THE FALLACY 
OF THE 
PRESENT THEORYofSOUND 
MOTT. THE FALLACY 
OF THE 
PRESENT THEORY OF SOUND 
BY 
HENRY A. MOTT, Jr., Ph.D., E. M., etc. 
v« ' 
PROFESSOR OF CHEMISTRY AND PHYSICS IN THE NEW YORK MEDICAL 
COLLEGE AND HOSPITAL FOR WOMEN 
AUTHOR OF 
Ttie Chemist's Manual“ Was Man Created “ Adulteration of Milk", 
Testing the Value of Rifles by Firing under Water”; “The Laws 
of Nature “ The Air We Breathe, and Ventilationsetc. 
NEW YORK 
PRINTED FOR THE AUTHOR BY 
JOHN WILEY & SONS 
15 Astor Place 
1885 Copyright, 1885, 
By HENRY A. MOTT, Jr. 
M. H. GREEN, 
74 and 76 Beekman Street, 
NEWYORK. PREFACE. 
To attack a theory which has been upheld for 2500 
years, and which has been and is sustained by the greatest 
living scientists, is certainly a very bold undertaking. 
The nature of the undertaking should not, however, 
deter truth from asserting itself, or deter any scientific 
man, with sufficient individuality and independence, 
from exposing the fallacy of the same, if such fallacy 
can be shown to exist. 
The author therefore makes no apology for thus 
coming to the front and joining Dr. A. Wilford Hall in 
exposing the fallacy of the present theory of sound, 
for he believes that it is the duty of every man to do his 
own thinking and not allow others to think for him. 
The old saying, 
‘ ‘ The name is but the shadow, which we find 
Too often larger than the man behind,” 
is too true to be overlooked. Great names often carry with 
them too much authority, and it requires a well-balanced 
mind to properly attach the correct importance which in PREFACE. 
IV 
many cases such names deservedly merit. To accept, 
therefore, the present theory of sound as correct because 
it is sustained by “great names,” and because on the 
authority of such names it is pronounced correct, without 
exercising any individuality of thought to inquire into its 
merits or demerits, would be only to impede the progress 
in search of truth, and not only impair the value of 
scientific deductions, but at the same time limit the pro- 
gress of science. 
That the reader may feel satisfied that other scientific 
men besides those mentioned in the following pages 
have arrived at the same conclusions as the author, he 
deems it advisable to introduce here the opinions of some 
well-known scientists on Dr, Hall’s discovery. 
Opinion of Dr. H. H. Adams, President of Wesleyan 
University. 
“ I have examined the new theory of sound—or rather, 
as it seems to me, the complete overthrow of the undulatory 
theory. Other members of the faculty have come to the 
same conclusion as myself.” 
Opinion op Prof. J. L. Kephart, A.M., of San Joaquin 
College, Cal. (formerly of Western College, Iowa). 
“ I have no hesitation in admitting that, in my opinion, 
the undulatory theory of sound is hopelessly shattered.” PREFACE. 
V 
Opinion of Peof. Osboen, LL.D., of Madison 
Univeesity. 
“The part on sound I prize very highly—a new 
departure that must be permanent and lead to many 
modifications of old notions.” 
Opinion of Heney 0. Cox, A.M., Peofessoe of Physi- 
cal Sciences, Pickaed Institute, Chicago. 
“ The first division of the hook is given to a discussion 
of the wave-theory of sound; and so completely does he 
show the absurdity of that hypothesis that we feel 
mortified to reflect that for fifteen years we taught it as 
science,” 
Prof. Thomas Munnell, A.M., former President of 
Hiram College, Ohio, no longer believes in the current 
theory of sound, and thinks it will not be long before the 
scientific leaders of this century will abandon it also. 
Prof. J. W. Spangler, President of the American 
College, Concepcion, Chili, S. A., states that “ the wave- 
theory of sound has been demonstrated [by Dr. Hall] 
to be a pure fallacy.” 
Prof. Jacob Chapman, A.M., of Exeter, H. H., 
formerly Professor of Mathematics in Dartmouth College, 
and who held the same position for years in the Franklin PREFACE. 
and Marshall College, and who believed in and tanght 
the wave-theory of sound, has declared that he has 
abandoned that theory as entirely wrong, 
Charles H. Goddaed, 8.A., LL.B., Professor of 
Physical Sciences and Biology in Nebraska College, at 
Nebraska City, has abandoned the wave-theory of sound 
as false. 
Peof. J. W. Lowbee, M.A., Ph.D,, former President 
of Columbia College, Ky., writes that he has totally 
abandoned the wave or undulatory theory of sound. 
Peof. C. H. Kieacofe, A.M., President of Hartsville 
(Indiana) University, states: “We no longer teach the 
wave-theory of sound as science, but as a theory worthy 
of consideration only as an example of what may be 
palmed off on the world as true science.” 
It must be agreed that the opinions here presented 
against the wave-theory of sound cannot be ignored as 
unworthy of notice by the eminent scientific men as- 
sailed ; for such an array of careful thinkers as above 
{and numerous others could be mentioned) who have 
without reservation denounced the wave-theory of sound 
as fallacious must certainly be entitled to respect and 
consideration. 
If Prof. Helmholtz, Tyndall, Lord Raleigh, Sir 
William Thomson, in Europe, and Prof. Rood and 
Mayer, in this country, wish to retain the respect and PREFACE. 
confidence of thinking people, they will at once 
endeavor either to defend the theory of sound, or like 
men come boldly to the front and acknowledge that it is 
fallacious. I cannot conceive of an educated scientist, 
especially one who respects his name and values the 
opinion others may hold of his ability, integrity, and 
honor, who could under the present state of facts remain 
silent; especially if he has been a teacher of the theory 
which is now not only questioned but denounced as false 
by prominent scientific professors in our colleges and 
universities. 
Their silence, if such should prove to be the case, 
could only be attributed to defeat and cowardice. For 
no matter how well educated they may be, it must be 
acknowledged that other men are educated also, and that 
such men command the respect and confidence of think- 
ing people; their opinions are of value, however, only in 
proportion as their deductions are logical and consistent 
with facts; so that if they should err in denouncing the 
current theory of sound,—and if this was demonstrated 
by an acknowledged supporter of the theory,—such a 
man who should expose their false deductions would cer- 
tainly be respected, while a man who is unwilling to de- 
fend his assertions is not entitled either to respect or con- 
sideration. 
Author. PREFACE. 
N'OTE. 
The author would be greatly indebted to any reader 
of this book if he would kindly forward to him any pub- 
lished review or criticism of the same, whether in favor 
of or against it. Such courtesy will be promptly 
acknowledged. 
Author. 
61 Broadway, New York City, N. Y., U. S. A. LEOTUEE 
ON 
THE FALLACY OF THE PRESENT 
THEORY OF SOUND.* 
Ladies and Gentlemen : 
“The object of science is not to find out what we 
like or what we dislike ; the. object of science is truth.” 
Galileo has stated that the truth or falsity of an hypo- 
thesis must be judged by the weight of the facts and 
the force of mathematical deductions, and not by super- 
ficial appearances or the plea of authority based about 
what philosophers may have taught. This line of reason- 
ing clearly applies to the present theory of sound which 
I have the pleasure of directing your attention to this 
evening. Simply because the wave-theory of sound was 
* Lecture delivered before the New York Academy of Sciences, 
December 8, 1884. Held at Columbia College. 6 
THE FALLACY OF THE PRESENT THEORY OF SOUND. 
inaugurated by Pythagoras 2500 years ago, and has been 
sustained by Newton, Laplace, Helmholtz, Tyndall, 
Mayer, Rood, Blaserna, and a score of other distinguished 
scientists, is no reason why such theory should not be 
judged by “ the weight of facts and the force of mathe- 
matical deductions.” 
Too many theories which have had the indorsement 
of scientists have been exploded to permit of the accept- 
ance of anything in science on trust, or believing any- 
thing to be positively correct and true just because it is 
sanctioned by the indorsement of a long and immortal 
line of scientific names, especially if the subject has not 
received the most scrutinizing scientific examination from 
every possible standpoint. 
Theories in science are of great value to deduce explar 
nations for various unsolved problems; and when the 
correct theory is discovered which will explain and con- 
form with any particular problem under consideration in 
all its details, as known, then the theory ceases to be a 
theory and becomes a law. The assumption, however, 
of necessity must always exist, if the law be accepted as 
correct that we are either acquainted with all the details 
respecting the problem under consideration, or that if 
any new facts or details should afterwards turn up they 
would conform to the law. If they do not so conform, 
then the so-called law reverts back to the nature of a THE FALLACY OF THE PRESENT THEORY OF SOUND. 
7 
theory requiring either modification or complete anni- 
hilation. It is to the complete annihilation of the undu- 
latory theory of sound that your attention is directed. 
In 1877 Dr. A. Wilford Hall published a work on 
the Evolution of Sound, in which he carefully considered 
step by step the present undulatory theory of sound as 
elucidated by the distinguished authorities already 
referred to. It is needless for me to say that he has, not 
only in my opinion, hut also in the opinion of numerous 
scientific men, shown the fallacy of the present theory of 
sound, otherwise I would not he here this evening to 
present before a scientific body, in a lecture, the sum and 
substance of the numerous fallacies pointed out by him 
and other scientists besides myself who have carefully 
investigated the subject. 
To proceed properly it will be best for us to review 
with some care the present theory which has been so 
very generally accepted as correct, and which is at this 
moment being taught by all the schools and leading 
universities of the world, with the main object of cor- 
rectly enlightening students and searchers of truth as to 
how we hear or appreciate sound. But before I proceed 
I must respectfully ask your most critical and analytical 
attention to the present theory of sound, which I shall 
endeavor to conscientiously lay before you as it is 
expounded by such men as Tyndall, Helmholtz, Lord 8 
THE FALLACY OF THE PRESENT THEORY OF SOUND. 
Rayleigh, Mayer, Rood, Sir William Thomson, Blaserna, 
and other distinguished scientists and recognized authori- 
ties on acoustics, with the belief that you will see in the 
theory, independent of facts I shall give later on, suffi- 
cient impossibilities and contradictions to cause you 
to wonder why such a theory could be entertained at all. 
Professor Rood has defined sound as a sensation pro- 
duced when vibrations of a certain character are excited 
in the auditory apparatus of the ear, and states that these 
vibrations are generated by progressive tremors in the 
atmosphere, called sound-waves.* This definition, while 
setting forth briefly the present theory of sound, will not 
be sufficiently elaborate for us to-night, so I will there- 
fore enter into much fuller explanation, based, as I have 
already stated, upon the propounded facts of the various 
authorities on this subject. 
These authorities state that when a body capable of 
emitting a (musical) sound—a tuning-fork, for example 
—vibrates, it moulds the surrounding air into sonorous 
waves, each of which consists of a condensation and a 
rarefaction, and in the condensed portion the air is above, 
and in the rarefied portion is below, the average tem- 
perature, and this change of temperature produced by the 
passage of the sonorous wave itself virtually augments 
* Johnson’s Cyc.; Acoustics (0. N. Rood). THE FALLACY OF THE PRESENT THEORY OF SOUND. 
9 
the elasticity of the air and makes the velocity of sound 
about one sixth greater than it would be if there were no 
change of temperature.* But the average temperature 
of the air is unchanged by the waves of sound, as we can- 
not have a condensed pulse without having a rarefied one 
associated with it, and the temperature of the rarefaction 
is as much lowered as it is raised in the condensation; f 
so that from a vibrating body, such as the tuning-fork 
referred to at the end of a second from the time it com- 
menced its vibrations, the foremost wave would have 
reached a distance of 1095 feet in the air at 0° C. or 
1120 feet at 15° C. The prong of the vibrating fork in 
its swift advancement compresses the air immediately in 
front of it, causing the particles of air to crowd together, 
and when it retreats it leaves a partial vacuum behind it 
as the air-particles separate more widely,% the function 
of the fork being to carve the air into these condensa- 
tions and rarefactions,§ and they, as they are formed, 
propagate themselves in succession through the air. If 
a ball is urged against a number of balls placed in a 
groove, the motion thus imparted to the first ball is 
delivered up to the second; the motion of the second is 
delivered up to the third; the motion of the third is 
* Tyndall, Lectures on Sound (Ist ed.), pp. 29, 45, 46. 
t Tyndall, loc. cit. p. 39. 
§ Tyndall, loc. cit. p. 63. 
X Tyndall, loc. cit. p, 28. 10 
THE FALLACY OF THE PRESENT THEORY OF SOUND. 
imparted to the fourth: each ball after having given up 
its motion returning itself to rest, the last ball only of 
the four flies away. Thus is sound conveyed from parti- 
cle to particle through the air; the particles filling the 
cavity of the ear being finally driven against the tym- 
panic membrane, which is stretched across the passage 
leading to the brain, setting this membrane which 
closes the drum of the ear into vibration,* so that it 
bends once in and once out by each pulse.f In this 
transferrence of the vibrations of the air into the laby- 
rinth, it is to be observed that though the particles of 
the air themselves have a comparatively large amplitude 
of vibration, yet their density is so small that they have 
no great moment of inertia, and consequently when their 
motion is impeded by the drum-skin of the ear they are 
not capable of presenting much resistance to such an 
impediment or of exerting any sensible pressure against 
it 4 
But still Professor Tyndall says that if we hear one 
sound louder than another, it is because the ear is hit 
harder in the one case than in the other by the vibrating 
air-particle. § 
At this point it appears proper to describe briefly the 
* Tyndall, loc. cit. pp. 4, 5. 
X Sensations of Tone (Helmholtz), p. 199. 
§ Tyndall, loc. cit. p. 11. 
f Tyndall, loc. cit. pp. 49-60. THE FALLACY OF THE PRESENT THEORY OF SOUND. 
11 
formation of tlie ear as relates to the membrana tympani. 
This membrane separates the cavity of the tympanum 
from the bottom of the external meatus. It is a thin 
semi-transparent membrane, nearly oval in form, some- 
what broader above than below, and directed very 
obliquely downwards and inwards. Its circumference is 
contained in a groove at the inner end of the meatus, 
which skirts the circumference of this part except above. 
The handle of the malleus descends vertically between 
the inner and middle layers of this membrane, as far 
down as its centre, where it is firmly attached, drawing 
the membrane inwards, so that its outer surface is con- 
cave, its inner convex. 
“This membrane is composed of three layers, an 
external (cuticular), a middle (fibrous), and an internal 
(mucous.)” 
“ The fibrous layer consists of fibrous and elastic tis- 
sues. Some of the fibres radiate from near the centre to 
the circumference; others are arranged in the form of a 
dense circular ring round the attached margin of the 
membrane,” 
The tensor tympani draws the membrana tympani 
inwards, and thus heightens its tension. 
“ The laxator tympani draws the malleus outwards, 
and thus the membrana tympani, especially at its fore- 
part, is relaxed.” The stapedius muscle by inclining 12 
THE FALLACY OF THE PRESENT THEORY OF SOUND. 
the stapes backwards is supposed to compress the fluid 
contents of the vestibule. 
The tympanum is traversed by a chain of movable 
bones which connect the membrana tympani with the 
labyrinth, and serve to convey the vibrations communi- 
cated to the membrana tympani across the tympanum to 
the internal ear. The outer wall is formed by the mem- 
brana tympani, a small portion of bone being seen above 
and below this membrane. It presents three small aper- 
tures: the inter-chordse posterius, the Glaserian fissure, 
and the inter-chordae anterius. Through the first the 
chorda tympani nerve enters the tympanum; the aper- 
ture of the inter-chordae anterius being above the Glase- 
rian fissure, and through it the chorda tympani nerve 
leaves the tympanum.* 
It might here be stated that the membrana tympani 
is claimed to be capable of responding to an immense 
variety of waves or impulses. “A catholicity of the kind,” 
says Prof. Rood very truthfully, “ has not thus far been 
observed in experiments on membranes artificially 
stretched, whose range is found to be far more limited.”f 
The vibrations produced within the membrana tym- 
pani by the waves of sound are transmitted to the mem- 
* See Gray’s Anatomy, pp. 697-699. 
f Johnson’s Cyc.: Acoustics (Rood). THE FALLACY OF THE PRESENT THEORY OF SOUND. 
13 
branous covering of the fenestra ovalis by means of tbe 
cliain of bones within the cavity of the tympanum, and 
through secondary vibrations produced within this mem- 
brane the impulse is transmitted to the fluid of the 
vestibule. According to some authorities, the jarring of 
the otoliths against the filaments of the vestibular nerve 
affords, at this latter point, a perception of the intensity 
of the sound which is being appreciated by the ear.* 
The vibrations now travel along the fluids of the scala 
vestibuli of the cochlea and of the semicircular canals, 
thus passing in two different directions. 
The little sacs f contain, attached to their walls, small 
crystals of carbonate of lime in contact with the nerves ; 
and their function, as it appears, is to render us sensible 
of simple short sounds or shocks which probably would 
not affect the rest of the vibratory apparatus. They act 
as drags on the nerves when the latter vibrate with the 
Water in which they are bathed and thus produce sensa- 
tion. These sacs contain also, in connection with the 
nerves, certain microscopic hairs that are quite elastic and 
brittle, and probably capable of being set into vibration 
when the particular notes to which they are tuned are 
presented to them, just exactly as a tuning-fork can be 
* Darling and Ranney, Essentials of Anatomy, p. 596. 
f Rood, loc. cit. 14 
THE FALLACY OF THE PRESENT THEORY OF SOUND. 
set in vibration by the waves proceeding from a second 
fork of the same pitch. 
In the semicircular, canals, according to some observers, 
the direction from which the sound springs is perceived, 
while the vibrations carried along the scala vestibuli are 
transmitted to the filaments of the auditory nerve in the 
organ of Corti and those connected with the membrana 
basilaris, thus affording the perception of the note and 
the quality of the sound perceived. After reaching the 
apex of the cochlea the vibrations are transmitted from the 
scala vestibuli downwards along the tympani secundaria, 
which covers tho, fenestra rotunda, where the vibrations 
are lost; being no longer transmitted, on account of the 
absence of any conducting medium. The free entrance 
of air to the cavity of the tympanum, or the middle ear, 
affords an equal density of air upon either side of the 
membrana tympani, and thus insures a vibration of that 
membrane in absolute unison with the vibrations of the 
sound which it is called upon to record.* 
The function of the organ of Corti in the cochlea is 
described as follows : When the vibrations reach the end 
of the auditory nerve, some of the numerous rods or 
fibres of the Corti arches which bristle around the ap- 
pendages of this nerve will be strongly excited by such 
* Darling and Ranney, loc. cit. p. 596. THE EALLACY OE THE PRESENT THEORY OE SOUND. 
15 
vibrations as are in unison with them, and some will not; 
so that simple tones of different pitch will excite different 
fibres, showing that this wonderful organ discovered by 
Marchese Corti is a musical instrument, with its cords so 
stretched as to accept the vibrations of different periods 
and transmit them to the nerve-filaments which traverse 
the organ.* 
If the sound is a compound, or the form of the wave 
abnormal, this sound is, according to Helmholtz, analyzed 
into its constituents, since the cords (and rods) can only 
execute normal vibrations; and we see finally that the 
clang tint is the sensation produced by the simultaneous 
action of two or more of these strings upon their appro- 
priate nerve. The cochlea contains about 3000 of these 
strings, and if with Helmholtz we suppose that 200 of 
them are useful for rendering us sensible of tones not 
used in music, there will remain for the musical tones 
proper 2800 for the seven octaves, or 400 for each octave, 
33|- for each half-tone.f 
The final vibrations are sent along the auditory nerve 
to the brain, where they are translated into sound. 
The abnormal sounds perceived when the Eustachian 
tube is obstructed by swelling of the mucous lining 
during attacks of severe influenza are due, in great 
* Tyndall, loc. cit. p. 324. 
f Rood, loc. cit. 16 
THE FALLACY OF THE PRESENT THEORY OF SOUND. 
measure, to the impaired entrance and exit of air. It is 
customary for gunners when firing large cannon to stand 
with the mouth open, since by so doing the vibrations 
of the air produced by the explosion are transmitted 
through the Eustachian tube as well as through the 
auditory canal, and by neutralizing each other the drum 
membrane stands almost motionless, and little, if any, 
sound is perceived.* 
The motion of the sonorous wave, says Tyndall, must 
not be confounded with the motion of the particles which 
at any moment form the wave; for during its passage 
every particle concerned in its transmission makes only a 
small excursion to and fro, the length of the excursion 
being the amplitude of the vibration f on which the 
loudness or intensity of a note depends, as well as it de- 
pends on the difference of density between the condensa- 
tions and rarefactions. So that, if two forks were made to 
vibrate so that the condensations of the one will coincide 
with the condensations of the other, and the rarefactions 
of the one with the rarefactions of the other, thus sup- 
porting each other, a sound of greater intensity will be 
produced than that of either vibrating alone.;]: It is 
evident, however, that at each point in the mass of air at 
* Darling and Ranney, loc. cit. p. 596. 
\ Tyndall, loc. cit. p. 44. % Ty 
% Tyndall, loc. cit. p. 358. THE FALLACY OF THE PRESENT THEORY OF SOUND. 
17 
each instant of time there can be only one single degree 
of condensation, and that the particles of air can be mov- 
ing with only one determinate kind of motion, having 
only one single determinate amount of velocity, and 
passing in only one single determinate direction.* So that 
two different degrees of density produced by two differ- 
ent systems of waves cannot coexist in the same place at 
the same time; although the air is competent to accept 
and transmit the vibrations of a thousand instruments at 
the same time,f each particular sound passing through 
the air as if it alone were present $ the pitch of each 
note depending on the number of aerial waves which 
strike the air in a second. 
Tyndall states that when the tympanic membrane is 
shaken by the shock of a series of pulses at regular inter- 
vals, it cannot come instantly to rest.§ And Helmholtz 
states that an elastic body set into sympathetic vibration 
by any tone [whether in unison or not] vibrates sympa- 
thetically in the pitch or with the vibrational number of 
the exciting tone; but as soon as the exciting tone ceases, 
goes on sounding in the pitch or vibrational num- 
ber of its own proper tone.]] This in the face of the fact 
stated by him that membranes tuned to be in unison with 
* Helmholtz, loc. cit. p. 40. 
X Tyndall, loc. cit. p. 281. 
11 Helmholtz, loc. cit. p. 215. 
f Tyndall, loc. cit. p. 287. 
§ Tyndall, loc. cit. pp. 49, 69. 18 
THE FALLACY OF THE PRESENT THEORY OF SOUND. 
the combinational tones are set in sympathetic vibration 
immediately upon both generating tones being sounded 
simultaneously, but remain at rest if only one or other of 
them is sounded.* 
To close the consideration of this side of the undula- 
tory theory, I will add that Tyndall states that when we 
try to visualize the motions of the air having one thou- 
sand separate tones,—to present to the eye of the mind 
the battling of the pulses, direct and reverberated,—the 
imagination retires baffled at the attempt.*}* And he 
might have added, the shallowness and fallacy of the un- 
dulatory theory of sound was made apparent. He, how- 
ever, does express himself as follows: “Assuredly no 
question of science ever stood so much in need of revision 
as this of the transmission of sound through the atmos- 
phere. Slowly, but surely, we mastered the question, 
and the further we advanced the more plainly it appeared 
that our reputed knowledge regarding it was erroneous 
from beginning to end.”:}: 
How for the other side of the discussion, or to demon- 
strate what this paper calls for: The Fallacy of the Pres- 
ent Theory of Sound. 
To do this it will be advisable to divide the considera- 
* Helmholtz, loc. cit. p. 235. 
X Tyndall, loc. cit. p. 328, 329. 
f Tyndall, loc. cit. p. 257. the fallacy of the present theory of sound. 
19 
tion of this subject up into different heads. We will 
therefore consider (1) the Agitation of the Air; (2) 
Mobility of the Atmosphere', (3) Resonance', (4) Heat 
<vnd Velocity of the supposed Sound-waves; (5) Tuning- 
fork; (6) Decrease in Loudness of Sound; (T) The 
Dhysical Strength of the Locust; (8) Barometric Theory 
of Sir William Thomson; (9) Elasticity and Density of 
the Air; (10) Interference and Beats; and (11) The 
Mernbrana Tympani and the Corti Arches. 20 
THE FALLACY OF THE PRESENT THEORY OF SOUND. 
Agitation of the Air. 
The wave-theory of sound is inferred from the fact 
that when a body is excited by a blow or from any 
cause it is known that the body vibrates more or less, 
and is capable of inducing the vibration to a greater or 
less extent of any body with which it is in contact, and in 
fact will cause the vibration of bodies such as membranes, 
etc., which are in close proximity to it, provided the 
two bodies are connected by an elastic medium—such as 
air, for example. Thus far experiments are able to sus- 
tain this; and from these facts it is assumed that instead 
of the vibration (more strictly speaking, agitation) of the 
air having a very limited existence, not exceeding thirty 
feet even from the effect of blowing a steam-whistle, 
and which agitation does not travel more than five feet 
in a second, the vibrations or supposed air-waves are 
sent off and forth, so that a steam-siren can be heard for 
from twelve to fifteen miles by the final vibration of the 
membrana tympani by the action of these so-called 
waves. I fail to find recorded one experiment which 
shows the existence of vibrations, unless in the imme- 
diate vicinity of thier source, except, of course, the THE FALLACY OF THE PRESENT THEORY OF SOUND. 
21 
sympathetic vibration of bodies in perfect unison, or 
experiments conducted in tubes. If it were desirable to 
show the agitation of the air produced by a vibrating 
body, the numerous experiments and photographs made 
of the disturbances produced in the air by a body under 
such conditions would answer admirably; but that we 
have a right to assume because there are such vibrations 
or agitation near the source of the sound, that they 
extend beyond a certain limit and by condensations and 
rarefactions of the air produce air-waves which are 
propagated in some cases for fifty miles, and in other 
cases over one hundred miles, is too preposterous a pro- 
position to be entertained, as I propose presently to 
demonstrate. 
It is claimed that because a string of an instrument 
swings greatest when the tone is loudest, hence the loud- 
ness of a tone at a distance from the sounding body must 
necessarily depend on the amplitude of the oscillating air- 
waves, the supposed law being “that the intensity or 
loudness of a sound is proportional to the square of the 
amplitude of the sound-wave.” 
But unfortunately the oscillating air-waves or agita- 
tion of the air, instead of travelling as supposed 1120 feet 
a second, absolutely do not and cannot move away from 
fhe string a total distance of more than a dozen inches, as 
will be shown.  THE FALLACY OF THE PRESENT THEORY OF SOUND. 
The bugler may blow directly through his horn with- 
out producing tone, and exert all his lung-power and he 
cannot stir a sensitive gas-jet twelve feet distant; while 
the air-waves (agitation) he thus produces do not travel 
more than four feet a second, as determined by Dr. Hall. 
I have failed to cause a candle-flame to flicker when per- 
forming the same experiment fifteen inches from the 
flame. When the bugler adjusts his lips to the mouth- 
piece in such a manner as to cause the horn and its air- 
column to generate tone by the proper molecular vibra- 
tion, he manufactures and sends off the supposed air- 
waves with less than one fourth the lung-power he em- 
ployed before, which is supposed to set the entire atmos- 
phere into oscillation throughout 36 cubic miles, causing 
every particle of air to change its position from a 
state of rest into a “ small excursion to and fro.” And 
still if the instrument is placed within two inches of the 
candle-flame, I have found that the same will not be 
affected; and yet not one writer on sound seems to 
be able to see the difference between the sound of an 
explosion and its concussive shock, which would knock 
a man lifeless to the ground if standing near a maga- 
zine. 
The lowest tone of an organ is stated by Prof. 
Blaserna to have 16 vibrations to the second, and a 
consequent wave-length of 10 feet. It thus follows, says THE FALLACY OF THE PRESENT THEORY OF SOUND. 
23 
Dr. Hall,* that in the sound of such an organ-pipe the 
air-particles (as a whole) are obliged to travel 35 feet and 
back 16 times each second in order to pass from the space 
occupied by the centre of rarefaction to the centre of 
condensation and back. They would thus move with a 
velocity in one direction of 560 feet a second, or at the 
rate of 381 miles an hour, which would produce a tornado 
of more than double the velocity necessary to sweep a 
village into ruins! If there was the least truth in the 
wave-theory, the sound of a church-organ should get up 
a cyclone which would blow a cathedral into atoms! For 
the air, says Prof. Carter, must move with a given veloc- 
ity and exert a certain pressure, irrespective of the dis- 
tance through which the air-particles move—a fact no 
one can dispute. 
It would appear at least reasonable to inquire, If a 
given vibrating body can produce air-waves which can 
cause the membrana tympani to vibrate and thus produce 
sound, say, four hundred feet away from it, and that to 
avoid any possibility of failure of an experiment directed 
to the object of proving the existence of these so-called 
sound-waves, such experiments should be conducted at 
least beyond the known or possible sensitive action of the 
necessary agitation accompanying any disturbance of a 
* Problem of Human Life: chapter Evolution of Sound, p. 141.  THE FALLACY OE THE PRESENT THEORY OF SOUND. 
medium in which a body is in the act of vibrating, why 
are not the experiments conducted, say, one hundred feet 
away, using funnels to concentrate the air-waves ? 
The answer is simple : Because sound is not propagated 
by air-waves, and consequently there are no waves to 
concentrate. Why is it that no one has thought to attach 
to the tympanic membrane of the ear a bristle which 
can rest against a revolving cylinder covered with lamp- 
black, so that when a sound is made, say, fifty feet off, a 
register of the supposed vibrations of the membrane of 
the ear would be made in wave-lines on the cylinder, 
just as would result from speaking into a tube having a 
diaphragm at one end, with the bristle attachment placed 
against a blackened revolving cylinder within the dis- 
tance of thirty feet from a steam-whistle ? 
The fact is, there would be no wave-lines produced, 
because there would be no vibrations of the air at the 
distance of fifty feet from the source of sound, and the 
tympanic membrane would not vibrate: and this in the 
face of the fact that the sound of the human voice can 
be heard through the air of this locality ten times this 
distance, and 160 times the distance in the arctic regions 
over a sheet of ice, as attested to by Captain Parry on 
his return from his polar expedition. 
The experiment given by Prof. Tyndall to show how 
the waves of sound can cause a candle-flame to flicker 25 
THE FALLACY OF THE PRESENT THEORY OF SOUND. 
or be extinguished by clapping two books together in 
front of a long tube directed toward the flame is cer- 
tainly a most childish experiment; for if he had simply 
clapped the books together, with the backs of the same to 
the tube, the flame would not have even flickered and 
certainly not have been extinguished. It was the puffs 
of air, in the first instance, which caused the flickering 
and the extinguishing of the flame, and not the supposed 
sound-waves. But fearing that some one might think this 
was the case, he put in the end nearest the book a piece 
of paper liberating smoke, and because on clapping the 
book thq first time no smoke issued from the other end, 
he held that this was conclusive evidence that the 
flickering and extinguishing of the flame was due to 
sound-waves and not to puffs of air. Why did not Prof. 
Tyndall keep on rapidly clapping the books when they 
were facing the end of the tube? It was because he 
knew that the smoke would soon issue and destroy 
the experiment. There is one thing he took good care 
to do, and that was to put the smoking paper at the large 
end of the tube, where it would have a long distance to 
travel in order to get out, instead of putting it at the 
end near the candle-flame, when one rapid clapping of the 
books would have sent the smoke out and destroyed the 
experiment altogether. 
No one has disputed the fact that the human voice, as 26 
THE FALLACY OF THE PRESENT THEORY OF SOUND. 
well as other sounding instruments, does produce a succes- 
sion of air-waves capable of passing off for a limited dis- 
tance around. But these air-waves have been shown to 
be only an incidental effect of the motion generating the 
sound, and not by any means the sound itself. For a cir- 
cumscribed distance around the sounding body the waves, 
passing off with exactly the force and rapidity of the 
accompanying sound-discharges, will, of course, by im- 
pinging upon a sensitive membrane, throw it into forced 
vibration, in exact conformity to the original vibration 
which generated the tone and the accompanying wave- 
motions which are thus sent off. Such forced tremors 
occur whether the membrane is in unison with the 
sounding body or not, but cannot occur outside of the 
limited distance traversed by such incidental air-waves 
unless in unison.* As a proof that sound and air-waves 
are two separate and distinct phenomena, it is evident 
that the membrane of a telephone could be moved back 
and forth by any direct mechanical means other than air- 
waves, such as a delicate system of levers, acting on it 
with all the variety of rapidity, varying amplitude, and 
force which govern its motion when certain words are 
spoken into the mouthpiece; it would produce precisely 
the same result on the varying intensity of the electric 
*Hall, loc. cit. p. 534. the fallacy of the present theory of sound. 
current and strength of magnet, and would consequently 
Reproduce the same variety of movement in the mem- 
brane of the telephone at the other end of the line by the 
receiver, causing the words to he repeated there alone 
by mechanical means the same as if they had been 
originally spoken into the mouthpiece by means of the 
vocal organs. As a proof of this we have only to look 
at Mr. Edison’s phonograph, which actually accomplishes 
the equivalent of what has just been described, but with- 
cut levers. Dr. Hall * says: “ I have not the least doubt 
but that the wonderful mechanical genius of an Edison, 
a Gray, or a Bell can, and possibly will, yet produce a 
Purely mechanical means of operating on such a mem- 
brane through some kind of key-board and levers, by 
a deaf and dumb person may learn to talk in oral 
U'ords by the manipulation of keys, the same as he might 
learn to play a tune on the piano without being able to 
hear it.” 
From the marvellously delicate effect developed by 
h*Tof. Hughes’s instrument by which the step of a fly can 
be heard through the electric wire miles away, it cannot 
be possible that the movement of a fly’s foot can exert 
efficient physical force to alternately compress and 
expand a solid glass tube or a stick of carbon, and in this 
* Loc. cit. p. 525. 28 
THE FALLACY OF THE PRESENT THEORY OF SOUND. 
manner alternately strengthen and weaken the electric 
current passing through the wire. Everything tends to 
favor the opinion being formed by able scientific thinkers 
that something more than mechanical air-waves is neces- 
sary to produce the infinitely delicate effects generated 
at the transmitting device of a carbon telephone, or 
microphone as it is sometimes called. Some of the 
greatest physical investigators do not hesitate to claim 
that even the more delicate telephonic effect produced 
through the Bell diaphragm cannot be attributed to its 
mechanical or bodily vibrations toward and from the 
pole of the magnetized bar. The eminent Scotch phy- 
sicist Dr. Ferguson* states as a proof that but a portion 
of these effects can come from the vibratory motion of 
the transmitting membrane; that a solid iron plate an 
inch thick in place of the membrane has produced trans- 
missions of speech, and that even the naked end of a 
magnetized bar has done the same thing without the 
intervention of any kind of diaphragm or plate. Dr. 
Ferguson says: “I would, in the first place, take excep- 
tion to the vibratory theory of Bell, viz,, that it is the 
vibrations of the disk to and from the pole of the mag- 
net, in excursions proportionate to the intensity, pitch, 
and quality of the vocal sounds, that electrically affect the 
*Sci. Am. Suppl., No. 120. 29 
THE FALLACY OF THE PRESENT THEORY OF SOUND. 
instrument; and in so doing I only express the dissatis- 
faction with it of almost every one who deals with the 
telephone. Consequently mere vibrations of the iron 
disk are insufficient to account for its action.” 
He holds that the molecules, which are simply the 
smallest particles of the iron, are actually displaced and 
caused to change in their relative position to each other 
by the action of “ external sound,” and that this sonorous 
contact generates currents of electricity. How, says Dr. 
Hall, if “ external sounds” can actually produce electri- 
city in a steel bar or in the iron disk of a telephone as 
Well as vibratory motion, it is plain that sound must be 
something more than mechanical air-waves. This view 
is fully confirmed by Mr. Edison* himself, who says: 
“ I discovered that my principle [the alternate compres- 
sion and expansion of carbon by sound-waves], unlike all 
other acoustical devices for the transmission of speech, 
did not require any vibration of the diaphragm; that, 
in fact, sound-waves could be transformed into electrical 
pnlses without the movement of any intervening 
mechanism.” 
Before closing this section of the subject it may be 
Well to refer to the supposed fact that light, as well as 
sound, is credited with being produced by wave-motion. 
* Prescott, Telephone, p. 226. 30 
THE FALLACY OE THE PRESENT THEORY OE SOUND. 
It is well known that sonnd can be heard* even with 
one ear closed, and with the open ear turned directly 
away from the sounding body, and even when shielded 
from it by a large obstructing surface like that of a 
building, though, of course, the sound is not so dis- 
tinctly heard as if the ear opened directly toward the 
sonorific body, and without any intervening impediment; 
whereas, light cannot swerve to the right or to the left 
the smallest fraction of an inch, and cannot be seen at 
all, even in the slightest degree, unless it enters the eye 
in a direct line either from the luminous body or from 
some reflecting surface. 
If air-waves can lap around the head and enter the ear 
on exactly the opposite side, then ether waves—if there 
be such an all-pervading substance as ether, and if there 
be any truth in the undulatory theory of light—should 
do the same thing, and thus enable us to see a candle at 
a distance in a dark night with the back of the head 
directly toward it. These two results are thus so diamet- 
rically opposite that the supposed wave-motion of two 
perfectly analogous substances—air and ether—cannot 
explain both. If light be due to wave-motion, then sound 
cannot be, and vice versa; or perhaps neither one of them 
is due to wave-motion, which comes nearer the truth. 
* Hall, loc. cit. p. 160. THE FALLACY OF THE PRESENT THEORY OF SOUHT). 
31 
Mobility of the Atmosphere. 
Will any one explain how a pnlse can continue on in 
a direct line in advance of a fork’s prong, while at the 
same time they take into consideration*the mobility of 
the air ? It is certainly a well-known fact that the air can 
get out of the way of a body passing through it and 
thus pass around and behind it, and neutralize the effect 
in the disturbed portion, without the motion being trans- 
mitted more than a few inches from the centre of dis- 
turbance. Because air will move out of a cylinder where 
it is enclosed when forced to do so by a piston, is no 
reason why we should assume that a fly, by moving its 
wings and thus stirring the atmosphere, would actually 
continue the same displacement “to every other point 
of the atmosphere.” It must be remembered that, 
unfortunately for the wave-theory, the air is not enclosed 
in a tube. The idea that the mobility of a body is 
related to or depends on its compressibility could not be 
entertained, as the mobility of the air which can be com- 
pressed to a liquid is about the same as quicksilver, one 
part of which is only compressible in 440,000 parts for 
each atmosphere of pressure.  THE FALLACY OF THE PRESENT THEORY OF SOUND. 
How a scientific man sucli as Tyndall conld even 
“ roughly” compare tlie motion imparted to balls confined 
in a groove, already referred to, to air-particles possess- 
ing lateral mobility,* and which are free to slip around 
and not practically be pushed at all, is certainly, to say 
the least, incomprehensible. The credit of referring to 
the mobility of the atmosphere for the first time in any 
work on sound is due to Dr. Hall; and it alone, if no 
other argument could be advanced, is sufficient to destroy 
the wave-motion or spring-power of the air unless con- 
fined. 
* Hall, loc. cit. p. 261. THE FALLACY OF THE PRESENT THEORY OF SOUND. 
33 
Resonance. 
Tyndall states that “so thin a body” as a harp-string 
vibrating to and fro, while capable of moulding the air 
into condensations and rarefactions travelling with a 
velocity of about 1100 feet a second,* cannot throw the 
air into sonorous vibrations, and that this effect is pro- 
duced by the large surface with which the string is 
associated. This idea is certainly untenable. ISTo one 
disputes that the large surface or board of the harp 
necessarily receives a tremor from the vibrating string 
bearing against it, but such tremor can only be regarded 
as incidental, or as the effect of the motion which pro- 
duces the tone and not such motion itself. If viewed 
otherwise, the sounding-board would be the controlling 
mechanism in the production of tone; and consequently, 
instead of playing a secondary part to the string, which 
bas but a hundredth part of the vibratory effect on the 
air, the board should take possession of the sound and 
change its pitch to its own vibratory rate, whereas the 
string, not a thousandth part so large in area, retains its 
* Tyndall, loc. cit, p. 88. 34 
THE FALLACY OF THE PRESENT THEORY OF SOUND. 
perfect pitch, mastering and annihilating that of its 
powerful coadjutor: and this must he true of all 
stringed instruments besides the harp, such as the lute, 
piano, and violin.* If the wave-theory were correct, 
that resonance is really caused by the vibratory motion 
of the board, then evidently each string as soon as 
sounded should lose its own identity and be forced to 
conform to the normal pitch of the sounding-board; but 
this is not true, as the tone of a string never changes its 
pitch in being transferred to and augmented by the sound- 
ing-board : and we all can see how important it is that 
it should not, for in the case of the piano, which has 85 
separate strings, all having their own rate of vibration or 
pitch which we wish to preserve, the string vibration 
would be lost in the one vibrational pitch of the sounding- 
board, which we know does really augment the sound by 
resonance. Hence resonance must receive some other 
explanation than that given by the wave-theory, f 
Tyndall sets forth in his work under the head of 
Resonance an experiment to show the length of the 
column of air in a jar which resounds to a tuning-fork. 
Using one which vibrated 256 times a second, and of 
necessity having a length of 4 feet 4 inches to its sono- 
rous wave, he detached it from its case and struck it 
*Hall, loc. cit. pp. 83, 84. 
f Hall, loc. cit. p. 84. THE EALLACT OF THE PRESENT THEORY OF SOUND. 
35 
against a pad, the sound produced being hardly audible; 
he then held it over a glass jar and poured in water very 
gently until the column of air reached the proper height, 
when the sound burst forth with extraordinary power. 
The re-enforcement of the sound is known as resonance, 
fey measuring the length of this column of air he found 
it to be 13 inches. The length of the wave emitted by 
the fork is 52 inches. Hence, says Tyndall, the length of 
the column of air which resounds to the fork is equal to 
one fourth of the length of the sound-waves produced by 
the fork. 
If this statement were true it would argue in favor of 
the wave-theory; but unfortunately Dr. Hall found that 
a straight jar gave the greatest resonant depth not at 13 
inches but at Ilf inches, thus making the wave-length 
47 inches instead of 52, as it should be according to the 
wave-theory. This would make the velocity of sound 
1002 feet a second at 60° F., instead of 1120 feet a 
second. Perhaps Laplace might orginate a new formula 
of heat and cold to account for this discrepancy of 118 
feet a second. 
To obtain a resonant depth of 13 inches, it would be 
necessary to expand the mouth of the jar and carry the 
expansion a sufficient distance down; but such a jar is not 
an ordinary straight jar, and must be expanded to great 
nicety to produce the required result. A straight jar will 36 
THE FALLACY OF THE PRESENT THEORY OF SOUND. 
invariably give a resonant depth of Ilf inches. A jar 
with a given bell-shaped month gave a depth of 12f 
inches, while one with a contracted mouth gave a depth 
of Ilf. The honest straight jar gave, as stated, always 
Ilf inches: and this disputes the wave-theory of sound 
by just 118 feet a second. These experiments can be 
easily verified and the fallacy of the wave-theory demon- 
strated. THE FALLACY OF THE PRESENT THEORY OF SOUND. 
37 
Heat and Velocity of Sound-Waves. 
Hewton, independently of tlie necessities of the wave- 
theory, calculated the exact relative density and elasticity 
of the air, which when applied to the admitted require- 
ments of the theory made the velocity of sound in air at 
the freezing temperature 916 feet in a second, whereas 
the well-known observed velocity was 1090 feet, thus 
showing an undeniable discrepancy of 174 feet a second 
between the observed and the required velocity, or a 
deficit of about one sixth against the wave-hypothesis. 
When this fact was made known, the undulatory 
theory of sound should have been abandoned as a practi- 
cal absurdity contradicting in its fundamental principles 
the observed facts of nature. Laplace, the great French 
mathematician, came to the front and proposed using the 
heat generated in the condensations of the supposed sound- 
waves. 
This was based on the fact that sound travels faster in 
heated air than in cold ; and as heat also adds to the elastic- 
ity of the compressed portion of the wave, it was assumed 
that the excursion of the air-molecules into the heated or 
condensed portion and out again would be executed more 
rapidly than if no heat or augmentation of elasticity were  THE FALLACY OF THE PRESENT THEORY OF SOUND. 
generated ; and lienee it was concluded tliat the velocity 
of a given sound would be sufficiently increased by this 
change of temperature to make up the required 174 feet a 
second, or add the one sixth discrepancy pointed out by 
Newton.* So that “an augmentation of velocity of about 
two feet for every single degree centigrade” f is obtained, 
from which we deduce that for 174 feet the condensed 
half of a sound-wave must be raised 87 C. (156°.6 F.). 
Surely the actual distance the air-particles would have to 
travel to and fro cannot be “infinitesimally small” if 
by such motion any appreciable generation of heat and 
cold is to be expected. The real question which is of 
interest here is the amount of pressure to the square 
inch, in avoirdupois, which would be required to generate 
the 87° C. or 156°.6 F. necessary for the additional veloc- 
ity of 174 feet a second. 
To determine this point, an experiment was con- 
ducted in a glass tube having a thermometer in it, as also a 
tight-fitting piston, when Dr. Hall found, making liberal 
allowances, that with a pressure of 15 pounds to the square 
inch the actual heat generated was five degrees. Apply- 
ing this deduction, if we find a cubic inch of air requires 
15 pounds pressure (reducing it to one half its bulk) to 
raise its temperature 5 degrees, how much pressure will it 
* Tyndall, loc. cit. pp. 29, 45, 46. 
f Tyndall, loc. cit. p. 25. 
X Hall, loc. cit. p. 144. 39 
THE FALLACY OF THE PRESENT THEORY OF SOUND. 
require to raise tlie temperature of the same cubic inch 
87 degrees ? Rejecting fractions, we have 255 pounds as 
the result. 
Therefore any sound in passing through the air must 
produce an atmospheric pressure in the condensed portion 
of its waves of 255 pounds to each cubic inch to raise its 
temperature 87° C., which is necessary to add 174 feet a 
second to the velocity of sound. If this does not look 
absurd, it would he only necessary to calculate the abso- 
lute pressure which a mosquito must produce throughout 
a room of given dimensions in order to generate sufficient 
heat to thus add one sixth to the velocity of its sound. 
One more illustration may be interesting; and we will 
select iron this time as the medium, through which sound 
travels 16,822 feet a second. The same condensations and 
rarefactions take place in iron as in air, and heat must be 
generated by each condensation ; but unfortunately when 
iron is once heated to any degree whatever it cannot in- 
stantly become cool, so that heat generated by one con- 
densation of the iron could not have time to subside in 
any calculable degree before its re-enforcement by another, 
that by another, and so on, at the rate of 440 a second, 
if the pitch should be that of A, or the same as that of the 
second string of the violin. “It is thus,” says Dr. Hall,* 
*Hall, loc. cit. p. 235. 40 
THE FALLACY OF THE PRESENT THEORY OF SOUND. 
“ perfectly manifest, according to the wave-theory, that a 
locust by singing for one minute, sitting on a mass of 
iron, ought to raise its temperature to incandescence; 
for however little heat a single condensation would pro- 
duce, this rapid accumulation, without time for subsidence, 
would necessarily accomplish this miraculous result.” 
But as a fact there is no heat generated by the passage 
of a sound; there can be no condensations and consequent- 
ly no waves of sound. 
According to General Duane and other scientific men 
of our Signal Service as well as in the service of other 
nations, fog-horns and steam-sirens are often heard many 
times further against a violent gale than with it. 
Tyndall recognizes this fact, which he verified by his 
experiments off South Foreland.* Yet Prof. Rood states 
it has been found “experimentally that sound moves 
quicker with the wind and slower against it, the final 
velocity being in the one case equal to the sum, in the 
other equal to the difference, of the velocity of the wind 
and that of the sound-wave itself. ”f It is no wonder that 
Tyndall said, “Plainly, therefore, something else than 
the wind must be influential in determining the range of 
sound.” Surely, if sound is attributable to air-waves, such 
waves even from the most powerful fog-horn in the 
service could not travel against a gale even a dozen feet. 
* Tyndall, loc. cit. p. 396. 
f Johnson Cyc. THE FALLACY OF THE PRESENT THEORY OF SOUND. 
41 
The Tuning-Fork. 
With the above facts before ns, let us look into the dis- 
tance travelled in one second by the prongs of a tuning- 
folk or string of an instrument. 
Prof. Carter has conducted an experiment on the slow 
movement of a tuning-fork’s prongs, first shown by Hall, 
which is certainly worthy of careful consideration. The 
following is the result of his experiment as stated by him: * 
“ I used a large Koenig fork of 256 vibrations. Strik- 
ing it heavily and holding it upright in my fingers, I found 
that its sound was clearly audible, either held to the ear 
or through a long rubber tube, at the end of four min- 
utes. By means of a finely graduated scale I easily meas- 
ured the amplitude of the fork’s swing, I found it to be 
at first FT (it) an inch. At the end of fifteen seconds 
it had reduced to FT of an inch amplitude. At the end 
of fifteen seconds more its motion was barely visible 
against the sky. How, I can see a line of of an inch 
in breadth, which proves that the amplitude had again 
diminished to one fourth. In the third fifteen seconds 
* Microcosm, Dec. 1883, p. 154. 42 
THE FALLACY OF THE PRESENT THEORY OF SOUND. 
the motion had become totally invisible even through a 
good magnifier. Safe to assume another fourth, or a re- 
duction of amplitude to of an inch for each swing. 
“Now there are sixteen times fifteen seconds in four 
minutes; hence I have the of an inch swing reduced 
by four as a divisor sixteen times, or in round numbers 
to -3-4000000000 °f an i each swing. As the 
prong swings through this amplitude, counting both 
directions, 512 times in a second, we have the entire 
distance the prong travels, while sounding audibly, but 
the rjsFFTUTir an inch in a second. There are in 
round numbers 31,500,000 seconds in one year. Hence 
the prong moves at the rate of only about one inch in 
four years. Allowing one half for the swifter travel of 
the prong at the centre as compared with its average 
travel throughout a swing [which is too much], and we 
have the astounding fact that the fork continues to pro- 
duce audible sound while its prongs, at their swiftest 
motion, are not travelling at a velocity of more than one 
inch in two years. . . . Let physicists dispose of these 
figures, if they can, or forever after hold their peace.” 
Helmholtz * says: “ The pendulum swings from right 
to left with a uniform motion. . . . Near to either end of 
its path it moves slowly, and in the middle fast. Among 
* Helmholtz, loc. cit. p. 28, THE FALLACY OF THE PRESENT THEORY OF SOUND. 
43 
sonorous bodies which move in the same way, only very 
much faster, we may mention tuning-forks.” Dr. Hall 
says: “We now earnestly ask every candid student of 
science to examine this unavoidable teaching of the 
wave-theory in the light of the absolute facts here de- 
veloped, that the prongs instead of £ swiftly advancing ’ 
(as Tyndall says) sound audibly when moving more than 
25,000 times slower than the hour-hand of a family clock, 
and more than 300,000,000 times slower than any clock- 
pendulum ever constructed, instead of £ very much faster1 
as Helmholtz teaches. Surely with such an overwhelm- 
ing demonstration as this against the truth of a theory 
of science, such theory ought not longer to bear sway 
over the minds of intelligent teachers in our colleges 
and universities, nor be longer taught as true science 
to the perversion of the minds of young students.” * 
The question has been asked me, which one of two 
conical pendulums is moving more rapidly—one that 
makes one swing around a circle to travel, say, ten inches 
in one second, or a pendulum which makes, say, 100 
swings in a second but whose aggregate circular travel is 
only ten inches in one second. The impression was 
that the pendulum making 100 swings in a second un- 
questionably moved the faster. 
* Microcosm, Dec. 1883, p. 155. 44 
THE FALLACY OF THE PRESENT THEORY OF SOUND. 
The absurdity of this line of thinking I made apparent 
by a simple illustration: Given three men who can 
walk one mile in ten minutes; one proposes to walk once 
around, a circle exactly one mile in length, another four 
times around a circle one quarter of a mile in length, and 
another ten times around a circle—one tenth of a mile 
in length—all three accomplishing the aggregate mile in 
ten minutes. Surely the three men walk at the same speed 
or velocity, and their collision against an object would be 
exactly the same, and their effect upon the air in the view 
of compressing or condensing it would be exactly the 
same. 
Again, given a conical pendulum which by one swing 
travels around a circle whose circumference is one inch 
and does it in one second, and a conical pendulum mak- 
ing 100 circular swings in one second but whose aggregate 
distance of travel is only half an inch in that second. It 
must be plain that the conical pendulum making 100 
swings in one second is only travelling with one half the 
speed or velocity of the other, and can compress or 
condense an object only one half the extent that the first 
could. 
Let us take another illustration, for this argument 
is fatal to the wave-theory, and it alone shows the im- 
possibility of the so-called undulatory motion of the air 
in the production of sound. ISTow let us compare the THE FALLACY OF THE PRESENT THEORY OF SOUND. 
45 
conical pendulum to the reciprocating pendulum. As- 
sume a conical pendulum swinging around a circle 
whose diameter is the length of swing of any particular 
reciprocating pendulum. Again, assume the reciprocating 
pendulum swinging forward and back to the extent of 
the diameter of such circle, Mow it is a fact, attested 
to by Prof. Meyer, and one which can be easily verified, 
that at the centre of the width of swung or amplitude of 
the reciprocating pendulum, which of necessity is the 
centre of the circle, the velocity of the pendulum at this 
point is as swift or great as the velocity of the conical 
pendulum at any point in its path or swung. 
The reciprocating pendulum, however, in the same time 
does not travel as far or as great a distance as the conical 
pendulum. This is owing to the stops, starts, and slowing 
of motion from the centre of its swung towards its ends. 
Its greatest velocity as stated at the centre, however, is 
the same, no greater and no less. The difference in the 
distance travelled forward and back is substantially 
equal to the difference between twice the diameter of a 
circle and its circumference. 
Again, the swiftest motion of a reciprocating pen- 
dulum in going and returning, including stops, starts, and 
slowing of motion, is substantially as much faster than 
its average motion as the circle is greater than twuce its 
diameter. 46 
THE FALLACY OF THE PRESENT THEORY OF SOUND. 
In other words, while the reciprocating pendulum is 
making one excursion in one direction, the conical pen- 
dulum is making one half the circumference, or about one 
and a half, while the other is making one. The swiftest 
velocity, therefore, of the reciprocating pendulum in 
one excursion is about one half times faster than its aver- 
age velocity. 
It is a well-known fact that a pendulum of a given 
length takes just as long to vibrate or swing one inch 
forward and back as it would to vibrate or swing 100 
inches forward and back. This is due simply to the fact 
that to make it move through 100 inches it requires 
more force and consequently it goes faster than it would 
if only moving through one inch. This must not be 
mistaken to mean that the pendulum moves or swings as 
rapidly through the one inch as it does through the 100 
inches; the fact is, while it makes the swing in the same 
time it goes just 100 times slower. 
What we are interested in, therefore, is not the time 
it takes a pendulum or a prong of a tuning-fork to swing 
through a given distance, but what velocity of motion 
the pendulum or prong has at any period of its motion. 
The velocity of a prong of a tuning-fork and the dis- 
tance it travels in progressive swings are always on the de- 
crease. The number of vibrations do not change ; hence 
the pitch is maintained. Its intensity is what varies, and THE FALLACY OF THE PRESENT THEORY OF SOUND. 
does so as the amplitude of the prong’s vibration becomes 
less, and it continues to decrease until the prong comes to 
rest. 
Lord Raleigh,* speaking of sonorous waves, says it is 
necessary to have “ a knowledge of the energy which 
must be expended in a given time in order to generate 
them.” Nothing could be more important to us right 
here. It is the velocity of a body that hits or is capable 
of compressing or condensing, and not the stops and 
starts which one man said to me was the cause of the 
prong of a tuning-fork condensing air in front of it. 
Just imagine a prong of a tuning-fork while standing still 
or at a stop condensing anything. This is too absurd 
to dwell on. 
Now, as I have clearly shown, as the amplitude be- 
comes less and less while the tuning-fork sounds, the 
velocity of the prong also becomes less and less, and the 
blow it can give, or its supposed ability to condense the 
air, becomes less and less as it keeps on sounding. Let 
us therefore apply these facts, which I challenge any one 
to contradict, to the results obtained by Prof. Carter. 
It will be remembered that with a fork, after being 
struck, making 256 vibrations, he was able to hear the 
same distinctly for four minutes, during which time the 
* Nature (1877), vol. xvi. p. 114, 48 
THE FALLACY OF THE PRESENT THEORY OF SOUND. 
amplitude of the prong’s swing had diminished to 
woToTffirFoo an indl; and as the prong swings 
through this amplitude, counting both directions, 512 
times in a second, the entire distance the prong travelled, 
while still sounding audibly, was only 133000000' an 
inch in one second, or, at its swiftest motion, only one 
inch in two years—more accurately, one and one-half 
inches in four years. 
Now, I would submit the following proposition: As- 
sume a prong moving at a velocity no faster than the 
hour-hand of a clock. Does any one pretend to say 
that such a prong could compress the particles of the air 
into condensations and by its retreat leave a “partial 
vacuum” behind it, or a rarefaction, and thus send off 
sonorous air-waves? 
It is certain Tyndall * does not believe any such non- 
sense, for he says: “ When a common pendulum oscil- 
lates it tends to form a condensation in front and a rare- 
faction behind. But it is only a tendency/ the motion 
is so slow, and the air is so elastic, that it moves away in 
front before it is sensibly condensed, and fills the space 
behind before it can become sensibly dilated. Hence 
waves or pulses are not generated by the pendulum,” 
Now, this being admitted by one of the highest authori- 
* Tyndall (3d ed.), loc. cit. p. 38. 49 
THE FALLACY OF THE PRESENT THEORY OF SOUND. 
ties on the current system of acoustics, will some one 
please enlighten me how a prong when only travelling 
one and one-half inches in four years, or travelling 25,000 
times slower than the hour-hand of a clock already referred 
to, or 300,000,000 times slower than any clock-pendulum 
ever constructed, can “ mould ” or “ carve the air” into 
condensations and rarefactions and thus produce sound- 
waves ? Do not forget the fact that a prong of a tuning- 
fork advancing and retreating only one inch in one 
second is not only going with a velocity 123,000,000 
times greater than the prong of the tuning-fork in Car- 
ter’s experiment, which made 256 double vibrations, but 
it can exercise 123,000,000 times the force towards con- 
densing the air. 
No, gentlemen! Your wave-theory has been shown by 
the above to be incorrect, absurd, and fallacious, and you 
might as well reject the same and look around for some 
other theory that will not make its supporters the laugh- 
ing-stock of intelligent men. 
Before leaving this part of the subject it will be well 
to refer briefly to the 50 
THE FALLACY OF THE PRESENT THEORY OF SOUND. 
Frequent Change op Direction of the Prongs of 
■ a Tuning-Fork. 
It has been suggested that when Tyndall and other 
authorities on acoustics speak of the prong of a tuning- 
fork “swiftly advancing,” they really refer to “rapid 
change of direction,” so that by the rapid or, more 
properly, “frequent” change of direction of the prong 
of a tuning-fork the air is moulded or carved into con- 
densations and rarefactions. For when a strip of iron 
say four feet in length is put in a vise and pulled aside 
and then let go, while it will oscillate transversely, it will 
not produce sound, for its oscillation or change of direc- 
tion can be counted; if, however, the strip be removed 
and again adjusted so that only two feet of it are now 
free to move, it will oscillate four times as frequently; 
if one foot free, it will oscillate sixteen times as fre- 
quently as at first; if six inches free, sixty-four times as 
frequently, and so on. The oscillations now become so 
rapid, the number of them in a second (i.e., their fre- 
quency) become so great, that they can no longer be 
counted directly; we now hear sound—the shorter the THE FALLACY OF THE PRESENT THEORY OF SOUHD. 
51 
vibrating part the more rapid becomes the vibration, 
consequently the shriller the sound.* 
Again, it has been suggested that when a body oscil- 
lates in a large circular swing covering, say, ten feet, it 
ought to stir the air only gradually; but when the body 
having the same length of cord oscillates 100 times 
around a circle having a circumference of yLT- of a foot, 
it travels the aggregate distance of ten feet in the same 
time. The same air is acted upon oftener in this case than 
in the former, and it has not time to regain its normal 
position before it is acted on .again and again, and for 
this reason the air ought to be churned up more in this 
case than in the former. Applying this same argument 
to the prong of a tuning-fork in its excursion to and fro, 
it follows that, as no sound is heard until the vibration 
or change in direction of the prong is very frequent, the 
cause of the formation of sonorous waves is due to this 
churning motion or agitation. Let ns examine this sup- 
posed plausible solution of the problem, and if its 
absurdity can be shown, the hope of forming sonorous 
waves by a vibrating body will be completely blasted, 
as it has been shown that the slow motion of a tuning- 
fork’s prong cannot produce them, and that the stops 
and starts cannot produce them, and therefore they can- 
not be produced at all, which is unquestionably the case. 
*See Daniels, Prio. Phys. p. 366.  THE FALLACY OF THE PRESENT THEORY OF SOUND. 
It must not be forgotten that the particles constituting 
a sonorous wave must make a small excursion to and 
fro to the extent of the amplitude on winch the intensity 
depends. To induce a particle to make such excursion it 
is evident that the particle must be hit, and this particle 
must hit its neighboring particle, and the new particle 
thus hit must also perform its excursion, and so on with 
the rest of the particles constituting the wave. iNbw to 
hit the first particle it must be agreed that the prong of 
a fork must advance and must have some velocity, and 
certainly more than a clock-pendulum, which on account 
of its slow motion, according to Tyndall, only tends to 
form a sonorous wave, and that it is only a tendency. 
Daniels* also states that “air will not oscillate in 
waves such as can be propagated to a distance, unless 
there be some well-marked compression or rarefaction 
produced at the centre of disturbance.” . . . “ A vibrat- 
ing body before it can act as a sounding body must pro- 
duce alternate compressions and rarefactions in the air, 
and these must be well marked. If, however, the vibrat- 
ing body be so small that at each oscillation the surround- 
ing air has time to flow round it, there is at every oscil- 
lation a local rearrangement—a local flow and reflow of 
the air; but the air at a distance is almost wholly unaf- 
* Loc. cit., p. 367. 53 
THE FALLACY OF THE PEESENT THEOEY OF SOUND. 
footed by tins.” “As a general rule it is advisable,” says 
Daniels, “when sound is to be heard at a distance, to 
make the sources of sound of the largest size convenient. 
Smallness of size may, however, be compensated by 
quickness of vibration.” “Thus the chirp of certain 
insects is produced by such extremely rapid move- 
ments—as many as 12,000 to-and-fro vibrations per 
second—that the air is alternately compressed and rarefied 
on each side of the wings or in the neighborhood of the 
stridulating organs without having time to flow around 
them.” It is evident from this that even Prof. Alfred 
Daniel seems to indicate that “ frequent change of direc- 
tion” is equivalent to velocity of motion, and that “ fre- 
quent change of direction” can itself actually produce 
condensation and rarefaction. The fallacy of such ideas 
I now propose undertaking to showT. 
It has been shown that the prong in Carter’s ex- 
periment while sounding audibly did not travel but 
FToooooooinr °f an inch, and its greatest aggregate travel 
was only at the rate of 1|- inches in four years. 
Try and form some conception of the meaning of such 
figures, if possible. If you cannot, bear in mind this one 
fact: that even one billion (say nothing of 64) exceeds 
all the seconds of time in thirty-two years. 
To illustrate by values within the range of our intel- 
lectual grasp. Suppose a body, a lead-pencil for ex- 54 
THE FALLACY OF THE PRESENT THEORY OF SOUND. 
ample, to be moved slowly through the air at the rate 
of one inch in an hour, and that at the end of an inch 
it stops, and then immediately goes another inch in 
an hour, either in the same direction or in the opposite 
direction: would such motion, if repeated a thousand 
or a million times, condense the air and send off a 
pulse? Any one would answer, No. Would the same 
rate of motion divided into halves—that is, half an inch 
in half an hour, and then stop, and repeat another half- 
inch in half an hour, and so on—come any nearer con- 
densing the air ? Common-sense answers, No! Then 
let the pencil move a sixtieth of an inch at the same 
velocity, that is, in one minute, and stop, and then move 
another sixtieth in another minute and stop, and so on a 
thousand times, the same distance at the same velocity 
each time: could such reduction of distance and division 
of time change the result or the effect on the air if the 
same velocity were maintained ? An ignoramus would 
intelligently answer, No! He could also understand that 
no possible division of the original inch and the original 
hour into segments could condense the air, and that mil- 
lions of stops and starts of the pencil during the hour, 
each motion having no greater velocity, would produce 
no more effect on the air in the way of condensing it 
than would the first single motion of an inch in an hour. 
Thus when the prong in Prof. Carter’s experiment THE FALLACY OF THE PRESENT THEORY OF SOUND. 
55 
moved the OTO-0 000 oof °f an inch at one swing, or at 
the velocity of inches in four years, it could no more 
condense the air or drive off a pulse than would the same 
prong travelling inches in four years at one contin- 
uous motion. Surely no educated man could come to 
any other conclusion. 
It must therefore he conceded that nothing hut the 
swift velocity of a hody through the air can produce an 
atmospheric pulse. ISTo matter whether the movement 
of a hody he long or short—whether it consist of one 
motion or a succession of motions in one direction, or a 
succession of motions in opposite directions—slow 
motion in a fluid or mobile medium can only displace 
the particles. Should the prong of the tuning-fork in 
Carter’s experiment stop and start in one and the same 
direction at no greater velocity, it could no more con- 
dense the air by the second movement than by the first; 
nor could its stops and its starts in the opposite direction 
at no greater velocity produce any different result than 
by its first movement. If two such movements at such 
velocity could no more compress the air than could one, 
then three, five, ten, ten-thousand, or ten-million such 
separate motions, each at no greater velocity, would be 
incapable of producing a condensation or sending off a 
pulse. This is certainly an axiomatic and self-evident 
truth. Once more I ask you to bear in mind that it is 56 
THE FALLACY OF THE PRESENT THEORY OF SOUND. 
agreed that velocity of motion is all there is to consider, 
since the stops manifestly can do nothing, being motion- 
less. After a body has stopped moving there cannot he 
the slightest difference which way it goes as to the com- 
pressing effect on the air, whether in the direction it was 
pursuing before it stopped, in the opposite direction, or 
in some other direction. Its effect on the air will be 
precisely the same, according alone to its velocity. If 
its velocity is too slow to condense the air at any one 
motion, then two, ten, or a million similar motions can 
add nothing to velocity or condensing power. Hence 
the numerous cha/nges of direction constitute a factor 
entirely outside of this problem of condensing the air, 
since each separate movement is to be considered inde- 
pendently, or by itself, the same as if no other movement 
had been or was to be made; and being almost infinitely 
too slow to send off a condensation or pulse, it demon- 
strates the wave-theory of sound to be false. 
President Barnard states :* “If the foreign body [a 
prong of a tuning-fork or other body] exerts but one 
impulse and then remains at rest, only a single tremor 
will pass through the medium and there will be no 
vibration.” This is not even theoretically true; for a 
single forward motion and stop should produce a wave, 
* Johnson’s Cyc.: Vibration. THE FALLACY OF THE PIIESENT THEOKY OF SOUHD. 
57 
but the time required should be longer; tbe air-particle 
would move forward and be compressed, and would form 
a condensation. When tbe particle recoils after impart- 
ing its compression, a rarefaction of necessity must be 
produced, but not so quick as when tbe moving prong 
moves back or recedes as fast as it advances. 
Let us now inquire into tbe diameter of tbe particles 
of air and see if we cannot get a better idea of wbat tbe 
prong of a fork is supposed to do. Loscbmidt says : “ A 
cube whose sides is tbe a millimetre (.039368 
inch) (= 0.00000984 inch) may betaken as tbe minimum 
visible for observers of tbe present day. Such a cube 
would contain from 60 to 100 million molecules of 
oxygen and nitrogen.” And when we take tbe results 
obtained by Clerk Maxwell, Dupre, Lorenszy, abd Sir 
William Thomson, tbe diameter of tbe molecule is found 
to be between yguosoooo50000 to inro owoooo of an incll- To 
form some conception (says Thomson) of tbe degree of 
coarse-grainedness indicated by these conclusions, imagine 
a rain-drop, or a globe of glass as large as a pea, to be 
magnified to tbe size of tbe earth, each constituent mole- 
cule being magnified in tbe same proportion. Tbe mag- 
nified structure would be coarser-grained than a heap of 
small shot, but probably less coarse-grained than a heap of 
cricket-balls. So much for their size; and as regards 
their weight, Maxwell says it would require two hundred 58 
THE FALLACY OF THE PRESENT THEORY OF SOUND. 
million million million molecules of hydrogen to weigh 
one milligram (1 milligram = 0,01543 grain) ; and fur- 
ther, that the distance between them is 200 times greater 
than their diameter. Now, Prof. Pood has stated that the 
amplitude of sound-waves varies roughly from 0- to 
TTowoir an inch 5 while Lord Paleigh has determined 
that the note Fiv, which has 2730 vibrations (and a con- 
sequent wave-length of less than five inches), has an ampli- 
tude of somewhat less than one ten-millionth of a centi- 
metre, which is equal to one two-hundred-and-fifty-four 
thousandth (gg/o 0 <r) an inch. Now Tyndall dis- 
tinctly states * that the time required by a particle 
to execute a complete oscillation is that required by a 
sonorous wave to move through a distance equal to its 
own length. Supposing the length of the wave to be 
8 feet, and the velocity of sound in air of our present 
temperature to be 1120 feet a second, the wave in ques- 
tion will pass over its own length of air in of a 
second; and this is the time required by every air-particle 
that it passes to complete an oscillation, for at the end of 
a second from the time the prong of a tuning-fork com- 
menced its vibration the foremost wave would have 
reached a distance of 1120 feet. In large organs the lowest 
note is C", with vibrations, having a wave-length 
* Sound (3d ed.), p. 97. THE FALLACY OE THE PRESENT THEORY OE SOUND. 
59 
of over 60 feet; the highest musical note of an orchestra 
being probably the Dv of the piccolo-flute, with 4752 vibra- 
tions, having a wave-length of 2.8 inches. The range, 
however, of the ear is given by Helmholtz and Depretz 
between 16 vibrations, with a consequent wave-length of 
70 feet, and 38,000 vibrations, with a consequent wave- 
length of 0.352 inch, or about one third of an inch. 
Taking the lowest note, then, the length of time required 
for a particle of air to make a complete oscillation is -Jg- 
of a second, and the highest -g-s l oT of a second. 
In Carter’s experiment the length of time a particle of 
air is supposed to oscillate is of a second, as there are 
supposed to be just 256 sonorous waves of four feet four 
inches in the first 1120 feet, and so on. How let us 
apply these facts. Assume the prong of the fork in 
Carter’s experiment to advance 6400'000000t °f an inch, 
it is exceedingly questionable if it would hit a molecule at 
all. As I have stated, the space between the molecule is 
200 times its diameter; and second, the distance travelled 
by the prong is over 12 times less than the diameter of 
the smallest of molecules, or 266 times less than the 
diameter of the largest of molecules. It is evident that 
the prong would have to do some fine engineering to 
strike even one of the largest of molecules, assuming that 
an oxygen or nitrogen molecule is as large as 
of an inch. How as the prongs of this fork make only 60 
THE FALLACY OF THE PRESENT THEORY OF SOUND. 
256 vibrations in one second, it is quite certain that only 
one molecule could be hit in one second, if any are hit 
at all. Suppose the fork did hit a molecule : what good 
would that do \ for according to the current theory the 
molecules of the air at 60° F. are in rapid vibration; and 
if they were hit, the slow motion of the prong surely could 
not affect them sensibly. If a man attempts to hit a ball so 
as to send it off in the air to a distance, he brings his bat 
around with great velocity; if he did otherwise the ball 
would simply drop down in front of him. So that if the 
molecule is not hit with considerably swifter velocity than 
a pendulum could hit it, no sensible effect would be pro- 
duced, In Carter’s experiment it was shown that the prong 
advanced at each vibration °f an inch, blow, 
as Prof. Pood has stated that the amplitude of an air-par- 
ticle varies roughly between -gV an(l ttofotto' °f an inch, 
according to the intensity, let us take the smallest distance, 
say the 10 0o o oir °f an In 80 doing we find that the 
prong in Carter’s experiment travels a distance 64,000 
times less than the amplitude of the particle taken; and as 
every vibration of the prong is supposed to form a new 
wave, and the length of time in Carter’s experiment the 
particle has to complete its excursion to and fro is 
part of a second, as the prong vibrates 256 times in the 
second, the air-particle must of necessity move to and 
fro in each case at least 64,000 times faster than the THE FALLACY OF THE PRESENT THEORY OF SOUND. 
61 
prong advances, or than its velocity. Just imagine a 
bullet travelling “its distance” (for an air-particle has 
“ its distance” to travel, which is its amplitude) at 64,- 
000 times greater the velocity than the gases which gave 
it its motion. The above argument has nothing to do 
with the transmission of the pulse, hut simply refers to 
the motion of a particle of air and of the distance it 
must travel in its excursion. It must certainly be ad- 
mitted that reason disappears when such things are 
believed in. It therefore must be clear to every one by 
this time that a vibrating body cannot produce condensa- 
tions and rarefactions and thus send off sonorous waves. 
Hence the wave-theory of sound is false and must of 
necessity be abandoned, except perhaps to illustrate how 
plausible a theory can be and still at the same time not 
be vested with one element of truth. 
The present hypothesis compels scientists to assume 
that there are two entirely distinct principles of wave- 
motion in the atmosphere: one suited to their sound- 
theory, which will travel 1120 feet a second; and another 
class adapted to common-sense, which will not move more 
than four or five feet a second—both manufactured in sub- 
stantially the same manner. For example, “they all know* 
and would readily admit, if a string or a piece of wire be 
* Hall, loc. cit. p. 118. 62 
THE FALLACY OF THE PRESENT THEORY OF SOUND. 
moved back and forth In my hand through the air with 
the most perfect pendulous regularity, and caused to 
travel at an aggregate velocity even ten times greater 
than it is possible for it to obtain when sounding, that 
the air-waves will not travel over four or five feet a second, 
if that fast, and will not be able to make headway through 
the dense air a dozen feet till they will entirely die out. 
But the moment the same string moves through the air 
with its two ends supported in such a manner as to gener- 
ate tone, though with an aggregate velocity not one tenth 
as great, then, presto! it sends off air-waves, according to 
these learned physicists, which travel 1120 feet a second, 
or more than 200 times as fast!” 
If the string oscillates less than sixteen times a second 
it makes no sound, and consequently the air-waves are 
slow waves; but if it should oscillate forty or fifty times, 
then the waves start off with a velocity of 1120 feet a 
second. Can any well-balanced intellect see either consis- 
tency, sense, or science in this arbitrary and absurd dis- 
tinction % 
As sound-waves are claimed to be “ of a precisely simi- 
lar nature” and “ essentially identical ” and move “ ex- 
actly in the same way as water-waves,” as is claimed by 
Tyndall, Helmholtz, and other authorities, we must devote 
a few minutes to this comparison. By an original in- 
vestigation, Dr. Hall, after experimenting with water- THE FALLACY OF THE PRESENT THEORY OF SOUND. 
63 
waves of all sizes, has deduced the following law hitherto 
unobserved by any writer on sound : “ that wave-velocity 
is always exactly in proportion to wave-length, or dis- 
tance from crest to crest” This law, then, inevitably 
breaks down the wave-theory of sound, since it is a 
well-known fact, and universally admitted by physicists, 
that there is no difference in sound-velocity under the 
same conditions of temperature, etc., between the high- 
est notes, such as D, of the piccolo-flute, with a theoreti- 
cal wave-length of less than three inches, and the low E, 
for example, of the double bass, with a theoretical wave- 
length in air of twenty-eight feet. This must of neces- 
sity be the case, for a band can be heard a quarter of a 
mile away the same as a few feet away, and each sound, 
whether high or low, reaches the ear in perfect time: the 
rhythmical relation to each other would be destroyed by 
any difference in velocity. The velocity, however, of 
water-waves diminishes with the distance, and their 
wave-lengths contract or shorten in the exact ratio as 
their amplitude becomes less. These being facts, then, 
a wave of sound should travel slower and slower the 
farther it gets away from the generating instruments, 
while it should also become higher and higher in pitch 
by the contraction of its wave-lengths, as this is exactly 
the manner in which water-waves are propagated. 
In water-waves, any wave which happens to be a small 64 
THE FALLACY OF THE PRESENT THEORY OF SOUND. 
fraction larger than the one preceding it must necessarily 
gain slowly on the one in advance, till at last overtaking 
it the two blend into a single wave of about double the 
normal size of waves constituting that system ; the same 
thing then continues, until at last immense king-waves 
are produced. JSTow if sound consisted of wave-motion 
at all, or if air-waves were possible as the cause of sound- 
phenomena, we should certainly hear in every sustained 
musical tone an occasional outburst, or sonorous explosion, 
whenever one of the atmospheric king-waves should hap- 
pen to accumulate and dash against the tympanic mem- 
brane. As no such sonorous effects are ever observed, it 
becomes clearly manifest that sound does not travel by 
means of air-waves at all, or by any principle analogous 
to undulatory motion. 65 
THE FALLACY OF THE PRESENT THEORY OF SOUND. 
Decrease in the Loudness of Sound. 
Tyndall,* speaking about tbe propagation of sound 
from an exploding balloon, says: “ Take tbe case of a shell 
of air of a certain thickness with a radius of one foot, 
reckoned from the centre of explosion. A shell of air of 
the same thickness but of two feet radius will contain four 
times the quantity of matter; if its radius be three feet, 
it will contain nine times the quantity of matter, and so 
on. Therefore the quantity of matter set in motion aug- 
ments as the square of the distance from the centre of 
the explosion. The intensity or loudness of sound dimin- 
ishes in the same proportion.” 
Tyndall has not taken into consideration that the en- 
tire range of many sounds is less than a foot. Take the 
midge, for example. According to the law, then, if the 
distance from the midge be two feet, the loudness of the 
sound will be one fourth; if the distance be three feet, 
the loudness will be one ninth; if the distance be four 
feet, the loudness will be one sixteenth, and so on. Yet 
the sound entirely ceases within a single foot. To employ 
“ feet,” then, in computing the rates of decrease in the 
* Tyndall (Ist ed.), loc. cit. p, 10. 66 
THE FALLACY OF THE PRESENT THEORY OF SOUHD. 
loudness of the sound of a gnat would be to measure about 
as much out of proportion one way as it would be enor- 
mously too small when applied to the sound of the siren. 
Dr. Hall says: “We may state it as a truism which no 
one will question, that the measure to be employed in 
computing such proportional decrease in the intensity of 
particular sounds, if we estimate by the square of the dis- 
tance at all, must always and of necessity vary exactly 
in proportion to the intensity of the different sounds at 
the start; or in other words, as the range of the different 
sounds varies.” 
The supposed law that the intensity of sound dimin- 
ishes as the square of the distance is recognized and 
claimed by all wave-theorists, and in support of this an 
experiment is freely cited in the text-books. “ Four bells 
at forty feet will exactly equal in intensity of sound one 
bell at twenty feet.” “ There is not,” says Prof. Carter, 
“an acoustician on earth who has ever publicly ques- 
tioned that statement and experiment until Hall’s work 
appeared—and here I make the sweeping statement that 
not one of the i trained experimenters ’ ever once tried 
to perform that experiment, but simply took it in theory 
alone. This is a fatal mistake. I myself first tried the 
experiment with a very complete apparatus, and was aston- 
ished to find that instead of four equalling one at double 
distance, four equalled one at thirty times the distance.” THE FALLACY OF THE PRESENT THEORY OF SOUND. 
67 
The Physical Strength of the Locust. 
There is a well-known insect, one of the locustidse 
(a saltatorial family of the order orthoptera), whose 
stridulations can he heard a distance of more than a mile, 
as attested to by Darwin and others. This insect weighs 
less than a quarter of a pennyweight, and can, by simply 
rasping its legs across the nervures of its wings (for this 
is the way its tone is produced), according to the wave- 
theory, create a physical agitation and displacement of 
the air which converts four cubic miles of atmosphere 
into waves consisting of condensations and rarefactions, 
the compressed portion of which contain a sufficient 
augmentation of heat above the normal heat of the atmos- 
phere to add one sixth to the elasticity of the air and 
the velocity of sound. Dr. Hall has made some calcula- 
tions which cannot fail to be interesting, showing what 
the consequence of this would be if true. 
In the four square miles in which this insect can be 
heard there are in round numbers 16,000,000,000 square- 
inch columns of air, each exerting a pressure on the earth 
and in all directions of about fifteen pounds—in the aggre- 
gate 120,000,000 tons. How, since sound can only travel 
by means of “air-waves,” and as air-waves can be con- 68 
THE FALLACY OF THE PRESENT THEORY OF SOUND. 
stituted only of condensations and rarefactions, and as a 
condensation can only take place by the particles of air, as 
Prof. Tyndall says, “ crowding closely together,” or a rare- 
faction occur except by the particles of air separating 
“more widely apart” and as every particle of air con- 
stituting a sound-wave, according to the same high 
authority, must necessarily make “a small excursion to 
and fro” every time a wave passes, it inevitably follows, 
if this theory be true, that this insect, by simply moving 
his legs, displaces all the particles of air constituting 
these 16,000,000,000 inch columns for a mile high, and 
restores them to their place again 410 times each second 
(its tone being very nearly A, or that of the second string 
of the violin), and continues this process of thus churning 
the atmosphere into condensations and rarefactions a full 
minute at a time.* 
When we apply the power exercised by the locust 
(that could not move an ounce of weight) to the mem- 
brana tympani, we obtain some additional information 
which is still more enlightening and interesting.- It is 
agreed by all scientists that if an ear were present in 
any portion of the four cubic miles of air, the sound of 
the locust could be heard and the membrana tympani 
would bend once in and once out by each vibration, or 
*Hall, loc. cit. p. 130. THE FALLACY OF THE PRESENT THEORY OF SOUND. 
69 
440 times in one second of time. It is evident that there 
is in this membrane some weight or inertia to overcome ; 
this weight Dr. Hall has determined to be at least 
half a grain for each membrane. How, by a simple 
calculation which any schoolboy can verify, it is found that 
there is room enough in tins area, in round numbers, for 
65,000,000,000,000,000 of these tympanic membranes, as 
the membrane is not over a quarter of an inch square: which 
would give us a ponderable mass of 4,000,000,000,000 lbs., 
or two thousand million tons of tympanic membrane, 
which this trifling insect, according to the wave-theory of 
sound, is capable of throwing into rapid vibratory motion 
by the mechanical operation of moving its legs, moving 
the same once in and once out 440 times a second. As 
forty million people (nearly the whole population of the 
United States) could conveniently stand within four 
square miles permeated by the sound of this insect, their 
5000 lbs, of tympanic membrane would bend once in and 
once out 440 times in one second. And as the whole 
population of the earth is estimated at 1350 million, and 
as this number of individuals could stand conveniently in 
eleven and one half square miles, their 231,222 lbs. of 
tympanic membrane would, according to the wave-theory, 
bend once in and once out, about 1000 times a second, 
by the sound from a steam-siren, or 440 times a second 
by the stridulation of thirty-four locusts. 70 
THE FALLACY OF THE PRESENT THEORY OF SOUND. 
Another illustration will, I think, be all that is neces- 
sary to establish the value of the wave-theory of sound. 
We will select iron this time as onr medium instead of 
air, as we did in the case of the illustrations on heat. 
Imagine a locust stridulating in the centre of a mass of 
iron one mile in all directions. It is admitted that he could 
be heard, and about sixteen times quicker than in the air, 
by placing the tympanic membrane in actual contact with 
the iron at its surface. How, since a mass of iron is all 
thrown into wave-motion, and since, according to Prof. 
Eood, the amplitude of waves of sound will vary roughly 
from to 1000 ooo~°f an inch> ie iron must be moved 
at least to this extent; which could be easily verified, 
as Prof. Pood has been able to measure ¥0 o*o 0 0 part 
of an inch. The mass of iron thus displaced would 
weigh not less than 729,719,050,612 tons, and would be 
so moved by the strength of the locust, as it is permeated 
by its sound in all directions, as in the case of air, and 
every molecule must perform the wave-amplitude of the 
theory, or an excursion to and fro. 
The wave-length would naturally be over sixteen times 
as great as in air. It would follow from this, if the note 
were the low E of the double bass, which has forty vibra- 
tions to the second, that the length of the iron wave would 
be of necessity 176 feet from crest to crest. 
It may be well to mention here that Prof. Mayer THE FALLACY OF THE PEESENT THEOEY OF SOUND. 
71 
states * that a given sound in passing tlirougli tlie atmos- 
phere and producing its condensations actually increases 
the “density” of the “compressed half” of the wave 
-e4-j over the normal density of the air. Applying this, 
to the determination of the physical strength of the locust 
we have the modest amount of five thousand million tons; 
while if the calculation is based on the estimated heat 
which this pressure must necessarily generate to meet the 
requirements of Laplace these figures are thrown into the 
shade, making the physical energy of the locust equal 
to 132,566,207,938,560,000 lbs., or in round numbers 
66,000,000,000,000 tons, f 
On the theory of Sir William Thomson, the locust 
could only produce sound according to the law which 
changes barometric pressure,—that is, by the changes in 
the weight of the atmosphere,—as will be shown farther 
on. Therefore, as the locust can be heard over four 
square miles of the earth’s surface, or over an area of 
15,844,448,400 square inches, its mechanical strength, by 
moving its vibratory apparatus, can add 60,000,000 lbs., 
in round numbers, to the weight of the atmosphere. For 
if the barometer rises only one tenth of an inch, it shows 
that the weight of the atmosphere has actually increased 
* See Appleton’s Encyc.; article Sound, by Alfred Mayer, 
f Hall, loc. cit. p. 145. t Sci. Amer. Suppl. 
fSci. Amer. Suppl.  THE FALLACY OF THE PRESENT THEORY OF SOUHD. 
34 grains to each square inch on the surface of the earth 
at that locality in order to produce such change. 
Surely this fact is sufficient to show the absurdity of 
the current doctrine of acoustics. 
Prof. P. Kelso Carter * has made some interesting cal- 
culations (which do not seem out of place here) in rela- 
tion to the hell employed by Messrs. Colladon & Sturm 
under water to determine the velocity of sound. Two 
questions, says Carter, must be asked: 
1. What caused the actual motion of the water? 
2. How much was actually (not theoretically) moved ? 
In this problem the actual amplitude of the supposed 
vibration of the water-particles is not of the slightest 
consequence. The fact is the particles moved, and 
moved at a specified rate [within their amplitude]. 
Carter deduced the following undeniable facts : 
1. This remarkable bell (the sound of which was heard 
nine miles off) actually set in vibration particles of water 
in twenty cubic miles [estimated nine miles long and 
broad, with a depth of one fourth of a mile]. 2. This 
amount of water weighs 920 trillion tons. 3, The dead- 
weight resistance offered by this water to every impulse 
amounts to two trillion tons. (This supposes the impulse 
to be given at the smallest cross-section.) 4. This dead- 
* Microcosm, vol. iii. p. 262. THE FALLACY OF THE PRESENT THEORY OF SOUND. 
73 
weight was positively overcome 400 times in a second as 
long as the bell was heard. 
In this calculation, to meet the objection which might 
be urged that the sounding body only moves the first 
layer of the water, and the motion is communicated and 
handed over to the next with some loss, and so on, it 
makes no difference how thick or how thin a “ first layer” 
be taken. Carter has taken no thickness at all. It is 
indisputable that the amount of square surface will offer 
the resistance he has given. The only questions are: 
1. How great is the cross-section of the water moved ? 
2. How much resistance to such a rate of motion does 
water oifer to the square foot ? 
It is a principle laid down by Archimedes that any 
force whatever which proceeds or radiates from a centre 
diminishes as the square of the distance along any given 
line. How suppose the bell in the above case to vibrate 
one inch. Then the initial impulse given to the water 
will be one inch in amplitude. While the molecules of 
water next the bell will move one inch, no one can invent 
a reason for the next molecule to move any farther. 
Applying the above-mentioned principles, Carter finds 
as the force goes on, at nine miles it would be reduced to 
irsTo 0000 o o q °f an hieh, which is less than of the 
diameter of an ultimate molecule, so called, of hydrogen. 
But as this molecule is supposed to have a vibratory path  THE FALLACY OF THE PRESENT THEORY OF SOUND. 
200 times its diameter, then the reduced to yfoVof* 
As the vibratory motion of the hydrogen molecule in its 
path has never been heard, it is plain that an impulse to 
affect the auditory nerve must exceed it, as it is about 
thirty times less. 
This argument of Prof. Carter certainly settles the 
locust question, and sustains the deductions made to show 
what a locust would be called on to do if the wave-theory 
of sound were correct. THE FALLACY OF THE PRESENT THEORY OF SOUND. 
75 
The Barometric Theory of Sir William Thomson. 
As this is the very latest interpretation of the present 
theory of sound, it seems appropriate to devote a few 
minutes to its consideration. 
According to Sir William,* as stated briefly before, 
sound is “ exceedingly sudden changes of pressure acting 
on the tympanum of the ear, through such a short time 
and with such moderate force as not to hurt it, but to 
give rise to a very distinct sensation which is communi- 
cated through a train of bones to the auditory nerve.” 
To explain : It is a “ sudden change of pressure,” and it 
differs from a gradual change of pressure” as seen on 
the barometer only in being more rapid—so rapid that 
we perceive it as sound. 
If by any means a fall of the barometer could happen 
“ amounting to a tenth of an inch and taking place in a 
thousandth of a second,” says Sir William, “it would affect 
us quite like sound: a sudden rise of the barometer would 
produce a sound analogous to what ‘happens’ when I 
clap my hands.” 
* Sci. Am. Suppl. 76 
THE FALLACY OF THE PRESENT THEORY OF SOUND. 
By means of a regular barometric tube, with its sen- 
sitive column of mercury completely exposed to the air 
of a room by removing the cork from the enlarged por- 
tion of the chamber at its base, so that the slightest 
change of atmospheric pressure might be instantly ob- 
served in the rise or fall of the top of the column, the 
instrument being properly secured at a convenient height 
for close observation with a powerful magnifier, Dr. Hall, 
with the assistance of careful scientific witnesses, deduced 
the following:* that “Ho vibratory or wave motion of 
the air caused by a moving body, let the disturbances or 
pulses be slow or rapid, produces the slightest effect upon 
the barometer even in a closed room, and directly at the 
exposed mercury, as demonstrated by actual experiment. 
Therefore sound is not produced in our sensations by 
air-waves or atmospheric pulses sent off from a vibrating 
body, and consequently the wave-theory breaks down in 
the hands of its greatest modern champion.” 
* Microcosm, Nov. 1884, p. 125. THE FALLACY OP THE PEESENT THEOEY OP SOUND. 
77 
Elasticity and Density. 
Tyndall states a supposed law as follows: 
“ The velocity of sound in air depends on the elasticity 
of the air in relation to its density. The greater the 
elasticity the swifter is the propagation; the greater the 
density the slower is the propagation.” 
What, then, is elasticity ? It is a property of a body 
analogous to that of ductility, malleability, porosity, 
fusibility, etc., and in no manner or degree does it or can 
it exert mechanical force or aid in overcoming the inertia 
of a body: “its whole office* being to permit a cer- 
tain kind of motion or quality of effect through the ap- 
plication of adequate mechanical force.” So that the 
elasticity of the air could not add one grain of force to 
the original mechanical energy of the locust, in the 
illustration already given, by which it could displace the 
air by overcoming its inertia. 
It must of necessity be conceded, if the above law were 
correct,—if a body could be found having great density 
and no elasticity,—sound should not travel through such 
* Microcosm, vol. iii. p. 219, 78 
THE FALLACY OF THE PRESENT THEORY OF SOUND. 
a substance at all. Such a body we have practically in 
lead, which is one of the densest metals and is almost 
entirely devoid of elasticity. Miller says : * “By elasticity 
we understand the resistance that a body offers to com- 
pression or to extension, and the property which it pos- 
sesses of regaining its former volume when the pressure or 
tension is withdrawn.” When heat is applied to lead, its 
particles are so soft that they slide over each other, 
according to the current theory, in the act of expansion, 
and do not return to their original position. A leaden 
pipe of a few feet long, if used for conveying steam, be- 
comes permanently lengthened by some inches in a short 
time, f This would not be the case if lead had more 
elasticity. How, then, is it possible for lead to transmit 
sound-undulations 4030 feet per second, as Tyndall 
states, when the velocity of sound through water is 
practically the same, or 4Y14 feet ? The density of lead is 
just about eleven times that of water, and Tyndall says, 
“ Other things remaining the same, an augmentation of 
density always produces a diminution of velocity.” 
Hence the velocity of sound in lead should certainly be 
very much slower than in water, if it should have any 
velocity at all, according to the law. Tyndall further 
states that “ elasticity is measured by compressibility,” as 
* Chem. Phys., parti, p. 48. 
f Miller, loc. cit. p. 289. THE FALLACY OF THE PRESENT THEORY OF SOUND. 
79 
is stated in as many words by Miller’s definition of elas- 
ticity just given. Which is the more compressible, lead 
or water, when the coefficient of compression of sea-water 
is known to be only 0.0000436, and lead, as is known, can 
be compressed in the cold, being similar to putty ? 
Professor Tyndall gives the velocity of sound along the 
fibre of pine-wood as 10,900 feet, and across the rings 
4611. ISTow, says Prof. Carter,* in the name of common 
reason, is not pine-wood infinitely more compressible 
than water ? Is it not therefore much less elastic ? And 
is it not also only a little lighter or less dense ? Well, 
then, put these facts together, and as the densities are 
very nearly alike, surely the velocities ought to be the 
same. 
If it is maintained that the elasticity of the air con- 
stantly adds force to the impulse imparted to the same by 
the locust, so that the locust does not have to exert much 
force to set the atmosphere into vibrations, either, says 
Dr. B. S. Taylor, “ the doctrine of the unalterable 
quantity of energy must be given up or else the un- 
dulatory theory of sound ” must be abandoned. This 
doctrine, however, is perfectly safe, for elasticity, as 
already stated, is a mere property of a body and cannot 
add one grain of force to the supposed work of the locust, 
* Microcosm, Nov. 1884, p, 104. 80 
THE FALLACY OF THE PRESENT THEORY OF SOUND. 
or the work the locust would of necessity have to per- 
form if the wave theory of sound were correct; hut as it 
is not correct, we can protect the locust as well as the 
doctrine of the constant equivalence of energy. 
As I have just had occasion to refer to the “ impulse,” 
it is best for me to say a few words about it, for the 
majority of people think that all a vibrating body has 
to do is to start or form a so-called sonorous wave and 
the “impulse” will safely carry it at the rate of 1120 
feet through the air. “An impulse is the effect of 
a blow,” and “ the measure of an impulse in producing 
a change of velocity of a body is the increased (or 
decreased) momentum produced in the body.” “ The 
work done by an impulse (being) measured in the same 
way as for finite forces.” All the effects, therefore, says 
DeYolson Wood, of an impulse are measured in the same 
way as the total effects produced by a finite force. 
The idea of an impulse contributing one grain of 
force over and above, or even exactly as much as, the 
force that excited it, is absurd. What interests us here 
is the velocity of an impulse. Newton thought an im- 
pulse was transmitted through a molecule of a body in- 
stantaneously. This is incorrect, even according to the 
present theory of the constitution of bodies. Matter is 
supposed to be composed of molecules acted upon by at- 
tractive and repulsive forces. Molecules are therefore THE FALLACY OF THE PRESENT THEORY OF SOUND. 
81 
not in contact according to tins view. If the distance 
between the molecules he increased within the limits of 
the action of the forces, both forces are diminished; and 
if the distance is lessened, both are increased, but not in 
the same proportion. Applying these facts, then, a mole- 
cule of air after receiving a blow is first compressed 
(which requires time) before it can move towards its 
neighbor in front of it; and when so moving it excites 
and increases the forces; the neighboringmolecule is then 
compressed, each molecule performing its own motion 
forward and back, and so on until the original force is 
overcome. From this it is evident that in the trans- 
ferrence of a pulse a given amount of time is required and 
a given amount of the original force is utilized to do work. 
Now, it is a fact that the impulse in an elastic medium 
travels with considerable rapidity; but such rapidity can 
be easily ascertained by experiment, and has been done. 
If the propagation of sound wTas attributed to some 
other cause than the vibrations of condensations and rare- 
factions of the air, no physicist would assume (for it is a 
mere assumption) that an impulse can travel at the rate 
of 1120 feet a second through air. It is only on account 
of the first assumption that an “impulse” has been 
credited with such a wonderful performance. Experi- 
ments made within the domain of practical limits (leav- 
ing the consideration of the so-called light-pulses and 
sound-pulses out) do not justify any such conclusion.  THE FALLACY OF THE PRESENT THEORY OF SOUND. 
Interference and Beats. 
It is claimed that the so-called sound-waves under cer- 
tain conditions produce interference, and this is claimed 
to be especially conclusive evidence in favor of atmos- 
pheric wave-motion. It is certainly essential to the 
theory that such interference should exist, as sound- 
waves, according to Helmholtz and other scientists, are 
“essentially identical” with and “precisely similar” to 
water-waves; as when two equal systems of water-waves 
travel together in such manner that the crests of one 
system coincide with or fall into the furrows of the 
other system they will mutually destroy or neutralize 
each other producing a level, or nearly so. So it is 
claimed that if the condensation of one wave of sound 
should fall into the rarefaction of another wave of sound 
of the same intensity, according to Tyndall the result 
would be “ absolute silence;” while if the condensation 
of the one coincided with the condensation of the other, 
and the rarefactions the same way, then by this “ coinci- 
dence” a sound will be produced which will be four 
times the intensity of either. This supposed law of 
interference of sound-waves has no foundation in science THE FALLACY OF THE PRESENT THEORY OF SOUND. 
83 
or fact, as I will now undertake to show; and if I succeed 
in doing so, the so-called wave-theory will not have a 
foundation to stand on. 
The double siren, which must be familiar to you all, is 
an apparatus by which it is claimed that the so-called 
interference can be demonstrated. To use Tyndall’s own 
words :* “ Where the circle is perforated by 12 orifices, 
the rotation through of its circumference causes the 
apertures of the upper wind-chest to be closed at the 
precise moment when those of the lower siren are 
opened, and vice versa. It is plain, therefore, that the 
intervals between the puffs of the lower siren, which 
correspond to the rarefactions of its sonorous waves, are 
here filled by the puffs or condensations of the upper 
siren. In fact, the condensations of the one coincide with 
the rarefactions of the other, and the absolute extinction 
of the sound of both sirens is the consequence.” Tyndall 
further states that this statement may seem to exceed 
“ the truth; for when the handle is placed in the position 
which corresponds to absolute extinction, you still have 
a distinct sound.” He claims that the “aerial disturb- 
ance breaks up into secondary waves which associate 
themselves with the primary waves of the instrument.” 
The turning of the upper siren through FT of its circum- 
* Tyndall, loc. cit. p. 291. 84 
THE FALLACY OF THE PRESENT THEORY OF SOUND. 
ference utterly extinguishes fundamental tone. But 
we do not extinguish its octane. To discuss the merits 
of this seems too absurd, for “ In the name of science and 
reason—in the name of acoustics and common-sense— 
what should have been expected but this very result V * 
By operating the two sirens together, so that the 12 
puffs of the upper siren alternated with the 12 puffs of 
the lower siren, surely 24 puffs were obtained the same 
as if he had used one siren with 24 holes instead of 12. 
The result of necessity must be the raising of the funda- 
mental note to its octave. Tyndall should have known 
this instead of resorting to talk about “ secondary waves 
associating themselves with primary waves,” etc., when 
he distinctly teaches that no octave, from whatever 
instrument, can be produced without doubling the number 
of vibrations which caused its fundamental tone. 
Prof. Helmholtz was the first to make the mistake. 
He says :f “ The puffs of air in one box occur exactly in 
the middle between those of the other, and the two prime 
tones mutually destroy each other. . . . Hence in the 
new position the tone is weaker because it is deprived of 
several of its partials [over-tones]; but it does not 
entirely cease; it rather jumps up an octave.” We 
have heard the reason why “ the tone is weaker” in the 
* Hall, 100, cit. p. 288. f Helmholtz, loc. cit. p. 240. 85 
THE FALLACY OF THE PRESENT THEORY OF SOUXTD. 
new position according to Helmholtz and Tyndall, 
and now we will hear the true explanation given by 
Dr, Hall: That the weaker tone is due simply to the fact 
that it was constituted of a single series of 24 successive 
puffs or vibrations to a revolution, while the prime tone 
was composed of two series of 12 double or unison puffs 
which necessarily re-enforced each other, and by which 
means their intensity was increased fourfold.* 
Prof. Tyndall showed how the number of vibrations 
of a particular fork could he ascertained by the siren. 
He says the siren makes 334 puffs of air in a second, and 
he further distinctly says that one puff is one wave of 
sound. "With the siren, then, a single puff of air escaping 
through a hole in a disk constitutes a vibration, or a 
pulse, or a sound-wave. But with the fork the case is 
very different. Here we see that a single puff or motion 
does not constitute a vibration, but only half a vibration.f 
In the matter of the siren, says Prof. Carter, £ 384 puffs 
of air issue from a tube in a second. Each puff is a 
motion forward from the mouth of the tube; there is no 
backward motion in any sense whatever. 
How we would like Prof. Tyndall to explain how a 
puff of air, that has only one motion “ to” and not “ fro,” 
can, by his own definition, be called a wave of sound or 
f Tyndall, loc. cit. p. 69 
* Hall, loc. cit. p. 295. 
% Microcosm, Dec. 1883, p. 145. 86 
THE FALLACY OE THE PRESENT THEORY OF SOUND. 
a vibration. He insists on it that a vibration mu 
consist of two motions equally distinct, one forward and 
tbe other backward, or else it is only a “semi-vibra- 
tion.” 
The puff is not suddenly checked and reversed as in 
the case of a fork’s prong, but is left to expend itself 
against the yielding atmosphere. The stream is sud- 
denly cut off, but no one will be so foolish as to claim 
that the stoppage of the supply of wind is a reversed 
motion. If it is, then the stoppage of wind constitutes 
the vibrating body, for the Professor assures us that the 
vibrating body must make the “ excursion to and fro.” 
If any one declares that the starting and stopping of 
the air constitutes the necessary double motion, they can 
be referred to the tuning-fork, which manifestly stops 
and starts at each end of its swing, or four times in a 
complete excursion to and fro. 
The facts are that the puff of air makes only a “ semi- 
vibration,” or a single motion forward, while the fork- 
prong makes a double motion “ to and froand notwith- 
standing this difference, the siren and the fork produce 
precisely the same note when listened to in the ordinary 
way. 
The siren produces sound by using the air itself as the 
agent, and conveys the sound through itself to the ear. 
In this case one motion or semi-vibration produces the THE FALLACY OF THE PRESENT THEORY OF SOUND. 
87 
effect on the ear of certain notes in the scale. The fork 
produces sound in itself and does not convey this sound 
to the ear at all, hut is forced to hand it over to another 
medium, air, to convey it to the ear. In this case a 
double vibration is necessary to produce the same note. 
Prof. Carter asks the following question: If sound 
is produced by a vibrating piece of steel, and were my 
ear buried in the steel itself, would I hear anything? 
By the aid of Tyndall’s admission that a single air-puff 
actually produces the same effect on the ear as a double 
fork-vibration, Carter has been able to discover that 
“ When the ear is in the vibrating body a single or semi 
vibration produces the same effect as that produced by a 
double or complete vibration when the ear is not in the 
sounding body.” 
If two unison * forks be sounded over the resonant 
jars of proper depth placed one half a wave apart, their 
tone can be heard exactly the same in line as at right 
angles, or when a whole wave-length apart; while 
according to the testimony of Prof. Helmholtz the 
very highest authority on the subject, such sounds are 
destitute of accompanying over-tones. 
The necessity for referring to “ clang-tints” or “ over- 
tones” of the “ highly composite” siren resulting from 
* Hall, loc. cit. p. 287. 88 
THE FALLACY OF THE PRESENT THEORY OF SOUND. 
its “ secondary waves- whicli associate themselves with 
the primary waves” is at once dispelled. The real value 
of the siren, then, is to show that the pitch of every fun- 
damental sound, from whatever instrument, corresponds 
precisely to the number of vibrations in a second which 
generates the tone.* 
Let ns consider for one moment a harp-string. Here 
we have condensations sent off on one side by the very 
identical motion which generates and sends off the rare- 
factions on the other side of the string, and at exactly the 
same instant of time. So that, according to the theory of 
interference by half wave-lengths, the rarefactions on 
one side of the string would react and reflect upward a 
given distance, just in time to coalesce with the con- 
densation from the other side, since they occur synchro- 
nously and both travel with the same velocity; and hence 
the two systems of waves from the two sides of the 
string must necessarily produce complete interference 
and cause “absolute silence” in a vertical direction, if 
there is a shadow of truth in the wave-theory. 
It seems needless to say you know that no such in- 
terference takes place. It may be advisable to refer 
briefly to the apparatus of M. Koenig, the principle of 
which was first proposed by Sir John Herschel, the ob- 
* Hall, loc. cit. p. 303. THE FALLACY OF THE PRESENT THEORY OF SOUND. 
89 
ject being to divide a stream of sound into two branches 
of different lengths and afterward cause the branches to 
reunite and to interfere with each other. Koenig’s ap- 
paratus, which must be familiar to you, carries out this 
idea. Tyndall states that when the parts are properly 
adjusted the sound of a fork is extinguished. This 
statement is false, for no such thing as silence occurs, 
since the sound of the fork is not diminished in intensity 
more than one quarter, as any sound-expert would readily 
admit; and by a modification of Koenig’s instrument 
the effect has been proved to be due to the result of 
resonance, and due to either the re-enforcement or op- 
position of the two vibrating air-columns of the two 
tubes; * and it has been further shown that any resonant 
effect produced by dividing the sound into two streams 
ean be equally obtained by a single stream in connection 
with a closed resonant tube of certain depth. As the 
Koenig apparatus has always been considered as con- 
clusive evidence in favor of this law of interference be- 
tween sound-waves, scientists cannot help but be in- 
debted to Dr. Hall for exposing its fallacy and thus 
annihilate completely the supposed law of interference, 
the very foundation of the present wave-theory of sound. 
* Hall, loc. cit. p. 311. 90 
THE FALLACY OF THE PRESENT THEORY OF SOUND. 
Beats. 
If we employ two organ-pipes which give slightly differ- 
ent tones, assuming both their waves start fairly together, 
the supposed condensations and rarefactions being in har- 
mony, this state of things cannot long remain so, owing 
to the inequality of their length. Hence in this experi- 
ment we must expect to have alternations of sound and 
silence, the tone rising and swelling to a maximum, then 
dying away again to repeat itself, etc. These alter- 
nations are called beats, and furnish even to the un- 
musical ear a very accurate means of judging of the 
identity of musical tones. 
According to Helmholtz, discord is due to the presence 
of the beats; and Hood * states “ that when from any 
cause these beats follow each other at the rate of about 
33 in a second the discord is at its maximum, becoming 
more tolerable with twice this number, and finally 
disappears altogether as their number is increased to 
about 120 in a second. On the other hand, if the beats 
follow quite slowly—for example, at the rate of three 
* Johnson’s Cyc. THE FALLACY OF THE PRESENT THEORY OF SOUND. 
91 
to five in a second—the effect is not unpleasant, and can 
even be employed in music, suggesting as it does the 
idea of trilling. It is evident from tins that the sinking 
and swelling of the sounds of two beating instruments 
result “ alone,” according to the wave-theory, from the 
alternate coincidence or interference of the air-waves 
themselves sent off from such sounding bodies. This 
I deny, as I have clearly shown that no such interfer- 
ence between two supposed systems of air-waves can take 
place, since not the slightest weakening of two unison 
tones occurs when two vibrating bodies are sounded half 
a wave-length apart. Dr. Hall * maintains that the 
operation which alternately augments and diminishes 
the intensity of tone, as the oscillations of two forks cross 
each other’s path in changing from synchronous to alter- 
nate vibration, has nothing to do with air-waves or any 
motion of the air-particles whatever, but takes place in 
the instruments themselves or in their potential and 
practical sympathetic attraction for each other, without 
regard to the coincidence or interference of such useless 
nonentities as these so-called atmospheric condensations 
and rarefactions. 
Suppose, for example, two forks mounted upon their 
resonant cases and tuned sufficiently out of unison to pro- 
* Hall, loc. cit. p. 305. 92 
THE FALLACY OF THE PRESENT THEORY OF SOUND. 
duce, say, one beat to the second. If sounded in close 
proximity to each other or in a position of strong sym- 
pathetic attraction, a listener stationed a hundred feet 
away from them will distinctly hear their beats—will in 
fact hear them as far away as the sound of the forks is 
audible. But let the two forks while sounding be quietly 
separated only a few feet toward the right and left of the 
listener, and though he will continue to hear their united 
sounds in full force, yet the beats will entirely cease, 
showing that they result from the sympathetic influence 
of the two forks upon each other owing to their affinity, 
and not to the alternate interference and coincidence of 
the two systems of supposed air-waves a hundred feet 
away, or at the ear of the distant observer, as the wave- 
theory teaches. THE FALLACY OF THE PRESENT THEORY OF SOUND. 
93 
The Membrana Tympani and the Corti Arches. 
The description of the membrana tympani has been 
given already, so only a few additional facts will be of 
interest. 
The upper border * of this membrane is 7 mm. nearer 
to the entrance of the external auditory canal than the 
lower. The posterior border is about 5 mm. nearer this, 
entrance or meatus than the anterior. It makes an angle 
of 55° with the axis of the auditory canal. Its general 
shape is elliptical or funnel-shaped. The horizontal 
diameter is Bto 8.5 mm., and vertical 8.5 to 9 mm. Its 
thickness is not quite 0.1 mm.; in other words, about the 
same as very fine letter paper. Mr. Shrapnell considers 
the function of the membrana flacceda is to protect the 
more tense fibres, deadening the effect of the sudden and 
loud sound, or of coughing and sneezing, when by yield- 
ing it saves the tense fibres from being ruptured. In the 
hare and sheep, whose sense of hearing is very acute, this 
structure is remarkably developed, f The existence of a, 
* St. John Roosa, Diseases of the Ear (1884). 
f London Med. Gaz., vol. x. p. 120. 94 
THE EALLACT OE THE PRESENT THEORY OE SOUND. 
minute opening in the membrane at its upper margin 
called the Eivinian foramen has been proved, as air may 
be occasionally heard to whistle through it, although it 
cannot be seen by the unaided eye.* 
Double hearing sometimes occurs, and Mr. Homes ex- 
plains it by a defective action of the radiated muscle, 
which was not exerted with the same quickness and force 
in one ear as in the other, so that the sound was half a 
note too low, as well as later in being impressed upon the 
organ. Nearly all such cases observed are amongst 
musicians, f 
The membrana tympani when viewed through the 
auditory canal shows a triangular spot of light. The 
apex of this spot is at its greatest concavity and is called 
the umbo, and is due to this and the inclination of the 
membrane. It is reflected light.:}: 
According to Dr. St. John Eoosa, § “the presence of 
the membrana tympani in whole or in part is not essen- 
tial to fair hearing power.” This was first clearly proved 
by Sir Astley Cooper, |( 
Eoosa, however, says “ that it is very important to good 
hearing in some cases, [as] is shown by the numerous in- 
* Kessel-Stricker, Handbook of Histology, p. 953. 
+ Phil. Trans, of Royal Soc. London, 1880, pt. i. 
% Politzer, Membrana Tympani, p. 26. 
| Phil. Trans. London, 1800, p. 155. 
§ Loc. cit. p. 252. THE FALLACY OF THE PRESENT THEORY OF SOUND. 
95 
stances in which an artificial membrana tympani raises 
the hearing power from a very low degree to a higher 
one.” This fact can be readily explained, and will be 
below. 
Sir Astley Cooper * was the first to puncture the mem- 
brana tympani to cure deafness, and he cites four cases 
which by such treatment were made to hear distinctly. 
Hunold punctured every membrana tympani to which 
he could get access, and he reported the brilliant result 
of curing or improving seventy cases out of a hundred. 
While this has been questioned, Michaelis succeeded in 
improving the hearing of 3300 of the cases treated by 
him. Karl Himly wrote a commentary upon the opera- 
tion, to show that it was only in exceptional cases that 
puncturing the membrane was of any value. The truth 
of the matter, as it appears to me, is that if it were not 
for the middle or inner ear being liable to get inflamed 
or diseased, the puncturing of the membrane would be 
performed very much oftener than it is. 
Sufficient cases on record prove, however, what we are 
more interested in—that, for the perception of sound, the 
membrana tympani can be completely removed and the 
subject will hear as well, if not better, without it as with 
it. Therefore the beautiful idea of the necessity of the 
* Phil. Trans. Royal Soc. London, 1801. 96 
THE FALLACY OF THE PRESENT THEORY OP SOUND. 
tympanic membrane vibrating once in and once out for 
each vibration and being hit harder by the air-particles 
to produce intense notes than if notes less intense are 
sounded, or the idea that such membrane is necessary at 
all except to oblige a supposed wave-theory, I think from 
the above is clearly established, as the medical student re- 
ferred to by Sir Astley Cooper in his work lost his 
tympanic membrane but could hear very well. The real 
value of the tympanic membrane is then simply to keep 
the cold and dust out of the middle ear, which otherwise 
might become inflamed or diseased. 
Just imagine how accommodating, says Prof. Cox,* 
the tympanic membrane is supposed to be by the high 
authorities. If the notes C 2 (256 vibrations), E2 (320), G2 
(384), and C 3 (512) of the piano be struck simultaneously, 
according to the wave-theory this membrane is supposed 
to vibrate within the same second in and out 256, 320, 
384, and 512 times. And each sound-wave is supposed 
to go through the air as if it alone were present. Does 
this not look absurd, and is it not a valuable discovery 
which proves that sound-perception does not depend on 
the vibration of the membrana tympani at all ? When 
the middle ear is diseased, the hearing can be benefited 
by a hearing-trumpet or audiphone. 
* Microcosm, Sept. 1884, p. 60. THE FALLACY OE THE PRESENT THEORY OF SOUND, 
97 
Sir "William Thomson in his lecture coolly instances 
a case of a deaf man hearing music by holding a stick be- 
tween his teeth pressed against the piano while he was 
playing it, not seeming to recognize the fact * that this 
conduction of sound to the auditory nerve by means of 
the solid bones of the head was a flat overturn of his 
pretentious barometric philosophy. 
Prof. Helmholtz states that the drum-skin, as well as 
every other membrane, must have some definite pitch as 
the “ the vibrational number of its own proper tone 
hence has claimed to have proved that this membrane is 
toned to a relatively deep note as a result of its funnel- 
like shape. He says that the tone cannot be exactly de. 
termined, but it is certainly not higher than 700 vibra- 
tions. So that if the highest note but one in a seven- 
octave piano-forte (G), with 8400 vibrations in a second, 
should be sounded, the tympanic membrane at once is 
coerced into an abnormal rate of nearly 3000 oscil- 
lations out of tune, assuming the vibrational number of 
the membrane to be 440, or the note A, and this too by 
“ sympathetic vibrationand then, contrary to all known 
mechanical or acoustical laws, it drops that motion and 
takes up a new rate of 440 vibrations a second, without any 
known or exciting cause whatever to superinduce it, since 
* Hall, loc. cit. p. 304. 98 
THE FALLACY OF THE PRESENT THEORY OF SOUND. 
we are told by Helmlioltz tbat “ as soon as the exciting 
tone ceases it goes on sounding in the pitch or the vibra- 
tional number of its own tone.” “ Hence A must be 
sounding,” says Hall, “in my ear as a perpetual monotone,, 
while an orchestra is playing, filling up every interval 
which occurs in any piece of music I hear.” 
As the vibrational number of any stretched membrane 
depends on its size, weight, and tension, and as it is 
evident that no two drum-skins can combine these ele- 
ments to exactly the same degree in different individuals, 
it follows that with one person A would be the pre- 
dominant or loud note, with another B or Bb, with an- 
other C or Off, with another D, and so on through the 
chromatic scale, or possibly through several octaves. 
Fortunately, however, such trash as this need not confuse 
us, as I have already shown that the tympanic membrane 
can be punctured or removed and the subject will hear 
as well, and in many cases better, without it as with it. 
A word before closing, in relation to the rods of Corti, 
which have already been referred to in the first part of 
this paper. Helmholtz insists that they “ must be dif- 
ferently tuned and their tones form a regular progressive 
series of degrees through the whole extent of the 
musical scale.” The “ differently tuned ” strings of a 
piano-forte in order to produce its seven octaves are not 
only compelled to vary in length from feet to If THE FALLACY OF THE PRESENT THEORY OF SOUHD. 
99 
inches, the difference being as Ito 40; the size and weight 
must also differ, the weight of the highest and lowest 
strings of the piano-forte in order to “form a regular 
progressive series of degrees through the whole extent of 
the musical scale” being 1 to about 1600, 
Hensen, however, shows that the difference between the 
longest and shortest of these Corti rods is only about one 
half, or as 1 to 2, while no perceptible difference in size 
is recorded which is necessary in the strings of a piano- 
forte. C. Hasse has shown that these microscopic pro- 
cesses, so essential to the wave-theory of sound, have no 
existence at all in the ears of birds ! Yet the mocking- 
bird can distinguish, analyze, and imitate the finest shade 
of pitch equal to a prima donna! Away, then, to the 
winds goes the Corti lute of 3000 strings, as Prof. Tyndall 
calls it. 
As regards the unisonant vibration of the antennse or 
so-called “auditory hairs” of the mysis or opossum- 
shrimp, as also the vibration of the so-called variously 
tuned fibrils of the antennse of the male mosquito as 
spoken of by Mayer,* these motions must be regarded 
as simply reactive instead of unisonant, being first heard 
by the animal through the proper auditory organs with- 
out any motion whatever of such parts, and then reflected 
* Am. Jour. Sci., Aug. 1874. 100 
THE FALLACY OF THE PRESENT THEORY OF SOUND. 
back upon the antennae or fibrillae through the nervous 
system of the creature, thus causing the tremor which is 
noticed by experimenters as the supposed direct result of 
unisonant action. The filing of a saw or some peculiar 
scraping movement of a slate-pencil, for instance, will 
often react through the nervous system unpleasantly upon 
the teeth, and with some temperaments, so to set them 
on edge as to be almost unendurable. No one, of course, 
would suppose that such impressions on the teeth could 
occur from the direct or objective action of sound- 
pulses, since a deaf person would perceive no such effect. 
Let scientists, says Dr. Hall, test the question of 
unisonant vibration of antennae on a dead opossum- 
shrimp or a mosquito, if they wish to show the absurdity 
of their deductions. THE FALLACY OE THE PRESENT THEORY OE SOUND. 
101 
Conclusion. 
In conclusion of tins lecture, I would state that 
numerous other arguments could be added to show con- 
clusively the fallacy of the wave-theory of the sound, but 
time will not permit; and I question whether any more 
arguments can be necessary, for Prof. Huxley * has said; 
“ Every hypothesis is bound to explain, or at any rate 
not to be inconsistent with, the whole of the facts it pro- 
fesses to account for; and if there is a single one of these 
facts which can be shown to be inconsistent with (I do 
not merely mean inexplicable by, but contrary to) the 
hypothesis, such hypothesis falls to the ground—it is 
worth nothing. One fact with which it is positively in- 
consistent is worth as much and is as powerful in nega- 
tiving the hypothesis as five hundred.” 
My object this evening, as I have stated before, was to 
show the fallacy of the wave-theory of sound first demon- 
strated by Dr. Hall, and to point out just such facts as 
Huxley speaks of, and to show that it is a fallacy of 
science handed down from age to age like the Ptolemaic 
* Origin of Species, p. 140. 102 
THE FALLACY OF THE PRESENT THEORY OF SOUND. 
system of astronomy till a Copernicus arose, and his aide- 
de-camp Galileo, to show the world a more excellent sys- 
tem. 
Now, gentlemen, while I submit the arguments and 
facts presented in this paper to your careful considera- 
tion, with the hope that you will weigh the facts and 
mathematical deductions with the greatest of care and 
with the one view before you of searching for truth and 
accepting the same when found, I am willing to risk the 
fallacy of the wave-theory upon the correctness of one 
single objection, and that is the slow instead of swift 
movement of the tuning-fork when sounding audibly 
and its inability to produce sonorous sound-waves at all 
as required by the current theory of acoustics. 
If any scientist can fairly and logically meet and 
answer this argument, I will gracefully acquiesce. 
Otherwise the wave-theory should be abandoned at once 
as a mistake, for one single fact which is positively op- 
posed to an hypothesis, according to Huxley, overturns it 
as completely as would five hundred such opposing facts. 
I know some scientist will say, We adopt the current 
theory provisionally for want of a better one. This I pro- 
pose to give at some future time. All that I ask now is 
to have the fact admitted that the wave-theory is falla- 
cious. lam satisfied that there are scientific men who 
have so much faith in the correctness of the wave-theory THE PALLACY OP THE PRESENT THEORY OP SOUND. 
103 
of sound that it would be difficult to convince them that 
the theory could be incorrect. Their faith might be lik- 
ened unto the Arabic adage: “If the pitcher fall on the 
stone, so much the worse for the pitcher; and if the 
stone fall on the pitcher, so much the worse for the 
pitcher”—always worse for the pitcher, or for any argu- 
ments which attack a theory that has been upheld for 
2500 years, and more especially when such theory has 
been and is sustained by the ablest living scientists. 
Let the investigation commence, but do not waste time 
attacking the less important points; proceed at once 
to the strong ones, such as the arguments referring to 
the tuning-fork and to so-called interference, and let the 
world know whether the wave-theory is the stone or 
whether it has been shown to be the pitcher by the argu- 
ments advanced this evening.