
mical masses,  moving in space about their common centre of
gravity, were  by any cause whatever, for example by the re-
sistance of the surrounding medium, caused to fall together,
the question again arises, How great is the thermal effect cor-
responding to this process  of mechanical combination ?
    Even though the elements  of the orbits (that is, their ex-
centricity) may be  unknown, we can  nevertheless  calculate
from the given weight and volume of the masses  in question
the maximum and the minimum of the required effect.  Thus
let  it be supposed, for the sake of an example, that our earth
had been divided into tAvo  equal  globes which had united in

   * The idea that the meteors here referred  to owe their  light to a me-
shanical process—whether friction, or the compression of the air—is not
new; but  without a knowledge of the mechanical equivalent of heat it
could have no scientific foundation. 
             COLLISION  OF COSMICAL MASSES.          355

the manner described : calculation teaches us that the amount
of heat which would have been evolved in such a case Avould
considerably  exceed that Avhich  an equal weight of matter
could furnish by the most intense process of chemical action.
   It is more than  probable that the earth has come  into  ex-
istence in some such way, and that in consequence our sun, as
seen from the  distance of the fixed stars, exhibited at  that
epoch a transient burst of light.  But Avhat took place in our
solar system  perhaps millions of years ago, still goes on at
the  present time here and there among the fixed stars; and
the  transient  appearance of  stars, which  in some cases, like
the celebrated star of Tycho Brahe, have at first an extraor-
dinary degree of brilliance, may be satisfactorily explained
by assuming the falling together of previously invisible  double
stars.
   Contrasting Avith  such explosive bursts of light  is  the
steady radiation,  shown  continuously through enormous pe-
riods, by the  greater number of fixed stars,  and among them
by our  sun.   Do these  appearances, which in  so  special a
manner tempt to higher  speculations, constitute a real excep-
tion  to the exhaustion of a cause in producing its effect, which,
in accordance with  the foregoing considerations, we  have re-
garded as an  estabhshed law of Nature ? or does the smaU
sum  of human knowledge authorize us in  supposing that here
also  there is an equivalence between performance and expen-
diture, and in searching for the conditions  of that equivalent ?
   To enter further upon  this subject Avould lead us beyond
the  intended scope  of this  publication ; and I therefore close
in the hope that  the  reader Avill please to supplement  by his
oavd  reflection much that in this tract has  been left unsaid 
 
         SOME THOUGHTS



              OK THE




CONSERVATION OF FORCE.





          B? Pu. FARADAY. 
   Michael Faraday, son of a smith, was born in London' in 1V.U.   Ho
was taught reading, writing, and arithmetic at a day-school, and in all other
things educated himself.   At thirteen he was apprenticed, to a bookbinder,
choosing this vocation in order to be among books.  He was early fond of ex-
periment, and averse to trade;  and being taken to hear some lectures of Sir
Humphrey Davy at the Royal Institution, he resolved to pursue science, and
wrote to Davy asking his assistance in obtaining a place.  Davy favored his
application, and in 1813, at the age of twenty, he was appointed assistant in
the laboratory of the Royal Institution.  In 1820 he discovered the chloride
of carbon, and in 1823 effected the condensation of chlorine and other gases.
On this account Davy became jealous  of him, and discouraged the idea of
recommending him for election to the Royal Society, which, however, took
place in 1824.  In 1820, Oersted announced his celebrated  discovery of
electro-magnetism, and Faraday at once entered upon an investigation of the
relations of magnetism and electricity.  In  1831 he  commenced his cele-
brated series of Experimental Researches in Electricity, which  extended to
three volumes, published in 1839, 1844, and 1855.  In 1827  he published
his admirable work on "Chemical Manipulations," and, in 1830, a valuable
paper on " The Manufacture of Glass  for Optical Purposes."   In 1833 he
became Professor of Chemistry in the^loyal Institution, and he has received
numerous honors from the learned societies of Europe.   In 1835 he received
a pension of £300 a year, and in 1858 the Queen allotted him a residence in
Hampton Court.  Dr. Faraday has talents of a high order, both as an orig-
inal investigator and as a lecturer.  Advanced in years, he has now retired to
a considerable extent from active duty, but is still in the vigor of his powers,
as is shown by his recent lectures to juvenile audiences in the Royal Insti-
tution. 
THE  CONSERVATION  OF  FORCE.
      YAKIOUS circumstances induce me at the present mo-
       ment to put forth a consideration regarding the  con-
servation of force.   I do not suppose that  I  can  utter any
truth respecting it that has not already presented itself to the
high  and piercing  intellects  Avhich move Avithin the exalted
regions of science;  but the  course of my own investigations
and vieAvs makes me think that the consideration may be of
service to those persevering labourers (amongst whom I en-
deavour to class myself) who, occupied in the comparison of
physical ideas Avith fundamental  principles,  and continually
sustaining and aiding themselves by experiment and observa-
tion, delight to labour for the advance of natural knowledge,
and strive to foUoAV  it into undiscovered regions.
   There is no question Avhich hes  closer to the root of aU
physical knowledge  than  that which inquires whether force
can be destroyed or  not.  The progress of the strict science
of modern times  has tended more  and more to produce the
conviction that "force can neither be created  nor destroyed;"
and to render daily more manifest the value of the knowledge
of that truth in experimental research.  To admit, indeed,
that force may be destructible or can altogether disappear,
would be to admit  that  matter could be uncreated; for we
know matter only by its forces ;  and though one of these is 
360          THE CONSERVATION OF FORCE.

most  commonly referred to,  namely, gravity, to prove  ita
presence, it is not  because gravity has any pretension, or any
exemption, amongst the forms of force as regards the princi-
ple of conservation, but  simply that being, as far as we per-
ceive, inconvertible in its nature and unchangeable in its man-
ifestation, it offers an unchanging test of the matter which we
recognize by it.
    Agreeing with those who  admit the conservation of force
to be a principle in physics, as large and  sure as that of the
indestructibility of matter, or the invariability of gravity, I
think that no particular idea of force has  a right to unlimited
or unqualified acceptance that  does not include assent to it;
and also, to definite amount  and definite disposition of the
force, either in one effect or another, for these are necessary
consequences ; therefore  I urge, that the conservation of force
ought to be admitted as a physical principle in aU our hypoth-
eses, whether partial or general, regarding the actions of mat-
ter.   I have had doubts in my own mind whether the consid-
erations I am about to advance are not rather metaphysical
than physical.  I am unable to define what is metaphysical in
physical science ; and am exceedingly adverse  to the  easy and
unconsidered admission of  one supposition upon another, sug-
gested as they often are by very imperfect induction from a
smaU number of facts, or by a very imperfect  observation of
the facts themselves ; but, on the  other hand, I think the phi-
losopher  may be bold in his  apphcation of principles which
have  been developed  by close inquiry,  have  stood  through
much  investigation, and continuaUy increase in force.  For
instance, time is growing up dahy into importance as an  ele-
ment in the exercise of  force.  The earth moves in its orbit
in time ; the crust of the earth moves in time ; hght moves in
time;  an electro-magnet requires  time for its charge  by an
electric current; to inquire, therefore, whether power, acting
either at sensible or insensible distances,  always acts in time,
is not to be metaphysical; if it acts in time and across space, 
ACTION OF FORCES IN TIME.
361
it must act by physical  lines of force;  and our view of the
nature of the force  may be affected to  the  extremest degree
by the conclusions which experiment and observation on time
may  supply;  being, perhaps, finally determinable  only  by
them.  To inquire after the possible  time  in which gravita-
ting,  magnetic, or electric force is exerted, is no more  meta-
physical than to mark  the times of the hands  of a clock in
their  progress ; or that of the temple of Serapis and its ascents
and descents ;  or the periods of  the occultations of Jupiter's
sateUites ;  or that in which the hght from them  comes to the
earth.  Again, in some of the  known cases  of action in time,
something  happens whUst  the  time  is passing which did not
happen before, and  does not continue  after; it is, therefore,
not metaphysical to expect an effect in every case, or to en-
deavour to discover its  existence and  determine its nature.
So  in regard to the  principle of the  conservation  of force ; I
do not think that to admit it, and its consequences, whatever
they may be, is to be metaphysical; on the contrary, if that
word have any apphcation to  physics,  then I think that any
hypothesis, whether of heat, or electricity,  or gravitation, or
any other form of force, which either willingly or unwillingly
dispenses with the principle of  conservation, is more  liable to
the charge than  those which,  by including it, become  so far
more  strict and precise.
    Supposing that the truth of the principle of  the conserva-
tion of force is assented to, I come to its uses.  No hypothesis
should be admitted, nor  any assertion of a fact  credited, that
denies the  principle.  No vieAV should  be  inconsistent or  in-
compatible with it.  Many of our hypotheses in  the present
state  of science may not comprehend  it, and  may be unable
to suggest its consequences ; but none  should  oppose or con-
tradict it.
    If the principle be admitted, we perceive at once that a
theory or definition, though it may not  contradict the princi-
ple, cannot be  accepted  as sufficient or complete unless the
         16 
362          THE CONSERVATION OF FORCE.

former be contained in it;  that howeAer weU or perfectly the
definition may include and represent the state of things  com-
monly considered under it, that state or result is only partial,
and must not be accepted as exhausting the power or being
the fuU equivalent, and  therefore cannot be considered as
representing its whole nature; that, indeed, it may express only
a very smaU  part of the whole, only a residual phenomenon,
and hence give us but httle indication of the full natural truth.
AUowing the principle its force, we ought, in every hypothe-
sis, either to  account for its consequences by saying what the
changes' are when force of a given  kind apparently disappears,
as when ice thaws, or else should leave space for the idea of
the conversion.   If any hypothesis, more or  less  trustworthy
on other accounts, is insufficient in expressing it or incompat-
ible with it, the place of deficiency or opposition  should be
marked as the most important for  examination, for there lies
the hope  of  a discovery of new laws  or a new condition of
force.   The  deficiency should never be accepted as satisfac-
tory, but be  remembered and used as a stimulant to further
inquiry; for  conversions  of force may  here be  hoped for.
Suppositions  may be accepted for  the time, provided they are
not in contradiction with the principle.   Even an increased or
diminished capacity is better than nothing at  aU, because  such
a supposition, if made, must be consistent with the nature of
the original hypothesis, and may, therefore, by the apphcation
of experiment, be converted into  a further  test  of probable
truth.   The  case  of a  force simply removed or  suspended,
without a transferred exertion in some other direction, appears
to me to be absolutely impossible.
    If the principle be accepted as true, we have a right to
pursue  it to  its consequences, no matter what they may be.
It is, indeed, a duty to do  so.  A theory may be  perfection,
os far  as  it goes, but a consideration  going  beyond it, is not
for that reason to be shut out.   "We might as weU accept our
limited horizon as the  limits of the world.   No  magnitude, 
RELATION  OF GRAYTTY.
363
 either of the phenomena or of the results to be dealt Avith,
 should stop our exertions to ascertain, by the use of the prin-
 ciple, that something remains to be  discovered, and to trace
 in Avhat direction that discovery may he.
    I will  endeavour to Ulustrate  some of the  points Avhich
 have  been urged, by reference, in the first instance, to a case
 of poAver, which  has long  had  great  attractions for me, be-
 cause of its  extreme simplicity, it3  promising nature, its uni-
 versal presence, and in  its invariability under hke circum-
 stances ; on Avhich, though I have  experimented* and as yet
 faUed, I think experiment Avould be weU bestowed, I mean the
 force of gravitation.  I believe I represent the received idea
 of the gravitating force aright in saying that  it is a simple at-
 tractive  force exerted between  any  two  or  all the  particles or
 masses of matter, at every sensible distance, but with a strength
 varying inversely as the square  of the  distance.   The  usual
 idea of the force implies direct action at a distance ;  and such
 a vieAV appears to present  little  difficulty except to NeAvton,
 and a feAV, including myself, who in  that respect  may be of
"like mind Avith him.
    This idea of gravity appears to me to ignore  entirely the
 principle of the conservation of force; and  by the terms of
 its definition, if taken in an absolute sense, " varying inversely
 as the square of the distance," to be in direct opposition to it,
 and it becomes  my duty now to point out where this contra-
 diction occurs, and to use it  in iUustration of the principle of
 conservation.  Assume  tAvo particles of matter, A and B, in
 free space, and a force in each or  in both by which they gravi-
 tate towards  each other, the  force being  unalterable for an
 unchanging distance, but varying inversely as the square of
 the distance Avhen the latter  varies.   Then, at the distance of
 ten, the force may be estimated as one ; Avhilst at the distance
 of one, that is, one-tenth of the former, the force will be one
* Philosophical Transactions, 1851, p. 1. 
364          THE CONSERVATION  OF FORCE.

hundred ;  and if we  suppose an elastic  spring  to be intro-
duced betAveen the tAvo as a measure of  the attractive force,
the poAver compressing it wUl be a hundred times as much in
the latter  case as in the former.  But from whence can  this
enormous increase of power  come?  If Ave say  that it is the
character of this force, and  content ourselves with that as a
sufficient answer, then  it appears to me we  admit a creatioh
of power and that to an enormous  amount; yet  by a change
of condition, so small  and simple as to fail in leading the least
instructed  mind to think that it can be a  sufficient  cause, Ave
should admit a result  which would equal the  highest  act  our
minds can appreciate of the working of infinite  power upon
matter; Ave should let  loose the highest  law in physical  sci-
ence which our faculties permit us to perceive, namely, the
conservation of force.   Suppose the two  particles, A and B,
removed back to the greater distance of ten, then  the force of
attraction would  be  only a hundredth part of  that they pre-
viously possessed; this, according to the  statement that the
force varies inversely as the square  of  the distance, would
double the  strangeness of the above results; it would be an
annihilation of force—an effect equal in  its infinity  and its
consequences with creation, and only within the  power of Him
Avho has created.
    We have a right to view gravitation under every form that
either its definition or its effects can  suggest to the mind ;  it
is our privUege to do so with every force  in nature ; and it  is
only by so doing that;we have succeeded,  to a large extent, in
relating the various forms of power, so as to derive one from
another, and  thereby obtain  confirmatory evidence  of  the
great principle  of the  conservation of force.   Then let us
consider the two particles, A and B, as attracting each other
by the force  of gravitation, under  another view.  According
to the definition,  the force depends upon both particles, and  if
the particle A or B were by  itself,  it could not gravitate,  that
is, it could have no attraction, no force of gravity.    Suppos- 
          THE  CASE  OF GRAVITATING PARTICLES.      305

ing A to exist in that isolated state  and without gravitating
force, and  then B placed in relation to it, gravitation comes
on, as is supposed, on  the  part of both.  Now, Avithout try-
ing to imagine how  B, which had no  gravitating force, can
raise up gravitating force in A ;  and how A, equally without
force  beforehand, can raise up force in B, stUl, to imagine it
as a fact done, is to admit a creation of force in both parti-
cles ;  and so to bring ourselves within the impossible conse-
quences Avhich  have been already referred to.
    It may be said Ave cannot have an idea of one particle by
itself, and so the reasoning fails.   For my part I can compre-
hend a particle by itself just as easily as many particles ; and
though  I cannot concei\"e the relation  of a lone particle  to
gravitation, according to the limited aIcav which is at present
taken of that force, I can conceive its relation to something
which causes gravitation, and with Avhich, whether the parti-
cle is alone, or one of a universe of other particles, it is al-
ways related.   But the reasoning upon a lone particle does
not fail; for as the particles can be separated, we can easUy
conceive of the particle B being removed to an  infinite dis-
tance from A, and  then the power in A avUI be infinitely di-
minished.   Such removal of B wiU  be as if it were annihi-
lated  in regard to A, and the force in A wiU be annihilated
at the same time ; so that the case of a lone particle and that
where different  instances only are considered become one, be-
ing identical Avith each other in their consequences.   And  as
removal of B to an infinite  distance is as regards A annihUa-
tion of B, so removal to the smallest degree is, in  principle,
the same thing with displacement through infinite space ;  the
smaUest increase in distance involves annhiilation of poAA'er;
the annihilation of the second particle, so as  to have A alone,
involves no other consequence in relation to  gravity;  there is
difference in degree, but no difference in the  character of the
result.
    It seems hardly necessary to observe, that the same hne 
366
THE CONSERVATION OF FORCE.
of thought grows up in the mind, if we consider the  mutua
gravitating action of one particle and many.  The particle A
will  attract the particle B at the distance of a mile with a
certain  degree  of  force;  it wiU attract a  particle C at  the
same distance of a mile with  a power equal to that by Avhich
it  attracts B; if myriads  of  like particles be placed at  the
given distance of a mUe, A wUl attract each with equal force ;
and  if other particles be  accumulated round it, within and
without the sphere  of tAvo miles diameter, it wUl attract  them
all with a force varying  inversely Avith the  square of the dis-
tance.  How are we to conceive of this force growing up in
A to a million-fold or more, and if the surrounding particles
be then removed, of its diminution in an equal degree ?   Or,
how are we to  look upon  the power  raised up  in aU these
outer particles by the action of A on them,  or by their action
one  on another, without admitting, according to the  hmited
definition of graA'itation, the facUe generation and annihilation
of force?
   The assumption which we make for the time with regard
to the nature of a power  (as gravity, heat, etc.), and the
form of words in which we express it, that is, its definition,
should be consistent with the  fundamental principles of  force
generally.   The conservation of force is a fundamental  prin-
ciple ;  hence the assumption with regard to a particular  form
of force  ought to  imply what becomes of the force when  its
action is increased or diminished, or its direction changed; or
else  the assumption should admit  that it is deficient on that
point, being only half  competent to represent the force ; and,
in any case, should not be  opposed to the  principle of conser-
vation.  The usual definition  of  gravity as an attractive force
between the particles of matter varying inversely  as the square
of the distance, whilst it  stands as a fuU definition of  the
power, is inconsistent with the principle of the  conservation
of force.   If we accept the  principle, such a definition  must
be  an imperfect account  of  the whole of the  force, and is 
        GRAVITATION BUT PARTIALLY UNDERSTOOD.    36?

probably only a  description  of one exercise  of that power,
whatever the nature of the force itself may be.  If the defi
nition be  accepted as tacitly including  the conservation of
force, then it ought to admit that  consequences  must occur
during the suspended or diminished degree in its power as
gravitation, equal in  importance to  the  power suspended or
hidden ; being in fact equivalent to that diminution.   It ought
also to admit, that it  is incompetent to suggest or  deal with
any of the consequences of that changed part or condition of
the force,  and cannot tell whether they depend on, or arc  re-
lated to, conditions external or internal to the gravitating par-
ticle ; and, as it appears to me, can say neither yes nor no to
any of the arguments or probabihties belonging to the subject.
    If the definition denies the occurrence of such contingent
results, it  seems to me to be unphilosophical;  if it simply ig-
nores them, I think it is imperfect and  insufficient;  if it ad-
mits these things, or any part of them, then it prepares the
natural philosopher to look for  effects and  conditions as yet
unknown, and is open  to any degree of development of the
consequences and relations of power; by denying, it  opposes
a dogmatic  barrier to improvement; by ignoring, it  becomes
in many respects  an inert thing, often much in the way; by
admitting, it rises to the dignity of a stimulus to investigation,
a pilot to human science.
    The principle of the conservation of force would  lead us
to assume, that when  A and B attract each other  less, be-
cause of  increasing  distance,  then some  other exertion of
power, either within or without them, is proportionately grow-
ing up ; and again, that when their distance is diminished, as
from  ten  to one, the poAver of attraction, now increased  a
hundred-fold, has  been produced out of some other form of
power which has been equivalently reduced.  This  enlarged
assumption of the nature of gravity is not more metaphysical
than the half assumption ; and is, I beheve, more philosophi-
cal and more in accordance with all physical considerations. 
368
TIIE CONSERVATION  OF FORCE.
The half assumption is, in my view of the matter, more dog«
matic and irrational than the Avhole, because it leaves it to be
understood that power can be created and destroyed almost at
pleasure.
    When the equivalents of the various forms of force, as far
as  they are  knoAA-n, are  considered, their differences appear
very great;  thus, a grain of water is knoAvn to have electric
relations  equivalent to a very powerful flash of lightning.  It
may therefore be supposed that a very large apparent amount
of  the force causing  the phenomena of  gravitation, may be
the equivalent of a very small change in some unknown  con-
dition of  the bodies, Avhose attraction is varying by change of
distance.   For my own  part,  many considerations  urge  my
mind tOAvard the idea of a cause of  gravity, Avhich is not res-
ident in  the particles of  matter  merely, but constantly in
them, and aU space.  I have already put forth considerations
regarding gravity which partake of this idea,* and  it seems
to have been unhesitatingly accepted by  NeAvton.f
    There is one wonderful  condition of  matter, perhaps its
only true  indication,  namely, inertia; but in  relation to  the
ordinary  definition of gravity, it only adds to the difficulty.
For if we consider two  particles of  matter at a certain dis-
tance apart, attracting each other under  the poAver of gravity,
and free to approach, they wiU  approach ; and when at only
half the distance, each wiU have had stored up in it, because of
its inertia, a certain amount of mechanical force.  This must

   * Proceedings of the Royal Institution, 1855, vol. ii., p. 10, etc.
    \ " That gravity should be innate, inherent, and essential to matter, so
that one body may act upon another at a distance,  through a vacuum, with-
out the mediation of any thing else, by and through which their action and
force may be com eyed from one to another, is to me so great an absurdity
that I believe no man who has in philosophical matters a competent fac-
ulty of thinking, can ever fall into it.   Gravity must be caused by an agent,
acting constantly according to certain laws; but whether this agent be ma-
terial or immatei ial I have left to the consideration of my reader."—Set
Newton's Third Letter to Bcnticy. 
          INERTIA, GRAVITY, AND  CONSERVATION.       369

be due to the force exerted, and, if the conservation principle
be true, must have consumed an equivalent proportion of the
cause of  attraction;  and yet, according to the  definition of
gravity,  the attractive force is  not  diminished  thereby, but
increased four-fold, the force growing up within  itself tho
more rapidly, the more it is occupied  in producing other force.
On the other hand, if mechanical force from without be used
to separate  the  particles to twice their distance, this force is
not stored up in momentum or by inertia, but disappears ; and
three-fourths of the attractive force at the first distance disap-
pears Avith it.   How  can  this be ?
    AVe knoAv not the physical condition or action from Avhich
inertia results ;  but inertia is always a pure case of the  con-
servation  of force.  It has a strict  relation to gravity, as  ap-
pears by the proportionate amount of the force which gravity
can  communicate to  the  inert body; but it appears to have
the same  strict relation to other forces acting at a distance as
those of magnetism  or electricity, when they are  so  applied
by the tangential balance as to act independent of the gravi-
tating force.  It has  the hke strict relation to force communi-
cated by  impact, pull,  or in any  other way.   It enables a
body to take up and  conserve a given  amount of force until
that force is transferred to  other bodies, or  changed into an
equiA-alent of some other form; that is aU that we perceive
in it; and we cannot find a more  striking  instance amongst
natural, or  possible phenomena, of the  necessity of the  con-
servation  of force as a law of nature ; or one  more  in  con-
trast with the assumed variable condition of the gravitating
force supposed to reside in the particles of matter
    Even  gravity itself furnishes the strictest proof of the con-
servation  of force in  this, that its  power is unchangeable for
the  same distance; and  is by that in striking  contrast Avith
the variation which we assume in regard to the cause of grav-
ity, to account for the results at different distances.
   It wiU not be  imagined for a moment  that I am opposed 
370           THE  CONSERVATION  OF FOECF.
to what may be caUed the law of gravitating action, that is,
the laAv by which all the known effects  of gravity are gov
erned; what I am considering is the definition of the force of
gravitation.  That the result of one exercise of a power may
be inversely as the  square of the  distance, I believe and ad-
mit ; and I know that it is so in the case  of graAnty, and has
been verified to an  extent that could hardly have been within
the conception even of Newton himself Avhen he gave utter-
ance to the law; but that the totality of  a force can be  em-
ployed according to that law I do not believe, either in rela-
tion to gravitation, or electricity, or magnetism, or any other
supposed form  of power.
    I might have drawn reasons for urging a continual  recol-
lection of,  and  reference to, the  principle  of the conser\ation
of force from other forms of power than  that of gravitation ;
but I think  that when founded  on gravitating phenomena,
they appear in their greatest simplicity; and precisely for this
reason, that gravitation  has not yet been connected by any
degree of convertibility with  the other forms of force.  If I
refer for  a few minutes to these other  forms, it is only to
point in  their  variations, to  the proofs of the  value  of the
principle laid down, the consistency of the knoAvn phenomena
with it, and the suggestions of research and  discovery which
arise from it.   Heat, for instance, is a mighty form of power,
and its effects have been greatly developed  ; therefore, assump-
tions regarding its nature become useful  and necessary,  and
philosophers try to define it.  The most probable assumption
is, that it is a motion of the particles of matter ; but a view,
at one time very popular, is, that it consists  of a particular
fluid of heat.   Whether it be viewed in one way or the  other,
the principle  of conservation is admitted, I believe, with aU its
force.  When transferred from one portion to another portion
of like matter, the fuU amount of heat appears.  When trans-
ferred to matter of  another kind an  apparent excess or defi-
ciency often results; the word " capacity" is then introduced, 
USES  OF THE PRINCIPLE.
371
which, AvhUe it acknowledges  the principle of conservation^
leaves space for research.  When employed in changing the
state of bodies, the appearance and disappearance of the heat
is provided for consistently by the assumption of enlarged or
diminished motion, or else space is left by the term " capa-
city" for the  partial  views  which remain to be de\'eloped.
When converted into  mechanical force, in the steam  or  air
engine, and so brought into direct contact with gravity, being
then easily placed in  relation  to it, still the conservation of
force is fully respected and wonderfully sustained.   The con-
stant amount of heat developed in the whole of a A'oltaic cur-
rent described  by M. P.  FaArre,* and the present state  of the
knowledge of  thermo-electricity,  are  again fine, partial, or
subordinate  illustrations of  the principles of conservation.
Even Avhen rendered radiant, and for the time giving no trace
or signs of ordinary heat action, the assumptions  regarding
its nature have provided for  the belief  in the conservation of
force,  by admitting  either that it throws the  ether into an
equivalent state, in sustaining  which for the time the  power
is engaged; or else, that the motion of the particles of heat
is  employed  altogether  in their own  transit  from place to
place.
   It is true that heat often  becomes evident or insensible in
a manner unknovra  to us ;  and we have a right to ask AA'hat
is happening when the heat disappears  in one  part,  as  of the
thermo-voltaic  current, and  appears in another; or when it
enlarges or changes  the  state of bodies ; or what would hap-
pen, if the heat being presented, such changes were purposely
opposed.  We have a right  to ask these questions, but not to
ignore or deny the  conservation of force; and one of the
highest uses of the principle is to suggest such inquiries.  Ex-
plications of simUar points are continually produced, and wiU
be most abundant from the  hands of those who, not desiring
* Comtcs Rendus 1854, vol. xxxix., p. 1212. 
372          THE CONSERVATION OF FORCE.

to ease their labour by forgetting the principle, are ready to
admit  it, either  tacitly, or, better still, effectively, being then
continuaUy guided by it.  Such philosophers believe that heat
must do its equivalent of work; that if in  doing Avork it
seem to disappear, it is  stiU producing its equivalent effect,
though often in a manner  partiaUy or  totally unknoAvn ; and
that if it give rise to another form of force (as Ave imperfectly
express it), that force is equivalent in power to the heat which
has disappeared.
    What is caUed chemical attraction affords equaUy instruc-
tive and suggestive considerations in relation to the principle
of the  conservation of force.  The indestructibility of indi-
vidual  matter is one  case, and a most  important  one, of the
conservation of chemical force.   A molecule  has  been en-
dowed with powers which  give rise in it to various  qualities,
and these never change, either in their nature or amount.   A
particle of  oxygen  is  ever a particle of oxygen—nothing can
in the least wear it.  If it  enters into combination and disap-
pears as oxygen—if it pass through a thousand  combinations,
animal, vegetable, mineral—if it lie hid for a thousand years
and then be evolved, it is oxygen with its first  qualities, nei-
ther more  nor  less.  It has  all its  original force,  and only
that; the amount of force which it disengaged when hiding
itself has again to be employed in a reverse direction when it
is set at liberty; and if, hereafter, we should decompose oxy-
gen, and find it compounded of other particles, Ave should only
increase  the strength  of the proof of the conservation  of
force, for we should have  a right to  say of these  particles,
long as they have  been hidden, all that we could say of the
oxygen itself.
    Again, the body of facts included in the theory of definite
proportions, witnesses to the  truth of the conservation  of
force ;  and though we knoAv little of the cause of the  change
of properties of the acting and produced bodies, or how the
forces of the former are hid  amongst  those of the latter, we 
            CHEMICAL ACTION AT A DISTANCE.         373

do not for an  instant doubt the conservation, but are moved
to look for the manner in which the forces  are, for  the time,
disposed, or if they have  taken up another form  of force, to
search what that form may be.
    Even chemical action at a distance, Avhich is in such an-
tithetical contrast with the ordinary exertion of chemical affin-
ity, since it can produce effects miles  away from the particle0!
on which they depend, and which are  effectual only by forces
acting at insensible distances,  stiU  proves the  same thing, the
conservation of force.   Preparations can be made  for a chem-
ical  action in  the simple voltaic circuit, but until the circuit
be complete that action does not occur ;  yet in completing wc
can so arrange the circuit, that a distant chemical action, the
perfect equivalent of the  dominant chemical  action, shaU be
produced;  and this result, whilst it  establishes the electro-
chemical equivalent of power, establishes the principle of the
conservation of force also, and at the same time  suggests
many  collateral  inquiries which  have yet to  be made  and
answered,  before all that concerns the conservation in  this
ease can be understood.
   This  and other  instances of chemical action at a distance
carry our inquiring thoughts on from the facts to the physical
mode of  the exertion of force ;  for the qualities wliich seem
located and fixed to  certain particles of matter appear  at a
distance  in connection with particles  altogether  different.
They also lead our thoughts to the conversion  of one form of
poAver into another;  as, for instance, in the  heat which the
elements of a  voltaic pile may either shoAV at the place where
they act  by their combustion or combination  together, or in
the distance, where the electric spark may be  rendered mani-
fest ;  or  in the  wire  of fluids of the different parts of the
circuit.
   When we  occupy ourselves Avith the dual forms of power,
electricity, and magnetism, Ave find great latitude  of assump-
tion,  and necessarUy  so, for  the  powers  become  more  and 
374
THE CONSERVATION OF FORCE.
more complicated in their conditions.  But stiU  there is  no
apparent desire to let loose the force of the principle of con-
servation, even in those cases where the appearance and dis-
appearance  of force  may seem  most evident  and striking.
Electricity appears when there is consumption of no other
force than that  required for friction; we do not  know hoAv,
but we  search to knoAv, not  being wiUing to  admit that the
electric  force can arise out of nothing.  The two  electricities
are developed in equal proportions ;  and having appeared, we
may dispose variously of the influence of one upon successive
portions of the other, causing many changes in relation, yet
never able to  make  the  sum of the force of one kind in the
least  degree.exceed or come  short of the sum  of the other.
In that  necessity of equality, we see another direct proof  of
the conservation of force, in the midst of a thousand changes
that require to  be developed in  their  principles  before we
can consider this part of science as even moderately known
to us.
    One assumption with regard to electricity is, that there is
an  electric fluid  rendered evident by excitement in plus and
minus proportions.    Another assumption  is,  that there are
two  fluids  of  electricity, each  particle  of each repeUing  all
particles hke itself, and attracting aU particles of the  other
kind always, and with a force proportionate  to the inverse
square  of the distance, being so far analogous  to the  defini-
tion of gravity.   This hypothesis  is antagonistic to the law
of the conservation of force, and  open  to all the  objections
that have been, or may be, made  against the ordinary defini-
tion of gravity.  Another assumption is, that each particle  of
the two electricities  has a given amount of power, and can
only attract contrary particles with the  sum of that amount,
acting upon each of two with only hah0 the power it could in
like  circumstances exert upon  one.  But various  as are the
assumptions, the conservation of force (though wanting in the
Becond)  is, I think, intended to  be included in  aU.  I  might 
               OPENING OF NEW PROBLEMS.           375

repeat the same observations nearly in regard to magnetism-
Avhether to be assumed as a fluid, or two fluids or electric cur
rents—whether the external  action be supposed to be action
at a distance, or  dependent on an external condition and
lines of force—still, all are intended to admit the conserva-
tion of power as  a  principle to which the  phenomena are
subject.
    The principles  of physical knowledge are  now so far de-
veloped as to  enable us not merely to define  or describe the
known,  but to  state reasonable expectations regarding the
unknown;  and I think the principle  of the  conservation of
force may greatly aid experimental philosophers in that duty
to science,  Avhich consists  in  the enunciation of problems  to
be solved.   It wiU lead us, in any case Avhere the force re-
maining unchanged in form is  altered in direction  only, to
look for the neAV disposition of the force ; as in the cases of
magnetism, static  electricity, and perhaps gravity, and to as-
certain  that as a whole it remains unchanged  in amount—or,
if the original force disappear, either  altogether or in part, it
AviU lead us  to look for  the new condition or form of force
wliich should  result, and to develop its  equiA'alency to the
force that  has disappeared.  Likewise, when force is devel-
oped, it will cause us to consider the previously-existing equivr-
alent to the force so appearing;  and  many such cases there
are  in chemical action.  When force disappears, as in the
electric or magnetic induction after more or less discharge,  or
that of  gravity with an increasing distance, it AviU suggest  a
research as to whether the equivalent change is one Avithin
the  apparently acting  bodies, or one external  (in part)  to
them.  It wUl also raise up inquiry as to the nature of the
internal or external state, both before the change and after.
If supposed to be  external, it will suggest the necessity of a
physical process, by Avhich the power is communicated from
body to body; and in  the  case  of external action, wiU lead
to the inquiry Avhether, in any case, there can be  truly action 
376
THE CONSERVATION OF FORCE.
at a distance, or whether the ether, or some Other medium, it
not necessarily present.
    We are not permitted as yet to see the nature of the source
Of physical  power, but we are  alloAved to see much of the
consistency existing amongst  the various forms in Avhich it is
presented to us.   Thus, if, in static electricity, we  consider
an  act  of induction, we can  perceive  the consistency of all
other like acts of induction with it.   If we then take an elec-
tric current, and compare it Avith this inductive  effect, Ave see
their relation and consistency.   In the same manner Ave have
arrived at a knowledge of the consistency of magnetism  with
electricity, and also of chemical action  and of heat Avith all
the former; and if we see not the consistency betAveen gravi-
tation with any of these forms of force,  I am strongh of the
mind that it is because of our ignorance only.   Hoav imper-
fect Avould our idea of an electric current noAV be, if  we Avere
to leave out of sight its origin, its static and  dynamic induc-
tion, its magnetic influence, its chemical and  heating  effects ;
or our idea of  any one of these  results,  if we left any of the
others unregarded ?  That there should be a power of gravita-
tion existing by itself, having no relation to the other natural
powers, and no respect to the law of  the  conservation of force,
is as little likely as that there should be a principle of levity
as weU as of graA'ity.   Gravity may be only the residual part
of the other forces of nature, as Mositi  has  tried to show;
but that it should fall out from the law of  aU other force, and
should be outside the reach either of further experiment  or
philosophical conclusions, is not probable.   So Ave must strive
to learn more of  this outstanding power, and endeavour to
avoid any definition of it which is incompatible  with the prin-
ciples of force generally, for all the phenomena of nature lead
us to belie\-e  that the great and governing law is  one.  I
would much rather  incline  to  believe  that bodies  affecting
each  other  by gravitation  act  by lines of force of definite
amount (someAvhat in the manner of magnetic  or electric in- 
       MENTAL QUALIFICATIONS  FOR THE INQUIRY.    377

duction, though with polarity), or by an  ether pervading  all
parts of .space, than admit that the conservation of force
could be dispensed Avith.
    It may be supposed, that one  who has little or no  mathe
matical knoAvledge should hardly assume a right to judge oi
the generality and force  of a  principle  such as that which
forms  the  subject of these  remarks.  My apology is  this: I
do not perceive that a mathematical mind, simply as such, has
any advantage OA*er an equally acute mind not mathematical,
in perceiving the nature and poAver of a natural  principle of
action.   It cannot of itself introduce  the knowledge  of any
neAv principle.   Dealing Avith any and every amount of static
electricity, the mathematical mind has balanced and adjusted
them Avith Avonderful  advantage, and  has  foretold  results
which the  experimentalist can do no more  than Arerify.   But
it could not discover dynamic-electricity, nor electro-magnet-
ism, nor magneto-electricity, or  even  suggest them;  though
when once discovered by the experimentalist, it can take them
up  Avith extreme facUity.
    So in respect of the force of gravitation, it has  calculated
the results of the power in such a wonderful manner as to
trace the known planets through  their courses and  perturba-
tions, and in so doing has discovered a planet before unknown ;
but there  may be results  of the gravitating force of other
kinds than attraction inversely as the square of the distance,
of Avhich it knows nothing, can  discover  nothing, and  can
neither assert nor  deny their possibility or occurrence.  Under
these circumstances, a principle  which  may be accepted as
equally strict Avith mathematical knoAvledge, comprehensible
without it, applicable by all in their philosophical logic, Avhat-
ever form  that may take, and aboA-e aU, suggestive,  encour-
a™in°-, and instructive to the mind of the experimentalist,
should be the more earnestly employed and the  more fre-
quently resorted to Avhen Ave are  labouring  either to discover
new regions  of science, or to  map out and develop those 
378
TEE CONSERVATION OF FORCE.
which are known into one harmonious whole ; and if in such
strivings, Ave, Avhilst applying the principle of conservation,
see but imperfectly, stiU Ave should endeaA'our to see, for even
an obscure and distorted vision is better than none.   Let us,
if we can, discover a new thing  in  any shape;  the true  ap-
pearance and character wiU be easily developed afterwards.
    Some  are  much surprised that I should, as  they think,
venture to oppose the conclusions of Newton; but here there
is a mistake.  I do not oppose  Newton on  any point; it is
rather those who sustain the idea of action at a distance, that
contradict  him.  Doubtful as I ought to be  of myself, I  am
certainly very glad to feel that my convictions are in accord-
ance with his conclusions.  At the same time, those who  oc-
cupy themselves Avith such matters  ought not to depend alto-
gether  upon authority, but should  find  reason within them-
selves,  after careful thought  and consideration,  to use and
abide by their own judgment.   Newton himself, Avhilst refer-
ring to those Avho  were judging his  views, speaks  of such  as
are competent to form an opinion in such matters, and makes
a strong distinction between them and those wrho were incom-
petent for the case.
   But after  all,  the principle of the conservation of force
may by some be denied.   WeU, then, if it be unfounded even
in its apphcation to the  smaUest part of  the  science of force,
the proof must be within  our reach, for aU  physical science
is so.  In  that case, discoveries as  large or larger than any
yet made, may be  anticipated.  I do not resist the  search for
them, for  no one  can do harm, but" only good, who works
Avith an earnest and truthful spirit  in  such a direction.  But
let us not  admit the destruction or creation of force without
clear and  constant proof.  Just as  the chemist  OAves all  the
perfection of his science to his dependence on the certainty
of gravitation  applied  by the balance, so may the physical
philosopher expect to find the greatest security and the utmost
aid in the principle of the conservation of  foi ce.  AU that 
             SUPPLEMENTARY CONSIDERATIONS.        379

wc  have that is good and safe, as the steam-engine, the elec-
tric-telegraph, &c, Avitness to that principle—it would require
a perpetual motion, a fire Avithout heat, heat Avithout a source.
action without reaction, cause with  effect, or effect Avithout a
cause, to displace it from its rank as a law of nature.
    During  the  year that has passed since the publication of
the foregoing views regarding gravitation, &c, I ha\'e come to
the  knoAvledge  of  various  observations  upon them, some
adverse, others favourable : these have given me no reason to
change my oaati mode of viewing  the subject; but some of
them make  me  think that I have not stated the matter with
sufficient precision.   The word " force" is understood  by
many to mean  simply " the tendency of a body to pass from
one  place  to another," which is equivalent, I suppose, to the
phrase " mechanical force ; " those who so restrain its  mean-
ing  must have  found my argument very obscure.  What I
mean by the word " force," is the cause of a physical action;
the  source  or sources of all possible changes amongst the
particles or materials of the universe.
    It seems to me that the idea of the conservation of force is
absolutely independent of any notion we may form  of the
nature of force or its ATarieties, and is as sure  and may be as
firmly  held  in  the  mind, as if we,  instead of being very
ignorant, understood perfectly every point about the cause of
force and  the varied  effects it can  produce.  There may be
perfectly distinct and separate  causes  of what  are  caUed
chemical actions, or electrical .actions, or gravitating actions,
constituting  so  many forces;  but  if the " conservation  of
force " is a good and true principle,  each of these forces must
be subject to it:  none can vary in its absolute amount; each
must be  definite  at aU  times, whether for a particle, or for aU
the particles in  the  universe ;  and the sum also of the three 
380           THE  CONSERVATION OF FORCE.
forces  must be equaUy unchangeable.  Or, there may be but
one cause for these three sets of actions, and in place of three
forces we may really have but one, convertible in its manifes-
tations ;  then the proportions between one set of actions and
another,  as the chemical and the electrical, may become very
variable, so as to be utterly inconsistent with the idea of the
conservation of  two  separate  forces  (the  electrical  and
the chemical), but perfectly consistent with the consercation
of a force, being the common cause of the two or more sets
of action.
    It is  perfectly true that we cannot always trace a force by
its  actions, though we admit its conservation.   Oxygen and
hydrogen may remain mixed for  years without shoAving any
signs of  chemical  activity ;  they may be  made at any given
instant to  exhibit active  results, and  then assume a new
state, in which again they appear as passive bodies.  Now,
though we cannot clearly explain what the chemical  force is
doing, that is to say, what are its  effects during  the  three
periods before, at, and after the active combination, and only
by very vague assumption can approach to  a feeble concep-
tion of its respective states, yet we do not suppose the creation
of a new portion of force for the active  moment of time, or
the less  beheve  that the  forces belonging to the oxygen and
hydrogen exist unchanged in their amount at all these periods,
though varying in their results.   A part may at the active
moment  be thrown off as mechanical force, a part as radiant
force, a part disposed of Ave knoAv not how ; but believing, by
the principle  of conservation, that  it is not  increased or
destroyed,  our thoughts  are directed to search out  what
at  aU and every period it is doing, and how it is to be
recognized  and  measured.   A problem,  founded  on the
physical truth of nature, is stated, and, being stated, is on  the
way to its solution.
    Those who admit the possibility  of the common origin of
aU physical force, and also acknowledge the principle  of con- 
SUPREMACY OF THE  PRINCIPLE.          381
servation, apply that principle to the sum total of the force
Though the amount of mechanical force (using habitual lan-
guage  for  convenience sake) may  remain  unchanged  and
definite  in  its character for a long time, yet when, as in the
coUision of tAAro  equal inelastic  bodies, it appears to be  lost,
they find it in the form of heat;  and whether they admit  that
heat  to be a continued mechanical action (as is most proba-
ble), or assume some other idea,  as that  of electricity, or
action of a heat-fluid, stiU  they  hold to the principle of  con-
servation by admitting that  the sum  of force, i. e. of the
" cause of action," is the same, Avhatever character the effects
assume.  With  them the  convertibility of heat, electricity,
magnetism, chemical action  and motion, is a famUiar thought;
neither can  I perceive any reason why they should be led to
exclude, a priori, the cause of  gravitation from association
Avith the cause of these  other phamomena respectively.   All
that they  are  limited by  in their various  investigations,
whatever directions they may take, is the necessity of mak-
ing no assumption  directly contradictory of the conservation
of force applied to the sum of all the forces concerned, and to
endeavour to discover the  different  directions in which the
various parts of the total force have been exerted.
    Those  Avho   admit  separate  forces  inter-unchangeable,
haA'e  to show that  each of these forces is separately subject
to  the principle  of conservation.  If gravitation be such a
separate force, and yet its  power  in the action of two  par-
ticles be  supposed to be diminished  fourfold by doubling the
distance,  surely  some new action, having  true  gravitation
character, and that alone, ought to appear, for how else can
the totality of the force remain  unchanged?  To define the
force as " a simple attractive force exerted betAveen any  tAvo
or aU the particles of matter, with  a strength varying in-
versely as the square of the distance," is not to answer  the
question; nor does it indicate or even assume what  are  the
other complementary results which occur;  or aUow the sup- 
382
THE CONSERVATION OF  FORCE.
position that  such are necessary : it is simply, as it appears
to me, to deny the conservation of force.
   As to the gra\itating force, I do not presume to say that I
have the least idea of Avhat occurs in tAvo particles when their
power of mutually  approaching each other is  changed by
their  being placed at different distances ; but I  have a strong
conviction, through  the influence on my mind of  the doctrine
of conservation, that  there  is  a change; and  that the  phe-
nomena resulting from the change will probably appear some
day  as the result of careful research.   If it be  said that
" 'twere to consider  too  curiously to consider  so," then I
must dissent: to  refrain  to  consider would be to ignore the
principle of the conservation of force, and to stop the inquiry
which it suggests—whereas to admit the proper logical force
of the principle in our hypotheses and considerations, and to
permit its guidance  in a cautious yet courageous  course of in-
vestigation, may give us power to enlarge the generalities Ave
already possess in  respect  of  heat, motion, electricity, mag-
netism,  &c,  to associate gravity with  them, and  perhaps
enable us to know Avhether  the essential  force of gravitation
 (and other attractions) is internal or external  as respects the
attracted bodies.
    Returning once  more  to the definition of the graAitating
power as " a  simple attractive force exerted between any two or
all the particles or masses  of matter at every sensible distance,
but  with  a strength varying inversely as the square of the
distance," I ought perhaps  to  suppose there are many who
accept this as a true and sufficient description of the force, and
Avho  therefore, in relation to it, deny the principle  of conser-
vation.  If both  are accepted  and are thought to be consist-
ent  with  each  other, it  cannot be difficult  to add words
which shaU make "varying strength"  and "conservation"
agree together.   It cannot be  said  that the definition merely
applies to  the  effects of gravitation as far as we know them.
So understood, it would  form no  barrier  to  progress;  for, 
        DEFINITION OF  THE  GRAvrTATTNG POWER.     383

that particles at different distances  are  urged toAvard  each
other with a  power varying  inversely as  the  square of the
distance, is  a truth: but the definition  has not that mean-
ing;  and Avhat I  object  to  is  the  pretence  of knowledge
which the definition sets up Avhen it assumes to describe, not
the partial effects of the force, but the  nature of the force
as a whole. 
 
THE CONNECTION AND EQUIYALENCE
            OF FOECES
          By Prof. J. VON LIEBIG.
17 
   Justus von Liebio, born  at Darmstadt in  1803, after spending  ten
months in an apothecary's shop, entered the University of Bonn in  1819,
and  afterwards graduated in  medicine in Erlangen.  In 1822 he went to
Paris, where he studied chemistry two years.  In 1824 he read a paper on
the Fulminates before the French Institute, which attracted the attention of
Humboldt, by whose influence  he was appointed adjunct Professor of Chem-
istry in the University of Giessen.  He became  professor of this institution
in 1826, and established here  the first laboratory in Germany for teaching
practical chemistry.  In  1840 he published his " Chemistry in its applica-
tions to Agriculture and Physiology," in the form of  a report to the British
Association.  In 1842  he reported to the same body his work on "Animal
Chemistry."  About  the same time  appeared his  "Familiar Letters  on
Chemistry," which has since been rewritten and much extended.   He is the
author abo of various  other valuable works.  He remained  at Giessen  till
1852, when he became professor and president  of the laboratory in  the
University of Munich.  In 1854 his friends in Europe contributed and pre-
sented to him £1,000, and in I860 he became President of the Academy of
Sciences in Munich.   Professor Liebig is a bold and  intrepid investigator,
and an ardent writer, who has  made a  profound  impression  upon his age.
While some of his views have  not been accepted in the chemical world, and
indeed have been abandoned by himself, others have taken  their place  as
valuable additions to the  body  of scientific truth.   The charge that some of
his doctrines have proved erroneous does not disturb him; ia the true scien-
tific  spirit he replies, " Show me the man who makes no mistakes, and I  will
Bhow you a man who has done nothing." 
THE CONNECTION AND  EQUIVALENCE
                   OF  FOECES.
   IT is well knoAvn that our machines create no power, but
    only return what they have received.  The motion of a
 clock is produced by a weight or a spring; but it is the power
 of the  human arm applied to stretch the spring or elevate the
 weight, which is expended in the movement of the wheels and
 pendulum in twenty-four hours, or in eight or fourteen days.
    A water-wheel sets in motion, in a mUl, one or more  miU-
 stones ; in a foundry, one or more hammers;  in saltworks
 or mines  it pumps  or raises weights to certain heights; in
 factories, it communicates movements to looms, spinning ma-
 chines,  and roUers.  In aU these  instances, the work  per-
 formed by the water-wheel is due to the force exerted by the
 faUing water on the buckets, Avliich sets the wheel in motion ;
 and this force must  be greater than the resistance presented
 by the  different machines in operation.  The performance of
 the machine is measurable by this force.
   The Avork of a steam-engine is executed by the movement
 of a piston upAvards and downwards by the pressure of steam,
 just as a water-Avhcel is moved by  the pressure  of  water.
The cause of this pressure is heat, wliich is derived from the
chemical process of combustion, and is absorbed by  Avater.
By this heat, steam is produced, and the necessary expansion 
388   THE CONNECTION AND EQUIVALENCE OF FORCES.

obtained for the movement of the piston.   It  is heat, in this
last form, which  performs the  mechanical work of the  ma-
chine.
   Every force acts by producing pressure either from or tow-
ards the centre of motion.  In every machine in  operation
the amount of poAver is always measurable by the resistance
overcome ;  and this again can be expressed by corresponding
Aveights, which that power is capable of raising to  a certain
height.   If one man raises by a pump, in one minute, 150 lbs.
of water, and another  200 lbs.; or if one horse  draws to a
certain distance a load of 20 cwt., and another a load of 30
CAvt.,  it is  evident that these numbers express the relative
working power of these two men or horses.   In  mechanics,
the working power of  every machine  is expressed  in horse
power, that is, a force capable of elevating in each second 75
kilogrammes (=2 J lbs. avoirdupois) to a height of one meter
(39*37 inches).
   The whole power communicated to a machine is  not actu-
aUy  avaUable,  but is in part lost by friction.  For if  two
machines possess  the same power, it is found that the greater
quantity of work wUl be executed by the one which has to
overcome the  smaUer amount  of  friction.   In  mechanics,
friction  is always regarded as  acting  in direct opposition to
motion in every machine.  It was believed that the working
power of a machine could be absolutely annihUated by it.
    As the proximate cause of the cessation of motion, friction
was a palpable fact, and could as such be taken into account;
but a fatal error was committed in giving a  theoretical view
of its mode of  action.  For if a power coidd be annihilated,
or, in other words, have nothing as its effect, then there Avould
be no contradiction involved in the belief, that out of nothing
also power could be created.  To this erroneous idea we may
partly trace the behef, held for centuries by most able men, in
the possibUity of discovering a machine which should renew
within itself its own power as it was expended, and  thus ever 
           STATEMENT OF  MATEr's ARGUMENT.        389

continue in motion,  without the necessity for any external
motive force.   The discovery of such a perpetual motion was,
indeed, worthy of every effort.   It would be as valuable as
the bird which lays the golden eggs ; for by its means labour
would be performed,  and money made in abundance without
any expenditure.
    A mass of facts, hitherto uninteUigiblo, ha\re had much
light  thrown upon them by a  more  correct A'iew of natural
forces, for  which we are indebted to a physician, Dr. Mayer,
of Heilbronn,  and which, by the investigations of the  most
eminent natural philosophers and mathematicians, has attained
a significance and importance scarcely to be foreseen.
    According to Dr. Mayer, forces  arc  causes, in which full
apphcation of the  axiom must  be  found,  that every cause
must produce an effect which corresponds and is equal to the
cause.  Causa cequat effectum.   Thus if a  cause C produces
an  effect E,  then C = E.  Should  the  effect  E become the
cause of another effect e, then also E = e = C.  In such a
chain of causes and effects no link, or part of a link, can ever
become nothing = nothing.   Should a given cause C have pro
duced its  corresponding  effect E, then C ceases to exist, for
it has been converted into E.  Consequently, as C passes into
E, and the latter into e, it follows that aU these causes, as far
as relates to their quantity, possess the property of indestructi-
bility, and to  their quality that of convertibility.  In number-
less cases  we see  a  motion cease,  Avithout its usual effects
being produced, such as  lifting a weight or load; but as the
force  which  has caused the motion  cannot  be reduced to
nothing, the question arises; what form has it assumed.  Ex-
perience giAres the ansAver,  by shoAving that wherever motion
is arrested by friction, a blow, or concussion, heat is the re-
sult.  The motion is the cause of the heat.
    The rapid friction of  two plates of metal  can  raise  their
temperature to  redness,  and cause the ebullition of water if
the  friction takes place below  its surface.  In hke manner, 
390  THE CONNECTION AND EQUIVALENCE OF FORCES.

by rapid motion the iron tires of carriage wheels become fre-
quently so hot that they cannot be touched.  In grinding
needle-points the steel is  heated to redness, and the detached
particles burn Avith sparks.   The wooden  breaks of raUway
carriages become  frequently so hot by friction that their sur-
face emits an empyreumatic odour.  By the friction of an
iron grater, particles of white sugar can be melted and heated
eo far as to acquire the taste of burnt sugar (Caramel).  The
heat evolved by the friction of two pieces of ice is sufficient to
melt them.
    In  the English steel-foundries a  bar  of steel 10 or  12
inches long,  by being heated at one end in a forge, is welded
by  hammering to another slender bar, 10  or 12  feet long,
without the necessity of further direct apphcation of heat—a
point of great importance for the  preservation of the good  *
quality of the steel.   Every spot on which the powerful blows
of the  hammer rapidly descend, becomes red hot, and to the
spectators the red glow of heat  appears to run up  and down
the bar.  This glow is produced by the blows of the hammer,
and corresponds to an amount of heat sufficient to raise many
pounds of water to the boiling point; whUst  the end of the
bar heated in  the fire would scarcely by itself raise to the
same temperature as many ounces of water.
    According  to  the preceding  views a precise  connection
exists between the bloAvs of the hammer  (the cause) and the
heat produced  (the  effect) ;  and natural philosophers have
devised the most ingenious experiments to show this relation.
The working power is in this case converted into heat.  If
the view of  Mayer be correct, then should Ave by this amount
of heat thus obtained, be able to reproduce the same amount
of work, viz., the  same number of blows of the hammer.  But
a closer vieAV of the point shows that we  require to  elevate
the hammer, and that therefore its Avorking  poAver was not  ■
inherent, but only lent to it.  The  hammer was elevated by a
Avater-wheel set in motion by a certain weight of water falling 
         MECHANICAL POWER  CHANGED  TO HEAT.      391

 on its buckets.  Thus to raise a hammer weighing ten pounds
 to the height of one foot requires at least the faU of ten pounds
 weight of water from a height of a foot.  It Avas then, properly
 speaking, this Aveight of falhng water Avhich produced the
 heat through  means of the  hammer.   By simply altering the
 arrangement  of the machinery,  the same force  would have
 caused a mill-stone to revolve with great rapidity on its axis,
 or raised by friction two iron disks to a red heat.
    From experiments instituted to elucidate this  point, it has
 been established that 13,500 blows of a hammer, weighing 10
 pounds, faUing on a bar of iron from a height of one foot, pro-
 duce an  amount of heat sufficient to raise one  pound of water
 from the freezing point to that of ebullition.   This fact may
 be represented in another Avay by saying,  that 1,350 cwts. of
 Avater, faUing from a height of one foot, wUl raise the temper-
 ature of 1 lb. of  water from freezing to the boiling point; or
 1,350 lbs. of water faUing from the same height wUl raise one
 pound of Avater one degree in temperature, or  in other words,
 that  this  amount  of heat corresponds to a working  power,
 capable of elevating 13] cwt. to the height of one foot.
    Wherever motion  is lost in a machine  by friction or by
 concussion, there is always  produced a corresponding amount
 of heat.   When, on the  other hand,  a certain  quantity of
 vrork is  performed by heat, there disappears, AAith the me-
 chanical  effect obtained, a  certain amoitnt of heat, which is
 expressed by saying that the heat lost by one pound of water
 in faUing one degree in temperature, is equal to the elevation
 of 13 j cwt. to the height of one foot.   This quantity of heat
 becomes  then the equivalent or value of the working power
 expressed by the above numbers.
   This constant relation between heat and mechanical move-
 ment has been confirmed in  the most varied  manner.  A rod
 of metal is extended by a weight, and on its removal resumes
 its original  length, provided certain limits be not exceeded.
The  same effect is produced by heat;  and it  is evident thai 
392  THE CONNECTION AND EQUIVALENCE OF FORCES.

an equal force must be exerted by the rod in its extension
as  in its contraction.  Now, experiment has shown that the
relation  expressed by the numbers above  given, must exist
between  a given  extension of a bar of iron, and the heat or
weight Avhich has caused that extension, viz., that a quantity
of heat sufficient to raise  a  pound of water one degree in
temperature, wiU, when communicated to a bar of iron, en-
able it to elevate a weight of 1,350 lbs. to the height of one
foot.
    An interesting application of this fact was long ago made
in the Conservatoire des Arts et Metiers, in Paris.  In this
building, which was formerly a conA'ent, the nave of the church
was converted into a museum for industrial products, machines,
and implements.  In its arch, traversing its  length, appeared
a crack,  which graduaUy increased  to the  width of several
inches, and permitted the passage of rain and snow.  The
opening could easily have been closed by stone and hme, but
the yielding of the side waUs  would not have been prevented
by  these means.  The Avhole  buUding was  on the point of
being puUed down, when a natural philosopher proposed the
foUowing plan, by which the object was  accomphshed.   A
number of  strong iron rods were firmly fixed at one end to a
side waU of the nave, and after passing through the opposite
waU Avere  provided  on  the outside with  large nuts, which
were screwed up tightly to the wall.  By applying  burning
straw to the rods, they extended in length.   The nuts by this
extension being now removed several  inches from the Avail,
were again screwed tight to it.  The rods on cooling con-
tracted with enormous  force, and  made  the side Avails ap-
proach each other.   By repeating  the operation the crack
entirely disappeared.  This building with its retaining rods
is still in existence.
    The working power of a machine,  set  in motion by elec-
tricity, can be expressed by numbers, in the same way as the
mechanical effect of heat.   An electrical current is generated 
           ELECTRICITY  CONVERTED  INTO HEAT.        393

by a rotating magnet or by solution  of zinc in the galvanic
battery.   Such a  current, in circulating  through  a thick or
thin wire, exhibits the same deportment as  a fluid flowing
through a wide or narrow tube.   As a given quantity of fluid
requires more time or greater pressure to  pass through a nar-
roAv tube than through a large, so a thin wire offers a greater
resistance than a thick one to the passage  of a current of elec-
tricity.  The  current  is thus retarded and  diminished,  one
portion only passing through the conductor, the other being
converted into heat.   According to the amount of heat thus
produced  by the conversion of the electricity,  a  conducting
Avire of platinum  can be fused,  one  of gold  fused and con-
verted into Arapour,  and a  considerable  quantity of water
brought into violent ebuUition by passing the current through
a thin platinum wire wound round a glass  tube  in a spiral
form.
    If the electrical current  circulates through a Avire wound
spirally round a bar of iron, the latter  is converted into a
powerful  magnet capable of 'attracting and carrying seAreral
hundred weights of iron.  The electrical is converted into the
magnetic  force,  by which a machine may be set  in motion.
The power of attraction communicated to the iron bar is in
exact proportion to the  amount  of electricity circulating in
the surrounding Avire, and this current is  again dependent on
the property of the conductor.   That  portion  of electricity
Avhich  in  the  conductor  is converted into heat, produces no
power  of  attraction in the  iron bar.  It foUows, from the
foregoing, that the quantity of electricity which circulates, of
that Avhich produces heat, and the amount of magnetic power
convertible into working power, stand in the same relation to
each other, as the working power produced in a machine by
the pressure of falhng water to the heat generated by friction
and concussion in  the same  machine.  The  same amount of
electricity which, when converted into heat by the resistance
of the conductor, raises by one degree the  temperature of one* 
394   THE CONNECTION AND EQUIVALENCE OF FORCES.

pound of  water, generates a magnetic force capable of ele-
vating a weight of 13} cwt. to the height of one foot.
   If the metallic wire through which the electricity  is cir-
culating, be cut, and both ends immersed  in Avater, a chemical
decomposition of the water into hydrogen and oxygen takes
place.  The circulating electricity is converted into chemical
affinity, and into a power of attraction wliich causes the sep-
aration of the elements of water.  "With the evolution of the
hydrogen  and oxygen aU traces of the electrical  current dis-
appear.  The power to produce heat and magnetic force, the
usual effects  of the electrical current, is apparently in this
case annihilated, and in its place we obtain two gases, one of
which, hydrogen, when burned in oxygen, reproduces  water
and  evolves heat.   Now it has been proved,  by careful ex-
periments, that an electrical current of a given  strength,
which, when converted into heat in a conductor, is capable
of raising the temperature of a pound of water by one degree,
wiU  produce by the decomposition of water a quantity of hy-
drogen, by the combustion of which  one  pound of water can
also  be elevated one degree in temperature.
   The heat and power of attraction which were apparently
lost  by the decomposition of the water,  had only become
latent, so  to  speak, in the elements  of water.  This heat is
again set  free on the reunion of these elements, and if con-
verted into working power, would produce the  same  result
(viz., raising a given weight a foot high) as would have been
effected by a magnetic power generated by a quantity of elec-
tricity circulating  round a bar of iron,  equal to that Avhich
Avas originaUy employed in the decomposition  of the water.
    The electrical  current is the consequence of a  chemical
action, and  the amount  of electricity which circulates can
therefore  be  measured by the  quantity of zinc which  is dis-
solved.  The chemical force (affinity)  is converted by  the
solution  of the zinc into a  corresponding quantity of elec
tricity; and this again in the conductor into its equivalent of 
THE MOTIVE-FORCE OF  PLANTS.
395
 heat, or into magnetic force, or, as in the  case of the decom-
 position of water, into  chemical force.  In no case is there a
 diminution or increase of force.  If,  according to the materi-
 alist, matter is indestructible, the same holds good with regard
 to force.  It is not extinguished; its apparent  annihUation,
 its disappearance, is only a conversion into some  other form.
    We  know now the origin of the heat and light which
 warm and Uluminate our dwellings, of the heat and power
 generated in our bodies  by the vital  process.   Plants are the
 one source of all materials used  for the  production of heat
 and hght, and of that nourishment which must be daily taken
 to maintain the phenomena of vitality.   The  elements  of
 plants are earthy  in their  nature,  and are obtained from
 water,  earth, and air.   In plants,  certain inorganic com-
 pounds—carbonic  acid, water, and  ammonia—are decom-
 posed.   The carbon of  the carbonic acid, the hydrogen  of
 the water, and the nitrogen of the ammonia, are retained as
 constituents of their organs, but the  oxygen of the carbonic
 acid and of the water are  returned as gas to the air.  With
 out hght, however, plants cannot grow.
    The  vital process in plants exhibits itself as directly oppo-
 site in its ciiaracter to the chemical process in the formation.
 of salts.
    Carbonic acid, water, and zinc, when brought together pro-
 duce a certain effect  on each other.   In virtue  of  chemical
 affinity there is formed a white powdery compound, contain-
 ing carbonic acid, zinc,  and oxygen from  the  water, and
 hydrogen is at the same time evolved.
    In  plants, the  hving bud or part of the plant takes the
 place of the zinc.  By their growth are formed, from carbonic
 acid and water, compounds containing carbon and hydrogen
 or carbon and the elements of water, and oxygen is at the
 same time evolved.  Sunlight acts in hving plants like elec-
tricity, which arrests the natural attraction of the  elements of
 water,  and separates them from each  other. 
 396  THE CONNECTION AND EQUIVALENCE OF FORCES.

    Without the hght  of the sun plants cannot grow.  The
 living germ, the green leaf,  owe to the sun their poAver of
 transforming earthy elements into living, vigorous structures.
 The germ may, indeed, be evolved under ground without the
 action of hght, but  only when it breaks through the surface
 of the  soU does it first acquire the power, by the sun's rays,
 of converting inorganic elements into its own structure.  Tho
 iUuminating and heating rays of the sun, in thus bestowing
 life, lose their oaati hght and heat.   Their power now becomes
 latent in the ne\v  products of the  frame,  which haA'e been
 produced under their influence from carbonic acid, Avater, and
 ammonia.  The  light and heat with Avhich our dwelhngs are
 Uluminated and warmed are but those bestowed by the sun.
    The food of men and animals  consists  of tAvo classes of
 materials, Avhich differ totaUy in their nature.  One  class is
 destined to the production of blood and the maintenance of
 the structure of the body;  the other is similar in composition
 to ordinary materials  for combustion.   Sugar, starch, the
 gum of bread, may be  regarded as  transformed woody fibre,
 for we can prepare them  from this substance.  Fat, in it.5
 amount of carbon, resembles closely mineral coal.  We heat
our bodies as we do stoves, by combustibles  AAiiich possess the
 same elements as wood and coal, but which differ essentially
 from them by being soluble in the fluids  of the body.
    The elements of nutrition  from which the temperature of
 the body is derived, evidently produce no mechanical power ;
 because power is  but converted heat,  and the heat which
 maintains and elevates the temperature  of the body does not
 produce any other effect than that of warmth.
    AU those mechanical operations constantly taking place in
 the hving body, in the movement of organs and limbs, are
 dependent on an  accompanying change in the  composition
 and properties of those highly complex sulphur and nitrogen
 constituents  of the muscles, which, though furnished by the
blood, are in the first instance  deriAred directly from the food 
             DERIVATION OF ANLAIAL POAVER.          397

of man.   The change of position in the elements of these
complex  bodies, attendant  on their rearrangement into new
and simpler compounds, necessarily gives rise to motion ; and
the molecular movement of the particles in a state of change
is transferred to the muscular mass.   Chemical action is thus
evidently the source of mechanical poAver in bodies.
   The elements of the food of men  and animals which give
rise to power and heat, are produced in living plants only by
the action of sunlight.  The rays of  the  sun become latent,
so to speak, in them in the same way as the current of elec-
tricity becomes latent  in the hydrogen by decomposition of
water.
   Man, by food, not only maintains  the perfect structure of
his body, but he daUy lays in a store of power  and heat, de-
rived in  the first instance  from the  sun.  This power and
heat, latent  for a time, reappears and again becomes active
AArhen the hving structures are resolved by the vital processes
into their original elements.
   The rays of the sun add daily to the store of indestructi-
ble forces of our terrestrial body, maintaining life and motion.
Thus, from beyond the limits of our earth, the body, the more
earthly vessel, derives aU  that may be called good  in it, and
of this not a single particle is ever lost. 
 
            THE CORRELATION
                  OP THE
PHYSICAL  AND VITAL  FORCES
        By Dr. WILLIAM B CARPENTER. 
    William Benjamin Carpenter, the eminent English physiologist, Avas
born in the early part of this century, and graduated as doctor of medicine
in Edinburgh in 1839.  He commenced  practice in Bristol, but has been
chiefly occupied  as  a lecturer and author.  LTis most  important works  are
the "Principles ot  General and  Comparative  Physiology" (1839),  the
" Principles of Human Physiology " (1846), which reached a fifth edition in
1855, and " The Microscope, its Revelations and Uses" (1856).  He is  the
author of various minor, but valuable works, and of many elaborate papers
in the cyclopedias and scientific periodicals.  For many years he was editor
of the " British and Foreign Medico-Chirurgical Review."   He was  elected
a member of the Royal Society in 1814, and is  now Professor of Medical
Jurisprudence in University College, London;  Lecturer on General Anatomy
and Physiology at the  London  Hospital  and  School of Medicine, and  Ex-
aminer  in Physiology and Comparative Anatomy in the University of Lon-
don.  In 1850 he published an able paper in the Transactions of  the Royal
Society on the " Mutual Relations of the Vital and Physical  Forces," and
has published upon the same general subject, the essays which close this vol-
ume, in the new  Quarterly Journal of Science for the present year.  Dr. Car-
penter is an able and original thinker, as well as a voluminous writer, and has
made many valuable contributions to the  progress of physiological science. 
ON THE CORRELATION  OF  THE  PHYS-
         ICAL AND VITAL  FORCES.
 I.—RELATIONS  OF LIGHT AND HEAT TO THE VITAL  FORCES
                       OF PLANTS.

    IN every period of the  history of Physiology, attempts
    have  been  made to identify aU the forces acting in the
 Living Body with those operating in the  Inorganic universe.
 Because  muscular force, when brought to bear on the bones,
 moves them according to the mechanical laws of lever action,
 and because the  propulsive poAver of the heart drives the
 blood through the vessels according to the rules of hydraulics,
 it has been imagined that the movements of living bodies may
 be explained on physical principles ; the  most important con-
 sideration of all, namely, the source of that contractUe poAver
 which the living muscle possesses, but which the dead  muscle
 (though having the same chemical composition) is utterly in-
 capable  of exerting, being  altogether  left out of view.  So,
 again, because the digestive  process, whereby food is reduced
 to a fit state for  absorption, as AveU as the formation of va-
rious products of the decomposition that is continuaUy taking
place in the  living body, may be  initiated in the  laboratory
of the chemist;  it has been  supposed  that the  appropriation 
4:02  COERELATION OF PHTSICAL AND VITAL FOECES.

of the nutriment to the production of the living  organized
tissues of Avhich the several parts of the body are composed,
is to be regarded as a chemical action—as if any combination
of albumen and gelatine, fat and starch, salt and bone-earth,
could make a hving Man without the constructive agency in
herent in the germ from which his bodUy fabric is evolved.
    Another class of reasoners have cut the knot which they
could not untie, by attributing aU the actions of hving  bodies
for which Physics and Chemistry cannot account, to a hypo-
thetical " Vital principle ;" a shadoAvy agency that does every
thing in  its own Avay, but refuses to be made  the subject of
scientific examination ; like the " od-force " or the  " spiritual
power " to Avhich the  lovers of  the marveUous are so fond of
attributing the  mysterious  movements of turning and  tUting
tables.
    A more scientific spirit, however, prevaUs among the best
Physiologists of the present day; who, whilst fully recogniz-
ing the fact that many of the phenomena of living bodies can
be  accounted for by the agencies Avhose operation they trace
in the world  around, separate  into a distinct  category—that
of vital actions—such as  appear to differ  altogether in kind
from the phenomena of Physics and Chemistry, and seek to
determine, from the study of the conditions under which these
present themselves, the laws of their occurrence.
    In the prosecution of this  inquiry, the  Physiologist will
find it greatly to his advantage to adopt the method  of  phUos-
ophizing which distinguishes the Physical science of the pres-
ent from that of the past generation; that, namely,  which,
whilst fuUy accepting the logical definition of the cause of any
phenomenon, as " the antecedent, or the concurrence of ante-
cedents on which  it is  invariably and unconditionally conse-
quent"  (Mill), draAVS  a  distinction between the dynamical
and the material conditions ;  the former supplying  the power
which does the Avork, wliUst the latter affords the instrumental
means through which that power operates. 
          DTXAMICAL AXD  MATEKIAL CO^DITIOXS.      403

    Thus if we inspect a Cotton Factory in fuU action, we find
 it to  contain a vast number of machines, many of them but
 repetitions of one another, but many, too, presenting the most
 marked  diversities in construction, in operation, and in result-
 ant products.   We see, for example, that one is supplied with
 the raw material, Avhich it cleans and dresses;  that another
 receives the cotton thus prepared, and " cards " it so as to lay
 its fibres in such an arrangement as  may admit of its being
 spun ; that another series, taking up the product supplied by
 the carding machine, twists and draws it out into threads of
 various degrees of fineness ;  and that  this thread, carried into
 a fourth set of machines, is woven into  a fabric which may
 be either plain or variously figured according to the construc-
 tion of the loom.  In every one of these dissimilar operations
 the force which is immediately concerned in bringing about the
 results is one and the same;  and the variety of its products is
 dependent  solely upon the diversity  of the material instru-
 ments through which it operates.   Yet these arrangements,
 hoAvever skilfully devised, are utterly valueless without the
 force Avhich brings them into play.  All the elaborate mechan-
 ism, the triumph of  human ingenuity in devising, and of skiU
 in constructing, is as powerless as a corpse without the vis
 viva  Avhich alone can animate it.   The  giant  stroke of the
 steam-engine, or  the majestic revolution of the water-wheel
 gives the required  impulse;  and the vast apparatus which
 was the moment previously in a state of death-like inactivity,
 is aroused to aU  the  energy of its wondrous life—every part
 of its complex organization taking upon itself  its peculiar
 mode of activity,  and evolving its own special product, in vir-
 tue of the  share it receives of the one general force distrib-
uted through the  entire aggregate of machinery.
   But if we carry back our  investigation a stage further, and
inquire  into the  origin of the force  supplied by the  steam-
engine or  the  Avater-wheel,  we  soon meet with a  new and
most  significant fact.  At our first  stage, it is true, we find 
404  CORRELATION OF  PHYSICAL AND VITAL FORCES.

only the  same  mechanical force acting through a different
kind of instrumentality;  the strokes of  the  piston  of the
steam-engine being  dependent upon  the  elastic force of the
vapour  of water, whilst  the revolution of the Avater-Avheel is
maintained  by  the  dovraAvard impetus of water  en masse.
But to what antecedent dynamical agency can Ave trace  these
forces ?   That agency in each case is Heat; a force altogether
dissimilar in its ordinary manifestations to the force which
produces  sensible motion, yet capable of being in turn con-
verted into  it and generated  by  it.   For it is from the Heat
apphed beneath the boiler of the steam-engine  that the  non-
elastic liquid contained in it derives aU that potency as elastic
vapour, which enables it to overcome the vast mechanical re-
sistance that is  set in opposition  to it.  And, in hke manner,
it  is the heat of the solar rays  which pumps  up  terrestrial
waters  in the shape of vapour,  and  thus supphes to Man a
perrenial  source of new power in their descent by the force
of gravity to the level from which they have been raised.*
    The poAver  of the steam-engine, indeed, is itself derived
more remotely from those  same  rays;  for the Heat apphed
to its boUers is but the expression of  the chemical change in-
volved in combustion ; that combustion is sustained either by
the wood wliich is the product of the vegetative  activity of
the present  day, or by the  coal which represents the vegeta-
tive life of  a remote  geological  epoch; and that vegetative
activity, whether present or past, represents  an equivalent
amount of Solar Light and Heat, used up in the  decomposi-
tion of the  carbonic acid  of the atmosphere,  by the instru-
mentality of the  growing  plant.-j-  Thus  in  either case we
come, directly or  indirectly, to Solar Radiation as the main-

   * See on this subject the recent admirable address of Sir William Arm-
strong at the Meeting of the British Association at Newcastle.
   f This was discerned by the genius of George Stephenson, before the
general doctrine of the Correlation of  Forces had been given to the world
by Mayer and  Grove. 
       ESTABLISHMENT OF THE GENERAL PRINCIPLE.   405

spring of our mechanical  power; the vis viva of our whole
microcosm.  Modern physical inquiry ventures even one step
further, and seeks the source of Light and  Heat of the Sun
itself.   Are  these, as formerly supposed, the result of com-
bustion,  or are they, as surmised by Mayer and Thomson,
the expression of the motive power  continuaUy generated in
the faU of  aerolites toAvards the Sun, and as continuaUy anni-
hilated by their impact on its surface ?   Leaving the discus-
sion of this question to Physical Philosophers, I proceed now
to my own proper subject.
    It is now about twenty years since Dr. Mayer first broadly
announced, in aU its generality, the great principle now known
as that of " Consolation  of Force;" as a necessary deduc-
tion from two axioms or essential truths—ex nihilo nil fit, and
nil fit ad nihilum—the validity of Avhich  no true  philosopher
would ever  have  theoretically questioned,  but of which he
was (in my judgment) the  first to appreciate the fuU practical
bearing.  Thanks to the labours of Faraday, Grove,  Joule,
Thomson, and Tyndall, to  say nothing of those of Helmholtz
and other distinguished Continental savans, the great doctrine
expressed by the  term  "Conservation  of Force" is now
amongst the  best-established generahzations of Physical Sci-
ence ;  and  every thoughtful Physiologist must desire  to see
the  same course of inquiry thoroughly pursued in regard to
the phenomena of hving bodies.   This ground was first broken
by Dr. Mayer in his remarkable treatise, " Die  Organische
Bewegung in ihrem Zusammenhange mit dem  Stoffwechsel"
("• On  Organic MoA'ement in its relation to Material Changes,"
Heilbronn, 1845) ; in which he distinctly set forth the princi-
ple that  the source  of all  changes in the living Organism,
animal as weU as vegetable, hes in the forces acting upon it
from without; whUst the changes  in its own composition
brought about by these agencies, he considers to be the imme-
diate source of the forces Avhich are generated by  it.
   In  treating of these forces, however, he dweUs chiefly on 
406  CORRELATION  OF PHYSICAL  AND VITAL FORCES.

the production  of Motion, Heat, Light, and Electricity  by
Uving bodies ; touching more slightly upon the phenomena of
GroAvth and Development, which constitute, in the eye of the
physiologist, the distinct province of vitality.  In  a memoir
of my own, " On the Mutual Relations  of the Vital and Phys-
ical Forces," published in the Philosophical Transactions for
1850,* I aimed to show that the general doctrine of the " Cor-
relation of the Physical Forces " propounded  by Mr. Grove,
was equaUy applicable to  those Vital  forces which must be
assumed as the moving powers in  the production of purely
physiological phenomena;  these forces being generated in
hving bodies by the transformation  of the  Light, Heat, and
Chemical Action supplied by  the  world around, and being
given back to it  again, either during  their life, or after its
cessation, chiefly in Motion and Heat, but  also to a less de-
gree in Light and Electricity.  This  memoir attracted but
little  attention at the time, being regarded, I beheve, as too
speculative ; but I have since had abundant evidence that the
minds of thoughtful Physiologists, as weU as Physicists, are
moving in the same direction;  and as the progress of science
since the publication of my former  memoir, would lead me
to present some parts of my scheme of doctrine in a different
form,f I venture to  bring  it again  before  the public in the
form of a sketch (I claim for it no  other title), of the aspect
in which  the apphcation of the principle of the  " Conserva-
tion of Force " to Physiology noAV presents itself to my mind.
   * At this date the labours of Dr.  Mayer were not known either to my-
self or (so far as I am aware) to any one else in this  country, save the late
Dr. Baly, who a few months  after the publication of my Memoir, placed in
my hands the pamphlet,  " Die Organische Bewegung;" to which I took the
earliest opportunity in my power of drawing public attention in " The Brit-
ish and Foreign Medico-Chirurgical Review" for July, 1851, p. 23V.
    f I have especially profited by a Memoir on the Correlation  of Physical,
Chemical, and Vital Force, and the Conservation of Force in Vital Phenom-
ena, by Prof. Le Conte (of South Carolina  College), in Silliman's American
Journal for Nov., 1859, reprinted in the Philosophical Magazine for 1860. 
            CHARACTEEICTTC3 OF VITAL ACTIVITY.       407

    If, in the first place, we inquire what it is that essentially
 distinguishes Vital  from every kind  of Physical  activity, we
 find  this distinction most  characteristically expressed in  the
 fact that a  germ endowed with  Life, developes itself into an
 organism of a type resembUng  that  of its parent; that this
 organism is the  subject of incessant  changes, which all tend
 in the first  place to the evolution of its typical form, and sub-
 sequently to its maintenance in that form, notAvithstanding the
 anfagonism of Chemical and Physical agencies, Avhich  are
 continually tending to produce its disintegration ; but that, as
 its term of  existence is prolonged, its conservative power  de-
 clines so as to become less and less able to resist these disinte-
 grating forces, to which it finaUy succumbs, leaving the organ-
 ism to be resolved by their agency into the components from
 which its materials were originaUy drawn.  The history of a
 living organism, then,  is one  of incessant change; and  the
 conditions of this change are to be found partly in the organ-
 ism itself, and partly in the external  agencies to  which it is
 subjected.   That condition winch is inherent in the organism,
 being derived hereditarily from  its progenitors, may be con-
 veniently termed its germinal capacity; its parallel in the  in-
 organic world being that fundamental  difference in properties
 which  constitutes  the  distinction  between one   substance,
 whether elementary or compound, and another;  in virtue of
 which each  " behaves" in its own characteristic manner when
 subjected to new conditions.
    Thus, although there may be nothing in the aspect or sen-
 sible  properties of the  germ of a Polype, to distinguish from
 that of a Man, we find that each develops itself, if the requi-
 site conditions be supplied, into its typical form, and no other;
 if the developmental conditions required by either  be not sup-
plied  we do  not find a different type evolved, but no evolution
at aU takes  place.*

   * It is quite true that among certain of the lower tribes, both of riant* 
408  CORRELATION  OF PHYSICAL AND VITAL FORCES.

    Now the difference  between a being of high  and a being
of low organization  essentiaUy consists in this: that in the
latter the constituent parts of the fabric evolved by the pro-
cess of growth from  the  original germ, are  similar  to  each
other in structure and endowments, whUst in  the former they
are progressively differentiated Avith the advance of develop-
ment, so that the fabric comes at last to consist of a number
of organs, or instruments, more  or  less dissimilar in struc-
ture,  composition, and  endowments.   Thus  in the  lowest
forms of Vegetable hfe, the primordial germ multiplies itself
by duphcative subdivision into an apparently  unlimited num-
ber of ceUs, each of them simUar to  every other, and capa-
ble of maintaining its existence independently of them.   And
in that lowest Rhizopod type of  Animal life, the  knowledge
of which is among the most remarkable fruits of modern bio-
logical research, " the Physiologist has a case in which those
vital operations which he  is elsewhere  accustomed to see car-
ried on by an elaborate  apparatus, are performed without any
special instruments whatever; a  little  particle  of apparently
homogeneous jeUy changing itself into a  greater variety of
forms than the fabled Proteus, laying hold of  its food without
members, swallowing it  without a mouth, digesting it without
a stomach, appropriating its nutritious material without absorb-
ent vessels or a circulating system, moving from place to place
without muscles, feeling (if it has any power to do so) with-
out nerves, propagating  itself without genital apparatus, and

and Animals, especially the Fungi and Entozoa—similar germs may devel-
op themselves  into very  dissimilar forms, according to the conditions un-
der which they are evolved;  but such diversities are only the same kind as
those which manifest themselves among individuals in the higher Plants and
Animals, and only show that in the types in question there is a less close
conformity to one pattern.  Neither in these groups, nor in that  group of
Foraminifera, in which I have  been led to  regard  the range of variation
as peculiarly great, does  any tendency ever  show itself to the assumption
of the characters of any group fundamentally dissimilar. 
THE LOWEST GRADE OF  LIFE.
409
not only this, but in many instances forming shelly coverings
of a symmetry and complexity not surpassed by those of any
testaceous  animals,"* Avhilst the mere  separation of a frag-
ment of this jelly is sufficient to originate a  new and  inde-
pendent organism,  so that any number  of these beings may
be produced  by the successive detachment of such  particles
from a single Rhizopod, each of them retaining (so far as we
have at present the  means of knoAving)  the characteristic en-
dowments of the stock from  which it was an offset.
    When, on the other hand, we Avatch the  evolution of any
of the higher  types of  Organization, Avhether  vegetable or
animal, we observe that although in the first instance the pri-
mordial cell multiplies  itself by duplicative subdivision into
an aggregation of celb, which are apparently but  repetitions
of itself and of each other,  this  homogeneous extension has
in each case a definite limit, speedily giving place to a struc-
tural differentiation, Avhich becomes more and more decided
with the progress of development, until  in that  most hetero-
geneous of all types—the Human  Organism—no two  parts are
precisely  identical,  except  those wliich correspond  to each
other on the opposite sides of the  body.   "With this structural
differentiation is associated a corresponding differentiation of
function; for whilst in the life of the most  highly developed
and  complex  organism we witness no act which is  not fore-
shadowed, however vaguely, in that  of  the  lowest and sim-
plest, yet we observe in  it  that  same  " division of labour"
which constitutes the essential characteristic of the highest
grade of civUization.  For,  in what  may be  termed the ele-
mentary form  of Human Society, in  which every individual
relies upon himself alone for the supply of aU his wants, no
greater result can be obtained by the  aggregate  action of the
entire community than its mere maintenance ; but  as each in-

   » See the Author's Introduction to the Study of the Foraminifera, pub-
lished by the Ray Society, 1862 : Preface, p. vii.
             18 
ilO  CORRELATION  OF PHYSICAL AND  VITAL FORCES.

dividual  selects  a special  mode of activity for himself, and
aims at improvement in that specialty, he finds himself attain-
ing a higher and  still higher degree of aptitude for it;  and
this  specialization tends to increase as opportunities arise for
new modes  of activity, until that complex fabric i3 evolved
which constitutes the most developed form of the Social State
wherein  every individual  finds the work—mental or bodhy—
for Avhich he is best fitted, and in which ho may reach the
highest attainable perfection;  while the mutual dependence
of the Avhole (Avhich is  the necessary result of this specializa-
tion of parts) is  such  that  every individual Avorks for the
benefit of all his  fellows,  as weU as for his  OAvn.  As it  is
only in such a state of society that the  greatest triumphs of
human ability become possible, so is it only in the most dif-
ferentiated types of  Organization that Vital Activity can  pre-
sent its  highest manifestations.  In the one case, as in the
other, does the result depend upon a process of gradual devel-
opment, in which, under the  influence of agencies whose na-
ture constitutes a proper object of scientific inquiry, that most
general form in Avhich the fabric—Avhether corporeal or social
—originates, eATolves itself .into that most special in Avhich its
development culminates.
    But notwithstanding the wonderful diversity of structure
and of endoAvments  which we meet with in the study of any
complex  Organism, we  encounter a harmonious unity or coor-
dination  in its entire aggregate  of actions, which is yet more
wonderful.  It is in this harmony or coordination, whose ten-
dency is  to the conservation of the organism, that the state  of
Health or  Normal  life essentiaUy  consists.  And  the  more
profound our investigations of its conditions, the more definite
becomes the conclusion to which we are led by the  study  of
them—that it is fundamentally  based on the common origin
of aU these diversified  parts in the  same germ, the vital en-
dowments  of which, equally diffused throughout  the  entire
fabric in those lowest forms of organization in which every 
       THE FUNDAMENTAL CHARACTERISTIC OF LIFE.   411

part is  but a repetition  of every other, are differentiated iu
the highest amongst a variety of organs, acquiring in virtue
of this differentiation a much greater intensity.
    Thus,  then,  we may take that mode  of Vital Activity
which manifests itself in the  evolution of the germ into the
complete organism repeating  the type of its parent, and the
subsequent maintenance  of that organism in its integrity, in
the one case as in the other, at the expense of materials de-
rivcd from external sources—as the most universal and niost
fundamental characteristic of Life ; and we  have now to con-
sider the nature and  source of the Force or Power by Avhich
that evolution is brought about.   The prevalent opinion  has
until lately been, that  this power is inherent in  the  germ;
which has been supposed to derive from its parent not merely
its  material substance, but a  nisus formativus, bildungstrieb,
or germ force, in virtue of which it buUds itself up into the
likeness of its parent, and maintains itself in that likeness
until the force is exhausted, at  the  same time  imparting a
fraction of it to each of its progeny.  In this mode of A'iew-
ing the subject, all the organizing force  required to build up
an Oak or a Palm, an Elephant or a "Whale, must be concen-
trated in a minute  particle,  only  discernible by microscopic
aid,  and the  aggregate of aU the germ-forces appertaining to
the descendants,  hoAvever numerous, of  a common  parentage,
must have existed in their original progenitors.  Thus in the
case of the successive viviparous broods of  Aphides, a germ-
foi ce capable of  organizing a mass of Using structure, Avhich
Avould amount (it has  been calculated)* in the tenth brood
to the bulk of five hundred miUions of stout men,  must have
been  shut up in the single  individual, weighing perhaps  the
l-1000th of a grain, from Avliich the first  brood Avas evolved.
And in hke manner, the germ-force which has organized  the

   *  See Prof. Huxley on the  " Agamic Reproduction of Aphi-j," in Linn.
Trans., vol. xxii., p. 215. 
412  CORRELATION OF PHYSICAL  AND  VITAL  FORCES.

bodies of aU the individual men that have Uved from Adam
to the present day, must have been concentrated in the body
of their common ancestor.   A more complete reductio ad ab-
surdum can scarcely be brought  against  any hypothesis ; and
we  may consider it proAed that  in  some way or other, fresh
organizing force is constantly being supphed from without
during the Avholc period of the exercise of its activity.
    When we look carefuUy into the question, however, Ave
find that what  the germ really  supphes  is not  the force, but
the  directive agency ; thus rather resembling the control exer-
cised by the  superintendent  builder, who is charged  with
Avorking out the design of the architect, than the bodily force
of the Avorkmen who  labour under his  guidance in the con-
struction of the fabric.  The actual constructive force, as we
learn from an  extensive survey  of  the phenomena of life, is
supplied by Heat, the  influence of which upon the rate  of
growth  and development, both  animal and ATegetable, is  so
marked as to have universally attracted the attention of Phys-
iologists, who, hoAvever, have for  the most part only recognized
in it a vital stimulus that caUs forth the  latent poAver of the
germ, instead of looking upon it  as itself furnishing the poAver
that does the work.  It has  been from the narrow limitation
of the area over wliich physiological research has  been com-
monly prosecuted,  that  the  intimacy of this relationship be-
tween Heat and the Organizing  force has not  sooner become
apparent.   "Whilst the vital phenomena of Warm-blooded ani-
mals, Avhich possess Avithin themselves the means of main-
taining a constant temperature, were made the sole, or at any
rate the chief objects of study, it Avas not likely that the in-
quirer Avould recognize the fuU influence of external  heat in
accelerating, or of  cold in retarding their functional  activity.
It is only when the survey is  extended  to  Cold-blooded ani-
mals and to Plants, that the immediate and direct relation be-
tAveen Heat and Vital Activity,  as  manifested in the  rate  of
growth and development, or of other changes  peculiar to the 
DYNAMICS OF GERMINATION.
413
living body, is unmistakably manifested.  To some of those
phenomena, Avhich afford the best illustrations of the mode
in which Heat acts upon the living  organism, attention wUl
noAV be directed.
    Commencing Avith the Vegetable kingdom, we find that the
operation of Heat as the motive power or dynamical agency,
to which the phenomena of growth and development are to be
referred, is  peculiarly well seen in the process of Germina-
tion.   The seed consists of an embryo which has already  ad-
vanced to a certain  stage of development, and of a store of
nutriment laid up as the material for its further evolution;
and in the fact that this evolution is carried on at the expense
of organic compounds  already prepared by extrinsic agency,
until  (the store of these being exhausted) the young plant is
sufficiently far advanced in its development to be able to elab-
orate them for itself, the condition of the germinating embryo
resembles that of an Animal.  Noav, the seed may remain
(under favourable circumstances) in a state of absolute inac-
tion during an unlimited period.   If secluded from the free
access of  air and moisture, and  kept at a Ioav temperature, it
is removed from  all influences that would on  the  one hand
occasion its  disintegration, or on the other, AArould caU  it into
active life.  But Avhen again exposed to air and moisture, and
subjected to a higher temperature, it either germinates  or  de-
cays,  according as the embryo it contains has or has not pre-
served  its vital endowments—a question Avhich only experi-
ment  can resolve.   The process of germination is by no  means
a simple one.   The nutriment stored up in the seed is in great
part in  the condition of insoluble  starch;  and this must  be
brought into a soluble form before it can be appropriated  by
the embryo.   The metamorphosis is effected by the agency of
a ferment termed  diastase, Avhich is laid up in the  immediate
neighbourhood of the  embryo, and which, when brought to
act on starch, converts it in the first instance into soluble dex-
trine, and then (if its action be continued)  into sugar.  The 
 414   CORRELATION OF PHYSICAL AND VITAL FORCES.

 dextrine  and sugar, combined with the albuminous and  oily
 compounds also stored up in the seed, form the "protoplasm,'-
 which is the substance immediately  supphed  to the young
 plant as the material of its tissues ; and the conversion of this
 protoplasm into various forms of organized  tissue, which be-
 come more and more differentiated as development advances,
 is obviously referable to the vital activity of the germ.  Noav
 it can be very easily shown experimentaUy that  the rate of
 growth in the germinating  embryo is so closely related (within
 certain limits) to the amount of heat supplied, as to place it3
 dependence on that  agency beyond reasonable question: so
 that we  seem fuUy entitled to say that Heat, acting through
 the germ, supplies the constructiAre force or power by Avhich the
 Vegetable fabric is buUt up.*  But there appears to be another
 source of that power in the  seed itself.  In the  conversion of
 the insoluble starch of the seed into sugar, and  probably also
 in a further  metamorphosis of a part of that sugar, a large
 quantity of carbon is eliminated from  the seed by combining
 Avith the oxygen of the air, so as to form  carbonic acid ;  this
 combination is necessarily attended Avith a  disengagement of
 heat,  which becomes very sensible when (as  in  molting) a
 large  number of germinating seeds are aggregated together;
 and it cannot but be regarded as probable that  the  heat thus
 evolved within the seed  concurs with that  derived from Avith-
 out, in supplying to the germ the force that promotes its evo-
 lution.

   * The effect of Heat is doubtless manifested very differently by differ-
 ent seeds; such variations being partly  specific, partly  individual.  But
 these are no greater than we see in the inorganic world: the increment of
 temperature and the augmentation of bulk exhibited by different substances
when subjected to the same absolute  measure of heat, being as diverse as
tho substances themselves.  The whole process of " Malting," it may be
remarked, is based on the regularity with which the  seeds of a particular
cpecies  may be at any time forced to a definite rate of germination  by a
definite increment of temperature. 
             DYNAMIC FUNCTIONS OF PLANTS         41."

   The condition of the Plant which has attained a more ad-
vanced stage of its development, differs from that of the ger-
minating embryo  essentiaUy in this particular, that the organic
compounds which it requires as the materials of the extensior
of the fabric are formed by itself, instead of being supplied to
it from without.   The tissues of the coloured surfaces of the
leaves and  stems, when acted on by light, have the peculiar
power of generating—at the expense of carbonic acid, water,
and  ammonia—various ternary and quaternary organic  com-
pounds, such as chlorophyll, starch, oil, and albumen; and of
the compounds thus generated, some are appropriated by the
constructive force of the  plant (derived from the heat with
which it is supplied) to the formation of new tissues ; AAiiilst
others are stored up in  the cavities of those tissues, Avhere
they ultimately serve either for the evolution of parts subse-
quently developed, or for the nutrition of  animals which cm-
ploy them as food.   Of the source of those peculiar affinities
by which the components of the starch, albumen, &c, are
brought together, we have no right to speak  confidently ; but
looking to the fact that these compounds are not produced in
any  case by the direct union of their elements, and that a de-
composition of binary compounds seems  to be a  necessary
antecedent of their  formation, it is scarcely improbable that,
as suggested by Prof. Le Conte (op. cit.), that source is to be
found in the chemical forces set free in the prehminary act of
decomposition, in Avhich  the  elements would be liberated in
that  " nascent condition" Avhich is well known to  be one of
pecuhar energy.
   The influence of Light, then, upon Vegetable organism ap-
pears to be essentially exerted in bringing about what may be
considered a  higher mode of chemical combination between
oxygen, hydrogen, and carbon, Avith the addition of nitrogen
in certain cases ;  and there is no  evidence  that it extends be-
yond this.   That the appropriation of the materials thus pre-
pared, and their conversion into organized tissue in  the opera- 
 4:16   CORRELATION OF PHYSICAL AND A'lTAL FORCES.

 tions of growth and development, are dependent on the agencj
 of Heat, is just as evident in the stage of maturity as in  that
 of germination.  And there is reason to believe, further, that
 an additional  source of organizing force is to be found in the
 retrograde metamorphosis of organic compounds that goes on
 during the whole life of the plant; of which metamorphosis
 the expression is furnished by the production of carbonic acid.
 This is peculiarly remarkable in the case of the Fungi, Avhich,
 being  incapable of forming new compounds  under the influ-
 ence  of light, are entirely supported by the organic matters
 they absord, and Avhich in this respect correspond-on  the one
 hand Avith the germinating embryo, and  on the other Avith
 Animals.   Such a decomposition of a portion of the absorbed
 material is the only conceivable source of the large quantity
 of carbonic acid they are constantly giving out; and it would
 not seem unlikely that the force supphed  by this retrograde
 metamorphosis of the  superfluous components of their food,
 which fall down (so to speak) from the elevated plane of " prox-
 imate principles," to the lower level of comparatively simple
 binary compounds, supphes a force which raises another por-
tion to the rank of living tissue, thus accounting in some de-
gree for the very rapid growth  for which this tribe of Plants
is so remarkable.  This exhalation of carbonic acid, however,
is not peculiar to Fungi and germinating embryos, for it takes
place during  the whole hfe of  floAvering plants, both by day
and by night, in sunshine and in shade, and from their green
as well as from their dark surfaces ; and it is not improbable
that, as in the case of the Fungi, its source lies partly in the
organic matters absorbed, recent investigations * having ren-
dered it probable  that Plants  really take up and  assimilate
soluble  humus, Avhich,  being a  more highly carbonized sub-
stance than starch, dextrine,  or cellulose, can only be con-

  *  See the Memoir of M. Risler, " On the Absorption of Humus " ir.
the " Bibliotheque Universelle," N. S., 1858, torn. L, p. 305. 
            PLANT-PRODUCTS STORES OF FORCE.        417

verted into compounds of the latter kind by parting with somo
of its carbon.  But it may also take place at the  expense  of
compounds previously generated by the plant itself, and stored
up in its tissues;  of wliich we seem to have an  example in
the unusual production of carbonic acid Avhich takes place at
the period of floAArering, especially in such plants as  have a
fleshy disk, or receptacle containing a large quantity of starch ;
and thus, it may be surmised, an extra supply of force is pro-
vided for the maturation of those generative products whose
preparation seems to be the highest expression of the  vital
poAver of the vegetable  organism.
    The entire  aggregate of organic compounds contained in
the vegetable tissues, then, may be considered as  the  expres-
sion, not merely of a certain amount of the material elements,
oxygen, hydrogen, carbon, and nitrogen,  derived  (directly or
indirectly) from the water, carbonic acid, and ammonia of the
atmosphere, but also  of a certain amount of force which has
been exerted in raising these from the loAver plane of simple
binary compounds, to the  higher leAel of complex,  " proxi-
mate principles ;" whilst the portion of these actually converted
into organized tissue may be considered as the expression of
a further measure of  force, which, acting under the directiA-e
agency of the germ, has served to build  up  the fabric in  its
characteristic type.  This constructive action goes on during
the whole Life  of the Plant, which essentially manifests itself
either  in the extension of the original  fabric (to which in
many instances  there seems no determinate limit), or in the
production of the  germs of neAV  and  independent organisms.
It is interesting to remark  that the development of the more
permanent parts involves the successional decay and reneAval
of parts whose existence  is temporary.  The  " fall of the
leaf"  is the effect, not the cause, of the  cessation of  that pe-
culiar functional activity of its tissues, which consists in the
elaboration of the nutritive  material required for the produc-
tion of wood.   And it would seem as if the duration of their 
418  CORRELATION OF PHYSICAL  AND VITAL  FORCES.

existence  stands in an inverse ratio to the energy of their ac-
tion ;  the leaves of "evergreens," which are not cast off until
the appearance of  a new succession, effecting their functional
changes at a much less rapid rate  than do those of  " deci-
duous " trees, whose term of life is far more brief.
    Thus, the final cause or purpose of the Avhole Vital Activ-
ity of the  Plant, so far as the  individual is concerned, is to
produce an  indefinite extension of the dense, Avoody, almost
inert, but permanent portions of the fabric, by the successional
development, decay, and renewal of the soft, active, and tran-
sitory ceUular parenchyma;  and according to the principles
already stated,  the descent of a portion of the materials of the
latter to the  condition of  binary compounds, which is  mani-
fested  in  the largely-increased  exhalation  of  carbonic acid
that takes  place from the leaves in the later part of the sea-
son, comes to the aid  of external Heat in supplying the force
by which  another  portion of those materials is raised to the
condition  of organized tissue.  The  vital activity  of the
Plant,  however, is further manifested in the provision made
for the propagation  of its  race,  by the  production  of the
germs  of new individuals ; and here, again, we observe that
whilst  a higher temperature is usuaUy required for the  devel-
opment of the  flower, and the maturation  of the  seed, than
that Avhich suffices to sustain the ordinary processes of vege-
tation, a special provision appears to be  made in some in-
stances for the evolution of force in the  sexual  apparatus it-
self, by the retrograde metamorphosis  of a portion of the or-
ganic  compounds  prepared by the previous nutritive  opera-
tions.   This seems the nearest approach presented in the
Vegetable  organism,  to what we shaU find to be an ordinary
mode  of activity in the Animal.   That the performance of
the generative  act involves  an extraordinary expenditure of
vital force  appears from  this remarkable  fact, that blossoms
which Avither and die as soon as the ovules have  been fertil-
ized, may be kept fresh for  a  long period if fertilization be
prevented. 
            RECONVERSION OF ORGANIC  FORCES.       419

   The  decay which is continually going on during the life
of a Plant restores to the inorganic world, in the form of car
bonic acid, Avater, and ammonia, a part of the materials draAvn
from it in the act of vegetation ; and a reservation being made
of those vegetable  products which are consumed as food  by
Animals, or which are preserved  (like timber, flax, cotton,
&c) in a state  of  permanence, the various forms of decom-
position which take place  after death complete that restora-
tion.  But in returning, however slowly, to the condition of
water,  carbonic acid,  ammonia,  &c, the constituents  of
Plants give forth an amount of heat  equivalent to that AAliich
they would generate by the process of ordinary combustion;
and  thus they restore to the inorganic world, not only the ma-
terials, but  the forces, at the expense of Avhich the vegetable
fabric was constructed.  It is for the most  part only in the
humblest Plants, and in a particular phase of their lives, that
such a restoration takes place in  the form of motion, this mo-
tion  being, like growth and development,  an  expression of the
vital activity of the  "Zoospores"  of Algoe,  and being ob-
viously intended for their dispersion.
   Hence we seem justified in affirming that the  Correlation
between heat and  the  organizing force of Plants is  not less
intimate than that which  exists between heat  and motion.
The  special  attribute of the vegetable germ is its power  of
utilizing, after its own particular fashion, the heat which it
receives, and  of applying  it as a  constructive power to the
building-up of its fabric after its characteristic  type. 
420  CORRELATION OF PHYSICAL AND VITAL  FORCES.
II—RELATIONS OF LIGHT AND HEAT TO THE VITAL FORCES
                       OF ANIMALS.

    Those of our readers who accompanied us through  the
first part of our  inquiry are aware  that it was our  object to
show, that as force is never lost in the inorganic Avorld, so
force is never created in the organic; but that those various
operations of vegetable  life Avhich  are sometimes Araguely
attributed to  the  agency of an occult "\ital principle," and
are referred  by more exact thinkers to certain Vital Forces
inherent in the organism  of the plant, are really sustained by
solar light and  heat.  These, we  have  argued, supply  to
each germ the whole power by which  it buUds itself up, at the
expense  of the materials it draws from  the Inorganic Uni-
verse, into the complete organism; Avhile the mode in Avhich
that power is exerted (generally as vital force,  specially  as
the determining cause of the form peculiar to each type)  de-
pends upon the "germinal capacity" or directive agency inher-
ent in each particular  germ.   The first stage in this construc-
tive operation consists in the production  of certain organic
compounds of a purely chemical nature—such as gum, starch,
sugar, chlorophyU, oil, and  albumen—at  the expense of the
oxygen,  hydrogen, carbon,  and nitrogen derived from the
Avater, carbonic  acid, and ammonia of  the atmosphere;
Avhilst the second  consists in the further elevation of a portion
*>f these  organic  compounds to the rank of organized tissue
possessing attributes distinctively vital.   Of the whole amount
of organic compounds generated  by the plant,  it is but a
comparatively smaU part (a) that  undergoes this progressive
metamorphosis into living tissue.   Another  smaU  proportion
(b) undergoes a retrograde metamorphosis, by which the orig-
inal binary components are reproduced; and in this  descent
of organic compounds to the loAver plane, the poAver con- 
GRADES OF ORGANIC ASCENT.
423
Burned in their elevation is given forth in the form  of heat
and organizing force  (as is specially seen in germination),
Avhich help to raise the portion a to a higher level.   But by
far the larger  part (c) of the organic  compounds generated
by plants remains  stored up in their fabric, Avithout undergo-
ing any further elevation;  and it is at the expense of these,
rather than  of the  actual tissues  of plants, that the life of
animals is sustained.
    When, instead of yielding up any portion of its substance
for the sustenance of animals, the  entire vegetable organism
undergoes retrograde  metamorphosis, it not only gives back
to the inorganic world the binary compounds from Avhich it
derived its own constituents, but in the descent of the  several
components of  its fabric to that simple condition—whether by
ordinary combustion (as in the burning of coal) or  by slow
decay—it gives out the equivalents of the light and heat by
which they were elevated in the first instance.
    In applying these  views to the  interpretation of the phe
nomena  of  animal life, we  find ourselves, at  the commence-
ment of our inquiry, on a higher platform (so to speak) than
that from Avhich we had to ascend  in Avatching the construe-
tiATe  processes of the plant.   For,  Avhilst the plant had first
to prepare the  pabulum for  its deAelopmental  operations, the
animal has this already provided for it, not only at the ear-
liest phase  of its  development, but during the whole period
of its existence; and  aU its  manifestations of vital activity
are dependent  upon a constant and adequate supply of the
same pabulum.   The first of these manifestations is, as in the
plant, the building-up  of the organism by the appropriation
of material supphed from external sources  under the directive
agency of the germ.   The ovum of the animal, like the seed
of the plant, contains  a store of appropriate nutriment pre-
viously elaborated by  the parent;  and  this store suffices for •
the development of the embryo, up to the  period at which  it
can obtain and digest  ahmentary materials for itself.  That 
 422  CORRELATION OF PHYSICAL AND VITAL FORCES.

period occurs, in the different tribes of animals, at very dis-
similar stages of the entire developmental  process.  In many
of the loAver classes, the  embryo  comes forth from the egg,
and  commences  its independent  existence,  in  a  condition
which, as compared with the adult form, would be  as  if a
human embryo were to be thrown upon the world to obtain
its own subsistence only a law Aveeks after  conception ; and its
whole subsequent groAvth and development takes place at the
expense of the nutriment which it ingests for itself.
   We have examples of this in  the class of insects, many of
which come forth from the egg in the state of extremely simple
and minute  worms, having scarcely any power of movement,
but an extraordinary voracity.   The eggs  having been depos-
ited in situations fitted to afford an ample supply of appropriate
nutriment (those  of  the flesh-fly, for example, being  laid in
carcases, and those of the  cabbage-butterfly upon a cabbage-
leaf), each larva on its emersion is as weU provided with ah-
mentary material as if it had been furnished with a large sup-
plemental yolk of its own ; and by avaUing  itself of this, it
speedily  grows to many  hundred or  even  many  thousand
times its original size, Avithout making any considerable ad-
vance in  development.  But having thus laid up in its tissues a
large additional store of material, it passes into a state which,
so far as the external manifestations  of  life are concerned,
is one of torpor, but Avhich  is reaUy  one of great develop-
mental activity : for it is during the pupa state that those new
parts are evolved, which  are  characteristic of the perfect in-
sect, and of which  scarcely a trace was discoverable in the
larva ; so that the assumption of this state may be likened in
many respects to a re entrance  of the  larva into the ovum.
On  its termination, the imago or  perfect insect comes forth
complete in  all its parts, and  soon manifests the locomotive
and  sensorial powers by which  it is  speciaUy distinguished,
and of which the extraordinary predominance seems to jus-
tify our regarding insects as the types of  purely animal  life. 
DEVELOPMENT OF INSECTS.
423
There are some insects whose imago-life has but a very short
duration, the performance of the generative act being appar
ently the only object of this state of their existence : and such
for the most part take no food whatever after their final emer-
sion, their vital activity being maintained, for the short period
it endures,  by the material  assimUated  during their larva
state.*  But those whose period of activity is prolonged, and
upon  whose  energy there  are  extraordinary demands, are
scarcely less voracious in  their imago  than  in their larva-
condition ;  the food  they consume  not being applied to the
increase of their bodies, AA'hich  grow very little after the as-
sumption of the imago-state, but chiefly to their maintenance ;
no inconsiderable portion  of it, hoAvever, being appropriated
in  the female to the production of OAra, the  entire mass of
which deposited by a single individual is sometimes enormous.
That  the performance of  the  generative  act  involves not
merely a consumption of material, but a special  expenditure
of force, appears from a  fact to be presently stated,  corre-
sponding to that already noticed in regard to plants.
    Noav if we look for the source of the  various forms of
vital  force—which  may  be distinguished as  constructive,
sensori-motor, and generative—that are manifested in the dif-
ferent stages of the  life of  an insect, we find  them to lie, on
the  one hand, in the heat with which the  organism is sup-
plied from external  sources,  and,  on  the other,  in the food
provided for it.   The  agency of heat, as the moving poAver
of the constructive operations, is even more distinctly shoAvn
in  the development of the larva within  the egg, and in the
.development of the imago within its pupa-case, than it is  in

    * It is not a little curious that in the  tribe of Rotifera, or Wheel-ani-
malcules, all  the males yet discovered are entirely destitute of digestive
apparatus, and are thus incapable of taking any food whatever; so that not
only the whole of their development within the egg, but the whole of their
active life after their emersion from it, is  carried on at the expense of the
Btore of yolk provided by the parent. 
421:  CORRELATION OF PHYSICAL  AND  VITAL FORCES.

the germinating  seed;  the  rate  of each of these processes
being  strictly regulated by the  temperature  to  which  the
organism is  subjected.   Thus  ova. which are ordinarily not
hatched untU the  leaves suitable for the food of their larvae
have been put forth, may be made, by artificial heat, to pro-
duce a brood in the winter ;  whUst,  on the other hand, if they
be kept at a low temperature, their  hatching may be retarded
almost  indefinitely without  the destruction  of their  vitahty.
The same is true of the pupa-state ; and it it remarkable that
during the latter part of that state, in Avhich the developmental
process goes on Avith extraordinary rapidity, there is  in cer-
tain insects  a special provision for  an elevation  of the tem-
perature of the embryo by  a process resembling incubation.
Whether, in addition to the  heat imparted from Avithout, there
is any addition of  force developed within (as in the germinat-
ing seed) by the return of a part of the  organic  constituents
of the food to the condition of binary compounds, cannot at
present be stated  with confidence:  the  probabihty is, how-
ever, that such a retrograde metamorphosis does take  place,
adequate evidence  of its occurrence during the incubation  of
the bird's egg being afforded  by the liberation  of carbonic
acid, which is there found to be an  essential  condition of the
developmental process.  During the larva-state there is very
little poAver of maintaining  an independent temperature,  so
that the sustenance of vital activity is stiU mainly  due  to
the heat supphed from without.   But in the active state of the
perfect  insect there is a production  of heat  quite comparable
to that of warm-blooded animals ;  and this is effected by the
retrograde metamorphosis of certain  organic constituents  of.
the food, of Avhich we find the expression in the exhalation of
carbonic acid and  water.  Thus the food of animals becomes
an internal source of heat, Avhich may render them independ-
ent of external temperature.
    Further,  a hke retrograde metamorphosis of  certain con-
stituents of the food is the  source  of that sensori-motor power 
VITAL  FORCES   OF INSECTS.
125
which is the peculiar characteristic of the animal  organism;
for on the one hand the demand for food,  on the  other the
amount  of metamorphosis  indicated by the  quantity of car-
bonic acid exhaled, bear a very close relation to the quantity
of that power Avhich is put forth.  This relation is peculiarly
manifest in insects, since their conditions of activity and re-
pose present a greater  contrast in their respective rates of
metamorphosis, than do  those of any other  animals.  Of the
exercise of generative force we have no similar measure ; but
that it is only a special modification of ordinary vital activity
appears from this circumstance, that the life of those insects
wliich ordinarily die very soon after sexual  congress and the
deposition of the ova, may be  considerably prolonged if the
sexes  be  kept apart so that  congress cannot take  place.
Moreover,  it has  been   shoAvn by recent inquiries into the
agamic reproduction of  insects and other animals, that the
process of generation  differs far  less from those reproductive
acts which  must be referred to the category of the  ordinary
nutritive processes, than had been previously supposed.
    Thus, then, we find  that in the animal  organism the de-
mand for food  has reference not merely to its use as a mate-
rial for the construction of the fabric; food  serves also as a
generator of force ;  and this force may be of various kinds—
heat and motor-poAver being the principal  but by no means
the only modes under which it manifests  itself.   We  shaU
now inquire what there  is peculiar in the sources of the vital
force which animates the organisms of the higher animals at
different stages of life.
    That the developmental force which occasions the evolu-
tion of the  germ  in the  higher vertebrata is really supphed
by the heat to  which the ovum is subjected,  may be regarded
as a  fact  estabhshed beyond all question.   In  frogs  and
other amphibia, which have no special  means of imparting a
high temperature to their eggs, the rate of development (Avhich
in the early stages can be readily determined with great exact- 
426  CORRELATION OF PHYSICAL AND  VITAL FORCES.

ness) is entirely governed  by the degree of warmth to which
the ovum  is subjected.   But in  serpents  there is a peculiar
proAision for supplying  heat; the female performing a kind
of incubation upon her eggs, and generating in her oavti body
a temperature much above that of the surrounding air.*  In
birds, the developmental process  can only be maintained by
the steady apphcation of external warmth, and this to  a de-
gree much higher than that which is needed in the case of
cold-blooded animals ; and we may notice two  results of this
application as very significant of the dynamical relation be-
tAveen  heat and  developmental  force—first, that  the period
required for the evolution of the germ into the mature embryo
is  nearly constant, each species  having  a  definite  period of
incubation—and  second, that the grade of development at-
tained by the embryo before its emersion is relatively much
higher than it is in cold-blooded vertebrata  generaUy; the
only instances in which any thing hke the same stage  is at-
tained without a special  incubation, being those in Avhich (as
in the turtle and  crocodUe) the  eggs are hatched  under the
influence of a high external temperature.   This higher devel-
opment is attained at the expense of a much greater consump-
tion of nutrient material; the store laid up in the " food yolk"
and " albumen" of the  bird's egg, being many times greater
in proportion to the size of the animal Avhich laid it, than that
contained  in the whole egg  of a frog or  a fish.    There is
eAidence in that hberation of carbonic acid which has  been
ascertained to go on in the egg (as in the  germinating seed)
during the whole of the developmental process, that the return
of a portion of the organic substances provided for the  suste-

   * In the Yiper the eggs  are usually retained  within the oviduct untL
they are hatched.  In the Python, which recently went through the process
of  incubation in the Zoological Gardens, the eggs were imbedded  in the
coils of the body; the temperature to which they were subjected (as ascer
tained by a thermometer placed in the midst of them) averaging 90° F.,
whilst that of the cage averaged 60° F. 
         DYNAMICS OF EMBRYONIC  DELELOPMENP.     427

nance of the embryo, to the  condition of simple binary com-
pounds, is an essential condition of the process ; and  since it
can scarcely be supposed  that the  object of this  metamor-
phosis can be to furnish heat (an ample supply of that force
being afforded by the body of the parent), it seems  not  un-
likely that  its purpose is to supply a force that concurs with
the heat received from Avithout in maintaining the process of
organization.
    The  development of the  embryo within the body, in  the
mammalia, imparts to it a steady temperature equivalent to
that of  the parent itself; and  in all save the implacental or-
ders of this  class,  that  development  is carried  stUl further
than in  birds, the new-born mammal being yet more com-
plete in all its parts, and its  size bearing a larger proportion
to that of its parent, than  even in birds.   It is doubtless ow-
ing in great part to the constancy of the temperature to AA'hich
the embryo is  subjected,  that its rate of development  (as
shoAvn by the fixed term  of utero-gestation) is  so uniform.
The supply of organizablc material here afforded by the OArum
itself  is  very  small,  and suffices  only for the very earliest
stage  of the constructive process; but a special provision is
very soon made for the nutrition of the embryo by materials
directly supplied by the  parent;  and the imbibition of these
takes the place,  during the Avhole  remainder of foetal life, of
the appropriation of the materials supplied in the bird's  egg
by the " food yolk" and " albumen."   To what extent a retro-
grade metamorphosis of  nutrient material takes place in  the
fcetal  mammal,  we have no precise  means  of determining;
since the products of that metamorphosis are probably for the
most part imparted (through the placental circulation) to the
blood of the mother, and  got rid of through  her  excretory
apparatus.   But sufficient evidence of such a metamorphosis
is  afforded by the presence of urea in the amniotic fluid and
of bihary matter in the intestines, to  make it probable that it
takes  place not less  actively (to  say the least) in the foetal 
 4:28  CORRELATION OF PHYSICAL  AND  VITAL FORCi:3.

 mammal than  it doe3 in the chick  in ovo.   Indeed, it is  im-
 possible to study the growth of any  of the higher organisms—
 which not merely consists in the formation of new parts, but
 also involves a A'ast  amount  of interstitial  change—Avithout
 perceiving that in the remodelling  Avhich is incessantly going
 en, the parts first formed must be removed to make  Avay for
 those which have to take their place.  And such removal can
 scarcely be accomphshed without a retrograde metamorphosis,
 which, as in the numerous cases already referred to, may be
 considered Avith great probabUity as setting free constructive
 force to be applied in the production of new tissue.
    If, noAV, Ave pass on  from the intra-uterine life  of  the
 mammalian organism to  that period of its existence which
 intervenes  between birth and maturity, we see that a tempo-
 rary provision  is made in the acts of lactation and  nursing
 for affording both food and Avarmth to the young creature,
 Avhich is at first incapable  of adequately providing itself with
 aliment, or of resisting external  cold without  fostering  aid.
And we notice  that the  offspring of man remains  longer  de-
pendent upon parental care than  that of  any other mammal,
in accordance with the higher grade  of development to be
ultimately  attained.   But when  the  period  of infancy  has
passed, the child,  adequately  supplied  with food, and pro-
tected by the clothing which  makes up for the deficiency of
other tegumentary covering, ought to be able to maintain its
own heat, save in an extremely  depressed temperature;  and
this it does by the metamorphosis of  organic substances, partly
derived from its own fabric,  and partly  supplied directly by
the food, into binary compounds.   During the whole period
of growth and  development, we find the  producing power at
its highest point; the circulation of blood being more rapid,
and  the amount of carbonic acid generated and throAvn  off
being much greater in proportion  to the bulk of the body,
than at any subsequent period of life.  We find, too, in tho
large amount of other excretions,  the evidence of a rapid 
            CONSTRUCTIVE FORCES OF ANDklALS.        429

metamorphosis of tissue ; and it can hardly be questioned (if
our  general doctrines be well founded) that the constructive
force that operates in the completion of the fabric wUl be de-
rived in part from the heat so largely generated by chemical
change, and in  part from the descent Avhich a portion of the
fabric itself is continuaUy making from the  higher  plane  of
organized  tissue to the loAver  plane  of dead  matter.  This
high measure  of vital activity can only be sustained by an
ample supply of food; which thus  supplies both material for
the  construction of the  organism, and the force  by whose
agency that construction is accomplished.
    How completely dependent the constructive process still is
upon heat, is shown by the phenomena of  reparation in  cold-
blooded animals ; since  not  only can  the  rate at Avhich they
take place be experimentally shown to bear a direct relation
to the temperature to Avhich  these animals are subjected, but
it has  been ascertained that  any extraordinary act of repara-
tion (such as the reproduction of a limb in the salamander)
wUl only be performed under the influence of  a temperature
much  higher than that required for  the maintenance of the
ordinary vital activity.  After the  maturity of the organism
has  been  attained, there  is no  longer any call for a larger
measure of constructive force than is required for the mainten-
ance of its integrity ; but there seems evidence that even then
the  required force has to be  supplied by a retrograde meta-
morphosis of a portion of the  constituents of the  food, over and
above  that which serves to generate  animal heat.  For it has
been experimentaUy found that, in the ordinary Ufe of an adult
mammal, the quantity of food necessary to keep the body in
its normal condition is nearly tAvice that which Avould be re-
quired to supply the " waste " of the organism, as measured
by the total amount of excreta  when  food is withheld; and
hence it seems almost certain that the descent of a portion of
the organic constituents of this food to the  lower level of sim-
ple  binary compounds  is a  necessary condition of the ele- 
 430   CORRELATION OF PHYSICAL  AND VITAL FORCED

 vation  of another  portion to the  state  of hving  organized
 tissue.
    The conditions  of animal existence, moreover, involve a
 constant expenditure of motor force through the instrumental-
 ity of the nervo-muscuhir apparatus ; and the exercise of the
 purely psychical poAvers, through the instrumentality of the
 brain, constitutes a further expenditure of forco, even Avhen
 no bodily exertion is  made as its result.   We have now to
 consider the  conditions  under which these forces  are devel-
 oped, and the sources from which they are derived.
    The doctrine at  present commonly received among physi-
 ologists upon these points  may be stated  as  follows :—The
functional  activity of the nervous and muscular apparatuses
involves, as its necessary condition, the disintegration of their
tissues; the  components of Avhich, uniting with  the oxygen
of the blood,  enter into neAV and simpler combinations, Avhich
are ultimately eliminated from the body by the excretory oper-
ations.   In  such a retrograde  metamorphosis of tissue, we
have two sources of the liberation of force :—first, its descent
from the condition of living, to that of dead matter, involving
a liberation of that force which Avas  originally concerned in
its  organization ;*—and second, the  further  descent of  its
complex organic components to  the  lower plane  of  simple
binary  compounds.   If we trace back these forces to their
proximate  source, Ave  find  both of them in the food at the

   * It was  by  Liebig ("Animal Chemistry," 1842) that the doctrine was
first distinctly promulgated which had been already more vaguely affirmed
by various Physiologists, that every production of motion by an Animal
involves a proportional disintegration of muscular substance.  But he seems
to have regarded the motor force produced as the expression only of the
 vital force by which the  tissue was previously animated ; and to have looked
jpon its disintegration by oxygenation as simply a consequence of its death.
The doctrine of the " Correlation of Forces " being at that time  undevel-
oped, he was not prepared to recognize a source of motor power in the ulte-
rior chemical changes which the substance of the muscle undergoes;  but
seems to have regarded them as only concerned hi the production of heat. 
             TEST OF  ANIMAL MOTOR FORCE.          431

expense  of which  the  animal organism is constructed; for
besides supplying the material of tho tissues, a portion of
that food (as already shown) becomes the source, in its retro-
grade  metamorphosis,  of the production of  the heat which
supplies  the constructiAre poAver, whilst another portion  may
afford, by a like descent, a yet more direct supply of organ-
izing force.  And thus Ave  find  in  the  action  of solar light
and heat upon plants—Avhereby they are enabled not merely
to extend themselves almost without limit, but  also to accu-
mulate in  their substance a store of organic compounds for
tho consumption of animals—the  ultimate source not only of
the materials required by animals for their  nutrition, but also
of the forces of various kinds which these exert.
    Recent investigations have rendered it doubtful, however,
Avhether  the doctrine that every exertion  of the functional
power of the nervo-muscular apparatus  involves the  disinte-
gration of a certain equivalent  amount  of tissue, really ex-
presses the Avhole truth.  It has been maintained, on the basis
of carefully-conducted experiments,  in the first place, that the
amount of work done by an animal  may be greater than can
be  accounted for by the ultimate metamorphosis of  the  azo-
tized constituents of its food, their  mechanical  equivalent
being estimated by the heat producible by the  combustion of
the carbon  and oxygen which they contain ;* and secondly,
that whilst there is not a constant relation (as affirmed by
Liebig) between the amount of motor force produced and the
amount  of disintegration of muscular tissue represented by
the appearance of urea in the urine, such a constant relation
does exist  between  the development of motor force  and the
increase  of carbonic  acid in the  expired air, as shows  that
betAveen  these  two phenomena there is a most intimate rela-

   * This view has been expressed to the author by two very high author-
ities. Prof. Uelmholtz and Prof. William Thomson,  independently of each
other, as an almost necessary inference from the data furnished by tha
experiments of Dr. Joule. 
 432   CORRELATION OF PHYSICAL AND VITAL FORCES.

 tionship.*   And the concurrence of these independent indica-
 tions seems to justify the inference that motor force may be
 developed, like  heat, by the  metamorphosis of constituents
 of food which are not converted into living tissue ;—an infer-
 ence which so fully harmonizes Avith the doctrine of the direct
 convertibility of these two forces, noAV estabhshed  as  one of
 the surest results of physical investigation, as to have in itself
 no  inherent improbability.  Of  the  conditions which deter-
 mine the generation of motor force, on the  one hand, from the
 disintegration of muscular tissue, on the other from the meta-
 morphosis  of the components of the food, nothing definite can
 at present be stated ;  but we seem to have a typical example
 of the former in the  parturient  action of the uterus, whose
 muscular  substance, built up for  this one  effort,  forthwith
 undergoes  a rapid retrograde metamorphosis;  Avhilst it  can
 scarcely be regarded as improbable that the constant activity
 of the  heart  and of the  respiratory  muscles, which gives
 them no opportunity of renovation by rest, is sustained not so
 much by the continual  renewal of  their substance  (of which
 renewal there is no histological  evidence whatever) as by a
 metamorphosis of matters external to  themselves, supplying
 a force which is manifested through their instrumentality.

   To sum up:  The life of  man, or  of  any of the higher
 animals, essentiaUy consists in  the manifestation  of forces
 of various  kinds, of Avhich the organism  is the instrument;
 and these  forces are  developed  by the retrograde  metamor-
phosis  of the organic  compounds generated by the  instru-
mentality of the plant,  whereby they ultimately return to the
simple binary forms (water,  carbonic  acid, and ammonia),
which  serve as the essential food of vegetables.   Of these
organic compounds, one portion (a)  is converted into the

   * On these last points reference is especially made to the recent experi-
ments of Dr.  Edward Smith. 
              SUMMARY OF  THE ARGUMENT.          433

substance of the Hving body, by a constructive force  which
(in so far as it is not supplied by the direct agency of external
heat) is developed by the retrograde metamorphosis of another
portion  (b) of the food.  And whilst the ultimate descent of
the first-named portion (a) to the simple condition from which
it was originaUy drawn, becomes one source of the peculiarly
animal  powers—the psychical and the motor—exerted by the
organism, another  source  of these may be found  in  a hke
metamorphosis of a further portion (c) of the  food which has
never been converted into living tissue.
    Thus, during the whole life of the animal, the  organism
is restoring to the world around both  the materials and the
forces which it draws from it; and after its death this resto-
ration is completed, as in  plants, by the final  decomposition
of its substance.   But there is this  marked  contrast between
the two kingdoms of  organic nature  in  their material and
dynamical relations to the  inorganic Avorld—that whilst the
vegetable is  constantly engaged (so to speak) in raising  its
component materials from a  lower plane to  the higher, by
means of the power Avhich it draws from  the  solar rays, the
animal, whilst raising one portion of these to a stiU higher
level by the descent of another portion to a lower, ultimately
lets  doAvn the whole  of what the  plant  had  raised;  in so
doing, however,  giving back  to the universe,  in  the form of
heat and motion, the equivalent of the light and heat which
the plant had taken from it.
19 
INDEX.
                   A

Air-£im, action of the, 219, 220.
Ancient method of inquiry, 317.
Ancients, philosophic aims of the, 13.
— their mode of explaining  phenomena,
    103.
Andrews. Dr., 135,162.
Animal force, derivation of, 423.
— heat, source of, 32-1.
— nutrition, 421.
— system, early conception of, 212.
Anomaly in expansion and contraction, 52.
Aphides, multiplication of, 411.
Aristotle, 817.
Astronomy, tendency of its progress, xi.
— difficulties of, 319.
— early development of, 320.
Atmosphere, limit of, 136.
— pressure of, 819.
Atomic theory, objections to, 164.
Atoms, question of existence of, li 17.
Authority, value of, 11.
Automatic machines, 211.
                   B

Bacon, Francis, philosophy of, 14.
Becquerel, M., 102,125.
Beclard, M., 175.
Bergmann on electrical effects, 35
Bessel, 241.
Brodie, Sir B., 175.
Buffon, 814.

                   C

Causation, Grove on, 15.
— secondary, 18.
Cause and effect, 251.
-------simultaneity of, 17.
Cause, nature of, 402.
Caoutchouc, anomaly of, 53.
Carbonic acid tho index of animal power,
    431.
Carnot, 224.
— on the transfer of heat, 70.
Carpenter, Dr., xxxi., xxxiv., 173.
— biographical notice of, 400.
Catalysis, 6,1G9.
Chemical action, what is it ? 153.
-----a cause of light, 162.
----produces  magnetism, 162.
-----the source of mechanical power, 397.
— affinity as a cause of motion, 152.
----a cause of heat, 159.
— force converted into electrical, 154.
Chemistry of plants, 395.
Clarke, Mr. Latimer, 129,181.
Clausius, Prof., xxviii., 10-1, 228.
Cohesive attraction, 171.
Cold regarded dynamically, 48.
Colding, Prof., 224.
Coleridge,  108.
Collision, effects of, 29.
Combustion, key to the phenomena of, C21,
Comets, Mayer on, 270.
Compression, heat resulting from, 32.
Conservation of force, importance  of the
    problem, 856.
Constancy or the sun's mass, 2S2.
Constructive action of plants, 417.
Cooling of the earth, 80.
Cordier, M., 307, 313.
Correlation of physical forces, meaning of
    the phrase, 3, 833.
---------the  problem to be solved, 1S9.
---------difficulties of the investigation,
    194.
Cosmogony, Grove on, SI.
Cotton factory as a distributor of forc>, 403.
                   D

Daguerre, M., 112.
Dalton, i;>7,15'J. 
INDEX.
i35
Darkness converted into light, 119.
Davy, Sir II., xxvii., 4,134, 245.
D:iv, variation in length of the, 303.
De Camlolle, 57.
IV<:iy restori-s heat to the universe, 411*.
De la" Kive, 57.
Dt-spritz, M., 76.
Democritus, 127.'
Descartes,  xi.
Desormcs, Clement, 75.
Development of the embryo; derivation
    of its force, 427.
Diathermancy, 278.
Differentiation  in  animal  development,
    4(.9.
Diminution of tho earth's volume, 303.
Discovery, conditions o(,  104.
Distinctions among  the forces imperfect,
    17*.
Dove, M.,  120.
Dufour, M., 06.
Dulong and lYtit, 189.
Dynamic function of the  germ, 412.
                   E

 Earth, age of, 245.
 — form of, 297.
 Earth's interior heat, 236, 300.
 -------proofs of, 3u2.
 —----reasonableness of, 803.
 Effect of electrical discharge upon gases,
    93.
 Electrical Induction, 84.
 Electricity, limitation of the term, 85.
 — from caoutchouc, 35.
 — the link among the other forces, 37.
 — as initiating other  forces, H'J.
 — what is it? 83.
 — produces chemical decomposition,  8 t.
 — atmospheric, 87.
 — intensity of, 69.
 — effect upon the terminals, 90.
 — molecular changes of conductors, 95.
 — hypothesis of a fluid  unnecessary, 98,
    lol.
 — animal, 99.
 — in what it consists, 101.
 — initiates motion, 104.
 — and heat, 106.
 — and light, 107.
 — produced by blowpipe flame, 155.
 Electro-chemical equivalence, 394.
 ----equivalents of power,  373.
 Electro-magnetic equivalence, 893.
 Emotions, correlations of, xxxiv.
 Ethereal medium, 128, 242, 271, 847.
 ----objections to, 183.
 Equivalent, meaning  applied to the term,
    829.
 Ericsson, Mr., 73.
 Eruian on friction of homogeneous  sub-
    stances, 83.
Essences, the search for, 14.
Euler, Leonard,  123.
Events can never be repeated, 193
Expansion, inequality of, 54.
I                    F
i  Falling bodies, highest velocity of, 337.
I----phenomena of, 318.
  — force, 253, 343.
  Faraday, Dr.,  discoveries of,  6, 85, 144,
      145.
  — biographical notice of,  353.
  Favre, M., 371.
  Faye's theory of comets, 41.
  Flower figures in ice, u(\
  Fizeau, M., 129.
  Forbes, Jas. D., xix.
  Force, indestructibility of, xii.
  — use of the doctrine, xiii.
  — importance of new views of, xxx.
  — Grove's definition of,  19.
  — imparted to machines, 218.
  — what is it ?  251.
  — definition of, 335.
  — meaning of the term, 830, 379.
  — living and dead, 333.
  — animal, derived from decomposition ot
      food, 432.
  Foucault, M., 129.
  Fourier, M., 809.
  Franklin, Dr„ xvii.
  Fresnel on heat repellancy, 41.
  Friction, definition of, 30.
  — producing electricity, 33.
  — of homogeneous substances, 83.
  — heat of, 3a9.


                    G
  Gassiot, Mr., 59,135.
  Gay Lussac, M., 107.
  Germ-force, 411.
  Germination, dynamics of, 413.
  Generative force in insects, 425.
  Gravity implies  a plenum, 86S.
  — in relation to  other forces, 170, 253.
  — is it a force ? 839,  340, 341.
  —> but half understood, 366.
  — relation to conservation of force, 363.
  Grove, aim of his essay,  19.
  — biographical notice of, 2.
  — claims of, 5.
  — electrical images on glass, 86.
  — discoveries  on the relations of heat to
      the gases of water, 05.
  Grotthus, 103.
  Growth in the mammalia, 423.
  Guillemin, M., 151.
                   H

Heat, material hypothesis  of, annihilated
    by Kumford, xxiii., xxiv.
— definition of, 39.
— dvnamical effects of, 40.
— latent, 41, 848.
— influence of structure over tho  con-
    dition of, 57.
— produces the various forces, 57.
— reflection of, 61.
— converted into light, 63. 
430
INDEX.
Heat {continued).
— chemical and magnetic influence of, 64.
— as producing motive-power, 0^.
— practical application of, 77.
— produced by  chemical  combination,
    cause of, 161.
— definition of, 226.
— force only available in the ccoling pro-
    cess, 228.
— universal law of, 261.
— sources of, 261.
— solar, its chemical origin, 266.
— developed by friction, 277.
— upon high mountains, 282.
— lost by volcanoes, 810.
— lost by the ocean, 311.
— and motion,  convertibility of, 323.
— and work, 326.
— converted into organizing force, 412.
Helmholtz, 175.
— biographical notice of, 210.
— claims  of, 224.
Henry, Prof., xxviii., 290.
Herschel,  Sir John, 119, 264.
Herschel,  Sir W., 118, 136.
— his hypothesis of the sun's action, 260.
Hipparchus, 243.
History of scientific discovery, xv.
Holtzmann, 351.
Horner, M., 812.
Hume on  causation, 16.
Huxley, Prof., 411.
Hydraulic ram, 4.


                   I
Indestructibility of matter, xii.
Inertia, relation to forces, 369.
Intellectual and physical forces, xxxv.
Intensity  of the sun's heat, 270.
Interaction of natural forces, 211.
Insects, development of, 422.
                   J

Joule, Dr. J. P., xxiv., 3, 33,151, 224, 312.
                   K
Kant, 23.
Karsten, 85.
Kirchoff's researches, 62.
Knoblauch, M., 56,118.
Knowledge, slow growth of, 12.
                   L

Laplace, 231, 242, 243, 291.
Latent heat, 41, 348.
Lavoisier, xii.
Leconte, Prof., xxviii.
Liebig, vi., 174,175, 238, 430.
— biographical notice of, 3S6.
Light, polarization of, 110.
— chemical action of, 111.
— affects all forms of matter, 115.
  Light (continued).
  — produces the other forces, 116.
  — influence of the recipient surface upon,
     120.
  — and sound, analogies of, 126.
  — and molecular changes, 180.
  — a motion of ordinary matter, 133.
  — its loss or absorption, 189.
  — function of, in organization, 415.
  Life of the higher animals, in what  it con
     sists, 432.
  Living force, 218.
  Littrow, 271.

                    M

  Machines compared with the  living sys-
     tem, 79.
  — driving force of, 214, 387.
  Muggi, Dr., 148.
  Magnetism  a directive force, 142.
  — influence of, upon light and heat, 145.
  — as an initiating force, 147.
  — static and dynamic, 149.
  Magneto-electric machines, 222.
  Marrion, Mr., 151.
  Masson, M., 135.
  Mathematics, function of, in  investigation,
     877.
  Matter, ultimate  structure  of may never
     be known, 1S7.
  Matteucci, 79, 84, 97,151,172,175.
  Mayer, Dr., 3.
  — Tyndall's estimate of, xxx.
  — biographical sketch of, 250.
  — physiological  commencement  of  hie
     inquiries, 324.
  — secures  his  discovery  against  rival
     claimants, 224.
 — various references  to,  xxix., 241, 327,
     850, 3S9, 465.
  Measure of the sun's heat, 264.
  Mechanical  problem, the modern, 212.
 — force and heat, 262.
 — origin of solar heat, 276.
 — equivalent of heat, 816; 391.
 ---------applications of, 353.
 Melloni, researches of, 59.
  Mental and  vital forces, xxxii.
  Metamorphosis retrograde in animals, 421.
  Meteorites,  270.
 — heat generated by, 234.
  Metaphysics in science, 360.
  Modern science, alleged materializing ten-
     dency of,  xi.
  Molecules, how the term is  employed by
     Grove,  39.
  Moon, effect of collision  with  the  earth.
     804.                               ^
  Mongolfier,  M., 4.
 Moral forces, correlation of, xxxvii.
  Morgan, Mr., 135.
  Morfchini, 117.
  Mossoti, 171.
  Motion, as an affection of matter, 25.
 — never destroyed, 21.
I — produces heat, 23.
\  — produces various forces, 87. 
EtfDEX.
437
Motion (continued).
— asi affection of matter, 186.
— vast effocts of, 217.
Mountain tops, heat of, 2S2.


                   N

Nebular hypothesis, 230.
Nerve-power, source of, 430.
New views, public acceptance of, 9.
New doctrine of forces, how  far accepted,
    xiv.
Newton, xiii., xviii., 241, 276, 232,368, 378.
— speculations on light, 137.
Niepce de St. Victor, M., 125.
Numbers the highest aim of investigation,
    320.
0
Oersted's discoveries, 5.
Optic axis of crystals, 171.
Organic beings, source of  their motions,
    237.
— kingdoms of nature, relations to each
    other, 433.
— co-ordination, 410.
— correlations, Grove on, 172.
Organization, distinction between high and
    low grades of, 408.
Origin of the sun's heat, 276.
Origin of terrestrial power, 236,340.
Page, Mr., 151.
Particles, in what sense tho term is used
    by Grove, 89.
Pasteur, M., 132.
Peltier, M., 96.
Perpetual motion, 191,  192, 212, 219, 221,
    223, 338.
Persistence of force, xxxix.
Photography, chemistry of, 111.
Physical science of the  present dislin-
    guished from that of the past, 402.
Planetary atmospheres, 137.
— motions, 267.
— system, structure of, 230.
Planets, temperatures of, 121.
Plants, chemistry of, 420.
Plenum, a universal, 134.
Plucker, 171.
Plurality of worlds, 122.
Poisson, M., 81.
Pouillet, M., 244, 264, 280.
Powell, Baden, on Newton's rings, 41.
Practical arts after the middle ages, 211.
Ptolemaic system, 11.


                   Q
Qualities of matter,'transference of, 15.
Rankinc, Mr., xxviii.
Regnault, M., 225.
Respiration in cold-blooded animals, 429.
Roget, Dr., 4.
Rotation of the  earth, diminution of the,
    299.
Royal Institution, foundation of the, xxx.
Rule for the  investigation of  nature, 316,
    318.
Rumford, Count, 4.
— summary of his claims, xv,
— sketch of, xvii.
— researches of, xx., 347.
R
Seebeck, Dr., 113.
Seguin, M., 4, 76.
Sensations of heat disturb the judgment,
    49.
Sensations, misleading, 174.
Science, tendency of,  toward immaterial-
    ism'xii.
— the great event in the general progress
    of, xvi.
— the true £-<',■>;>" *f, xxxi.
— discovery of its fundamental principle,
    316.
Simultaneous discovery, examples of, xv.
Social forces, correlation of, xxxvi.
Solar radiation, effects of, 236.
----origin of organic power, 240.
— heat, amount of, 243, 264.
— spots, 286.
— atmosphere, 2S8.
— radiation, dynamical effects of, 403,404.
Sondhauss, Mr., 120.
Sound and light, 259.
Specific heat, dynamic view of, 53.
Spectrum, analysis of, 62.
Spencer,  Herbert, on the persistence ol
    force, xxxix.
Steam engine, action of, 220.
Stephenson, George, 115.
Stewart, Balfour, 61.
Store of force in the universe, 282.
-------in the planetary system at present,
    234.
Structure  of bodies  as  affecting  heat-
    motion, 55.
Sun, cooling of, 265.
Talbet, Mr., 112.
Tension, a static force, 22.
Theories, immature, 110.
— new, how they are to be judged, 196.
— the test of, 276.
Theorizing,  what is it ?  193.
Thermography, 58.
Thilorier's experiment on carbonic acid, 48.
Thompson, Prof., 52, 227, 229.
Tidal wave, 241, 291.
Time as an  element of dynamic changes,
    860.
— an element  in  the  sequence  of phe-
    nomena, 17.
— necessity cf its early measurement, 320. 
438
INDEX.
Torricelli, 103.
Transmutation of force chemically illus-
    trated, 372.
Tyndall, xxx., 57.
                   TJ

U nits of heat pro iuccd in combustion, 261.
                   V

Vacuum, not yet obtained, 184.
Vital and physical forces, correlation of,
    xxxii.
— effects, crude explanations of, 401.
— activity, characteristics of, 407.
----of plants, purpose of, 418.
— principle, 402, 420.
Vis viva, 218, 263.
Volcanoes, loss of heat by, 810.
Volta, 153.
Voltaic arc, cause of light of, 88
                   W

Wartinann, Mr., 146.
Water,  expansion of,  as it approaches
    freezing, 50.
Water-power, force produced by, 215.
Watt, James, 75.
Wortheim, 96, 150.
Whewell, Dr., xxvi., 13G.
Wollaston, Dr., 136.
Wilson, Dr., 136.
Words, misguiding influence of, 94.
— their social import, 180.
Work performed by chemical force, 228.
Wood, Dr., 54,100.
                   T

Toung, Dr.  Thomas, xxvil., 124,125,12i
    129,133.

                   Z

Zodiacal light, 272.
THE END 
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lustration, the Class-Book is unsurpassed.—A. T. Teaclur.
   Prof. Youmans possesses a  rare faculty for bringing the  intricacies of science right
within the comprehension of the masses of readers, and his book presents all the in-
terest of a novel.—Boston Post.
   The most recondite topics are placed in a transparent light before the common mind,
the language is eminently choice and attractive, not an unwieldy paragraph, scarcely a
superfluous word can be found from the beginning to the end of tho work, and, in spite
of the extreme economy of expression, there is no apparent constraint or formality, but
every page  flows smoothly and gracefully along, presenting a rare model of lucid and
agreeable didactic statement—N. Y. Tribune.
   The chapters on the Mutual  Relations of the Forces, and on the Dynamics of Vege-
table  Growth, are  alone worth the price of the volume.—B. F. Zeggett, Prof. Hat.
Science, Whitewater College, Ind.
   The present  volume exhibits plentiful  traits of what we believe we have beforfl
called Prof.  Youmans' educational genius.—Metliodist Quarterly Review.
   Unrivalled as a practical treatise.  Its introduction on the "Origin and Nature of
Scientific Knowledge " should be read by every teacher.—Mass. Teacher.
   One of its peculiar merits is that it can all be taught.—Prof. Phelps, A7". J. Kor-
mal School.
   Clear, accurate, recent, and imbued with  the enthusiasm of its author.—Ii. M. Man-
ley, Pros. If. II. Fern. College.
   It is eminently terse and compact, is  amply and  lucidly illustrated, and few cf our
many class-books that have crossed the ocean and been welcomed in Europe, are calcu-
lated to do us more credit than  this admirable work,—N. T. Independent.
   A thorough  perusal of the book enables us to pronounce it the best elementary
chemistry that has been written in our language.  It is penetfcatcd by a fearless yet dis-
ciplined scientific spirit, and is completely up to the  level of the latest discoveries in
the science of which it treats.  We nave read it with all the interest usually given to
romance.—Neno Nation.
   This manual  is distinguished from most other Class-books in setting almost wholly
BSldo what is merely technical and experimental, for the sake of the completest possible
exhibition of the principles of the subject.   For the thorough student, and even for the
general reader, a careful, lucid, and connected exposition of the new views was needed.
such as we are glad to acknowledge in the  present volume.   The author has given an
Intellectual value to his treatise very much abovi?  the standwd aimed  at in similar
Torts.—Christian Examiner. 
D.  APPLETON  &  CO. S  PUBLICATIONS.
Chemical  Atlas  :

     Or  the Chemistry of Familiar Objects.  Exhibiting the General Princi-
       '  pies of the Science in a Series of Beautifully Colored Diagrams,
         and  accompanied by Explanatory Essays,  embracing the  latest
         views of the subject illustrated.  Designed for the use of Students
         in all Schools  where  Chemistry is  taught.   By EDWARD  L,
         YOUMANS.  Large Quarto,  105 pages.


   The Atlas is a reproduction (in book form), and a continuation of the

mode of exhibiting  chemical facts and phenomena adopted in the author's

" Chemical Chart."  The application of the diagrams is here much extended,

occupying thirteen plates,  printed  in  sixteen  colors, and accompanied  by

100  quarto  pages of beautifully printed  explanatory letter-press.  It is a

Chart in a portable  and convenient form, containing many of the  latest

views of the science which  are not found in the  text-books.  It is  designed

as an additional aid to teachers and pupils, to be used in connection with

the author's "Class-Book," or as a review, and  for individuals  who  are

studying alone.

   It is  intended to  accompany the  author's Class-Book of Chemistry, but

it may be employed  with convenience and advantage in connection with any

of the" school text-books on the subject.

                         From the Home Journal.
   "Hero we have science in pictures—Chemistry in diagrams—eye-dissections of all
the common forms of matter around us;  the chemical  composition and properties of
nil familiar objects illustrated to the most impressible of our senses by the aid of colors.
This is a beautiful book, and as useful as it is beautiful.  Mr. Youmans has hit upon a
happy method of simplifying and bringing out the profoundest abstractions of science,
so that they fall within the clear comprehension of children."

                      From the Utica Morning Herald.
   "An excellent idea, well  carried out.  The style is lucid and happy, the definitions
concise and clear, and the illustrations felicitous and appropriate."

                        From the Lawrence Sentinel.
   " We have devoted  some little time in looking over this Atlas, and comparing its
relative merits with similar treatises heretofore published, and feel bound to accord to
it the highest degree of approbation and favor."

                           From Life Illustrated.
   "' This method of using the eye in education, though not the royal road to knowlcd"o,
Is really the people's railroad—a means of saving both time and  labor.  This work°ia
worth for actual instruction in common schools far more than a set of apparatus, which
the teacher might not  be able to  use, while  every one  can teach from the Atlas.  Wa
pronounce it, without  exception, the best popular work on Chemistry in the English
linguage."
     •                  From the New  York Tribune.
   "Mr. Youmans is not a mere routine teacher of his favorite  science; he has hit
upon novel and effective methods for the illustration of its princij les.  In his writings,
us well as his lectures, he is distinguished for the comprehensive order of his state-
ments, his symmetrical arrangement of scientifio facts, and the happy manner in which
he addresses the intellect through the medium of ocular demonstration.  In this latst
respect, his method is both original and singularly ingenious." 
D.  APPLETON &  CO.'S PUBLICATIONS.
Chemical  Chart.
    By EDWARD  L. YOUMANS,  M. D.   On rollers, 5 feet by 6  in  sire
         New Edition.

    This  popular work accomplishes for the first time, for Chemistry, what
maps and charts  have for geography, geology, and astronomy, by presenting
a new and valuable mode of illustration.   Its plan is  to represent chemical
composition  to the eye by colored diagrams, so that numerous facts of pro-
portion,  structure, and relation, which are the most difficult in the  science,
are presented to the mind  through the medium of the eye, and may thus
be  easily acquired  and long retained.  The want of  such a chart has long
been felt by the thoughtful teacher, and no other scientific publication that
has ever emanated from the American press has  met with the universal
favor that has been  aocorded to this Chart.  In the language of  a distin-
guished  chemist, "Its appearance marks  an era  in the  progress of the
popularization of Chemistry."
    It illustrates  the nature of elements,  compounds, affinity,  definite and
multiple  proportions, acids,  bases, salts, the salt-radical  theory, double de-
composition, deoxidation, combustion and illumination, isomerism, com-
pound radicals, and  the  composition of the proximate  principles  of food.
It covers the whole field of Agricultural Chemistry, and is  invaluable as an
aid to public lecturers, to teachers in class-room recitation, and for reference
in the family.  The mode of using it is explained in the class-book.
          From the late Horacb Mann, President of Antioch College.
   " 1 think Mr. Youmans is entitled to great credit for the preparation of his Chart,
because its uso will not only facilitate acquisition, but, what  is of far greater import-
ance, will  increase the exactness and precision of tho otudent's elementary ideas."
  From Dr. John W. Draper, Professor of Chemistry in Vie University of N. Y.
   " Mr. Youmans' Chart seems to me well adapted to communicate to beginners a
knowledge of the definite combinations of chemical substances, and as a preliminary
to tho use of symbols, to aid them very much in the recollection of the examples it
contains.  It deserves to be introduced into the schools."
   "We cordially subscribe to the opinion of Professor Draper concerning tho vanw
lo beginners of Mr. Youmans' Chemical Chart.
   JonN  Torrey,  Prof, of Chemistry in the College of Physicians dk Surg. N. Y.
    Wm. H.  Ei.let, late Professor of Chemistry in Columbia College, S. C.
   James B. Rogers, Professor of Chemistry in. the University of Pennsylvania.""
    From Benjamin Silltman. LL.D. Professor of Chemistry in Yale College.
    I  have  hastily examined Mr. Youmans' new Chemical Diagrams or  Chart of
encmieal combinations by the union of the elements in atomic proportions.  The dosiga
appears to be an excellent one." 
D.  APPLETON &  VO.'S PUBLICATIONS.
The  Hand-Book  of Household  Science.

     A Topular Account of  Heat,  Light, Air, Aliment,  and  Cleansing, its
         their Scientific Principles  and  Domestic  Applications.   By E. L.
         YOUMANS, M.D.   12mo, Blustrated, 470 pages.
    Various books have been  prepared which  cross  the field of domestic

science at different points, but  this is the  first work that traverses and

occupies the whole ground.  Hardly a page can be opened to that does not

convey information interesting  and valuable to every person who dwells in a

house.  The work will be found not only of high practical utility,  but capti-

vating to the student, and unequalled in the interest of its recitations.

  From the Superintendent of Public Instruction in the State of Pennsylvania.
   "The daily and hourly importance of  the topics embraced in the work, their im-
perious claims upon public attention, and their intimate connection with  individual
and social welfare, together with the compendious arrangement and copious fulness of
information presented, and the cautious accuracy and precision of statement, make it a
publication of the highest practical value for both the household and the school.
                                    '• Very respectfully yours,
   liProf. Edward L. Youmans.                        HENRY C. HICKOK."

          From the Superintendent of Schools ofthe State of New York.
   "It embodies scientific information of the highest importance, arranged with much
care, and so clearly  stated that even  the ordinary mind can scarcely fail to grasp and
retain the truths it unfolds and illustrates. It would prove a most valuable  class-book
in our high schools,  and I am satisfied that an examination into its merits would result
in its general introduction into such institutions.   Very respectfully yours,
                      "H. 11. VAN DYCK, Superintendent Public Instruction."

                      From the Springfield Republican.
   " It is the work of a  man thoroughly scientific  and thorougly practical.  It is  no
extravagance to  say that a mastery of its contents will secure a better knowledge of
the applications  of  Chemistry, Physiology, and Natural Philosophy, to life and life's
concerns, than the combined treatises upon these subjects which are usually  found in
our school-rooms."

                        From tha Detroit Advertiser.
   "This is one of the most valuable and important books that has of late been issued
from the press.  It will  do more to elevate and connect the ordinary duties of  house-
hold life with the domain of science than any other work yet published.   It is so  ar-
ranged that the general reader and the man of science may refer to it with satisfaction:
but it is also a book which ought  by all  means to be introduced in our schools, and
which every  young woman who expects to be any thing more than a doll or parlor
»utomaton,"should study and become as familiar with as she is with her prayer-book.''

                 From the Philadelphia Saturday Courier.
   " Few persons realize—few persons begin to realize—the importance of  thoroughly
understanding the nature and effects of light, heat, air, and food;  yet the value- of such
knowledge can hardly be overstated.  Mr. Youmans' work is the clearest  and fullest
exposition of science in those relations that has yet appeared.  School committees and
persons directly interested in education, who have long been searching for a work of
this kind,  will rejoice to find the fruit of their quest in this manual.  It is a valuable
book, written for a valuable purpose: tho desire to  lift our ordinary domestic life inU
mo dignity of intelligence pervades it throughout, and tinctures it in the grain." 
 
 
 
 
 
 
 
V-f.