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THE INTERNATIONAL SCIENTIFIC SERIES.
SIGHT:
AN EXPOSITION OF THE PRINCIPLES
MONOCULAR AND BINOCULAR VISION
                   BY

          JOSEPH  LE CONTE, LL. D.,

AUTHOR OF '"ELEMENTS OF GEOLOGY, "RELIGION AND SCIENCE, AND PROFES:OR OP
    GEOLOGY AND NATURAL HISTORY IN THE UNIVERSITY OF CALIFORNIA.
WITH NUMEROUS ILLUS1RATIONS.
         NEW YORK:        ^L/,'T—  -
D. APPLETON" AND COMPANY,
1, 8, and 5 BOND STREET.
       1881. 
1
I  Tfc65
         COrYRIGHT BY
D. APPLETON  AND  COMPANY.
            1881. 
PEEFACE.
    In writing this treatise I have tried to make a book
that would be intelligible and interesting to the thought-
ful general reader, and  at the same time profitable to
even the most advanced specialist in.this department.
I find justification for the attempt in the fact that there
is not, to my knowledge, any work covering the same
ground in  the  English  language.   Yision has  been
treated either as a branch of optics or else as  a branch
of physiology of the nervous system.  Helmholtz's great
work on " Physiological Optics,'' of which there exist
both a German and  a French edition, is  doubtless ac-
cessible to scientists,  but this work  is so technical  that
it is practically closed to all but the  specialist.  I be-
lieve, therefore, that the work which I now offer meets
a real want, and fills a^real gap in scientific literature.
    The form in which  the subject is here presented
has been developed  entirely independently, and as the
result  of a conscientious endeavor  to  make  it clear to
students under my instruction.   As  evidence of this, I
would draw attention to the fact that, orrt of one hun-
dred and thirty  illustrations, only  about  twelve  have 
4
PREFACE.
been  taken from  other  writers.   On  those  points  in
which I differ, not only in form  but  in matter, from
other writers, I  am willing to abide the judgment  of
those best qualified to decide.
   I  have devoted a  large, perhaps some may think a
too large, space to the discussion of binocular  vision.
I have done so, partly because I  have devoted  special
attention to this department, partly because it is so very
imperfectly presented by other writers, but chiefly be-
cause it seemed to me by far the most  fascinating por-
tion of the whole subject of vision.
   As a means of  scientific culture, the study of vision
seems to me almost exceptional.   It makes use of, and
thus connects together, the sciences of Physics, Physi-
ology, and even Psychology.   It makes the cultivation
of the habit of observation and experiment possible to
all;  for the greatest variety  of  experiments may be
made without expensive  apparatus, or, indeed,  appa-
ratus  of any kind.  And, above all, it compels one to
analyze the complex  phenomena  of Sense in his own
person, and is thus a truly admirable preparation for
the more difficult task of analysis of those still higher
and more  complex phenomena which are embraced in
the science of Psychology.
Berkeley, California, May 20, 1880. 
ANALYTICAL  TABLE   OF  CONTENTS.
                        INTRODUCTORY.
                                                            PAGE
 The Relation of General Sensibility to Special Sense .     9
    Law of differentiation, 10; gradation among the  senses, 11;  in
        kind of contact, 13; in distance of perception, 13; in refine-
        ment of organ, 14.


                            PART  I.

                     MONOCULAR  VISION.

                          CHAPTER I.

 General Structure of the Human Eye, and  the  For-
      mation  of Images.       .       .      .      .       17
    Section I.—General Structure :  General form and setting, 17;
        illustrations, 18; the muscles, 18; illustrations of their action,
        19; the eyeball, 20; sclerotic,  20; cornea, 21; iris, 21; lin-
        ings, 22; choroid, 22; ciliary  musck, 22; retina, 22; con-
        tents of ball, 23 ; lens, 23 ; humors, 24.
    Section II.—Formation of the Image, 24; conditions of per-
        fect image, 25; experiment, 27; illustrations, 27 ; property
        of a lens, 27 ; proofs of a retinal image, 29 ; nodal point, 29.

                         CHAPTER n.

The Eye as an  Optical Instrument      .      .      .30
    Comparison with the camera, 30; chromatism, 31; correction  of
       chromatism, 31; aberration, 35  ; correction of aberration, 36 ;
       adjustment for light, 37; adjustment for distance, 40; accom-
       modation of the eye, 42; experiment illustrating, 42; theory
       of adjustment, 44; Helmholtz's view, 44. 
6            ANALYTICAL  TABLE OF  CONTENTS.
                          CHAPTER III.

Defects of the Eye as an Instrument
    Emmetropy, or normal sightedness, 46 ; myopy, or near-sighted-
        ness, 46; presbyopy, or old-sightedness, 48 ; hypermetropy,
        or long-sightedness, 51; astigmatism, 52.

                          CHAPTER IV.
Explanation of Phenomena of Monocular Vision     .   53
    Section I.—Structure of Retina, 53; optic nerve, 54; relations
        to the eye, 54; layers of retina, 55; bacillary layer, 55; cen-
        tral spot, 57; blind spot, 59; perception of color, 59; primary
        colors, 60 ; view of Brewster, 60; of Young, 60 ;  of Hering,
        60; theory of color-perception, 61; theory of Young, 61; of
        Hall, 61; color-blindness, 62; theory of, 63.
    Section II.—Functions of the  Retina : Law of outward pro-
        jection of retinal impressions, 64; compared with other senses,
        65; illustrations of this property, 66 ; phosphenes,  67; muscae
        volitantes, 67;  Purkinje's figures, 68; ocular  spectra,  69;
        corresponding points,  retinal  and spatial, 72; properties of
        the central spot, 73 ; function of the central spot, 74; mini-
        mum visible, 76; minimum tactile, 77 ;  blind spot, 78; ex-
        periments  illustrating, 78-81; why there is no visible repre-
        sentative of this  spot in field of view, 82; erect vision, 83 ;
        comparison with other senses, 84; explained by law of direc-
        tion, 85; illustrations of this law, 86.

                            PART II.

                      BINOCULAR  VISION.
                           CHAPTER I.
Single and  Double Images .        .       .       .        .90
  .  The two  eyes  as one instrument, 90; the binocular field,  91;
        double images, 92 ; experiments illustrating, 92-94; analogy
        with  sense of touch, 95;  single vision, 95; corresponding
        points of the two retinae, 96; law of corresponding  points,
        97 ; conditions of single vision, 99; horopter, 101; optic chi-
        asm, and its relation to the law of corresponding points, 101;
        theories of the origin of property of corresponding points,
        102; nativistic theory, 103 ; empiristic theory, 103; consen-
        sual adjustments, 104; two fundamental laws, 105.

                          CHAPTER II.
Superposition of External Images       .       .        .107
    Of the same object, 107 ; of different objects, 108; Case 1. Dis-
        similar objects, 108; experiments illustrating, 108-109 ; Case
PAGE
  46 
ANALYTICAL TABLE  OF CONTENTS.
7
        2.  Similar objects, 112;  experiments illustrating,  112-113;
        Case 3. Many similar objects regularly arranged, 115; experi-
        ments illustrating, 115;  dissociation of consensual adjust-
        ments, 117; experiment  illustrating, 118;  general conclu-
        sions, 118.

                           CHAPTER III.
 Binocular  Perspective     .       .          ■     .        ,   120
    Experiments illustrating, 120-123; stereoscopy, 125 ; stereoscopic
        pictures,  126; how taken, 127; combination of stereoscopic
        pictures, 128 ; with the naked eyes, 128 ;  experiments illus-
        trating, 129-133;  combination by the use  of the stereoscope,
        134;  inverse perspective,  135;  experiments illustrating, 136-
        141;  different forms of perspective,  142 ; aerial, 142 ; mathe-
        matical, 142 ; monocular or focal, 142; binocular, 143.

                           CHAPTER IV.
 Theories  of Binocular Perspective      .       .        .   145
    Wheatstone's  theory,  145 ; Brucke's theory, 147 ; Dove's experi-
        ment, 148; my own view, 151; return to  comparison of the
        eye with the camera, 152.

                           CHAPTER V.
 Judgment of Distance, Size, and Form    .       .        .   156
    Judgment of distance, 156 ; different modes of, 156 ;  size, 157; ex-
        periments illustrating, 158,159; form, 160; outline form, 160;
        solid form, 160; gradation of judgments, 160; retrospect, 162.


                            PART  III.

    ON SOME DISPUTED POINTS IN BINOCULAR  VISION.

                           CHAPTER I.
Laws  of  Ocular Motion   .....   164
    Section I.—Laws of Parallel Motion :  Listing's law, 164;
        experiments illustrating, 164-172; the statement of the laws,
        173;  contrary statement by Helmholtz explained, 175; rota-
        tion on optic axes  in parallel motion  only apparent, 176.
    Section II.—Laws of Convergent Motion,  177; the rotation
        in this case real,  178; difficulty in  experimenting, 178; ex-
        periments proving  rotation  on optic axes in  convergence,
        180-187; effect of elevation and depression of visual plane,
        188;  experiments illustrating, 188; cause of  the rotation,
        189;  laws of parallel and convergent motion contrasted, 189. 
8
ANALYTICAL TABLE  OF  CONTENTS.
                           CHAPTER II,
                                                               PAGE
The  Horopter       .       .        ,       .        .       .192
    Defined, 192; difference of opinion as to its nature, 193; Midler's
        horopteric circle, 194;  Claparede's view, 194; Helmholtz's
        results, 195;  Helmholtz's view as to the relation of apparent
        and real vertical meridian, 197; experiments testing its truth,
        198;  adverse conclusion reached, 201  ; Meissner's results,
        experiments proving, 203;  my  results confirm Meissner's,
        206;  experiments proving,  206-210 ; conclusions in regard to
        the horopter, 210; wherein I differ from Meissner, 211.

                          CHAPTER  III.

On some Fundamental  Phenomena  of  Binocular Vision
      usually overlooked, and on a New Mode of  Dia-
      grammatic Representation based  thereon .       .213
    Usual mode of representation untrue, 213;  experiments illustrat-
        ing, 214 ; heteronymous shifting of the two fields of view and
        experiments illustrating, 216-221; ceil cyclopienne, 217, 222;
        first law or law of  heteronymous shifting stated, 223; ho-
        monymous rotation of the two fields, 224;  experiments illus-
        trating, 224-227 ; second law or law of homonymous rotation
        stated, 228; statement of the two laws, 229;  determination
        of the interocular space, 230; experiments illustrating the
        necessity of the new mode, 231-237 ; application of the new
        mode to representation of stereoscopic phenomena, 238.  Some
        curious phenomena resulting from the  heteronymous  shift-
        ing of the fields of view, 245; to trace the outline of a picture
        where it is not, 245; to trace the  outline of a candle-flame on
        an opaque screen, 248; to see through a book or a deal board,
        250.

                          CHAPTER  IV.

Visual  Phenomena  in  Ocular Divergence      .       .   252
    1. In drowsiness, 252; 2. In other modes  of producing  diver-
        gence, 255; 3. Prevalence of law of corresponding points over
        law of direction, 258; diagrams illustrating, 259.

                          CHAPTER  V.

Comparative Physiology of  Binocular Vision  .       .   262
    Optic chiasm in lower animals, 262; divergence of eye-sockets
        263; when extreme, incompatible with binocular vision, 264 •
        central spot, 266; how far  it exists in  lower animals, 267 •
        importance of this spot, 267 ; general changes in the eye as
        we go up the vertebrate scale, 269. 
SIGHT.
              INTEODUCTORY.

 THE RELATION OF GENERAL SENSIBILITY TO SPECIAL
                       SENSE.

    Sensory nerve-fibers are cylindrical threads of mi-
 croscopic fineness, terminating outwardly in the sensi-
 tive surfaces and  sense-organs,  and inwardly in the
 nerve-centers,  especially  the brain.    Impressions  on
 their outer extremity are transmitted  along  the  fiber
 with a velocity of about one  hundred feet  per second,
 and determine changes in the nerve-centers,  which in
 turn may determine changes in consciousness, which we
 call sensation.  The simplest and most  general form of
 sensation is what is called general sensibility, or common
 sensation.   This is a mere sense of contact, an indefinite
 response to external impression.  It gives knowledge of
 externality—of the existence of the  external  world—
 but not of the properties of matter.  The lowest animals
possess this, and nothing more.   But, as we go up the
scale of animals, in order to  give that wider and more
accurate knowledge of the various properties of matter
necessary for  the  complex relations of  the  higher ani-
mals, sensory nerve-fibers are differentiated into several
kinds, so that  each may give clear knowledge of differ- 
10
INTRODUCTORY.
ent properties.  Thus, for example, the  first  pair  of
cranial nerves—olfactive—is specially organized to take
cognizance of certain impressions, called smells, and no-
thing else.  If, therefore, these nerve-fibers are irritated
in any way, even mechanically, by scratching or pinch-
ing, they do not feel but perceive an odor.   The second
pair of cranial nerves—the optic—is specially organized
in a truly wonderful  way to respond  to  the ethereal
vibrations called light, and nothing else.  If, therefore,
these  nerves be mechanically irritated, we do not feel
anything, but see a flash of light.   In a similar manner,
the eighth pair—auditive nerve—is  specially organized
to respond to sound-vibrations, and nothing else; and
therefore mechanical irritation of this  nerve produces
only the sensation of sound.  Similarly, the ninth pair,
or gustative nerve,  is organized for  the appreciation  of
taste  only; and, therefore,  a feeble  electric  current
through this nerve produces a peculiar taste.
   We have in these  facts only  an  example of a very
wide law, viz., the law of differentiation.  In the lowest
animals all the tissues and organs which are so widely
distinct in the higher animals are  represented by  an
unmodified cellular structure, performing all the func-
tions of the animal body, but in an imperfect manner.
Each  cell in  such an organism will  feel like a nervous
cell, contract like a muscular cell, respire like  a lung-
cell, or digest like a stomach-cell.   As we go up the ani-
mal scale, this common structure is differentiated first
into three main systems, viz., the nutritive or epithelial
system, the ?i<?ry<?-system, and the hlood-system : the first,
presiding over absorption and elimination, i. e., exchange
of matter between the exterior world and the organism :
the second, over exchange of force between exterior
and interior by  impressions  determining changes  in 
        RELATION  OF GENERAL TO SPECIAL SENSE.    \\

 consciousness, and by will determining changes in exter-
 nal phenomena; the third, presiding over exchanges be-
 tween different parts of the organism.  The first kind
 of exchange may  be likened  to foreign commerce;  the
 second, to exchange of intelligence by telegraphic com-
 munication with  foreign countries;  the third, to  the
 internal carrying trade.  These three systems  are very
 early differentiated  in the embryo, since they are sev-
 erally produced from the three primitive layers of  the
 germinal disk, viz., the endoderm,, the ectoderm, "and
 the mesoderm.
    Neglecting now all but  the second or nervous sys-
 tem as we still go up, this  is again differentiated into
 three sub-systems, viz., the conscio-voluntary, or sensori-
 motor,  the reflex,  and the  ganglionic, each  with its
 center and its afferent and efferent fibers.   Neglecting,
 again, the two others, and selecting only  the sensori-
 motor, the sensory fibers of this sub-system are again
 differentiated into five kinds, each to respond to a dif-
 ferent kind of impression, and perceive a different prop-
 erty,  viz.,  the  five  special  sense-fibers for  sight,  hear-
 ing, smell, taste, and touch.   Even these are probably
 again further differentiated; for the  perception of dif-
 ferent colors and  different  musical sounds  is probably
 effected by means of special fibers of the optic and  au-
 ditive nerves.   The following diagram (Fig.  1)  illus-
 trates these successive differentiations.
   Gradation among  the Senses.—Now all these higher
special senses may be  regarded  as the result of refine-
ments of common sensation—each a more refined touch.
Coarse vibrations are perceived by the  nerves of com-
mon sensation as a jarring.   "When the vibrations are
so rapid that there are sixteen complete  movements
back and  forth in a second, an entirely different sensa- 
12
INTRODUCTORY.
tion is produced, which we call sound.  The vibrations
are no longer perceived by the nerves of common sen-
sation, but a special nerve—the auditive—is organized to
respond to or co-vibrate with them.   As the vibrations
increase in number, they are perceived as  higher and
higher pitch, until they reach the number of about
Fig. 1.
    UNMODIFIED
CELLULAR STRUCTURE
40,000 in a second.  This is  the highest pitch the ear
can perceive, the quickest vibrations  the auditive nerve
can respond to.  Beyond this there  is absolute silence,
but only because we have no  nerve organized to co-
vibrate  with these  more  rapid undulations.   These
vibrations, inaudible to us, may possibly be perceived by
some lower animals, as, for example, insects;  we can not 
       RELATION OF GENERAL TO  SPECIAL SENSE.     13

tell.  After a long  interval, vibrations again appear in
consciousness as light.  The vibrations which produce
this sensation are so rapid—399,000,000,000,000 in a sec-
ond—that they can be conveyed only by the ethereal
medium.   For the perception of  these vibrations, a pe-
culiar and  wonderful organization  is necessary, found
only in the optic nerve.   Above the number just given,
ethereal vibrations are perceived  as different colors, in
the order seen in the spectrum, until  831,000,000,000,-
000 is reached.   Beyond  this we have no nerve capable
of responding.
    The  gradation among  the  special  senses may  be
shown in a different way.  In touch we require direct
and usually solid contact; in taste, liquid contact, for
unless a body is soluble it can not be tasted; in smell,
the contact  is gaseous, for  unless a body is volatile  or
vaporizable it can not be smelled.  In this last case,
the perception of objects at a distance  begins; still it
is by direct contact, for particles from the distant body
must touch the  olfactive nerve.  In  hearing, there is
no contact of the sounding body,  but the vibrations are
conveyed through a medium.  AVe perceive at a dis-
tance, limited only by the extent of the atmosphere and
the energy of the initial vibration.  In sight, finally, we
perceive objects at a distance which is  illimitable, the
vibrations being conveyed by a medium which is uni-
versal, and  too subtile to be  recognized except as the
bearer of light.
   Again, commencing with taste: In this sense we dis-
tinctly perceive  that the  sensation is subjective—is  in
us, not  in the body tasted.  In smell, there is an equal
commingling of subjectiveness and objectiveness.   AVe
distinctly perceive the sensation as in the nose, and yet
by experience wc  have learned  to refer it to an object 
14
INTRODUCTORY.
 at a distance.  In hearing, we already refer the cause
 so completely to a distant  object that there is but the
 smallest possible remnant  of a consciousness of sensa-
 tion in the ear; the sound does not seem to be in the
 car, but  in yonder bell.  Finally, in sight, the  impres-
 sion is so completely projected outward, and  the con-
 sciousness of anything taking  place in the eye so com-
 pletely lost, that it is only by careful  analyses that we
 can be convinced of its essential subjectiveness.
    The  order which we have  given above is also the
 order of increasing specialization and refinement of the
 senses.   But only in the two higher senses—only in
 those senses in which there is no direct contact, but the
 impressing force is conveyed  by means of vibration
 through  a medium—only in these highest senses do we
 find that, besides the specialization of the nerve-fibers
 to respond to peculiar vibrations, also an elaborate in-
 strument is placed  in front of  the specialized nerve in
 order to  intensify the impression and give it more defi-
 niteness.  It  is wholly by virtue of this supplementary
 instrument that we are able to  hear not only sound but
 music, or to see not only light but objects.   The lowest
 animals in which an optic nerve is found perceive light,
 but not objects; because, though the specialized nerve is
 present, the appropriate  instrument  is wanting.   It is
 on these two higher senses that fine art  is wholly and
 science is mainly founded.   The specialized nerve and
the instrument for intensifying  and making definite the
impression are together called the sense-organ.  It is of
the most highly specialized  of these nerves and the
most refined  of these instruments, the highest  of the
sense-organs, the eye, that we  are now about to treat.
   It may be well to bear in mind  and keep  distinct
what may be called the direct  gifts  of sight, and what 
       RELATION OF  GENERAL  TO SPECIAL SENSE.    15

are added by the mind as judgments based upon these
gifts.  The direct data are only light, its intensity, color,
and direction.  These are incapable of  further analysis,
and are therefore simple sensations.  Outline form may
possibly be added, though this may be analyzed  into a
combination  of  directions.  But solid form, size, and
distance, though they may seem to be immediately per-
ceived, are not direct perceptions, but only very simple
judgments based on  the data given above.  We only
state these facts now that they may be borne in mind.
We  hope to substantiate them hereafter. 
 
                     PAET  I.

          MONOCULAR  VISION.



                   CHAPTER I.

 GENERAL STRUCTURE OF THE  HUMAN EYE, AND THE
               FORMATION OF IMAGES.

     SECTION I.—GENERAL STRUCTURE OF THE EYE.

   General Form and Setting.—The eye is nearly spheri-
 cal in shape, and about an inch in diameter.  The socket
 in which it is set is not a hollow  sphere, but an irregular
 hollow  cone  or  pyramid.   Evidently,  therefore,  the
 deeper and smaller parts of the hollow must be filled
 with something else.  It is filled with loose connective
 tissue, containing  fat.   On this, as  on  a soft cushion,
 the eyeball rolls with ease in every direction.  The eye
 proper is really behind the shin,  or outer integument of
 the face, for the skin which covers the lids turns over the
 edge (Fig. 2,11) and passes under the lids, becoming here
 thin and tender mucous membrane;  it is then reflected
from the back part of the lid to the anterior surface of
the white portion of the ball (Fig. 2, a a), then passes for-
ward again over the ball as far as  the clear part, or cornea
(Fig. 2, c c c), and  then entirely over this, although very
closely attached.  If carefully dissected off, it would leave 
18
MONOCULAR VISION.
the eyeball behind it.  This mucous  covering of the
anterior portion of the eyeball is called the conjunctiva.
   Illustrations.—In ordinary inflammations of the eye,
it is this  mucous membrane which is  affected, and not
the eye proper.  Disease of  the eye  proper is a far
more serious matter.
   When motes get into the eye, they can not go be-
yond easy reach, viz., beyond the reflection of the mu-
cous membrane, from the lid to the ball, at the points a a.
   The Muscles.—We all know the rapidity and preci-
sion  with which, the eye turns in all directions.  This
is by means of  six slender muscles.  Four of  these are
Fig. 2.                        Fig. 3.
called the straight muscles, and two the oblique muscles.
The straight muscles all rise at the bottom of the con-
ical socket,  diverge as they pass forward,  and grasp
the eyeball above, below, on right and left side, just in
front of the middle or equator of the globe (Fig. 3).
They are called  severally  superior, inferior, external,
and internal rectus.  The first turns the ball upward,
the second downward, the third  to the  right, and the
fourth to the left, if we are speaking  of  the right eye.
This is their action expressed generally; but, by refer-
ence to  Fig. 20, on page 54, it is seen that the axis of 
          GENERAL STRUCTURE OF  THE EYE.        19

the eye is not  coincident with the axis of the socket,
and, therefore, the action of the superior rectus by itself
is not only to turn the eye upward, but  also to rotate
it a little on its axis inward toward the nose;  while the
inferior rectus  not only turns the eye downward, but
also rotates it a little on its axis outward.
    The oblique muscles are superior and inferior.  The
superior oblique (Fig. 3, b)  rises like  the  recti  at the
bottom of the  socket, passes forward, contracts to a
slender tendon, passes  through a loop situated  in the
forward part of the socket, on the inner (nasal) and up-
per side (Fig. 3, c); it then turns upon itself backward
and outward, passes  over the  globe obliquely across
the equator,  and is  attached  to  the sclerotic, or white
coat of the  eye,  on  the  outside,  a little  behind the
equator.   From its last direction it is evident that its
function is  to  turn the  eye outward  and downward,
and at the same time to rotate it  on its axis  inward, i. e.,
sinistrally for the right eye  and dextrally for the left.
The inferior oblique (Fig. 3, d) rises from the anterior,
inner, and lower portion of  the  socket, passes outward
and backward beneath the ball, and, crossing the equator
obliquely, is attached to the  ball on the outside, a little
behind the  equator.   From  its  direction it  is evident
that its function is to turn the eye  inward and upward,
and at the same time to rotate it  on its axis outward,
i. e., dextrally—or like the hands of a watch—for the
right and sinistrally for the left.
   Illustrations of these Actions.—If we  desire to  look
upward,  we  bring into action the two superior recti;
if downward, the two  inferior recti; if to the right, the
exterior rectus of the  right  and the interior rectus of
the left eye; if to the left, the external rectus of the
left and  internal of the right.  If we desire  to look at 
20
MONOCULAR VISION.
a very near object, as, for example, the root of the nose,
then the two interior recti are brought into action. But
we can not voluntarily bring into action the two exterior
recti to turn the eyes outward, nor the superior rectus
of one eye and the inferior rectus of the other, so as to
turn  the  one eye  upward and  the  other  downward.
The reason of  this is because such motions, so far from
subserving any useful purpose, would only confuse us
with double images, as will be explained hereafter, and
therefore have never been learned.
   Malpositions of the  eye, such as squinting, are the
result of too great contraction of one of the recti mus-
cles, usually the internal.  It is often cured by cutting
the muscle, and allowing it to attach itself to a new point.
   The Eyeball.—We have thus far spoken only of what
is external to the ball, viz., the socket, the muscles, etc.
We come  now to explain the structure of the ball itself.
Suppose, then, the  ball be removed  from the  socket,
and  the muscles and  connective  tissue be  dissected
away; let us  examine more minutely  its form and
structure.
   The eye thus separated is  nearly a  perfect  globe,
except that the front part is more protuberant  (Fig. 4).
   1. The outer investing coat,  except  the small pro-
tuberant front part, is a strong, thick, fibrous membrane
of a porcelain-white color, called the sclerotic.   This
is partly exposed in the living eye, and is called the
" white of the eye."  By its strength, toughness, and
elasticity  it  gives form without rigidity.  On this  ac-
count  the ball yields to pressure,  but quickly regains
its form.  It also serves as the  basis of attachment for
the muscles.  If we compare the eye  to  a globular
watch, then the  sclerotic represents the outer case.
   2.  The more protuberant part of the ball is covered 
           GENERAL STRUCTURE OF THE EYE.         21

with  a thick, strong,  but very  transparent membrane,
called the cornea (C, Fig.  4).   It  corresponds  to  the
crystal of the watch.   Its function is to admit the light,
and at the same time to refract it, so as to assist in form-
ing the image, as will be explained hereafter.
Section of the Eye.— 0, optic nerve; S, sclerotic; Ch, choroid; R, retina; r, vitre-
  ous body; Cm, ciliary muscle ;  Cj, conjunctiva; C, cornea;  /,  iris;  L, lens;
  *, aqueous humor; **, ciliary body or zohule of Zinn.

    3. Running  across from  the circle of  junction of
the cornea with the sclerotic, and thus cutting off the
more protuberant clear part  from the main part of the
ball, and  thus corresponding  in  position to the face of
the watch, there is an opaque, colored plate called the
iris, I.   It is the colored part of the eye, black, brown,
blue,  or gray, in different individuals.   This transverse
plate  is not  perfectly flat, but protrudes a little in the
middle.   In its center is a round hole, called the pupil, 
22               MONOCULAR  VISION.
corresponding in position with the hole in the watch
face for attachment of  the hands.  The pupil seems to
be jet black,  because the observer looks through  the
pupil into the dark interior of the ball.  The function
of the pupil is to admit, and at the same time regulate
the amount of, light.
   4. Linings.—Thus much is visible to the naked  eye
without  dissection.  But, if  the  ball be now carefully
opened, the part behind the iris  is found  to be lined
with  two thin membranes,  (a.)  Immediately in con-
tact with the sclerotic is the choroid, a thin membrane,
the cells of which are colored with  black pigment, which
gives it a deep-brown, velvety appearance.  Its function
is to quench the light as soon  as  it has done its work
of impressing the retina.  The anterior portion of  the
choroid,  separated  from the sclerotic,  drawn  together
as a curtain, and thickened  by muscular tissue, forms
the iris already described.  Just before separating from
the sclerotic to form the iris, it splits into two layers:
one, the anterior, goes to form the iris, as already said,
while the other, the posterior, is gathered into a circular,
plaited curtain, or series  of  converging folds, which
surrounds  the outer  margin  of  the lens (to  be pres-
ently described) like a dark, plaited collar.  These plaits,
or folds, seventy to seventy-two in number, are called
the ciliary processes (Fig. 5, and e, Fig. 19, p. 43).   Be-
neath this dark, plaited collar, and therefore in contact
with  the  sclerotic,  is  a  muscular collar, with radiating
fibers, called the ciliary muscle,  (b.) Within the choroid,
innermost and most important of all, is the retina.  This
is, in fact, a concave expansion of the  optic nerve  (0,
Fig. 4).   This nerve, coming from the brain, enters  the
eye-socket near its point,  penetrates the sclerotic  and
the choroid, then spreads out within as a thin, concave 
GENERAL STRUCTURE  OF THE  EYE.         23
membrane of  nerve-tissue, covering  the whole interior
of the  ball  as far forward as the ciliary collar.  Its
function  is  to receive and respond to the impressions
of light.  Its wonderful structure and functions will be
explained hereafter.
    5.  Contents.—The ball thus described is not hollow
and empty, but  filled with
refractive media, as transpa-
rent as finest glass.   These
are:
    (a.) Crystalline, or Zens.
—Immediately  behind   the
iris, and  in  contact  with it,
is found  the  crystalline.   It
is a  flattened ellipsoid, or
double convex lens, as clear
as  finest  glass,  about  one
third of an inch in diameter,
and One Sixth of an  inch in  Section of Era-a, sclerotic; b, cor-
 ...        _          .        nea; c, conjunctiva; d, iris; e, lens;
thickness, firm  enough  to    /, Cinary muScie behind the dark
handle easily, but elastic and    ciliary process*; g, retina; h, optic
           J '                   nerve.  (After Cleland.)
easily  yielding to  pressure.
On section it is found to consist of layers, increasing in
density from surface  to  center, as shown in  Fig. 5, e,
and in Fig.  13, on page 37.   The lens is invested with
a very thin, transparent membrane, capsule of the lens,
which not only invests it, but continues  outward as a
plaited curtain, to  be attached  to the sclerotic near  the
junction  of  the cornea.   The  elastic rigidity of  the
sclerotic pulls  gently on this curtain and  makes it taut,
and  the taut membrane in its turn presses gently on
the elastic compressible crystalline and slightly flattens
it.  We shall see the importance of this when we come
to speak of the adjustment of the eye for distance.
             2
 
24
MONOCULAR VISION.
   The perfect  transparency of the lens is obviously
necessary for distinct vision; cataract, a common cause
of blindness, arises from its opacity.
   The lens, with  its continuing curtain,  completely
divides the interior  of the ball  into two compartments,
an anterior and a posterior.
   (b.) The anterior  chamber  is  filled  with  a clear,
aqueous liquor, called the aqueous humor (Figs. 4 and
5), a small  portion of which is  behind the iris, but by
far the larger portion between  the iris and  the cornea.
The  two parts are in connection through  the pupil.  If
the cornea  be  punctured, the aqueous humor runs out,
the clear protuberant part of the eye collapses,  and the
sight is for the time ruined.   If, however, the wound
heals without scar,  or if the scar be to one  side of the
direct line of  sight, the cornea will fill again  and the
sight may be recovered.
   (c.) The posterior and much larger chamber is filled
with  a transparent, glassy substance, about  the consist-
ence  of soft jelly,  called the  vitreous humor.   This
humor is in direct contact with the lens and curtain in
front, and with the retina over its whole globular sur-
face.
        SECTION II.—FORMATION OF THE IMAGE.
   The eyeball, as thus described, may be regarded as
consisting essentially  of  two distinct portions, viz.: 1.
A nervous expansion, the retina, specialized for respond-
ing to light-vibrations; 2. An optical  instrument, the
lens  apparatus, placed  in front of the retina, and spe-
cially arranged to make the impression of light strong
and  definite, by means of an image.   These two are 
FORMATION OF THE  IMAGE.
25
 entirely different in their origin.  In embryonic devel-
 opment, the one is an outgrowth from the brain, the
 other an ingrowth from the epidermis and cutaneous
 tissues.   These afterward meet and  unite  to form this
 wonderful organ.
    Now the sole object of this complex instrument  is
 the formation of a perfect image on the retina.   With-
 out  images we would perceive light, but  not  objects;
 and distinctness  of objects  is exactly  proportioned to
 distinctness of  retinal images.  If the  image of  an ob-
 ject is distinct, the  object will be distinct;  if the image
 is blurred, the  object, both in outline and  in details of
 surface, will be blurred.  If there is no image, no object
 will be  visible.  Therefore  the image must  be a fac-
 simile of the real  object, for the apparent object will
 be a fac-siraile of the image.
   Conditions of a Perfect Image.—A serviceable  image
 must be sufficiently bright, and perfectly sharp and dis-
 tinct in outline.  Brightness only requires a  sufficient
 amount of  light.   In order  to be perfectly distinct,  it
 is necessary that rays from different points in the object,
 even the most contiguous, should not mix on the image,
 but all  the rays from each point on the object must be
 carried to its own point on the image.  Now, it  is im-
 possible that both of these conditions should be fulfilled,
 except  by some such arrangement as  we find  in the
 eye.
   For see : suppose  the light to enter by a hole only,
like the pupil;  and, further, in order that there be light
enough, let the  hole be somewhat large ; then the light,
diverging from  any  point, b, Fig. 6, ^4, of the object a b c,
and entering the hole h of  diaphragm d d, will form a
diverging pencil, and  spread  out over the  whole circle
V, on the screen s  s.   Similarly, the  rays  from a will 
26
MONOCULAR VISION.
spread out and form the circle a', and from c the circle
c'.  Thus it  is seen that rays  from widely different
points in the  object mix with each other on the receiv-
ing screen; much more, then, would rays from contigu-
ous points of the object mix.   In such a case, the mixing
is so great that no recognizable image is formed at  all.

                        Fig. 6.
As  the  hole becomes smaller, the circles of  dispersion,
a' V d',  become smaller in the  same proportion; and,
therefore, the light  from different points of the object
is more and  more  separated on the receiving screen,
and  the image becomes first recognizable,  then more
and more distinct.   But, in the mean time, the quantity
of light is becoming less  and  less, and therefore the
image fainter and fainter.   If we suppose the  hole  to
become a mathematical point, then one ray  only passes
from each point to the object, and goes to its own place
in the image (Fig. 6, B), and the conditions  of distinct-
ness are fulfilled; but the image is now infinitely faint,
and therefore invisible.   If, now, we try to increase the
brightness by increasing  the size of the hole, in propor- 
FORMATION OF THE  IMAGE.
27
tion as we  get brightness do we lose distinctness.  We
can not get both at the same time.
  Experiment.—Let a room with solid shutters be dark-
ened ; let one shutter  have a hole of  a few inches  in
diameter;  cover the hole with an opaque plate of sheet
iron, in which there is a very small hole, one tenth  to
one twentieth of an inch in diameter.  If, now, a sheet
of white paper be held a little way from the small hole,
an inverted image of the external landscape will be seen
on the sheet.  If we increase  the size of the  hole, the
image will be brighter, but also more blurred.
  Illustrations.—Many  simple experiments  may  be
made illustrating this principle. A pinhole in a card
will make an inverted image of a candle flame.  When
the sun is in eclipse, it may be examined without smoked
glass, by simply allowing it to shine through a pinhole
in a card upon a suitable screen.  In the shade of a very
thick tree-top the sun-flecks are circular like  the sun;
but during an eclipse they are crescentic, or even annu-
lar, according to the degree of  obscuration.  They are
always images of the sun.
   Property of a Lens.—Now a lens has  the remarkable
property of accomplishing  both these apparently oppo-
                        Fig. 7.
site ends, viz., brightness and distinctness at the same
time.  If an object, a c, be placed before a lens, L (Fig.
7), then all the rays diverging from any point, b, are 
28               MONOCULAR VISION.
bent so as to come together again at the point  V.   Of
the divergent  pencil, b L L, the  central  ray passes
straight through without deviation; rays a little  way
from  the central are bent a little; rays farther away
are bent more and more  according to  their angle  of
divergence, so that they all meet at the same point,  b'.
Similarly all the rays proceeding from a, and falling  on
the lens, are brought to the same  point, a', and  from c
to the point c', and so also  for every intermediate point.
Thus an image is formed which is both bright and very
distinct if the  receiving screen is suitably placed, i.  e.,
at the exact place where the  rays meet.  The  billions
of rays from millions of points of the surface of the
object are, as it were, sifted out by the law of refraction,
and each safely conveyed to its own point in the image ;
so that, for every radiant point of the object, there is a
corresponding  focal point  in the image.   But it is evi-
dent that the screen must be suitably placed, for,  if it
be placed too near, at 8' S;, the rays have not yet come
together; if too far, at 8" 8", the rays have already met,
crossed, and  again diverged.  In  both cases the image
will be blurred.
                        Fig. 8.
Diagram illustrating the Formation of an Image cn tub Retina.
   In all dioptric instruments images are formed in this
way.  It is in this way that images are formed in the
eye.   In Fig. 8 it  is seen that the diverging  pencils, 
FORMATION OF THE IMAGE.
29
from  points A and B of the object, which  enter the
pupil, are refracted by the lenses of the eye, and brought
to a focus  on the retinal screen at  a' b'.  Now, since
the rays from every intermediate point of the  object
will be similarly focused, we will have a perfect  image
of the object painted on the retina.
   This fundamental fact  may be proved in many
ways  by observations on the dead eye: 1.  If the eye
of an  ox be taken from the socket, and the sclerotic
carefully removed, so that the back parts of the eye are
somewhat  transparent, a miniature image of the land-
scape may  be seen there; or, 2.  If we  remove the eye-
ball of a white  rabbit, we will find that, on account of
the absence of black pigment in the choroid of these
albinos, the transparency of the coats of the eye enables
us to see the image, even through the sclerotic, or much
more  distinctly if the sclerotic be removed; or,  3. We
may remove all the coats of the dead eye and replace
them  by a film of  mica—the image will be very dis-
tinct ;  or, 4. The image may be  seen in the living eye
by means of the ophthalmoscope.
   By reference to the diagram, Fig. 8, it  is seen that
the central rays from all radiants cross each other in
the lens.   This point of ray-crossing is called the nodal
point.  It is a little behind the center of the lens. 
CHAPTER II.
       THE EYE AS AN OPTICAL INSTRUMENT.

   The further explanation of the wonderful mechanism
of the eye is best brought out by a comparison with some
optical instrument.   We select for this  purpose the
photographic camera.  The  eye and the  camera: the
one a  masterpiece of  Nature's, the other of human
art.
   We pass over, with bare  mention, some obvious re-
semblances,  in which, however, the superiority of the
eye is  evident: such, e. g.,  as the admirable arrange-
ment of  the lids for wiping  and keeping  bright while
using, and for covering when not  in use;  also, the ad-
mirable arrangement of muscles, by which the eye  is
turned with  the greatest rapidity and precision on the
object to be  imaged, so superior to the cumbrous move-
ment  of the camera  for the same  purpose.   We pass
over these and many other  minor  points to come  at
once to the main points of comparison.
   Take, then, the eye out of  the socket—the dead eye—
and the camera without its sensitive plate—with only the
insensitive ground-glass receiving plate.  They are both
now pure optical instruments, and nothing  more.   They
are both contrived for the same purpose, viz., the for-
mation of a  perfect  image on a screen properly placed. 
        THE  EYE AS AN  OPTICAL  INSTRUMENT.      31

Look into  the camera from behind,  andwe see  the
inverted image on the ground-glass plate ; look into the
eye from behind, and we see also an inverted  image on
the retina.  The end, therefore, is the same in the two
cases.  We now proceed to  show that the  means  by
which the end is attained are also  similar.
    1. The  camera is  a small, dark chamber, open to
light only in front, to admit the light from the object to
be imaged.  It is coated  inside with lampblack, so that
any light from the object to be imaged or from other
objects which may fall on  the sides will be  quenched,
and not allowed  to rebound by reflection, and thus fall
on the image and spoil it.   No light  must fall on  the
image except that which comes directly from the object.
So  the eye also  is a very small, dark chamber, open to
light only in front, where the light must enter from the
object to bo imaged, and lined with dark pigment, to
quench  the light as soon  as it has done its work of  im-
pressing its own point of the retina, and thus prevent
reflection and striking some other part, and thus spoil-
ing the image.
    2. Both camera and eye form their images by means
of a lens or a system of lenses.   The manner in which
these act  in  forming an image has already  been ex-
plained (page 28).  It is precisely the same in both cases.
But lenses which form a perfect image are very difficult
of construction.   There  are, especially, two  main  im-
perfections which must  be corrected,  viz., chromatism
and aberration.
    3. Correction of Chromatism.—In the image formed
by a simple, ordinary lens, all the outlines of figures are
found to be slightly edged with rainbow hues.  If we
look through such a lens at  an object, the outlines of
the object will be similarly edged with colors, especially 
32
MONOCULAR  VISION.
if  the  object lie near the margin of the field of  the
lens.   This is explained as follows :
   Ordinary sunlight, as  every one knows, consists of
many colors mixed together, the mixture producing the
impression of white.   If a beam of sunlight be made to
pass through a glass prism, the beam is bent: but more,
the different colors are unequally bent, so that they are
separated and spread out over a considerable space.  This
colored space  is  called the spectrum.   In Fig. 9  the
r-v, spectrum : r, red; o, orange; y, yellow; g, green; b, blue; i, indigo; v, violet,

straight beam, a b, is bent by the prism so as to become
a c d; this  is called refraction.  But also the different
colors are unequally bent; red is bent  least and violet
most, the other colors lying  between these extremes;
thus they are spread  out  over a considerable colored
space.   This  unequal refraction is  called dispersion.
If we look through a prism at objects, we will find that
the outlines of the objects will be edged with exactly
similar  colors.  Now all refraction is accompanied by
dispersion; therefore a simple, uncorrected lens  always
disperses, especially on the edges where the refraction is
greatest; and, therefore, also, the images made by such
a lens will be edged with  color.  Thus the light from
the radiant a (Fig.  10), being white light, is dispersed ;
the violet rays, being  more bent, reach a focus at a\ 
THE EYE AS AN  OPTICAL INSTRUMENT.      33
but the red only at a", the other colors  at intermediate
points.  There is, therefore,  no place where all  the
rays from  the radiant  come  to a  focus—there  is no
common focal point  for the radiant a.  The best place

                       Fig. 10.
for the receiving screen would  be 8 8, but even  here
there is  no perfect focus.   Evidently,  therefore, the
conditions of a perfect  image are not fulfilled.   This
defect must be corrected.  It is corrected in every  good
lens.
    In order to understand how this is done, it must be
remembered, first, that  concave  and convex lenses an-
tagonize, and, if of equal refractive power, neutralize
each other.   Therefore, a combination of a double con-
vex and a double concave lens, if  of same material and
of  equal curvature, like  Fig. 11,
A, will produce no refraction, be-
cause  the refraction produced  in
one direction by the convex lens
is completely destroyed by  refrac-
tion in the opposite direction by
the  concave lens.   Such a com-    g/ A          B
bination will therefore  make no
image.   In  order that such a combination should make
an image at all, it is necessary that the convexity should
predominate over  the  concavity,  as in  Fig. 11, B.
Again, it must be  remembered that dispersion is not
always in proportion to  refraction.  Some substances
 
34
MONOCULAR  VISION.
have  a  higher refractive power and  a comparatively
low dispersive power, and vice versa.   This is the case
with different kinds of glass.
   Now, suppose we select a glass with excess of refrac-
tive over dispersive power for our convex lens, and one
with excess of dispersive over refractive power for our
plano-concave lens  (Fig. 11, B), and cement  these to-
gether as a compound lens: it is evident that these may
be so  related that the plano-concave lens shall entirely
correct the dispersion of  the convex lens without neu-
tralizing its refraction, and therefore the combination
will be a refractive, but not a dispersive, lens, and there-
fore will make an image without colored edges.   Such
a compound lens is  called achromatic.
   This  is the  way in  which  art  makes  achromatic
lenses, and all good  optical instruments have lenses thus
corrected.  Now, the lenses of the eye are  apparently
corrected  in a similar manner.   The eye  consists of
three  lenses—the aqueous, the crystalline, and the vit-
reous.  These have curvatures of different kinds and
degrees: the aqueous lens is convex in front  and con-
cave  behind; the crystalline is bi-convex; the vitreous
is concave in front.   As its convex outer surface can not
be regarded as a refracting surface, since this is  in direct
contact  with  the  screen to be impressed, it may be con-
sidered  as a plano-concave lens.   The refractive powers
of the material of  these are also different:  that of the
crystalline being  greatest, and the aqueous least.  The
dispersive powers of these have not been determined,
but they  probably  differ in this respect also.  Thus,
then,  we  have  here also  a  combination of  different
lenses, of different  curvatures, and different refractive,
and probably dispersive, power, and for the same pur-
pose,  viz., correction of chromatism.  It is  an  interest- 
        THE EYE AS AN OPTICAL INSTRUMENT.      35

ing historic fact  that the hint for correction of chro-
matism by  combination of  lenses was taken  from the
structure of the eye by Euler, and afterward carried out
successfully by Dollond.  That  the chromatism of the
eye is substantially corrected is shown by the complete
absence of colored edges of strongly illuminated objects,
and the sharp definition of objects seen by good eyes.
By close observation and  refined methods, it  has been
recently shown that the chromatism of the eye is not
perfectly corrected.  It can be observed if we use only
the extreme colors, red and violet.*  But  the  degree of
chromatism is so  small as not to interfere at all with
the accuracy of vision.
   4.  Aberration.—Another defect, much more  diffi-
cult to correct, is  aberration.  The form of lens most
easily made has a spherical  curvature.   But  in such a
lens there is an excess of  refractive power in the mar-
ginal portions as compared with the central  portions;
an excess increasing with the distance from the center;
therefore the focal point for marginal rays is not the

                        Fig. 12.
same  as  for the central rays, but nearer.   In Fig. 12
the marginal rays, a r', a r', are  brought to a  focus at
a",  while the  central rays, a r, a r, are brought to a
focus  at  a'.  The  best  place for the  receiving screen
would be at 8 8, between these; but  even there the
image would not be sharp.   In such a lens there  is no
           * Helmholtz, " Popular Lectures," p. 216. 
36
MONOCULAR VISION.
common focal point for all the rays, and therefore the
conditions of perfect image are not fulfilled—the image
is blurred.  This defect must  be corrected.   It is cor-
rected in the best lenses.
   The aberration may be greatly decreased by the use
of diaphragms, which cut off all  but the central rays;
but in this case we  get distinctness at the expense of
brightness.  This may be done when the light is very
intense.  Again,  the aberration  may be reduced  by
using several very flat lenses, instead of one thick lens.
This plan is used in many instruments.   But complete
correction can only be made by increasing the refraction
of the central portions of the  lens, and this may con-
ceivably  be accomplished in two ways, viz., either by
increasing  the curvature of this  part  or by increasing
its density, and therefore its refractive index.   It is by
the former method  that art makes the correction.  By
mathematical calculation, it is found that the curve must
be that of an ellipse.  A lens, to make a perfect image,
must  not be a segment of a sphere, but of the end of
an ellipsoid of revolution about  its major axis. It is
justly considered one of the greatest triumphs of science
to have calculated  the curve, and of art to have carried
out with success the  suggestion of science.
   Art  has not been able  to achieve success  by the
second method.  It  is impossible so to graduate the in-
creasing density of glass from the surface to the center
of a lens as to correct aberration.  Now, it is apparently
this second method, or perhaps  both, which  has been
adopted  by nature.   The crystalline lens increases in
density and refractive power from surface to center, so
that it may be regarded as consisting of ideal concentric
layers, increasing  in density  and curvature until the
central nucleus is a very dense  and highly refractive 
THE  EYE AS AN OPTICAL INSTRUMENT.       37
spherule (Fig. 13).  The surface of the cornea has the
form of an ellipsoid of revolution about its major axis,
and therefore doubtless contributes to the same effect.
In looking at very near objects, the con-
traction of the pupil, also, by cutting off
marginal  rays, tends in  the same direc-
tion.   However the result may be ac-
complished, whether by one  or by both
methods,  it is certain that in good eyes
it is completely achieved, for the clear- Sl
ness of vision is wholly conditioned on   structi-be of tub
                                         Leu 8.
the sharpness of the retinal image.
    It is probable that  the peculiar structure of the crys-
talline lens  described  above  has also another important
use in the  lower animals, if not in  man.  Dr.  Ludi-
mar Hermann * has  shown that,  in a homogeneous
lens, while  the rays from radiants near the middle  of
the field  of view,  i. e., nearly directly in front, are
brought to a perfect focus, the rays from radiants situ-
ated near the margins  of the field of view, i. e., of very
oblique pencils, are  not brought to a focus.  Therefore
the picture formed by such a lens is distinct in the cen-
tral parts, but very indistinct on the margins.   Now,
this defect of a homogeneous lens, Dr. Hermann shows,
is entirely  corrected by the peculiar  structure  of the
crystalline; therefore  this structure confers on the eye
the capacity of seeing  distinctly over a wide field, with-
out changing the position of the point of sight.  This
capacity he calls periscopism.  We will hereafter, how-
ever, give reasons showing  that  this property  of the
crystalline can be of little value to man.
    5.  Adjustment for Light.—The delicate work done
by the camera and by the eve requires a proper regulation
        * "Archives des Sciences," vol. lxiii, p. 66.  1875.
 
38
MONOCULAR VISION.
of the amount  of  light.  In both, therefore, we want
some contrivance by which, when the light is very in-
tense, a large portion may be shut out, and when the
light is feeble,  a larger portion may be admitted.  In
optical instruments this is done by means of diaphragms.
In the camera we have brass caps with  holes of various
sizes, which  may be changed and adapted to the inten-
sity of the light.  In the microscope we have a circular
metallic plate, with holes of various sizes.  By revolv-
ing this  plate we bring a larger or  a  smaller hole in
front of the lens.
   In the eye the  same end is reached, in a far more
perfect manner, by means of the iris.  The iris (Fig.
             Fia. 14.
Hitman Eye, enlarged, with Part of Cornea and    Showing Structure
  Sclerotic removed.—a, sclerotic; b, cornea; c,        of Iris.
  choroid; d, iris; e, pupil; /, ciliary muscle. (Af-
  ter Cleland.)
14, d) is an opaque circular disk,  with a round hole,
the pupil, in the middle.   The  circumference of  the
disk is immovably fixed to the sclerotic at its  junction
with the cornea ; but the margin of the circular hole, or
pupil, is free to move.  The disk itself is composed of
two sets of contractile fibers, viz., the radiating and  the 
         TnE EYE  AS AN OPTICAL  INSTRUMENT.      39

circular (Fig. 15).   The radiating  fibers converge from
the outer margin of the  iris as a fixed point, and take
hold on  the movable margin of  the  pupil, and, when
they contract, pull open the pupil on every side, and
thus enlarge it  (Fig. 15, B).  The circular fibers are
concentric with  the pupil, and are especially numerous
and strong near the margin, forming there a band about
one-twentieth of an inch wide.  When they contract, they
draw up the pupil, like a string about the mouth of a bag,
and make it small (Fig. 15, A).  We may regard the
radiating fibers as elastic, and as contracting passively by
elasticity when stretched; and the circular fibers as con-
tracting actively under stimulus, like a muscle.  Further,
the circular fibers are in such sympathetic relation with
the retina, that a stimulus of any kind, but especially
its  appropriate  stimulus, light, applied to  the  latter,
causes the former to contract, the extent of  the con-
traction being of  course in proportion to the  intensity
of  the light.   If, therefore, strong sunlight impresses
the retina, the circular fibers immediately contract, the
pupil becomes small, and a large portion of the light is
shut out.  When  the light diminishes, as in  twilight,
the circular fibers  relax, the previously stretched radi-
ating fibers contract by elasticity, and enlarge the pupil.
At night the pupil enlarges still  more, in order to let
in as much  light as possible.   Finally, if  a  solution  of
belladonna  (which  completely  paralyzes  the circular
fibers) be dropped into  the eye, the pupil enlarges  so
that the iris is reduced to a narrow dark ring.
    Art, taking  the hint from  Nature, and striving  to
be not outdone, has recently constructed for the micro-
scope a diaphragm somewhat  on this plan.  It is com-
posed of many very thin metallic plates, partly covering
each other, so arranged as  to leave a polygonal hole  in 
40
MONOCULAR VISION.
the middle, and sliding over each  other  in  such wise
that by turning a milled head in one direction they all
move toward the central point and diminish the open-
ing, while by turning  in  contrary direction they  all
move away from the center and make the hole larger.
This is confessedly  a beautiful contrivance, but how
inferior to the admirable work of Nature !
    As already stated (page 37), contraction of the pupil
takes place not  only under the stimulus of light, but
also in looking  at very near objects.  The reason of
this is, that correction  of spherical aberration is thus
made more perfect.
    6. Adjustment for  Distance — Focal Adjustment.
—We have seen  that  a  lens, properly corrected for
chromatism and aberration, makes  a  perfect  image.
But the plate or screen which  receives the image and
makes it  visible must   be  placed exactly in the right
place,  i. e., in the  focus; otherwise the image will  be
blurred.  We reproduce here  (Fig. 16)  the diagram
                       Fig. 16.
on page  27, showing this.  It is at once seen that, if
the receiving  plate is too near the lens, i. e., at 8' 8',
the rays  from any radiant of the object will not yet
have come together at a focal point.   If  the receiving
screen be too far from the lens, at  8" 8", then the rays
moving in straight lines will have already met, crossed,
and again spread out. It is evident that there is but one 
         THE EYE  AS AN OPTICAL INSTRUMENT.      41

 place where the  image is perfect, viz., at the focal
 points, 8 8.  Now, if this place of  the image were the
 same for all objects at all distances, it would be  only
 necessary to find that place, and fix the receiving plate
 immovably there.   But the place of the image formed
 by any lens changes with  every change in the distance
 of the object.  As the object in front approaches, the
 image on the other side recedes from the lens.  As the
 object recedes, the image approaches the lens.  There-
 fore there must be an adjustment of the instrument for
 the distance of the object.
    There are only two possible ways in which this ad-
 justment can be made: Either (1st), the lens remaining
 unchanged, the screen must advance or recede with the
 image; or  (2d), the place of the screen remaining the
 same, the lens must  be changed so  as  always to throw
 the image  on the immovable screen.  The first is the
 mode of  adjustment used in the camera, the opera-glass,
 the field-glass, and the telescope;  the second is the
 mode usually used in the  microscope.  In  the camera,
 for example, when the object  comes  nearer, we  draw
 out the tube so as to carry the ground-glass plate a little
 farther back;  when the object recedes, we slide up the
 tube so as to bring the receiving plate nearer the lens.
 So in the opera-glass we elongate the tube for near ob-
 jects, and shorten  it for  more  distant.  In  the micro-
 scope, on the contrary, the image is usually thrown to
 the same place in the upper part of the tube.  If, there-
 fore, the object approaches nearer the lens (as it  does in
 higher magnification), we change the lens  so as to throw
 the image to the same place.
    How  is  this managed in the eye ?  It was long be-
 lieved  that  the adjustment  was on  the  plan  of the
camera.  Now, however, it is  known that  it is rather on 
42
MONOCULAR  VISION.
the plan of the microscope.  It was formerly thought
that, in looking at a near object, the straight muscles,
acting all together, squeezed the eye about the equatorial
belt, and increased its axial  diameter—in other words,
made it egg-shaped—and thus carried the retinal screen
farther back from the lens.  But now it is known that
the retinal  screen remains  immovable, and  the lens
changes its  form so as to throw the image to the same
place.
   Experiment.—This is proved in the following man-
ner : A person is chosen with good, normal young eyes.
The  experimenter stands in a  dark  room, in front of
                        Fig. 17.






                                  c®'"
A, eye observed;  B, eye of observer ; c, section of candle flame; /, a distant point of
          sight, and n a near point of sight. (After Helmholtz.)

the patient, A, with a lighted candle in his hand, a little
to one side, as in Fig. 17, C, while his own point of ob-
servation is  on the other side, B.  If the observer now
looks carefully, he will  see  in  the  eye of the patient
three images  of  the candle-flame :  first, one reflected
from the surface of the cornea, which is by far the bright-
est (Fig. 18, a); second, one from the anterior surface
of the  crystalline, much  fainter (Fig. 18, b);  third,
one  from the  posterior surface of  the crystalline, the
faintest of  all, and very small  (c).  Further, it will be
observed that  the first  and second are erect  images, 
THE  EYE AS AN OPTICAL INSTRUMENT.      43
because reflected from a convex surface, while the third
is  inverted, because reflected  from a concave surface.
Now directing the patient to gaze on vacancy, or a dis-
tant point,/,  Fig. 17, we observe carefully the  posi-
tion and size  of these several  images.
Then, if by direction  the patient trans-
fers the point of sight to a very near
point, n, without changing the direc-
tion, we observe that the images a and
c do not change, but the image b changes
its  position and  grows  smaller.  This
image is reflected from the anterior surface of the crys-
talline.   The  anterior surface of the crystalline, there-
fore, changes its form.  Again, the nature of the change
of the image, viz., that it becomes smaller, shows that this
anterior surface  becomes  more convex.   By careful ex-
amination the iris, too, may be seen to pwotrude a little

                        Fig. 19.
F, lens adjusted to distant objects; N, to near objects; a, aqueous humor; d, ciliary
                   muscle ; e, ciliary process.

in the middle.   Evidently, therefore, in adjusting the
eye to very near objects, the crystalline becomes thicker
in the middle, and pushes the pupil a little forward.
In the accompanying diagram, Fig. 19, the crystalline
lens is divided  by a  plane through the  center.  The
right side, JY, is adapted to near objects; the left, F,
to distant objects.
flP 
44
MONOCULAR VISION.
    Theory of Adjustment.—Thus much  may be con-
 sidered certain.  It is certain that in adjusting the eye
 for looking at very near objects, the lens becomes more
 convex.  But the question, "How  is  this done?" is
 more difficult  to answer.  Helmholtz thinks it is done
 in  the following manner : *
    It will be remembered that the lens is invested by
 a thin, transparent membrane, which extends outward
 from its edge as a circular curtain, and is attached all
 around to the sclerotic, thus dividing  the interior of
 the eye into two chambers—the anterior, filled with the
 aqueous, and the posterior, with  the vitreous humor.   It
 will be remembered, further,  that this membrane is
 naturally drawn tight by the  elastic  rigidity of  the
 sclerotic, and presses gently on the elastic  lens, flatten-
 ing it slightly.  This is the normal passive condition, as
 when gazing  at  a distance.  Now  there are certain
 muscular fibers (ciliary muscle, Fig. 19, d) which, aris-
 ing from the exterior fixed border of the iris just where
 it is attached to the sclerotic, run  backward, radiating,
 and take hold upon the outer edge of the lens curtain.
 When these fibers contract, they pull forward the tense
 curtain to a  smaller  portion of  the globe, and thus
 relax its tension.   The relaxing of the tension of  the
 curtain relaxes also the  pressure of the capsule on  the
 lens, which therefore immediately swells or thickens in
.proportion to the degree of  relaxation.   According to
 Helmholtz, then, we adjust  the eye to  near objects by
 contraction of the  ciliary muscle.  There  are  other
 views on this subject, but this seems the most probable.
    The normal eye in a passive state is adjusted to in-
 finitely distant objects.  By change of  the form of  the
 lens, it can adjust itself to all distances up to about five
              * "Optique Physiologique," p. 150. 
        THE EYE AS AN OPTICAL  INSTRUMENT.      45

inches.  The range  of adjustment or of distinct vision
is, therefore, within  these limits.  It is only at compar-
atively near distances, however, that the change is great.
Between twenty feet and  infinite  distance the adjust-
ment is almost  imperceptible.
   We see, then, that the mode of adjustment of the
eye  is somewhat like that  of the microscope; i. e., the
change is in the lens, not in the position of the receiv-
ing  screen.  Like the  microscope, but how infinitely
superior!   The microscope  has its four-inch lens, its
two-inch lens,  its  one-inch lens, its half-inch lens, its
quarter-inch, its tenth-inch, and  even its  fiftieth-inch
lens.  It changes one for another, according to the dis-
tance of the object.  But the eye changes its one lens,
and  makes  it a five-inch lens, a  foot lens, a twenty-foot
lens, a mile lens, or  a million-mile lens;  for at all these
distances it makes a  perfect image. 
CHAPTEE  III.
     DEFECTS OF THE EYE AS AN INSTRUMENT.

   In the preceding chapter we have attempted to bring
out, in a clear and intelligible form, the beautiful struc-
ture of the eye, by comparing it with the camera, and
showing  its superiority.  But  the eye of which we
have been speaking is the normal or perfect eye.   This
normal condition is called  emmetropy.  The eye, how-
ever, is not always a perfect instrument.  There are
certain defects of the  eye which  are  quite  common.
The principles involved in the construction of the nor-
mal eye may be still further enforced  and illustrated by
an explanation of these defects.   Let it be  observed,
however, that these defects must not be regarded as the
result  of imperfect  work  on the part of Nature, but
rather as  the effects  of  misuse of the eye, accumulated
by inheritance  for  many  generations.  They do  not
occur in  animals, nor  in  the same  degree in  savage
races;  and  most of them are also  very rare in persons
living for many generations in the  country.
   The most important of these defects are myopy and
presbyopy.
   Myopy,  Brachymetropy,  or Near - Sightedness.—The
normal or  emmetropic eye adjusts itself perfectly for
all distances,  from  about   five  inches  to  infinity.  It 
       DEFECTS  OF THE EYE AS AN  INSTRUMENT.    4f

 makes a perfect image of objects at all these distances.
 This is called its range of distinct vision.  It has but one
 limit, viz., the nearer limit of five inches.   Now in the
 passive state of the eye, as for  instance in gazing on
 vacancy, or when  the  eye is taken out of the socket as
 a dead instrument, it is prearranged for perfect image
 of  objects at an infinite distance.  Its focus of  parallel
 rays in a passive state is on  the retina.  For all nearer
 objects,  a voluntary effort  is necessary  to  throw the
 image on the  retina, which effort  is greater as the
 object is nearer, until it is  limited at the distance of
 about  five inches.  The normal  eye,  therefore, is like
 a camera, which, when pushed up as much  as possible,
 is arranged for making a perfect image of sun, or moon,
 or a distant landscape, but can by drawing  the  tube be
 adjusted  to  shorter and  shorter distances  up  to five
 inches, but not nearer.
    The  myopic eye,  on the other hand, is not  pre-
 arranged for perfect image of distant objects.  Its focus
 for distant objects (focus of  parallel rays) is not on the
 retina, but in front of  it.   The refractive power of the
 lenses  in their passive  state is too great, or else  the re-
 ceiving screen (retina)  may be regarded as too far back
 from the lens, viz., at S" S", Fig. 7, page 27.  The rays
 have already reached  focus, crossed, and again spread
 out  before they reach  the retina.  An object must be
 brought  much nearer before its  perfect image  will be
 thrown on the  retina.  Within  this  farther limit of
 perfect image, however, it has its own range of  adjust-
 ment, like  the normal  eye.   The range of the  normal
 eye  is  from  infinite distance to five inches.   In the
myopic eye  the range may be from a yard to four
inches, or from a foot to three inches, or from six inches
to two inches, or even from three inches to one inch,
             3 
48               MONOCULAR VISION.
according to the degree  of  myopy.   The amount of
ocular adjustment or change  in the lens to effect these
ranges is as great as  for the normal range from infinite
distance to five inches, but the latter is a far more use-
ful range.  The myopic eye, therefore, is like a camera
which was never intended to be used for taking distant
objects, which, therefore, when shortened to the greatest
degree, is still too long in the  chamber for distant ob-
jects, but is adapted only for near objects within a cer-
tain limited range.
    It is  evident, then, that,  the  defect of the myopic
eye being too great refractive  power of the lens in a
passive state, this defect may  be remedied by the use of
concave glasses, with concavity  just sufficient to correct
the excess of  refractive power,  and therefore to  throw
the image of  distant objects  back to  the retinal  screen
in the passive state  of the eye.  The eye  then adjusts
itself to all nearer distances, and becomes in all respects
a normal  eye.  From the nature of the defect (structural
defect), it is evident that the glasses must be worn habit-
ually.
    Presbyopy, or  Old-Sightedness.—This defect is often
called long-sightedness, or far-sightedness; but this is
a misnomer, based on a misconception of its true na-
ture.   It  is  obviously impossible to have an eye more
long-sighted than the normal eye, for this defines with
perfect distinctness  the most distant objects,  such as
the moon or the sun when the dazzling  effect is pre-
vented by smoked glass.   It is usually  regarded as a
defect the reverse of near-sightedness.   As near-sighted-
ness is the result of too great  refractive power in a pas-
sive condition, so this is supposed to be a too small refrac-
tive power in the same condition.  As the myopic eye
throws the focus of parallel rays in front of the retina, 
       DEFECTS  OF THE  EYE AS AN INSTRUMENT.     49

 so it is supposed the presbyopic eye throws the focus of
 parallel rays behind the retina, because the retina is too
 near the lens, at S' 8', Fig. 7, page  27.  It is further
 supposed that the change which takes place  with age is
 a flattening, and therefore a loss of refractive power, of
 the lenses of the eye.  It is constantly asserted, there-
 fore, that  the myopic eye may be expected to become
 normal with age.
    Now this view of the nature of presbyopy is wholly
 wrong.  The presbyopic eye  sees distant objects per-
 fectly  well, and precisely like the normal eye.   Its pas-
 sive structure is therefore unaltered.  It makes a perfect
 image of  distant objects on the retina, like  the normal
 eye.   Its  focus of parallel rays is on the retina, not be-
 hind it.   It is therefore normal in its passive state, or
 in its  structure.   The defect, therefore, consists not  in
 a change  of the structure  which originally adapted it
 to the imaging  of  distant objects, but in the loss  of
 power to  adjust for near  objects.  And this loss  of
 adjusting power is, again, probably the result of loss of
 the  elasticity of the crystalline lens.   In the normal
 young eye, when the ciliary muscle pulls forward the
 lens curtain, and thus relaxes its tension, the lens by its
 elasticity swells  and thickens, and becomes more refrac-
 tive.   In  the presbyopic eye, the  ciliary muscle pulls,
 and  the curtain or capsule relaxes its  tension, in vain;
 the lens,  for want  of elasticity,  does  not  swell  out.
 Therefore  the remedy for presbyopy is the use of con-
 vex  glasses, not  habitually, not in looking at distant
 objects, but only in looking at or imaging near objects.
 The  putting on of convex  glasses does not make the
presbyopic eye normal, as  the  use of concave glasses
makes  the myopic eye ; therefore they can not  be worn
habitually.  In looking at near objects, it uses  glasses; 
50
MONOCULAR VISION.
in looking at distant objects, the glasses are removed.
Myopy is a structural defect; presbyopy is afunctional
defect.   One is a defect of prearrangement of the instru-
ment ; the other is a loss of power to adjust the instru-
ment.  To compare with the camera again: the presby-
opic eye  is like a camera which was originally arranged
for distant objects, and by drawing the  tube could be
adjusted for near objects also,  but, through  age and
misuse and rust, the draw-tube has become so stiff that
the apparatus for adjustment no longer works.  It still
operates well for distant objects, but can not be adjusted
for nearer objects.   If we desire to image a near object
in such  a  camera, obviously we must supplement its
lens with another convex lens.
    From what has  been said it is evident that the
myopic eye does not  improve  with  age, and finally
become normal, as  many  suppose.   Myopic  persons
continue  to wear glasses of the same curvature  until
sixty or seventy years of age.   I have never known a
myopic person who  discontinued the  use of glasses as
he grew older.   The same change, however, takes  place
in the myopic as in the normal eye, i. e., the loss of ad-
justment.  In all young eyes there is a range of adjust-
ment between a nearer and a farther limit; in the nor-
mal eye it is between five inches, near limit, and infinite
distance,  the farther limit (if limit it can be called); in
the myopic eye the nearer limit may be two inches, the
farther limit  four inches, or it may be between  three
and  six inches, or four inches and  one foot, according
to the degree of myopy.  Now, with advancing age,
the nearer limit, i. e., the limit of adjustment, recedes.
In the normal eye it  is first eight inches, then one foot,
then three feet, etc.,  until, when adjustment is entirely
lost, it  reaches the farther limit, and  there is but one 
       DEFECTS OF THE EYE AS AN INSTRUMENT.     51

distance of distinct vision; but the farther limit, i. e.,
structural limit, does not change.  So also in the my-
opic eye,- with advancing age, the nearer limit or  limit
of  adjustment recedes, but  not  the farther limit  or
structural limit.  This remains the same.  But, as this
was always too near for useful vision, glasses must still
be worn.  Thus it is evident that  myopy and presbyopy
may exist in the same  individual.
    In extreme old age, when the  tissues begin to break
down, it is probable that  some  flattening of  the eye
may take place.  To such persons it would be necessary
to wear convex glasses, even for  distant objects.  But
this is not ordinary presbyopy.   In fact, it is probable
that most of such cases belong to  the next category.
    Hypermetropy.—We have dwelt on  the  two  most
common defects of  the eye, but  there are others less
common, which must be briefly characterized.  Hyper-
metropy is the true opposite of myopy.   Like the latter,
it is a structural defect, but  in the opposite direction.
In  this case the lens  is not sufficiently refractive for
the length of the chamber, or the  receiving screen is too
near (at 8' 8', Fig.  7) for the refractive  power of the
lens.   Therefore the  focus of parallel rays  is behind
the retina in  a passive state of  the eye.  The hyper-
metropic eye when young usually sees well at a distance,
but not near at hand, and therefore it is apt  to be con-
founded with  presbyopy.   The reason is, that a slight
adjustment adapts the eye for perfect retinal  image of
distant objects; but the near limit of its range of ad-
justment  is much farther off   than  in  the  normal.
When, however, the hypermetropic eye loses its power
of adjustment with age, then even distant objects can
not be seen distinctly.  Such persons, therefore, while
young, should habitually wear slightly convex glasses, 
52
MONOCULAR VISION.
which make their eyes normal.  When they grow old,
they are compelled to have two pairs of glasses, one for
distant objects and one for near objects ; one for walk-
ing and one for reading.   The hypermetropic eye may
be compared to a camera which, when entirely pushed
up, is too short  for  the  imaging of any objects what-
ever.  By drawing, it may be adjusted  for distant  ob-
jects, but not for  near objects.
   Astigmatism.—The form of a perfect eye is that of
a spheroid  of revolution  about the optic axis.  Its re-
fraction in a horizontal  and a  vertical  plane will be
equal.   This  is necessary to bring all rays to a perfect
point at the same distance.  But eyes are found in which
the horizontal curvature  of the cornea or of the crys-
talline, or both, is different from the vertical curvature.
Such eyes  are said to be astigmatic, because the rays
from any radiant  are brought to a focal  line, instead of
a focal point.  A very slight degree of astigmatism is
not uncommon, and often exists unknown to the patient. 
CHAPTER  IV.
EXPLANATION OF PHENOMENA OF MONOCULAR VISION.

       SECTION  I.—STRUCTURE OF THE RETINA.

   We have thus far  treated of  the eye, and compared
it with the camera, purely as an optical instrument, con-
trived  to  form an image upon a receiving screen suit-
ably placed.  We have also  treated of the defects of
the eye, as much as possible, from the  same  physical
point of view as  defects of an instrument.  But in both
the camera and the eye the image  is only a means to
accomplish a higher  purpose, viz., to  make a  photo-
graphic picture in the one case and to  accomplish vision
in the other.  We  have thus far spoken  as much as
possible only of  an insensitive screen, the ground-glass
plate in the one case  and the dead  retina in the other.
But in both, when accomplishing their real work, we
have a sensitive  screen, in which  wonderful changes
take place, viz.,  the iodized  plate in  the one  and the
living:  retina  in the other.  In order to understand the
real function of the eye in the living animal, it is neces-
sary that we study the  structure and  functions  of the
retina.
   Structure  of  the Retina.—The  retina,  as  already
stated, page 22, is a thin membranous expansion of the 
54
MONOCULAR VISION.
optic nerve.  These nerves, arising from the optic lobes
of the midbrain, appear first beneath the base of the
brain  as the optic roots, r r', Fig. 20, converge, unite,
and partially cross their fibers at the optic chiasm, ch ;
then,  again diverging,  enter  the  conical eye-sockets  a
little to the interior of the point; then pass through the
midst  of the fatty cushion behind the eye, surrounded

                        Fig. 20.
by the  diverging  recti muscles, and  finally  penetrate
the sclerotic at a point about one eighth of an inch to
the inside  of the  axes; then spread  out all  over the
interior of  the ball as  an  innermost coat, immediately
in contact  with the vitreous humor, and extend as far
forward as the ciliary processes, or nearly to the iris.
The wide extent of this expansion and  its  hollow con- 
STRUCTURE OF  THE RETINA.
55
cave form are necessary to give wideness to the field of
view.  By this means rays from objects, not  only in
front but far to the right and  left, above and below,
fall upon and impress the retina.
    The  thickness of  this nervous expansion  is  about
one hundredth of an  inch, or about  the thickness of
thin cardboard, at the bottom or thickest part, but thins
to one half that amount on  the anterior margins; yet,
under the microscope, a section through the thickness
shows that it is very complex  in its  structure,  being
composed of several very distinct layers.   We may first
represent it  on  a smaller  scale as composed  of  three
principal layers :  First, the innermost layer, /,  Fig. 21,

                         Fig. 21.
Generalized Section of Eetina, etc.— O, optic nerve; S, sclerotic; ch, choroid; E,
  retina; b, bacillary layer; g, granular and cellular layer; f, fibrous layer; V, vitre-
  ous humor; c, central spot.
in contact with the vitreous  humor, V,  is composed
wholly of fine interlaced fibers of the optic nerve.  This
nerve, o, is seen to pierce the sclerotic and the other
layers of the retina, and then to spread out as an inner-
most  layer.   Second, outermost of all, and therefore in
contact  with the choroid, ch, is a remarkable layer, com-
posed of cylindrical rods, like pencils set on end.  This
is called the bacillary layer (bacillum, a small  rod), or 
56
MONOCULAR  VISION.
layer of rods, b.  Third, between these is found a layer
composed of granules and nucleated cells, g.   This may
be called for the present the granular and nuclear layer.
Fig. 22.
Enlarged Section of Retina (after Schultze).—A, general view; B, nervous ele-
  ments; a, bacillary layer; e, external nuclear layer; d, external granular layer; e,
  internal nuclear layer; /, internal granular layer; g,  ganglionic layer; h, fibrous
  layer, consisting of fibers of optic nerve. 
             STRUCTURE OF  THE RETINA.           57

   Further, it will be seen that these layers  exist, all
three, in  every part  of the retina except  two spots.
These  are the  spots  where the optic nerve, 0, enters,
and the central spot,  c, which is in the axis of the eye.
Where the optic nerve enters, of course, no other layer
can exist  except the fibrous layer.   In the central  spot
the fibrous layer  is wholly wanting, and the  granular
and  nuclear layer is almost wanting, so that the retina
is here almost reduced to the bacillary layer.   For this
reason this spot forms a depression in the retina.
   But the extreme  importance of the retina requires
that  these layers be examined more closely.   For this
a much greater enlargement  is necessary.  Fig. 22 rep-
resents such enlargement.  The fibrous layer, h, requires
no further  description;  but  the granular and  nuclear
layer is seen to be composed of two distinct layers of
small granules, d and f and two layers of large nucle-
ated cells, c and e, and a layer of very large nucleolated
cells, g, from which go out  branching fibers.  These are
multipolar cells, or ganglia.  It  is further seen that the
bacillary layer  is composed of two  kinds of elements,
viz., slender cylindrical rods and larger cone-like bodies.
These are called rods and cones.  It is seen, still further,
that all these different elements of the retina are in con-
tinuous connection with each other, and with the fibers
of the optic nerve.
   The bacillary layer is of the extremest interest.  It
consists mostly of rods, but among these are distributed
the larger cones,  as in Fig. 23, A.  As we approach
the central  spot the cones become  more numerous, as
seen in B.  In the depression of the central spot {fovea
centralis)  we find only  cones, and  these are of much
smaller size than those in  other parts of  the retina, as
seen  in C.  The rods are about  3-^ inch in length and 
58
MONOCULAR  VISION.
^i—- inch in diameter.   The  cones are shorter and
about three times thicker than the rods, except in the
central depression, where they are nearly as small as the
rods, being there only jo^ot inch in diameter.   In this
spot, therefore, there are probably no less than one mil-
lion cones in a square ^ inch.
                        Fig. 23.
Bacillary Layer, viewed from the Outside Surface.—A, appearance of usual
  surface; B, appearance of surface of the raised margin of yellow spot; C, surface of
  central spot.

   Distinctive Functions of the Layers.—As the distinc-
tive  functions of the several sub-layers of the middle
layer (granular and nuclear) are unknown, we will treat
of only the three layers—inner, middle, and outer.  The
outer layer of rods and cones (bacillary) is undoubtedly
the true receptive layer, which corresponds to the iodized
film  of the sensitized plate of the camera.   These rods
and cones receive and respond to the vibrations of light;
they  co-vibrate  with  the undulations of  the  ether.
The inner or fibrous  layer  conducts the received im-
pression to  the optic nerve; for  each rod and cone is
connected by a slender  thread, continuous with  nucle-
ated cells of the granular layer and a fiber of the fibrous
layer.   The fibrous layer may, in fact, be regarded as a
layer of conducting threads  coming from the rods and
cones, which threads are then gathered  into a cord or
cable, the optic nerve, which in its turn finally conducts
the impression to the brain.   The function of  the mid-
dle layer is more obscure; but  nucleated nerve-cells,
and  especially multipolar cells, are always generators or 
STRUCTURE OF THE  RETINA.
59
originators of  nerve-force.   They  evidently have an
important function.  They probably act as little nerve-
centers ;  and many unconscious,  involuntary, or reflex
acts  of vision are probably performed by their means,
without referring the sensation to the brain.
   The manner in which the whole apparatus operates
is briefly as follows :  The light  penetrates through the
retina until it reaches the outer layer of rods and cones.
These are specially organized to respond  to or co-vibrate
with the undulations of light.   These vibrations are
carried through  the connecting  threads to the fibrous
layer, then through the fibers of  this layer to the optic
nerve, then along the fibers of the  optic nerve to the
gray matter of the brain, where  they finally determine
changes  which emerge into consciousness as the sensa-
tion of light.
    That we  have correctly interpreted the function of
the  layer of rods and cones  is rendered probable not
only by its very remarkable and  complex  structure,
adapting it  to responsive vibrations, but also by the
peculiar  properties of two spots on  the retina on which
all the  layers do not co-exist.   Just where the  optic
nerve enters, as shown in Fig. 21, page 55, the bacillary
layer is  necessarily wanting, and it is the only spot in
which this is the  case.   Now, this spot is blind (see page
78).  Again, just in the axis of  the  globe, or what
might be called the south pole of the eye, is the central
spot or central pit.   In this spot is  wanting  the fibrous
layer and  the whole  of the  middle layer,  except the
multipolar cells.   The bacillary layer is  here, therefore,
directly  exposed  to the action of light.  Now, this is
the most sensitive spot of the retina.
    Perception of  Color.—Color, like musical  pitch, con-
sists of  an  infinite number  of  kinds and shades; but 
60
MONOCULAR VISION.
these may be  reduced to a few primary  kinds, by the
mixture of which the intermediate shades may be sup-
posed to be made.   Newton made seven primary colors
in the solar spectrum;  but though these, and indeed
many more, may be considered distinct from the physi-
cal point of view, since they are the result of different
rates of ethereal vibration, yet they can not be all con-
sidered as primarily distinct sensations.  Brewster  re-
duced all color-sensations  to  three  primary,  viz., red,
yellow, and  blue.   Young made them red, green, and
violet.  This latter view is adopted by Helmholtz and
most modern writers.
    Recently, however, Hering * has reinvestigated the
whole subject with great acuteness, from the purely phys-
iological instead of  physical point of view, and arrives
at different  results.  Hering includes white and black
among his primary color-sensations, making  six  in all.
But, leaving out these as belonging rather to the cate-
gory of shades or nuances, according  to  Hering there
are four and  only four primary color-sensations essen-
tially distinct  from each other, viz., red, yellow,  green,
and blue.  Aside from all physical considerations, un-
doubtedly this is true.   These four  colors  are  essen-
tially distinct and irresolvable into any mixture of oth-
ers.   Again, according to Hering, these four are  re-
ducible to two complementary pairs, viz., red and green
on the one hand, and yellow  and blue  on  the other.
This  is also undoubtedly  true.  Finally, according to
Hering, complementary colors are the  result of opposite
affections of the retina, so that there are only two essen-
tially distinct color-affections of the retina, which, with
their opposites, produce the two pairs of complementary
colors : the one with its opposite produces red and green;
       * Hering, "Zur Lehrc von Licht-Sinne," Wien, 1878. 
STRUCTURE OF THE RETINA.
61
the other with its  opposite, yellow and blue.   This,
though more doubtful, seems a probable cause of com-
plementariness.
   Theory of Color-Perception.—Color-perception is un-
doubtedly  a simple perception, and irresolvable into
any other.   It  must, therefore, have its basis in retinal
structure.   Since light is  perceived by co-vibration of
retinal elements, and since the different  colors have
different rates  of vibration, there must be a correspond-
ing structure of the retinal elements, by means of which
they co-vibrate with each  of these  colors.   In  the ear
different rates of aerial vibration (musical pitch) are per-
ceived  by  means of rods  of different  lengths (rods of
Corti),  which  co-vibrate, each with its own  pitch.  It
seems probable, therefore, that different rods or cones co-
vibrate with different  rates of ethereal undulations, i. e.,
with  different  colors.   This is the commonly received
view, brought  forward first by Young.   It is supposed
that there are three  kinds  of rods or cones, which sever-
ally co-vibrate  with  the three primary colors of Young.
One kind responds to the slower vibrations of red, anoth-
er kind to those of green, and still  another to the more
rapid  vibrations of  violet.  When two  kinds  vibrate,
intermediate colors  are perceived.   When all vibrate
together, then  white light is perceived.  Or, to express
it differently, intermediate colors produce vibration of
two kinds, white light of all kinds, of  rods.  Or, if we
adopt  the  theory of Hering in regard to the primary
colors,  one  kind of  rod or  cone  responds to red  and
green, another kind  to yellow and blue.
    Very recently Stanly  Hall has proposed a  theory
which seems even more probable.*  He believes that
color is perceived by the cones alone ; further, that
   * "American Academy of Science and Art," vol. xiii, p. 402 (1878). 
62
MONOCULAR VISION.
different parts of the same cone vibrate with different
degrees of  rapidity, and therefore respond to different
colors, and that the conical form  is adapted  for  this
purpose.  In order to gain clearer conception,  we may
imagine each cone to be made up of a number of but-
tons of graduated sizes joined together.   These buttons,
on account of their different  sizes, would vibrate with
different degrees of rapidity, and therefore co-vibrate
with different colors.  White light, he supposes, vibrates
the whole series; red light, the thicker, and violet, the
thinner, portion of the series;  or, taking Hering's view
of the primary colors,  we may imagine that  red  and
green rays affect one portion, and yellow and blue rays
another portion, of the same cone.
   The subject of the mechanism of color  perception,
however, is yet in the region of speculation, though
probably of profitable speculation.   To pursue it  any
further would be unsuited to the character of this trea-
tise.
   Daltonism, or  Color-Blindness.—Many persons lack a
nice discrimination of shades of color.  Such persons
see colors perfectly well, but, from want of attention or
culture, have not learned to nicely discriminate  and
name them.  This must not be confounded with color-
blindness.  The color-blind  do  not  see  some colors as
colors at all.   The defect is not one of culture, but of
sensation.  We can best explain it by comparing the
eye and ear.
   The limits of the perception of sound-vibrations are
very wide,  viz., more  than eleven octaves.  The  limits
of perception of light-vibrations are far more restricted,
viz., only a little more than one octave.  Now  in many
ears the extreme limits are not perceived ; but this is not
considered  a defect, because there is no special use for 
STRUCTURE OF THE  RETINA.
63
the extremest range.  So in the eye.  Even the narrow
limits of the normal eye are sometimes not reached; but
in this case the usefulness of the whole range makes it
a serious  defect.  This is  color-blindness.  In the ear
the vibrations most  commonly unperceived are at the
upper end of the scale.  In the eye it is  usually the
lower end of the scale which is  defective, viz., red, or
red and green.   The  color-blind see yellow and blue,
but not red and green.
    This defect was first  brought to scientific notice by
the celebrated chemist Dalton, and after him has often
been  called Daltonism.  The peculiarities of Dalton's
vision were carefully investigated by Sir John Herschel,
and the first scientific explanation was given  by him.
Adopting  the view of Young of three primary colors,
Herschel regarded normal vision as  trichromic, but the
vision of  Dalton as dichromic, the red being wanting.
This  view certainly explained the  most  striking phe-
nomena of color-blindness, but it does  not  explain the
fact that green is wanting as well as red.  As shown by
Pole * (who is himself color-blind),  the phenomena are
far more perfectly explained on Hering's view of the
primary colors; and conversely, the phenomena of color-
blindness are a powerful argument in favor of Hering's
view.   Of the two pairs of  complementary colors of
Hering, one pair, viz., the red-green, is wanting in the
color-blind, while the other pair, yellow-blue, is perceived
as in normal vision.   The colors  and shades, therefore,
which are perceived by the color-blind are: 1, black and
white, and all intermediate shades of gray; 2, yellow in
all its shades; and, 3, blue in all its shades.  A. pure red
seems to them a dark gray; but if mixed with yellow, as
   * "Nature," 20, pp. 477, 611, 637 (1879); "Contemporary Review,"
May, 1880. 
64
MONOCULAR VISION.
are most reds, it appears yellow mixed with  gray, or a
kind of brown; or if mixed with blue (purple), it ap-
pears as blue mixed with gray, or slate-blue.  A pure
green appears simple gray ; a yellow-green, yellow mixed
with gray—i. e., brown ;  and a blue-green, slate blue.
   The cause  of this defect of vision is, of course, a
defect of retinal structure.   If we admit that the rods
and cones are the responsive elements, and that differ-
ent kinds of rods or cones respond to different primary
colors, then in the retina  of  the color-blind the rods or
cones responding to red  and  green are  wanting;  or,
by Hall's theory, the cones are so shaped that they re-
spond to only one complementary pair, viz., to yellow
and blue.
SECTION II.—FUNCTION OF THE RETINA, AND EXPLANATION
       OF THE PHENOMENA OF MONOCULAR VISION.

   There is  a certain peculiarity in the general  func-
tion  of the  retina,  optic nerve, and associated  brain
apparatus, which  must now be  explained  and clearly
apprehended,  in  order to understand the  phenomena
of vision.
   Law of Outward Projection of Retinal Impressions.—
An image is  formed on the retinal screen.   We have
seen  that the  whole object of the complex arrangement
of lenses placed in front of the retina is the formation
of images.  But we do not see the retinal images.  We
do not see anything in the eye, but something outside
in space.  It  would seem, then, that the retinal image
impresses the retina in a definite way; this impression
is  then conveyed  by the optic  nerve to the brain, and
determines changes there, definite in proportion to the 
FUNCTION  OF THE RETINA.
65
distinctness of the  retinal image;  and then the brain
or the mind refers  or  projects this impression outward
into space as an external image, the.sign and facsimile
of an object which  produces it.  We shall see hereafter
how important it is that we regard what we see as ex-
ternal images, the signs of objects which produce them,
and these external images  themselves as  projections
outward of retinal images.
    This law of outward projection  is so important  that
we will stop a moment to show that it is not a new law
specially made for  the sense  of sight, but only a modi-
fication of  a general law of sensation.  After doing so,
Ave will proceed to  illustrate by many phenomena, so as
to fix it well in the mind.
    Comparison with Other Senses.—The general law of
sensation is, that irritation or stimulation in  any portion
of the course  of a sensory fiber is referred to its periph-
eral extremity.  Thus, if the sciatic nerve be laid bare
in the upper thigh, and then pinched,  the pain is felt,
not  at the part injured, but at the termination of the
nerve  in the  feet  and  toes.   If  the  ulnar nerve be
pinched in the hollow on the inner side of the point
of the elbow,  pain  is felt  in the little and ring fingers,
where this  nerve is distributed.   In amputated legs,
as is well known, the  sense of the presence of a foot
remains, and often severe neuralgic pains are felt in the
feet and toes. The pain, which in this case is caused
by a diseased  condition of the nerves  at the point of
amputation, is referred to the place where the diseased
fibers were  originally  distributed.  In  nerves of com-
mon sensation, therefore,  injury or  disease, or stimu-
lation  of any kind in  any part,  is  referred  to  the
peripheral  extremity  of  the nerve-fibers.   Now  the
peculiarity of  the optic nerve is, that it refers impres- 
66
MONOCULAR  VISION.
sions not  to  its peripheral extremity only, but beyond
into space.
    But when we find great differences in the functions
of tissues, such  as occur in this case, we can generally
find the steps  which  fill  up the gap.   A  thoughtful
comparison  of  the phenomena  of  the different senses
will, we believe, reveal  these steps.  We repeat  here
what  has  already been said  in  a general way on  page
13.  Commencing with  the lowest of the  specialized
senses, the gustative, an impression on the nerves  of
taste  is referred,  as  in  the case  of  common  sensory
fibers, to  their  peripheral extremity: the sensation is
on the tongue.   In the case of the olfactive, we have a
sensation still at the  peripheral extremity, i. e., in the
nose, but  also a  reference to an external body at  a dis-
tance as its cause.   Here  the  objective cause and the
subjective sensation are separated, and both  distinct  in
the mind.   In  the case of the auditive nerve, the sen-
sation  is no  longer perceived,  or at least is very im-
perfectly  perceived, in  the  ear, but  is nearly wholly
objective, i. e., referred to the  distant sounding body.
Finally, in the case of the optic nerve, the  impression
is  so wholly projected outward that the very reminis-
cence of its subjectivity is entirely  lost.  We are per-
fectly unconscious of any sensation in the eye at all.
   Illustrations  of this Property.—We will now try to
make this property clear by many illustrative experi-
ments.
    Experiment  1.—If the retina or the optic nerve in
any portion of its course were irritated in any way, by
pinching,  by scratching, or by electricity,  we should
certainly not feel any pain at all, but see a flash of light.
But where ?  Not at the peripheral extremity only, not
in the eye, but beyond in the field of view.   Of course, 
FUNCTION OF THE RETINA.            67
this experiment can not be easily made.   It has been
made, however, by passing a spark of electricity through
the head or through the eye in such wise as to penetrate
the retina  or traverse  the  optic nerve.  The  phenom-
enon  has also been observed in cases of extirpation of
the eye at the moment of section of the  optic nerve.
(Helmholtz.)
   Experiment 2.  Phosphenes.—Press the finger into
the internal corner of the eye:  you perceive a brilliant
colored spectrum in the field of view on the opposite or
external side.   The spectrum thus produced has a deep
steel-blue center,  with a brilliant  yellow border, and
reminds one of the beauty spots on a peacock's feather
or a  butterfly's wing.   Remove the  pressure to any
other part, and the spectrum moves also, but retains its
opposite position in the field of view.   In this familiar
experiment the pressure indents the sclerotic and causes
a change or irritation on  the  forward portion  of  the
retina; and any change whatever on the retina is always
referred directly outward at a right angle to the point
impressed, and therefore to the opposite side of the field
of view.  These colored spectra have been called phos-
phenes.
   Experiment 3.  Jfuscce Volitantes.—If we gaze on
a white wall or ceiling, or, still better, on a bright sky,
we see  indistinct motes  floating  about in the field  of
view on the wall or sky, and slowly gravitating down-
ward.   Sometimes they are  undulating, transparent
tubes, with nucleated cells within;  sometimes they are
like inextricably tangled threads, or like matted masses
of spider's web;  sometimes they  are  slightly  darker
spots, like  faint clouds.   They are called muscm voli-
tantes, or flying gnats.  What are they ?   They are specks
or imperfections in the transparency  of the vitreous 
68               MONOCULAR VISION.
Fig.- 21.
humor.  As fishes or other objects floating in midwater
of a clear lake on  a sunny day cast their shadows on the
bottom ooze, even so these motes  in the clear medium
of the vitreous  humor, in the strong light of the sky,
cast their  shadows  on the  retinal bottom.   Now, as
already said, all changes in the retina, of whatever kind,
whether produced by images, or  shadows, or  mechani-
cal irritations, are projected  outward  into the field of
view, and appear there as something visible.
   Experiment  4-  Purkinje's Figures.—Stand in  a
dark room with a lighted candle in hand.  Shutting the
left, hold the candle  very near  the right eye, within
three or four inches, obliquely outward and forward, so
that the light shall strongly illuminate the retina.  Now
move the light  about  gently, upward, downward, back
                       and  forth, while you  gaze  in-
                       tently on  the  wall  opposite.
                       Presently the  field of view be-
                       comes  dark from the  intense
                       impression of  the light,  and
                       then, as  you  move  the  light
                       about, there appears  projected
                       on the  wall  and  covering  its
                       whole surface a shadowy, ghost-
                       like  image, like a branching,
                       leafless  tree,  or like  a great
                       bodiless   spider   with  many
                       branching legs.  What  is  it?
                       It is an  exact but  enlarged
image of the blood-vessels of the retina (Fig. 24).  These
come in at the  entrance of  the optic nerve, ramify in
the middle layer, and therefore in the strong  light cast
their shadows on the bacillary layer, of the retina.  The
impression of these shadows  is projected outward into
Internal View of the Eetina,
  showing the retinal vessels rami-
  fying over the surface, but avoid-
  ing the central spot.  (After
  Cleland.) 
FUNCTION OF  THE RETINA.
69
the field of view, and  seen  there as an enlarged shad-
owy image.  These have been called Purkinje's figures,
from the discoverer.
    Experiment 5.   Ocular  8pectra.—Look a moment
steadily at the setting sun, and then, turning  away the
eye, look elsewhere—at the sky, the ground, the wall:  a
vivid colored spectrum of the sun (or many of them, if
the eye has not been steady while regarding the sun) is
projected into  the field of  view, and follows all  the
motions of the eye.  This spectrum, on a bright ground,
like the sky, to my eve is first green, then blue, then
purple, and so gradually fades away.  The spectrum is
equally seen when the eye is shut; but then, being pro-
jected  on a dark ground, the color is apt  to be comple-
mentary to that of the same spectrum seen against  the
bright  ground of the sky.   It is first blue, then yellow,
then green, and so fades.   The explanation is obvious.
The strong impression of the image of the sun on  the
retina  induces  a change  which lasts  some time;  but
every  change in the  retina appears, by projection, in
the field of view.
    This experiment may  be made in an infinite variety
of ways.  If at night we  gaze  steadily at a candle- or
lamp-flame, or flame of any kind, and then turn away
and look at the wall, we see a vivid colored  spectrum
of  the flame,  which gradually changes its color  and
fades away.   In my own case, on  shutting the eyes,
the spectrum is first bright yellow, with deep-red border
and dark olive-green corona; then it becomes  greenish-
yellow, and  then green with red border, then red with
indigo  border, and so fades away.  With the eyes open
the changes are slightly different, and in some  stages
are complementary  to the  preceding.  Again,  if we
look a  moment through a window at a bright sky,  and 
70               MONOCULAR VISION.
 then quickly turn the eye to the wall, we will see a
 faint spectrum of the window with all its bars projected
 against the wall.  If we  look  intently and steadily at
 any object strongly differentiated from the rest of the
 wall  of  a room, as  a small picture-frame  or  a  clock,
 then look to some other part of the wall, the spectrum
 of the object will be  seen on  the wall and follow the
 eye in its motions. This experiment succeeds best when
 we are just waked up in the  morning, and while the
 retina is still sensitive from  long rest.
    The  experiment  may be varied  thus: Lay a small
 patch  of vermilion  red—such as a red  wafer—on a
 white sheet of  paper, and gaze steadily at it in a strong
 light for a considerable time,  and then turn  the eye
 to some other  part of the paper.   A spectrum of the
 wafer  will be seen,  because every difference in the
 retina will appear as a corresponding difference in the
 field.  It will be observed, also, that the spectrum will
 be bluish-green, i. e., complementary to the red of the
 object.   The reason seems to be that the long  impres-
 sion of the red produces a profounder change, or fatigue,
 in those rods or cones, or those portions of the cones,
 which co-vibrate with red; therefore, when we look
 elsewhere, of the different colors which make up white
 light, the retina is least sensitive  to red,  and therefore
 the other rays will predominate. Now these other rays,
 which with red make up white light, are what are called
complementary to red. A  mixture of  these makes a
bluish-green.   It is difficult, however, to account for  all
the phenomena of the colors of spectra by this  " law
of fatigue."
   Complementary spectra  may be  still more beauti-
fully seen by gazing on the brilliant contrasted colors
 of a stained-glass window, and then turning the  eyes 
FUNCTION  OF THE RETINA.
71
 on a white wall.  The whole pattern of the window
 will be distinctly seen in complementary colors.
    Let it be  observed here how  differently spectral
 images behave from objects.  AVhen we move the eyes
 about, the images of objects move about on the retina,
 but the objects  seem  to  remain unmoved.   Spectral
 impressions on the retina, on the contrary, remain in
 the same place, and therefore their external images fol-
 low the motions  of the eye.
    We are now  prepared  to generalize from these ob-
 servations.  It is evident that what we call the field of
 view is naught else than  the external projection into
 space of retinal  states.  All variations  of  state  of the
 one, whether they be images, or shadows, or mechanical
 irritation,  whether  they be normal  or  abnormal, are
 faithfully  reproduced  as  corresponding variations  of
 appearances in the other.  This sense  of  an external
 visual field is  ineradicable.  If we shut  our eyes, still
 the field  is there, and still it represents the state of the
 retina.  With the eyes open, we call it the field of view,
 filled with  objects; with the eyes shut,  it is the field
 of darkness—visible, palpable darkness, without  visible
 objects.   The one  is  the  outward projection  of  the
 active state  of the  retina, crowded  with its  retinal
 images; the other  is the  outward projection  of  the
 comparatively passive state of the retina, without  defi-
 nite images.  When we shut our eyes, or stand with
 eyes open in a perfectly dark room, the  field of dark-
 ness is an actual  visible  field, the outlines of which we
 can, at least imperfectly, mark out.  It is wholly differ-
 ent from a  simple  absence of visual impression.  We
 see a dark field in front, but nothing at all behind  the
 head.  The dark  field is also quite different from black-
ness.  If we must describe it as of any color, we should
             4 
72
MONOCULAR VISION.
say that it is a dark grayish or brownish field, full of
irregular,  confused, and  ever-shifting lines and cloud-
ings.  If  the retina has been previously strongly im-
pressed, spectra are seen on this  dark background when
the eyes are shut.  When the eyes are open, the same
spectra are seen on the bright ground of the sky or wall,
and the difference of  the background  makes the differ-
ence of the color  of the spectra in the two cases.
    Now the same inherent activity of the retina which
produces the sense of a dark field  with its confused mark-
ings and cloudings, will also, under certain circumstances
of peculiar sensitiveness of the retina, as after complete
rest in  the early morning, give rise  spontaneously to
more definite spectra, often of beautiful colors.  I have
often, in bed in the morning, watched with eyes shut
these splendid spectra, consisting  of  a colored patch
surrounded with a border of complementary color, each
color closing in  on the  center  and so vanishing, while
another border commences on the outside to close in in
the same  way.   Thus, just  as  impressions or  images
made normally on  the  retina  by  actual objects  from
without are projected into the  field  of view and seen
there as the true signs of objects,  even so  impressions
made on  the  retina  abnormally from within,  \>y the
mind or imagination, are also sometimes projected out-
ward, and become the delusive signs  of  external ob-
jects having no existence.  It is thus that the diseased
brain gives rise to delusive visual phenomena.
    Corresponding  Points, Retinal and  Spatial.—Further,
it  is  evident that every point—every rod or cone—in
the retina has its invariable correspondent in the visual
fieldj and vice versa.  Moreover, since the central ray of
the pencil of every radiant point in the external world
passes through the  nodal point of the  crystalline lens, 
FUNCTION  OF THE  RETINA.
73
it is evident that these lines must cross each other there.
In other words, the lines forming correspondent points
in space and on the retina cross each other  in the nodal
point, and therefore the positions of these correspondent
points,  external and  internal, are  completely  reversed.
Thus not only are the retinal images inverted, but the
relative positions of  these images are inverted, and the
position of every focal  point is the inverse of  its corre-
spondent radiant  point.  It is obvious, then,  that the
left  half of  the retina  corresponds with the right half
of the field  of  view, and the right half of the former to
the left half of the latter ; and so also the upper half of
the former corresponds to the lower half of the latter,
and  the lower  half of  the former to the upper half of
the latter.
    There are some peculiarities of vision which we are
now prepared  to explain.
    1. Properties of the  Central Spot, and of  its  Represen-
tative in the Visual Field.—We have already stated that
there are two spots on  the retina where the constituent
layers do not all exist.   The central spot is destitute of
all except the  bacillary layer; the blind spot,  of all ex-
cept the fibrous layer.
    The central spot {macula centralis) is a  small de-
pression not more than one thirtieth of an inch in diam-
eter, situated directly in the axis of the  eye, or  what
might be called the south pole of this globe.   It differs
from other parts of the retina (a) by wanting the fibrous
and granular layers; therefore the retina is much thin-
ner there, and the spot is consequently pit-shaped, and on
this account is  often called the fovea centralis, or central
pit.   Of course, the absence of other layers exposes the
bacillary layer here to the direct action of light.  It dif-
fers again (b) by the presence of a pale-yellow coloring 
74
MONOCULAR VISION.
matter in  the  retinal substance; hence it is sometimes
called macula  lutea—-the yellow spot.   It differs, again,
(c) in a finer organization than any other part of  the
retina.  The bacillary layer here consists only of cones,
and these are far smaller, and therefore more numerous,
than elsewhere;  being here, as already seen (page 58),
only xowo °^  an inc^ irL diameter.
   Function of the Central Spot.—Every point on the reti-
na, as already  seen, has its correspondent or representa-
tive in the field of view.   Now what is the representative
of the central  spot ?  It is evidently the point, or rather
the line, of sight.  From its position in the  axis of  the
eye,  it is evident that on it must fall  the image of  the
object or  part of the object looked at, or of all points
in the visual line or line of sight.   Now, if we look
steadily and attentively on  any spot  on the wall, and,
without moving the eyes, observe the gradation of  dis-
tinctness over  the field, we find that  the distinctness is
most perfect  at the point of  sight and a  very small
area about that  point, and  becomes less and less as we
pass outward  in any direction toward the  margins of
the field of view.  Standing two feet from the wall, I
look at my pen held at arm's length  against the wall,
and  of course  see the pen distinctly.  Looking still at
the same spot, I move the pen to  one side eight or ten
inches: I now no longer see the hole in the  back of the
pen.   I move it two feet or more to one side: I now
no longer see  the shape of the pen.  I see an elongated
object of  some  kind, but can not recognize  it as a pen
without turning my eyes and bringing its image on the
central spot.  Hence, to see distinctly a wide field, as
in looking at a landscape or a  picture, we unconsciously
and rapidly sweep the line of sight over every part, and
then gather up the combined impression in the memory. 
FUNCTION  OF THE RETINA.
75
   Now the point of sight with a very small area about
it corresponds to the central spot, and the margins of
the field  of view correspond to the extreme forward
margin of the retina.  Therefore the  organization of
the retina for distinct perception is most perfect in the
central spot, and becomes gradually less and less perfect
as we  pass  toward the anterior margin, where its per-
ception is so  imperfect that we  can not tell  exactly
where the field of view ends, except where it is limited
by some portion of the face.
   Now what is the use of this  arrangement?  Why
would it  not  be much better  to  see equally distinctly
over all portions of the field of view ?   I believe that
the existence of the central spot is  necessary to fixed,
thoughtful attention, and this again in its turn is neces-
sary for the development of the higher faculties of the
mind.   In passing down the animal scale, the  central
spot is quickly lost.  It exists only in man and the
higher monkeys.  In the lower animals, it is necessary
for safety that they should see well over a very  wide
field.  In man, on the contrary, it is much more neces-
sary that he should be able to fix undivided attention on
the thing looked at.  This would obviously be impos-
sible if other  things were seen with equal  distinctness.
This subject is more fully treated in the final chapter
of this work.
   It is  evident, then, that distinctness of vision is a
product of two factors, viz.: 1st, an optical apparatus for
distinct image on the retina;  and 2d, a retinal  organiza-
tion  for distinct perception of  the image thus  formed.
These  two  factors  are  perfectly independent  of  each
other.  If I hold  up my pen before my eye,  but very
near, and then look at the sky, the outlines of the pen
are blurred because the retinal image is so, but my per- 
76
MONOCULAR VISION.
ception is perfect.  I can observe with great accuracy
the exact degree of indistinctness.   But if I hold the
pen far to one side, say 90°, from the line  of sight—on
the extreme verge of  the  field of view—it is again in-
distinct, much more so than before, but from an entirely
different cause, viz., imperfect perception of the retinal
image.  In  fact, my perception is so imperfect that I
can not tell whether the image is perfect or not.   Thus
there are  two  forms  of indistinctness of vision, viz.,
indistinctness from imperfect retinal image, and indis-
tinctness from imperfect retinal  perception.  The for-
mer is an effect of the optical  instrument, the latter of
the organization of the sensitive plate.
    It  is evident  from the  above  that  an  elaborate
structure of the lens, for making very exact images of
objects on the margins of the field of view, would be of
no use to man for want of corresponding distinctness
of perception in the  anterior margins  of the retina.
Therefore, as already  stated on  page 37,  the peculiar
structure of the crystalline, viz., its increasing density
to the center, is of use to man only as correcting  aber-
ration, and not in conferring the faculty of periscopism.
In the lower animals, however, in which periscopism is
so important, this structure of the lens subserves both
purposes.   So far as this property is concerned, there-
fore, the structure in  man may be regarded as having
outlived its use.
    Minimum Visibile.—Is  there  a  limit to  the  small-
ness of a visible point ?  This question has  been dis-
cussed by metaphysicians.   But, as  usually understood
by them, there is no such thing as a minimum visibile.
There is no point so small that  it  can not be seen if
there be light enough.  For example : a fixed star may
be magnified 10 diameters, 100 diameters, 1,000 diam- 
              FUNCTION OF  THE RETINA.           77

eters, 5,000 diameters, and still it is to us a mathemati-
cal point without dimensions.   How much more, there-
fore, is it without dimensions to the naked eye!  And
yet it is  perfectly visible.  The only sense in which
science recognizes a minimum visibile  is the smallest
space or object which can be seen as a surface or as a
magnitude—the  smallest  distance  within which  two
points or two lines may approach each other and yet be
perceived as two points or two lines.   In this sense it
is  a legitimate inquiry; for there is here a real limit,
which depends on the perfection of the eye as an in-
strument  and the fineness of the organization of the
retina.
   We can best  make this point clear by  showing a
similar property, but far less perfect, in the lower sense
of touch.   There is also a minimum tactile.
   Experiment. — Take a pair of  dividers ;  stick on
each point a mustard-seed shot, so that  the  impression
on the skin shall not be too  pungent.   Now try, on
another person whose eyes are shut, the least distance
apart at  which  two distinct  impressions can be  per-
ceived.   It  will be found  that, on  the  middle of the
back, it is about  3 inches; on the arm or back of the
hand, it  is about  £  to £ inch; on  the  palm, about \
inch; on  the finger-tips, about tV or  tV mcri I  an(^ on
the tip of the tongue, about -fa inch, or less.
   Now, sight is a very refined tact, and the retina is
specially  organized for an extreme minimum tactile.
There is no doubt that the size of the cones of the  cen-
tral  spot  determines the  minimum visibile.   If  the
images of two points fall on the same retinal cone, they
will make but one impression, and therefore be seen as
one; but  if they are far enough apart to impress  two
cones, then they will be  seen as two points.  So  also 
78
MONOCULAR VISION.
of an object: if its image on the retina be sufficient to
cover two or more cones  of  the central spot, then  it
will be seen as a magnitude.  Taking the diameter of
central-spot cones to be T1nro" (which is the diameter
given  by  some),  the  smallest  distance  between  two
points which  ought to be visible at  five inches  dis-
tance is ToV¥ °f an mch.   This is found to be  about
the fact in good eyes.
   2. Blind Spot.—This is the spot where the optic nerve
enters the ball of  the eye.   Objects whose images fall
on this spot are wholly invisible.  It is for this reason
that the point of entrance  is always placed  out of the
axis, about ^ inch on the nasal side.   For, if it were in
the axis, of course the image of the object we looked
at would  fall on this spot,  and the object would conse-
quently disappear  from view.   The  structural cause of
the blindness of this spot we have already explained on
page 59.  It is the absence of  the bacillary layer.   The
existence  of the blind spot may be easily proved by
experiments which any one can repeat.
   Experiment 1.—Make two conspicuous marks, A and
B, a  few inches apart.  Then shut the left eye, and
           *k                          •
           A                           B
while looking steadily with the  right eye at  the left
object, A, bring the paper gradually  nearer and nearer:
at a certain point of approach  B  will disappear utterly.
Continue to bring the paper nearer, still looking steadily
at A: at a certain nearer point B will reappear.   The
explanation is as follows: At first, when  the paper is at
considerable distance, say 18 inches, the  image of A is,
of course, on the central spot,  for the axis of the eye  is
directed toward this point; but the  image of B falls a
little to the internal or nasal side of  the central  spot, 
FUNCTION OF THE RETINA.
79
Fig. 25.
viz., between the central spot and the blind spot.   Now,
as the paper comes nearer, the eye turns more and more
in order to regard A, the image of B travels slowly over
the  retina  noseward  until it
reaches the blind  spot,  and the
object disappears.  As the pa-
per  still approaches, the  image
of B continues to travel in the
same direction until it crosses
over the blind spot to the other
side, when  the  object immedi-
ately reappears.
    The accompanying diagram,
Fig.  25,  illustrates  this  phe-
nomenon.   Let  A and B rep-
resent the two  objects, and R
and L the positions of the right
and left eyes respectively. The
right is drawn,  but  the left,
being shut, is  not drawn,  but
only its position indicated by the
dot.  The central spot is  repre-
sented by  c, in the axis A c,
and  the blind spot by o,  where
the  optic nerve  enters.  It is
obvious that the image a of the
object A  will be  always  on c,
and  the  place of  the image of
B is on the intersection b  of
the  line B b with  the retina.
Now, as the eye approaches the objects A and B, it is
seen that the image b  of B travels toward  the blind
spot, o.   At the second position of the eye,  R', it  has
not reached it.   At the  third position, R", it is upon it.
 
80
MONOCULAR VISION.
At the fourth position, R'", it has already crossed over
and is now on the other side.  At the third  position,
R", the object B disappears from view.
   The distance at which the disappearance takes place
will, of course,  depend  on the distance  between the
objects  A and B.  If these are 3 inches apart, then
the disappearance on approach  from a greater distance
takes  place  at about  1  foot, and  the reappearance  at
about 10 inches.  If the objects  be 1 foot apart, then
the disappearance takes place at 48 inches, and  the reap-
pearance at 38 inches.
   Experiment 2.—Place a small piece of money on
the table.  Shutting the left eye,  look steadily with the
right  at a spot on the table a little to the left of the
piece, and move the piece slowly to the right while the
point of sight remains fixed; or else, the piece of money
remaining stationary, move the point of sight slowly to
the left. At a certain distance from the point of sight
the piece will disappear  from view.  Beyond this dis-
tance it will reappear.
   Experiment 3.—The experiment may be  varied  in
many ways.   If, when the object  B has  disappeared
from view in the  previous experiments, we open the
left eye and shut the right, and look  across the nose at
the object  B, then A will disappear.  Thus  we may
make them disappear alternately.   If, finally, we squint
or cross the eyes in such wise that the right eye shall
look at  the left object A, and the left eye at the right
object  B (the two, A and B, had best be similar  in
this case), then B will fall on the blind spot of the right
eye and A on the blind spot of the left eye,  and they
will both disappear; but a combined image of A and
B on  the central spots of the two eyes will be seen  in
the middle.   This, however, is a phenomenon of bin- 
FUNCTION  OF THE RETINA.            81
ocular vision, and will be  explained farther on  (see
page 107).
   Experiment  J^.—Any object, if not too large, may
be made to disappear by causing its image to  fall on
the blind spot.   For example: From where I now sit
writing the door is distant about 10 feet.  I shut my
left eye and look at  the door-knob.   I now slowly re-
move the point of sight and  make it  travel to the left,
but at the same level; when it  reaches about 3  feet to
the left, the door-knob  disappears;  when it reaches 4
feet, it reappears.  Precisely in the same way a bright
star  or planet,  like  Venus  or  Jupiter,  or  even  the
moon, may  be  made  to  disappear completely from
sight.
   Size of the Blind Spot.—As every point in the retina
has its representative in the visual  field, it is evident
that the size of the invisible  spot is determined by the
size of  the  blind  retinal  spot.  We may, therefore,
measure the latter by the former.  I have made many
experiments to determine the size of  the invisible spot.
At the distance of 3^ feet (42 inches) I find the invisi-
ble spot 12 inches from the point of sight,  and  3^ inches
in diameter; i. e., a circle of  3£ inches will entirely dis-
appear at  that distance.  Taking the nodal point of the
lenses or the point of ray crossing at f of an inch in front
of the retina (it is a very little less), an invisible spot of
3^ inches  at a distance of 3£  feet would require a blind
retinal spot of a little more than ■£§ inch in diameter.
At 36 feet distance the invisible area would be 3 feet;
it would  cover a man sitting on the  ground.   At  100
yards  distance the invisible area would cover a circle of
8 feet diameter.   In  a word, the angular diameter of
the invisible spot is a little more than 4£°.  Helmholtz
makes it a little larger than this. 
82               MONOCULAR  VISION.
   Representative in the Visual Field of the Blind Spot-
Since every condition of the retina has its visible repre-
sentative in the field of view, it may be asked, " If there
be a blind  spot, why do we not see it, when we look at
a white wall or bright sky, as a black spot, or a dusky
or dim spot, or a peculiar spot of some kind ?"   I an-
swer :  1. With both eyes open there are, of course, two
fields of view partly overlapping each other.  Now the
invisible spots  in these  two fields  do not correspond,
and  therefore objects  in the  invisible spot of one eye
are seen perfectly  by the other eye, and hence  there
is no invisible area for the binocular observer.  But it
will be objected that even with one eye we see no pecu-
liar spot on a white wall.  I therefore add: 2. That we
see distinctly only a very small  area about the point of
sight, and  distinctness decreases rapidly in going from
this  point  in any direction.   Therefore  the correspon-
dent or representative in the field of view may well be
overlooked, unless  it be conspicuous, i. e., strongly dif-
ferentiated from the rest of the general field.   3. But if
this were all, close  observation would certainly detect it.
The true reason is very different, and the explanation is
to be sought in an  entirely different direction. Writers
on this subject have expected to find a visible representa-
tive, and have sought diligently but in vain for it.  But
the fact is, they ought not to have expected  to find it.
The expectation is  an evidence of confusion of thought
—of confounding blackness or darkness with absence of
visual activity.   Blackness or darkness is itself but the
outward projection of the unimpressed state of the bacil-
lary layer; but there is no bacillary  layer here.   We
might as well expect to see a dark spot with our fingers
as in  the  representative of  the blind spot.   A  black
spot, or a  dark spot, or a visible spot of any kind, is 
FUNCTION  OF THE RETINA.
83
not the representative in space of a blind or insensitive
retinal  spot.  The true representative of a blind spot
is simply an invisible spot, or, in other words, a spot in
which objects are not seen.  If we could differentiate it
in any way, it would be visible, which it is not.  As it
can not  be differentiated in any way, the mind seems
to extend  the general ground color of the neighboring
field of view over it.  This is, however, a psychological
rather than a visual phenomenon.  It is  for a similar
reason that it is impossible to see any limit to the field
of view, except  where it is limited by the  parts of the
face, as nose, brows, etc.  There is a certain limit hori-
zontally outward  where vision  ceases, but  it is impos-
sible  to detect  any line  of demarkation  between the
visible and the invisible.
   3. Erect Vision.—Retinal  images  are  all inverted.
External images or signs of objects are outward projec-
tions of retinal images.  How, then, with inverted retinal
images, do we see objects  in their right  position, i. e.,
erect ?   This question has puzzled metaphysicians, and
many answers characteristic of this class of philosophers
have  been given.   The true scientific answer is found
in what is called the " law of visible direction."  This
law may be thus stated : When the rays from any radi-
ant strike the retina, the impression is referred back
along the ray-line  {central ray of the pencil) into space,
and therefore to its proper place.  For  example:  The
rays  from a star (which is a mere radiant point) on the
extreme verge of  the  field of view to the right  enter
the eye and strike the retina  on its  extreme anterior
left margin; the impression is  referred straight  back
along the ray-line,  and  therefore seen in its proper  place
on the right.    A star on the left sends its rays  into
the eye and strikes the right side of the retina, and the 
84
MONOCULAR VISION.
impression is referred back along the ray-line  to its ap-
propriate  place on the left.  So also points  or  stars
above  the horizon in front impress the lower portion
of the retina, and the impression is referred back at
right angles, or nearly at right angles, to the  impressed
surface, and therefore upward;  and  radiants below the
horizon, on  the ground, impress the upper half of the
retina and are referred downward.
   Comparison with  Other  Senses.—There  is  nothing
absolutely peculiar in this; but only  a general property
of sense refined to the last degree in the case of  sight,
owing to the peculiar and exquisite structure of the
bacillary layer of  the  retina.  For example:  Suppose,
standing with our eyes bandaged, any one should with
a rod  push  against our body.   We immediately infer
the  direction  of the  external rod by  the  direction of
the  push.  Or another example : Suppose we stood
naked in a pond of placid water, with  eyes  bandaged,
and  some one on shore agitated  the water; the advanc-
ing waves would  after a while reach us and tap gently
upon the  sensitive skin.   Could we not infer the direc-
tion of the  distant  cause  from the direction of the
blows ?  Is  it any wonder, then, that when  the rays of
light crossing one another in  the nodal point punch
against the interior  hollow of  the  retina, we should
infer the direction of the cause by the direction of the
punch; i. e., that  we should refer each radiant back to
its proper place in space ?
    Thus  it  is seen that it is in no wise contrary to the
general law of the senses, that  we should refer single
radiants, like stars, back to their proper place in space
and see them there.  But objects are nothing else than
millions of radiants, each with its own correspondent
focal point in the retinal image.   Each focal impression 
FUNCTION OF THE  RETINA.
85
is referred back  to its correspondent radiant, and thus
the external image is reconstructed in space in its true
position, or is rein verted in the act of projection.
   Law  of Visible  Direction.—After these illustrations
and  explanations we return to the law, and restate it
thus: Every impression on the retina reaching it by a
ray-line  passing  through  the  nodal point is referred
back along the same ray-line to its true place in  space.
Thus, for every radiant  point in the object  there  is a
correspondent focal point in  the retinal image;  and
every focal point is referred back along its ray-line to
its own  radiant,  and thus the external image  (object)
is reconstructed in its proper  position.   Or it  may be
otherwise  expressed thus:  Space  in  front  of  us is
under all circumstances the outward projection of  ret-
inal  states.   With  the  eyes open, the  field of view is
the outward projection  of the active or stimulated state
of the retina; with the eyes shut, the field of dark)iess
is  the outward projection of the unstimulated or pas-
sive  state of the retina.  Thus the internal retinal con-
cave with all its states is projected outward, and becomes
the external  spatial concave, and the two correspond,
point for point.   Now the lines connecting  the  corre-
sponding points, external and internal, cross each other
at the nodal point, and impressions reach the retina and
are referred  back into  space along these lines;  or, in
other words,  these  corresponding points,  spatial and
retinal,  exchange with  each other by impression and
external projection.  This would give the true position
of all objects and  of all radiants, and  therefore com-
pletely explains erect vision with inverted retinal image.
   We  see, then, that the sense of sight is not excep-
tional  in this  property of direction-reference.   But
what is exceptional  is the marvelous perfection of this 
86
MONOCULAR VISION.
property—the mathematical accuracy of its perception
of direction.   This is  the result  partly of the remark-
able structure of the  bacillary layer.   Every rod  and
cone has its  own  correspondent  in space, and the ex-
treme minuteness  and therefore  number of separably
discernible points  in space are measured by  the  mi-
nuteness and therefore number of the rods and cones of
the bacillary layer.  Also  the perpendicular direction
of the rods and cones to the retinal concave is probably
related  to the direction of projection of impressions
into space, and therefore to the accuracy of the percep-
tion of direction.
    Illustrations  of the Law of Direction.—There  are
many interesting  phenomena explained by this law,
which thus become illustrations of the law.
    Since inverted images on the retina are reinverted
in projection and seen  erect, it is evident that shadows
of  objects thrown  on  the retina, not  being  inverted,
ought to become inverted in outward projection, and
therefore seen in this  position in space.  This is beau-
tifully shown in the following experiment.
    Experiment  1.—Make  a pin-hole  in a  card, and,
holding the card at four or five inches distance  against
                  the sky before  the right  eye with
       IG'          the left eye shut, bring the pin-head
               I  very near to the open eye, so that it
     ^   ' »J   I  touches the lashes, and in the line of
       -4       I  sight:  a perfect inverted image of
               1  the pin-head will be seen in the  pin-
               |  hole.   If, instead  of one, we make
               |  several pin-holes, an inverted image
                  of the pin-head will be seen in each
pin-hole, as shown in  Fig. 26.  The  explanation is as
follows: If the pin were farther away, say six inches or 
FUNCTION  OF THE RETINA.
87
F13. 27.
more, then light from the pin would be brought to focal
points and produce an image  on the retina; and this
image, being inverted, would by  projection be  rein-
verted, and the pin would be seen in its real position.
In the above experiment, however, the pin is much too
near the retina to form an image.   But nearness to the
retinal  screen,  though unfavorable for  producing an
image, is most favorable for casting a sharp shadow y
and while retinal images are inverted, retinal shadows
are erect.  The light  streaming through the pin-hole
into the eye  casts an erect shadow of the pin-head on
the retina.   This  shadow is  projected  outward into
space, and by  the  law of direction is inverted in the
act of projection, and  therefore seen in this position in
the pin-hole.   It is further  proved to be the outward
projection of  a retinal shadow
by the fact that, by multiplying
the pin-holes or sources of light,
we multiply  the shadows, pre-
cisely as shadows of an object in
a room are multiplied by multi-
plying the lights in the room.*
    Experiment 2.—If we look
at a  strong  light,  such  as  the
flame of a candle or lamp, or  a
gas-flame, at  some  distance and
at night, and thus bring the lids
somewhat near together, we  ob-
serve  long rays streaming from
the light in  many  directions, but  chiefly upward and
downward.  Fig. 27 gives the phenomenon as I see it.
The explanation is as follows : In bringing the lids near
   * This phenomenon was first explained by the author in 1S71. See
" Philosophical Magazine," vol. lxi, p. 266.
 
88
MONOCULAR VISION.
together, the  moisture which  suffuses the eye forms a
concave lens, as  in Fig. 28 (hence  the  phenomenon is
much more conspicuous if there be considerable moisture
in the  eyes).  This watery lens will be saddle-shaped—
i. e., concave vertically and convex  horizontally.  Now
the rays from the light (Z, Fig. 27)  which penetrate the
center of the pupil will pass directly on without refrac-
tion except what is normal, and  make its image (Fig,

                       Fio. 28.
28, L') on the central  spot.  But the rays which strike
the curved surface of the watery lens will be bent upward
to b and downward to a.  Thus the  light, instead of
being brought to a focal  point, is brought to  a long
focal line, b a, on the retina, with the image of the light
in the middle at L'.  The upper portion of  this line
b L' will be projected outward and downward, and form
the downward streamers  of Fig. 27;  while the lower
portion of the retinal impression a L' will be projected
outward  and upward, and form the upward  streamers
of Fig.  27.   To prove this, while  the streamers  are
conspicuous, with the finger lift up the upper lid:  im-
mediately the lower  streamers disappear;  now press
down the lower  lid: immediately the  upper streamers 
              FUNCTION  OF THE RETINA.            89

disappear.   Also, by  shutting alternately one  eye and
the other, it will be seen that a b  (Fig. 27) belongs to
the right eye and a' V to the left.
    The much lighter diverging side-rays are more dif-
ficult to account for.  I attribute them to the slight
crinkling of the mucus covering the cornea in bringing
the lids together. 
PAET  II.
BINOCULAR   VISION.
                  CHAPTER  I.

           SINGLE AND DOUBLE IMAGES.

   The Two Eyes a Single Instrument.—We have thus
far treated only of the phenomena of monocular vision;
and all that we have said might still apply, almost word
for word, if, like the Cyclops Polyphemus, we had but
one eye in  the middle of the forehead.  But we have
two eyes; and these are not to  be considered as mere
duplicates, so that if we lose one we still have another.
On the contrary, the two  eyes act together as one in-
strument ; and there are many visual  phenomena, and
many judgments based upon these phenomena, which
result entirely from the use of two eyes as one  instru-
ment.  These form  the subject matter of Binocular
 Vision.  It must be  clearly understood that the distinc-
tive phenomena of  binocular vision require two eyes
acting as one.  We might have two  eyes, or  even, like
Argus, a  hundred eyes, and yet not enjoy the  advan-
tages of binocular vision; for each eye might see inde-
pendently.   This would still be monocular vision.
   The phenomena  of binocular vision are far less
purely physical  than those of monocular vision.   They 
SINGLE AND DOUBLE IMAGES.           91
are also far more  obscure, illusory, and difficult of an-
alysis, because far  more subjective and far more closely
allied to psychical phenomena.   From early childhood
I have  amused myself with  experiments in this field,
and  have thus acquired an  unusual voluntary power
over the movements of  the  eyes, and a still more un-
usual power of analysis of visual phenomena.  This has
always therefore been a favorite field for me; but with
a little practice any one may acquire similar power and
enjoy a similar pleasure.
   Binocular Field.—We have  said  that  the  field  of
view is naught else  than an  outward projection of ret-
inal  states.  AVith the  eyes open and the  retina in an
active or stimulated condition, we call it  the field  of
view •  with the eyes shut and the retina in a compara-
tively passive or unstimulated condition, we call  it the
field of darkness.  In either case, every  variation in
the  state of different parts  of  the retina, whether  by

                        Fio. 29.
shadows  or by images, or by its own internal  changes
or unstimulated activity, is faithfully represented in
external  space by spectra, external images, etc.  But
we have  two eyes, and therefore two retinae, and there-
fore also two fields of view, the external projections of 
92
BINOCULAR  VISION.
the two retinas.  These two fields of view partly over-
lap each other, so as to form a common or binocular
field.   Fig. 29 represents  roughly  the form  of these
fields in my own  case.  The right field, R, is  bounded
by the line of  the nose n  n on the  left, the brows  br
above, and the cheek ch below.  The field of the left
eye, L, is  bounded similarly on the  right by  the nose
n' n', the  brow br', and the cheek ch'.  Between the
lines  of the  nose, n n, n'  n',  is the rounded triangu-
lar space C F, which is the common or binocular field.
This common field is the only part  seen  by both eyes.
The two fields are left vacant on the extreme right and
left, because, projected on a plane surface, they are un-
limited in these directions.   This is the necessary result
of the fact that  in a horizontal direction the field of view
of both eyes is more  than 180°.
   Now, there  being two  retinae, there  are of  course
two retinal images of every external object; and since
retinal images are projected outward into space as ex-
ternal images,  we must have two external images  of
every object.  But we see  objects only by these exter-
nal images.  Why, then, with two retinal images—ay,
and two external images—for every object, do we not
see all objects  double f  I  answer:  We do  indeed see
all objects  double,  except under certain conditions.
   Double Images.—This phenomenon of double images
of all  objects, except  under  certain special conditions,  is
so fundamental  in binocular vision, and yet so commonly
overlooked by even  the most intelligent persons unac-
customed  to  analyze their visual impressions, that  it
becomes absolutely necessary first of  all to prove it by
detailing many experiments, which  every one  may re-
peat for himself.
   Experiment 1.—Holding up the  finger before the 
SINGLE AND  DOUBLE IMAGES.          93
eyes, look, not at the finger, but at the wall or the ceil-
ing or the sky.   Two transparent images of the finger
will be  seen, the left one  belonging to the right  eye
and the right one to the left eye.  We easily prove  this
by shutting first one and then the other eye, and observ-
ing which  image disappears.  The images  are  trans-
parent, or  shadowy, because  they do not  conceal any-
thing.   The  place covered by the  right-eye image is
seen by the left  eye, and the  place covered by the left-
eye image  is seen by the right eye.  If we alternately
shut one eye and then the other, the wide difference
between these places is at  once  evident.   Often there
is  an  alternation in  the distinctness of these shadowy
images—first one and then the other fading away,  and
almost disappearing from view.
    Experiment 2.—Point with the  forefinger at some
distant  object, looking with both eyes open at the ob-
ject, not the  finger.   Two fingers will be seen, one of
them  pointing  at the object  and the other far out of
range, usually to the right.
    Most persons find some difficulty at first in being
conscious  of  perceiving  two  images.  The reason is,
they do not easily separate what they know from what
they see.   They know  there is  but  one finger,  and
therefore they think they see but one.  The best plan
is  to shut alternately one eye and then  the other,  and
observe the places of projection of the finger  against
the wall; and then,  opening both eyes,  shadowy  im-
ages at  both these places will  be seen.  I have found
some  trouble in convincing  a few  persons, and have
found one  single person whom I could not convince,
that there were two images.  To such a person all that
I am  about to  say on binocular vision will be  utterly
unintelligible.   The whole cause of  the  difficulty in 
94
BINOCULAR VISION.
perceiving at once double images is, that we habitually
neglect one image unless  attention is specially drawn
to it.   I have found that nearly  all persons neglect
the right-hand image—i. e., the image belonging  to
the left eye.  In other  words,  they are right-eyed as
well as right-handed.  I have also tried the same ex-
periment on several left-handed persons, and have found
that these neglected the left image—i. e., the image be-
longing  to the right  eye.   In  other words,  they were
left-eyed as well as left-handed.   There is  no doubt
that dextrality affects the whole side of  the  body, and
is the result of  greater activity of  the left cerebral
hemisphere.  People are right-handed because they are
left-brained.
   I  pause a moment  in order to  draw attention here
to the uncertainty of some so-called facts of conscious-
ness.   I  have often labored to  convince a person, un-
accustomed  to  analyze his visual  impressions, of the
existence of double images  in his own case.    He would
appeal with confidence, perhaps  with some  heat, to  his
consciousness against my reason;   and yet  he  would
finally admit that I. was right and he was wrong.   So-
called facts of consciousness must  be scrutinized and
analyzed, and subjected  to the  crucible of  reason,  as
well as other supposed facts, before they should be re-
ceived.
   Experiment 3.—Place the two forefingers, one  be-
fore the  other, in the  middle plane of the head (i.  e.,
the vertical plane through the nose,  and dividing the
head  into two symmetrical halves), and separated by a
considerable distance—say  one  8 inches  and the other
18 to  20 inches from  the  eyes.  Now,  if we  look at
the farther finger, it will be of  course seen single, but
the nearer  one is  double; if we  look  at  the nearer 
SINGLE AND  DOUBLE IMAGES.          95
finger, this will be seen single, but the farther one  is
now double; but it  is impossible to see  both of them
as single objects at the  same time.  By alternately
shutting one eye and  then the other, we can observe
in either case which of the double images disappears.
Thus we will learn  that when we look at the  farther
finger, the nearer one is so doubled  that the left image
belongs to the right eye and the right image to the left
eye ;  while, on the contrary, when we look at the nearer
finger, the farther one is so doubled that the right image
belongs to the right  eye and the left image to the left
eye.  In the former case the images are said  to be het-
eronymous,  i. e.,  of  different  name, and  in the latter
case they are said to be homonymous, i. e., of the same
name, as the eye.
   Analogues of Double Images in  Other Senses.—When-
ever  it was  possible, we have traced the analogy of
visual phenomena in other senses.  Is
there any analogue of double vision to
be found in other senses?  There  is,
as may be shown  by the following ex-
periment : If we cross the middle fin-
ger over the forefinger until the points
are well separated, and then roll a small
round body like a child's marble about
on the table between the points of the
crossed  fingers, we will  distinctly per-
ceive  two marbles.  The points of the
fingers touched by the marble are non-
corresponding.  (Fig. 30.)
   Single Vision.—Therefore it is evident that when
we look directly at anything we see it single, but that
all things nearer or  beyond the point of  sight are seen
double.   We then come back  to our previous proposi-
 
96
BINOCULAR VISION.
tion, that we always see things double except under
certain conditions.   What, then, are the conditions of
single vision ?  I answer:  We see a thing single when
the two images of that thing are projected outward to
the same spot in space, and  are therefore superposed
and coincide.   Under all other conditions we see them
double.   Again, the two external images of an object
are thrown  to the same spot, and thus superposed  and
seen single,  when the two retinal images of that object
fall on what are called corresponding points (or some-
times identical points) of the two retince.   If they do
not fall on corresponding points of the two retinae, then
the external images are  thrown  to different places in
space, and therefore seen double.  We must now explain
the position  of corresponding points of the two retinae.
   Corresponding Points.—The retinae, as already seen,
are two deeply concave or cup-shaped expansions of the
optic nerve.   If R and Z, Fig. 31, represent  a projec-
tion of these two retinal cups, then the black spots C C.

                       Fn. 31.
in the centers of the bottom, will represent the position
of the central  spots.   If now we  draw vertical lines
(vertical meridians), a b, a' V, through the central spots,
so as to divide  the retinae into two equal  halves, then
the right halves would correspond  point  for point, and 
SINGLE AND DOUBLE IMAGES.          97
the left halves would correspond point for point;  i. e.,
the internal or nasal half of one retina corresponds  with
the external or temporal  half  of  the other, and  vice
versa.   Or, more accurately, if the concave retinae be
covered with  a system of rectangular spherical coordi-
nates, like the lines of latitude and longitude of a globe,
a b and x y being the meridian and equator, then points
of similar longitude and  latitude in the two retinae, as
d  d', e e', are corresponding.  Or, still  better, suppose
the two eyes or the two retinae to  be placed one upon
the other, so that they coincide throughout like geomet-
ric solids;  then the coincident points  are  also corre-
sponding  points.  Of course, the central  spots will be
corresponding points ; also points on the vertical merid-
ians, a b, a' b', at equal distances from the central spots,
will be corresponding;  also points  similarly situated in
similar quadrants, as d d', e e', etc.   It is probable that
the definition  just given is not mathematically exact for
some eyes.  It is probable that in some  eyes the appar-
ent vertical meridian which divides the retinae into cor-
responding  halves is not perfectly vertical, but slightly
inclined outward at  the top.  This would  affect all the
meridians slightly ;  but the effect  is very small, and  I
do  not find it so in my eyes.  We shall discuss  this
point again  (page 146).
   Law of Corresponding Points.—After this explanation
we reenunciate the law of corresponding  points: Objects
are seen single when their retinal images fall on corre-
sponding points.  If they do not fall on corresponding
points, their external images  are thrown to different
places in space, and therefore are seen double.
   Thus we see that the term  "■ corresponding points  "
is used in two senses, which must  be kept distinct in
the mind  of the  reader.  Every rod  and  cone  in  each 
98                 BINOCULAR VISION.
retina has its correspondent in external space, and these
exchange with each other by impression and projection.
Also every rod or cone of each retina has its correspon-
dent in a rod or cone in the other retina.  Now the law
of corresponding  points,  with which we are now deal-
ing,  states that the  two external or spatial  correspon-
dents of two retinal corresponding  points always coin-
                         Fig. 32.
                            A
R and L, two eyes; 0, center of rotation of ball, or optic center; x, point of crossing
   of ray-lines—nodal point; A, point of sight; D, some other point in the horoptoric
   circle A O 0'; cc', central spots; aa',d d', actual images of A and D.

cide with each other.   In order to distinguish these two
kinds of corresponding points from each other, the lat-
ter—i. e., corresponding points on the two retinae—are
often,  and perhaps best,  called  "identical  points," be-
cause  their  external  spatial  representatives  are really
identical.
    We will now apply the law.   If we look  directly at 
             SINGLE AND DOUBLE IMAGES.          99

any small object, it will be seen single, because the two
retinal images fall on corresponding or identical points,
viz., on the two central spots.  In Fig. 32 the two eyes,
R and Z, are turned directly on A.   The image of this
object will therefore fall on the central  spots c c', and
the object will  be  seen single.  Objects at nearly the
same distance, as for example D, a little to the right or
left or a little above or below the point of sight, are also
seen single; because the retinal images d and d' are on
correspondent halves—i. e., the internal or nasal half of
R and the external or temporal  half of Z—and at  the
same distance from the central spots c c', and therefore
on identical points.  Objects lying in a horizontal  cir-
cle passing through the point of sight and  the centers
of the eyes,  0 0', are usually supposed to be seen single.
This  is nearly true, except when the point  of sight is
very near.  This circle has been called the horopteric
circle of Miiller.
    Objects, as  already said, beyond or nearer than the
point of sight, are always seen double.   The reason is,
that their retinal images always fall on non-correspond-
ing  points.   This  is shown in  the diagram Fig.  33.
"While the two eyes, R and Z, are fixed upon ^1, this
object will be seen single,  for  its images, a and a',  fall
upon the central spots.  But if, while still looking at
A,  we  observe  B  and C, we shall  see  that both  are
double.  The reason is, that the images of B, viz., b b',
fall upon the two nasal or internal halves of the retinae,
which are non-corresponding; while the images  of C,
viz., c c', fall upon the two external or temporal halves
of the  retinae, which  are  also non-corresponding.  If
the external double  images be all referred to the plane of
sight, P P (which, however, is not the fact), as is usually
represented  in diagrams, then  the  position of the dou- 
100
BINOCULAR  VISION.
ble images will  be correctly  represented by  cc', bb'.
It is seen at a glance that the images c c' of C are het-
eronymous, while the images b V of B are homony-
mous.  Generally, all the field of view within the lines

                        Fig. 33.
                         B
of sight, A a, A a', belongs to the  temporal halves of
the retinae, while all outside of these lines belongs to
the nasal halves.  Or, again, double images formed by
impressions on the  two nasal halves of the  retinae are
homonymous, while those  formed  by impressions on
the two temporal halves are heteronymous. 
SINGLE AND DOUBLE IMAGES.          1Q1
   Definition of Horopter.—We have seen that the ob-
ject at the point of sight is seen single;  and all objects
at the same or nearly the same distance, but a little to
the right or left,  or  above or below, are also either
seen single, or else the doubling, if any, is usually im-
perceptible.  On  the  contrary,  all objects  farther or
nearer than the point of  sight are seen  double.  Now
the surface of single  vision—i. e., the surface passing
through  the point of  sight,  all  the  objects  lying in
which are seen single—is called the horopter.  Whether
there is such a surface at all, and if there is, what is its
form,  are questions upon  which  the acutest observers
differ.  Some  have made  it a plane, some a spherical
surface.   Some, by purely geometrical  methods, have
given  it  the most  curious  forms and properties; while
others, by purely experimental methods, have come to
the conclusion  that it  is not a surface at all, but a  line.
We  are not now prepared to discuss this question, but
shall return and devote to  it a special chapter.
   Supposed Relation of the Optic Chiasm to the Law of
Corresponding  Points.—In the optic chiasm,  Fig. 20,
page  54, there is certainly a partial (but only a partial)
crossing  of the fibers  of the two optic nerves.  Many
physiologists connect this fact with this remarkable law.
There is probably such a connection.   But many go far-
ther.   They think that some of the fibers of each optic
nerve cross over to the other eye, and some do not; and
that  those which cross over supply the internal or nasal
halves, and those  which do not cross over supply the
temporal  halves.  Thus, in the  diagram  Fig. 34, the
fibers of the right optic nerve-root 0, as  it comes from
the brain, go to supply the temporal half t of the right
retina, and, by  crossing, the nasal half n' of the left ret-
ina, and  these  are  corresponding halves.  So also the 
102               BINOCULAR VISION.

fibers of  the left optic nerve-root 0'  go to supply the
temporal  half t' of the left and nasal half n of the right
retina.  Still further, they think that the fibers coming
from corresponding or identical points, or rods, or cones

                         Fig. 34.
0 0\ optic roots; N N', optic nerves; R and L, sections of the two eyes; c c', cen-
   tral spots; n n', the nasal halves, and t V, the temporal halves, of the retinae.

in the  two retinae are not only thus carried by the same
optic root, but finally unite to form one fiber, or at least
terminate centrally in one brain-cell, and thus form  one
single  sense-impression.   It  is  almost needless to  say
that, while this is an interesting  speculation,  it is no-
thing more; for the supposed union of fibers from  cor-
responding rods or cones can probably never be either
proved or disproved.
    Theories of the Origin of this Law.—The perception
of direction and the correspondence of retinal and  spa-
tial points are certainly inherent properties of  the  ret-
ina, being connected with its structure.   The former—
i. e., the  perception of direction—we have seen,  is a
general property of sensory nerves, only developed  into
mathematical accuracy in the case of  the optic nerve ; 
             SINGLE AND  DOUBLE  IMAGES.          103

the latter—i. e., the correspondence of retinal and  spa-
tial points—is only the expression of  this mathematical
accuracy of perception of direction; and  both are  con-
nected with the structure of  the  bacillary layer.   Un-
doubtedly,  then, this property is innate and antecedent
to all experience.  What the infant learns by experience
is not direction, but  distance and size of  the object.
Direction is a primary datum of sense.  But  the prop-
erty of  corresponding  points  of the two  retinae and of
identical spatial points in the two fields of view seems to
be less absolutely simple and  primary.   The questions,
" Is  this property innate, instinctive,  antecedent to ex-
perience ? or is it  wholly the result  of  experience ?"
have been  long and hotly disputed by the profoundest
thinkers on this subject.   The  former view  has been
held by Miiller, Pictet, and others; the latter  by Helm-
holtz, Briicke, Prevost, and Giraud Teulon: the one is
called the nativislic, the other the empiristic theory.
    We shall not follow the history of this dispute, nor
detail the arguments brought  forward on each side; for
the tendency of modern science, under the guidance of
the theory of evolution, is to bring these two opposite
views together, and  reconcile them by  showing  that
they are both in a degree  true, and therefore not wholly
inconsistent with each other.  The difficulty heretofore
has been that anatomists and physiologists have studied
man too much apart  from other animals, and thus the
amount  of inherited,  innate, instinctive qualities has
been greatly underestimated by some  and overestimated
by others.   A new-born chicken, in a few minutes after
breaking the egg-shell, will  see an  object, direct the
eyes upon it, walk straight up to it, and seize it.   Evi-
dently there is in this case not  only a  perception of
direction, antecedent  to  all experience, but  also some 
104
BINOCULAR VISION.
perception of distance, and the wonderful, coordination
of muscles  necessary for standing  and walking,  and
directing the movements of the eyes.   A young rumi-
nant animal in  a few minutes after birth will stand and
walk, and direct its motions  by sight.   A bird of wild
species, hatched in a cage and kept in a cage until it is
fully fledged and its muscles are sufficiently developed,
if then thrown into the  air, will fly  away with ease,
although the coordination of many muscles in the act
of flying is something so marvelous that it could not be
learned in a lifetime of trial, unaided by inherited ca-
pacity.  Inherited powers are still more marvelous in
the case of insects.
   Manifestly,  then, the wealth  of capacities  in all di-
rections possessed  by the individual  is  partly inherited
and partly acquired by individual experience.  In ani-
mals the  inherited, in man the individually  acquired,
wealth predominates. But all wealth is acquired.  Even
that inherited  is ancestral experience accumulated and
transmitted by the law of heredity.   Even instinct is
" inherited experience."   Thus, then, it is evident that
the property of corresponding points of the two retinae,
and therefore of identical points in space, is partly in-
herited and partly acquired  by individual experience.
It is doubtless  wholly the result of experience, but not
wholly of individual experience.
   Consensual  Adjustments.—There  are therefore two
adjustments of  the eye in every voluntary act of sight,
viz., focal and axial.  In the former, each eye is adjusted
by the ciliary muscle to make a perfect image on the
retina;  in the  latter, the two  eyes are turned by the
recti muscles so that their axes shall meet on the point
of sight, and the  images  of  the object looked at shall
fall on the central  spots.   The one is an adjustment for 
SINGLE AND  DOUBLE  IMAGES.
105
distinct vision, the other for single vision.  There is
associated with these still a third  adjustment, but of
far less importance, viz., the adjustment of the pupil.
The pupil contracts and expands not only as the light
is  bright or faint, but also as the object is near or  far.
These  three adjustments take place together and with-
out distinct volition for each—i. e., by the one volun-
tary act of looking.  They are therefore consensual
movements, and usually regarded as indissolubly asso-
ciated.  We shall  show hereafter  that under certain
circumstances they may be dissociated.
    The two Fundamental Laws.—There are also   two
great and fundamental laws by which all visual phe-
nomena are explained, viz.,  the law of direction  and
the law of corresponding points.  The one gives  the
true position  of all points in space, and  therefore en-
tirely  explains the  apparent  anomaly  of  erect vision
with inverted retinal images; the other gives coinci-
dence  of corresponding points in the two fields of view,
and therefore entirely explains the second anomaly of
single  vision  with two retinal images.   Both may in
fact be called laws of corresponding points.  The  one
asserts  the  correspondence point  for point  of retinal
rods and cones with external space, with  ray-lines  con-
necting  and  crossing in  the nodal  point;  the other
asserts  a  correspondence  point  for point of the rods
and cones of the two retinae, and the coincidence of
their representatives in the two fields of  view.  From
the one law flow all the phenomena of monocular, from
the other all the phenomena of binocular  vision.
    All the phenomena of binocular vision are explained
by the law of corresponding  points.  But the phenom-
ena are  so  numerous, so  illusory,  and so  difficult of
analysis, that  the  connection  is by no means obvious. 
106
BINOCULAR  VISION.
The science of binocular vision consists in tracing this
connection, and  thus explaining  the phenomena.  It
will be our object, then, to take up all the most impor-
tant phenomena of binocular vision, and explain them
in this way. 
CHAPTEK  II.
       SUPERPOSITION OF ENTERNAL IMAGES.

    In the movements of one eye, or of the two eyes if
they move together equally in the same direction, as in
looking to one side or the other, or up  or down, ob-
jects seem  to stand still, and  the eyes or the  point of
sight  to sweep over them.   But if we move the eyes in
opposite  directions,  as  in converging the optic  axes
strongly and then allowing them to  become again par-
allel,  objects, or rather  their external images, seem to
sweep like trooping shadows across  the  field  of view;
or rather, the fields of view themselves seem to rotate,
carrying all their images with them,  in a direction con-
trary  to the motion of the eye, and therefore (since the
two eyes move in contrary directions) in directions con-
trary to each other.  This phenomenon is not very easily
observed, because it is best seen by simple convergence
of the eyes on a very near  point  in space, without any
object to direct the convergence,  or in trying to look at
the root of  the nose.  Divergence of the eyes may be
produced by pressing the fingers in  their external cor-
ners.  In  this case also  the  motion  of the images is
evident.
    Evidently, then, by voluntary motion of the eyeballs
in opposite directions, and the consequent motion of the 
108
BINOCULAR  VISION.
shadowy images  in opposite directions, we may (if we
observe the images and control the motion of the eyes)
cause them, whether  they belong to the same object or
to different objects, to approach each other and combine
successively.   Many  curious  phenomena  thus  result,
which it is necessary  to understand before we approach
the more  complex phenomena, and especially  before
we can explain the judgments based  upon, these  phe-
nomena.
    Combination of the Images of Different Objects.—We
have seen that the  combination of the two  external
images of  the same object produces single vision.  But
the external images  of  different objects may also  be
combined.  Under this head there are  several cases.
    1. Dissimilar  Objects.—We have seen that when the
two images of  an object fall on corresponding points of
the two retinae,  they are thrown  outward as external
images  to the same  point in space,  superposed, and
united, and therefore the object is seen single.   If, in-
stead of the two  images of the same object, the images
of two  different objects fall upon corresponding points,
evidently they also will  be thrown to the same place
in space and superposed.  In this case, however, there
being two objects, there will be  four retinal images,
only two of which will fall on corresponding points, and
also four external images, only two of  which will  be
superposed.  But we may confine our attention to the
superposed images, or else we may cut off the  others
from view, or prevent them from forming.
   Experiment 1.—If the left hand and the right fore-
finger,  or any two dissimilar objects, be held up  before
the eyes, say 8 to 10  inches apart, and  then the eyes  be
converged until the right eye looks exactly toward the
left hand and  the left eye toward  the  right forefinger, 
         SUPERPOSITION OF  EXTERNAL IMAGES.     109

then evidently the retinal images of these two objects
will  fall  on corresponding  points, viz., on the central
spots /  and their corresponding external images ought
to be thrown to the same  place and superposed.  Such
is actually the fact.  The phenomena as they actually
appear are as follows: As the eyes begin to converge,
the images of  both objects  double homonymously, and
we see now four images.  As the convergence increases,
the double images separate more and  more, until  the
left image (belonging to  the left eye) of the forefinger
and  the  right image of  the hand (this belongs to the
right eye) are brought  together  and  superposed, and
the forefinger  is seen lying in the palm of the  hand.
Of course, as already explained, there will be two other
images—one of the forefinger to the right, and belong-
ing to the right eye, and one of  the hand  to the left,
and belonging to the left eye.   By shutting alternately
one  eye  and then the other,  these belongings of  the
several images may be tested.
   Experiment 2.—Or,  again, the same combination
may take place without convergence of the eyes, thus:
Hold up  the two forefingers before the eyes a foot or
so distant, and a little  more than two inches apart  (it
should be equal to  the interocular distance), and against
a bright background like  a white wall or the sky.  Now
look at the wall or the sky: the two fingers will both
double, making four images;  but the two middle  im-
ages will  unite to  form what  seems to be one finger.
There  will be  therefore  apparently three images:  the
middle one  (the combined  images) is  opaque like  an
object; the other two,  uncombined, are transparent
like  ordinary double images.  In this  case,  as we  are
gazing beyond the finger, the double images are het-
eronymous.  It is  therefore the right-eye image of the 
110
BINOCULAR VISION.
right finger (the left of  its double images) and the left-
eye  image of the  left finger (the right of  its double
images) which combine in the middle.
   These facts and the  conditions  under which the
combination takes place are illustrated by the accom-
panying diagrams.  In Fig.  35  the right eye, R,  is
directed toward the object B, and the left  eye, Z, to-
Fig. 35,
*&-p
In hoth figures the letters are the same.  R and L, the two eyes; A and B, two ob-
  jects ; a'b, Fig. 35, and ab', Fig. 36, combined images; primed letters, left-eye im-
  ages ; c c, central  spots of retinae; n, the nose; P P, plane of objects; and p p,
  plane of sight.

ward the object A.  The retinal images of these, falling
on the central spots  c c, are superposed at the point of
sight (where the lines of sight intersect) and seen as a'b,
while two shadowy images, a and b', are seen to the right
and  left.   Their position in the  plane of sight, and as 
         SUPERPOSITION OF EXTERNAL IMAGES.      m

determined  by the law of direction, is given by con-
necting the points R A and Z B.  In Fig. 36 the right
eye, R, is directed  toward the object A, and the left
eye, Z, toward the object B.  The point  of sight  is
therefore beyond, at the  meeting of  the optic  axes or
lines of  sight.   There the combined images, ab', will
be  seen, while two other uncombined images will  be
seen at points determined by the law of direction, rep-
resented by continuing the lines R B and Z A  to the
plane of sight.   It  is evident that in this case the two
objects ^1 and B must not be farther apart than the
optic centers (interocular space); otherwise the lines of
sight will not meet in a point  of sight, and therefore
the two  images will not combine.   Simple  inspection
of the diagrams will  explain the  phenomena, if the
reader will  bear in mind that  capitals  represent ob-
jects  and small letters external images; and further,
that the primed small letters represent left-eye images,
the strong lines P  P  the actual  plane of the objects,
and  the  dotted  lines pp  the plane of sight or of the
images.
    Many persons will  not at first  succeed in making
these experiments,  on  account  of the difficulty  which
most persons experience in watching double images and
controlling the  movements of the  eyes.  To such we
would recommend the  following method : Let the two
objects set up before the eyes in the first experiment be
other than parts of the body of the observer—for ex-
ample, a card  and  a rod, or  two  rods.   Then, while
looking at the table on which the objects lie, hold up
the forefinger—or better, a pencil—between the eyes
and  the objects.  The  pencil will of course  be double.
Now, by bringing the  pencil  nearer or carrying it far-
ther, its double images  will separate  or close up.   Bring 
112
BINOCULAR  VISION.
the pencil into such  a  position that  its double  images
shall exactly coincide with the centers of the two ob-
jects which you  desire to combine.  If you now look
at the  pencil,  the ocular  convergence  will be  exactly
suitable for combining  the objects.
    In the cases thus far mentioned there is no illusion :
the combined images do not produce the appearance of
a real object, as  in the case of combined images of the
same object producing single vision ;  because, in the
first place, the  two objects are dissimilar, and therefore
the combination is not perfect; and, in the second place,
the illusion  is destroyed by the existence of the two
other uncombined images.  We next try—
    2. Similar Objects.—If the two objects, the  images
of which we desire to combine, are exactly similar, then
the combined image  wTill  be exactly like  a natural ob-
ject.  For example:
    Experiment 1.—Place two pieces of money of the
same kind on the table, being careful that the stamped
figures shall be  in the same position.  Now, looking
down upon  them, combine as before.   Not  only will
the outlines of the two  pieces  combine, but the stamped
figures in the minutest  details, so that the middle com-
bined binocular  image will have all  the appearance of
a real object.  This is illustrated by Figs. 37 and 38, in
which  the  position of  parts  is  reversed, because the
eyes are supposed to  be looking down.   In Fig. 37 the
two objects (coins), A and B, are combined by crossing
the eyes, and the combined or binocular opaque image
will be seen at  the point of sight as a'b, while  monocular
shadowy images, a and b', will be seen right and left.
In Fig. 38 the combination is made by looking beyond
the plane of the coins, and the coins in this case must
not be  more than an  interocular space apart.   The com- 
SUPERPOSITION OF EXTERNAL IMAGES.     H3
bined images, like a real opaque object, will be seen at
the point of sight ab', and the two shadowy monocular
images right and left, as before, only they are now het-
eronymous.
    In this case, though the combination is perfect, yet
the illusion is still not complete, because of the presence
of the accompanying monocular images; but the forma-
tion of  these may be prevented  by the use  of appro-
priate screens.
    Experiment 2.—If in the first experiment with the
money,  before combining, we hold  two cards, sc, sc',
Fig. 39, one  in either hand and at about half  the dis-
tance to the table (the best distance is the plane of com-
bination or plane  of  sight, for then there will be no
doubling of  the cards), in such position that the card
in the right hand, sc, will hide the right piece  A  from
the right eye  but not from the left, and the card in the 
114
BINOCULAR  VISION.
left hand, sc', will hide the left piece B  from the left
eye but not from the right, and then make the com-
bination by crossing the  eyes, the  combined  binocular
opaque image will be formed as before; but the mo-
nocular images will  not  appear, because there will be
Fig. 39.                Fig. 40.
no other retinal image formed  except  on the central
spots.   This is represented in  Fig. 39.  In  case we
combine beyond the plane of the objects, then a me-
dian screen, sc, Fig. 40, extending from the  root of
the nose n to the  table, midway between the  objects,
will  prevent the  formation of  the monocular  images,
as shown.
   But in these cases, although the union of the two
images  is perfect, and  although we see nothing but an
apparently solid opaque object, even yet the illusion is
not  absolute; partly because the table  is doubled and
therefore unreal, and partly because the eye is adjusted
to the point of sight, whereas the light comes from the 
         SUPERPOSITION OF EXTERNAL IMAGES.      H5

object, which  is either nearer as  in  Fig. 40, or farther
off as in Fig.  39, than that  point.  We will try there-
fore  still another case.
   3. Many Similar Objects regularly arranged.—The
illusion is most complete when we combine the images
of many  similar objects  regularly  arranged over the
whole  field of view, such  as  the regular  figures  of a
tessellated pavement or oilcloth,  or  of a regularly fig-
ured carpet of small pattern, or of a papered wall of
regular pattern, or the  diamond-shaped spaces of a wire
grating.  In such a case, when by convergence we  com-
bine two contiguous figures immediately in front, other
contiguous figures all over the plane also combine.  In
other words, by the  motion of the eyes in opposite  di-
rections in convergence, the images of the whole plane
of the figured surface are slidden by one eye to the left
and  by the other eye to  the right, until  combination
takes place again over the whole field.  When the  com-
bination is effected, if we hold the point of  sight steady,
the combined images  of the  figures, at  first a  little
blurred, become sharp and  clear; and then  the whole
figured plane  comes forward to the point of sight, and
appears there as distinctly as a real object, but  on a
smaller scale in  proportion  to the less distance.   This
is represented in Fig. 41, in which the strong line  P P
represents the plane of the regular figures  1, 2, 3,  4, 5,
etc.  When contiguous figures, 6 and 7, are united  by
convergence at the point of sight, and seen there,  then
all other contiguous figures, 1 and 2, 2 and 3, etc., all
over the plane, will  be similarly united, and the whole
plane with all  its figures will advance and  be distinctly
seen  at the distance p'' p'.   When by stronger conver-
gence alternate figures, 5 and 7, are combined at a nearer
point of  sight 5 on  the plane p" p"—or (which is the 
116
BINOCULAR VISION.
same) when we use  the plane p' p' first  obtained with
all its figures as a real object, and again combine con-
tiguous figures—the whole plane advances top" p", and
is seen as a distinct object with  a still smaller pattern
of figures.   Using  the plane thus obtained again as an
object, and  uniting its contiguous figures, the  whole

                       Fig. 41.
plane again advances still  nearer, and the figures  be-
come still smaller at p'" p'".  In this manner I have
often distinctly seen a regularly figured wall  or pave-
ment on six or  seven different planes coming nearer
and nearer, and becoming smaller and smaller, until the
nearest was within 3 inches of the eyes, and the figures 
         SUPERPOSITION OF EXTERNAL IMAGES.      H7

in exquisite miniature, and yet the whole so apparently
real  that  it seemed to me I  could rap my knuckles
against  the wall or pavement.  When  thus  looking at
the nearest  image, by a slight relaxation of convergence
we may drop the image and catch it on the next plane,
and  again drop it  to each successive plane, until it falls
to its natural place.
    If the figures of the pattern are  not larger than the
distance between  the optic centers (2£ inches), then it
is possible also to unite the figures beyond the real plane
—i.  e., on the plane P' P'.  In this  case the figures will
be proportionately enlarged, as shown  by the diagram.
But it  is difficult by this method to make the image
clear, the reason for which we shall soon see.
    In all cases of illusive images the head ought to be
held steady. If it be moved  from side to  side while
gazing at such an  image, the image will also move from
side  to side—in the same direction  as  the head if the
point of sight  be nearer than the  object, and  in the
opposite direction if the point of sight be beyond the
object.   It is necessary too, in all experiments on com-
bination of images, that the interocular line should be
exactly parallel with  the line  joining the objects to be
combined; otherwise  one image will  be higher  than
the  other.
    Dissociation  of Consensual Adjustments.—We have
said above that when the combination in case 3 (and so
also in the other cases) is first  obtained,  the image of the
figures is not  distinct, but afterward becomes clear and
sharp.  The reason is this:  The voluntary adjustment
of the optic axes (axial adjustment) to a nearer distance
than the object carries with it, by consensus, the focal
adjustment and pupillary contraction for the same dis-
tance.  But since the lenses  are adjusted for a nearer 
118
BINOCULAR VISION.
distance than  the object, the retinal image will be  in-
distinct.   The subsequent clearing of the image, there-
fore, is the result of a dissociation of the axial and focal
adjustments.   The optic axes are adjusted for the point
of sight or distance of the illusive image, and the lenses
are adjusted for the distance of the object.   Some per-
sons  do not find it easy to make this  dissociation, and
therefore  to make the illusive  image  perfectly clear.
To presbyopic persons it is not difficult, but normal
eyes  will find some, though not insuperable, difficulty.
   Now it becomes an interesting question :  When the
axial and focal  adjustments are thus  dissociated,  with
which one does the pupillary contraction ally itself?   I
answer, it allies itself with the focal adjustment.   This
may  be proved as follows:
   Experiment.—While the combination and the forma-
tion of the illusive image are taking place, let an assist-
ant standing behind observe the  pupil in a small mirror
suitably placed in front and a little to  one side of one
eye.   He  will  see that at  first  the  pupil  contracts
strongly,  associating  itself  with the  axial  and  focal
adjustments to the  point of sight;  but as soon as the
illusive image clears and becomes distinct, he will ob-
serve that the  pupil has enlarged again.
   General Conclusions.—It  is evident, therefore, that
the combination of the similar images of two different
objects may produce the same visual effect as the  com-
bination of the two  images of the same object.   In
other words, single vision,  or ordinary perception  of
objects, is by combination of  two similar images; and
it  makes no difference whether  the two images belong
to the same object or  to two different  but  similar ob-
jects.  This idea must be clearly apprehended and held
fast; otherwise all that follows will be unintelligible. 
         SUPERPOSITION OF EXTERNAL  IMAGES.      H9

   Again, it is evident that two objects may be seen as
one,  and, contrariwise, one object may be seen as two
images.  We see then the absolute necessity, in binoc-
ular  vision, that we should speak of seeing only external
images, the signs of objects.   They  are  usually—i. e.,
under  ordinary conditions—the  true  signs, but  often
untrue, deceptive, illusory signs.
6 
CHAPTEK  III.
             BINOCULAR PERSPECTIVE.

   Thus far we have investigated the case of flat ob-
jects, or of figures or colored spaces on a plane.  We
have shown how the images of these may be combined
at pleasure,  so  as to give the  illusory appearance  of
objects or figures at places and  of sizes different from
their real places and sizes.  We come now to the more
complex  case of solid objects of three  dimensions, and
of objects situated at different distances.   This brings
us to the important subject of the perception of depth
of space so far  as this  is connected with binocularity;
or, in other words, to the subject of binocular perspec-
tive.  We will  introduce the subject with  some simple
experiments.
   Experiment  1.—Place one  forefinger  before the
other in the median plane, as  in the experiment  on
page 94.   As already seen, when we look at the farther
finger, the nearer one is doubled  heteronymously; when
we look at the nearer finger, the farther one is doubled
homonymously.   We can not see  them  both  single at
the same time.  The reason is obvious.  If we shut one
eye, say the left, we see the fingers as  in Fig. 42,  I; if
we  shut the right eye, we  see  them as in  Fig. 42,  II.
Now these two can  not be combined,  because they are 
BINOCULAR  PERSPECTIVE.
121
different.  When we combine the images of the farther
fingers, a and a', the nearer, b and b', will not have come
together  yet,  and  will therefore be heteronymously
Fig. 42.
Fig. 43.
    a'
b'
R
B
II
double, as in Fig. 43, I;  when by greater convergence
we combine the images b and b' of the nearer finger,
then the images a and a' of the farther will have crossed
over and become homonymously double, as in Fig. 43,
II.  As  in previous experiments,  double images are
given in dotted outline, and left-eye images are marked
with primed letters, and combined images with capitals.
   Now, in this experiment we are distinctly conscious
of a greater convergence of the optic axes necessary to
combine the double images of  the nearer finger, and of
a less convergence to combine the double images of the
farther.  Thus the eyes range back and forth by greater
and  less convergence, combining the double images of
the one and the other, or  transferring the point of sight
from one to the other; and thus we acquire a distinct
perception of distance between the two.  It is literally
a rapid process of triangulation, the base-line being the
interocular distance.
   Experiment 2.—We take a rod about  a foot  long,
and  hold it in the median plane a little below the hori-
zontal  plane  passing  through  the  eyes, so  that we can
see along its  upper edge, the  nearer end about six or 
122              BINOCULAR VISION.
eight inches from the eyes.  If now, shutting the left
eye,  we observe  the  projection of the rod against the
wall, it will be  like this—  /  —a being the nearer
and  b  the farther end.   If we shut the right eye and
                                              b'\
open the left, the projection will be like  this—  \  ,.
These  lines are exactly like the retinal images formed
by the rod in the right  and left eyes respectively, ex-
cept that these images are inverted.  Or, to express it
differently, these lines would make images on the  right
and  left retinae respectively exactly like those made by
the rod ; they are the facsimiles of the external  images
of the  rod.   If we now open both eyes and fix attention
on the farther end, then the nearer end will be  seen
double  heteronymously,   and the  projection  will be
         B
thus—  A,   .  If,  on the contrary, we  look  at the
       at  \a'
nearer end, then this of  course will be single, but the
farther end will now be  double homonymously, and

the projection will  be thus—   \J  .  If, finally
                  we
A
look at the middle point, this point will of course be
seen single, but  both ends double, the one homony-
mously, the other heteronymously, and  the projection
will be thus—a)Ca,'   ^r? to  Put  it differently,  the
external  images of  the  two eyes are like these lines—
af    and   \  :  if these two be brought together so
as to unite the farther ends b b', then by greater con-
vergence the middle points, and then by still greater
convergence the nearer ends a a', the three  projections
above  given are obtained; but it  is obviously impossi-
ble to unite all parts and see  single the whole  rod at 
BINOCULAR PERSPECTIVE.
123
once.   Now, if we observe attentively, we find that in
looking at the rod  the eyes range back and forth by
greater or less convergence, uniting successively the
different parts, and thus acquire a distinct  perception
of the difference of distance or depth of space between
the nearer and the farther end.
    Experiment 3.—We  take next a small  thin book,
and hold it as before six to eight inches distant in the
median plane, a  little below the horizontal plane of
sight, so that  the back and the upper edge  are visible.
If we shut the left eye, we see the back, the upper edge,

and the whole right side, thus— il .   The retinal image

formed in the right eye is exactly like this figure, except
that it  is inverted; this figure  makes exactly the same
retinal  image as the book does in the right eye; it is
the facsimile of the external image of the book for the
right  eye.  If we shut the right eye  and open the  left,
we see the  back, the upper  edge, and  the  whole left

side, thus— In.  Now, if we  open both eyes, we must

and do see both these images.  If we look beyond the
book,  the two images  are  wholly  separated, thus—

if     II. If we look at the farther part, we bring these

two images  together so as to unite the farther  part and
see it single, but  the nearer part or back  is double,

thus—™J|.   If we look at the  nearer part or back,

then this is seen single, but  the farther edge is now

double, thus— am.   But by no  effort is it possible to
see it single in all parts at the same time, because these 
124
BINOCULAR VISION.
dissimilar external images can not  be wholly  united.
The eyes therefore range  rapidly back and forth, suc-
cessively uniting  different  parts  by  greater and less
convergence, and  thus acquire a distinct  perception of
distance between the back and front, and hence of depth
of space.
    After these simple illustrations we are  now prepared
to generalize.  It is  evident  that solid objects as seen
by two eyes form different mathematical  projections,
and therefore form different retinal images in the two
eyes, and  therefore  also  different external images.
Hence the images of the same object, whether retinal
or  external,  formed  by  the two  eyes, are necessarily
dissimilar if  the object occupies considerable depth of
space.   But dissimilar images can not be united wholly:
for when by stronger convergence we unite the nearer
parts, the farther will  be  double; and  when  by less
convergence we unite the farther  parts, the nearer will
be double.  Therefore the eyes run rapidly and uncon-
sciously back and forth, uniting successively different
parts, and thus acquire  the  perception  of  depth of
space occupied by the object.  But what is true of a
single object  is true of different objects placed one be-
yond the other, as  the two fingers in experiment 1, page
120.  We can not at the same time unite nearer and
more distant  objects, but the point of sight runs rapidly
and unconsciously back and forth, uniting them succes-
sively, and thus we acquire a perception of depth of  space
lying between them.   Therefore, the perception of the
third dimension, viz., depth or relative  distance, whether
in a single object  or in a scene, is  the result of the suc-
cessive combination of the different parts of the two
dissimilar images of  the object or the scene: dissimilar,
because  taken from different  points, viz., the two eyes 
BINOCULAR PERSPECTIVE.
125
with the  interocular distance between.   This  funda-
mental  proposition  will be  slightly modified in our
chapter on the theory of binocular perspective.   In the
mean time it must  be clearly conceived and held fast;
otherwise all that follows on stereoscopy will  be unin-
telligible.
                 STEREOSCOPY.

   We have already seen  (page 96) that in binocular
vision  we see objects single by a  combination of two
similar or nearly  similar images, and that therefore
(page 118) it makes no difference whether the images
are those of  the same object or of different objects, if
the images in the two cases are identical, and if we take
care to cut off the monocular images which are formed
in the latter case.   Hence, if we draw two  pictures of
a rod  in the two positions shown  in
Fig.  44, and then combine them by
converging the eyes, taking care to cut
off the monocular images as directed on
page 114, Fig. 39, the visual result will
be exactly the same as that of an actual
rod in the median line; and therefore it will look like
such a rod.  As in the case of the actual rod, by greater
or less convergence of the optic axes we may combine
successively different parts; and the eyes therefore seem
to run back and forth, and we have a distinct perception
of depth of space.   To produce the proper effect, the
two pictures of Fig. 44 ought to be combined at  a dis-
tance of not more than six or eight inches
   So  also in the  case of the book, page 123.  If we
exactly reverse the  case described there—i. e., if we
\ 
126
BINOCULAR VISION.
make two  pictures of a book as seen by one eye and
the other, and then combine  them, cutting off the mo-
nocular images—we have the exact appearance of an
actual solid book.  The only reason why the illusion is
not complete is, that there are other kinds of perspec-
tive besides the binocular; and in this case especially be-
cause there is not the same change of focal adjustment
necessary for distinct image as  in the case of  a real
object.
    Now this  is the principle of the stereoscope.   The
stereoscope is an instrument for facilitating the com-
bination of two such pictures, and at  the  same time
cutting  off the uncombined  monocular  images  which
would tend to destroy the  illusion.
    Stereoscopic  Pictures.—When we look at an  object
having  considerable depth in space, or at a scene, there
is an image of the object or scene formed on each retina.
These two images are not exactly alike, because they
are taken from different points of view.  Now suppose
we draw two pictures  exactly like these two retinal
images,  except inverted.   Obviously these two pictures
will make  images on the corresponding retinae exactly
like those made by the original object on the one retina
and the other, and therefore will  be exactly like this
object seen by  one eye and  then by the other.  Now,
we have seen the wonderful  similarity of the eye to a
photographic camera.   Suppose,  then, instead of  draw-
ing the pictures like the two retinal images, we photo-
graph them.  Two cameras are placed before an  object
or a scene with a distance between of two or three feet.
They are like two great  eyes with  large  interocular
space.   The sensitive plate  represents the  retina, and
the pictures  the retinal  images.   The photographic
pictures  thus taken can not  be exactly alike, because 
BINOCULAR PERSPECTIVE.
127
taken  from different  points.   They  will  differ from
each other exactly as the two retinal images of the same
object or scene differ, only certainly in a greater degree.
Therefore, if these two  photographs  be binocularly
combined as  in the experiments previously given, they
ought  to and  must produce a visual  effect exactly like
an actual object  or scene; for in  looking  at an object
or scene, we are only combining retinal images (or their
external representatives) exactly like  these pictures, be-
cause taken in the same way.
    This is substantially the manner in which  stereo-
ssopic  pictures are  taken.  It  is not  always  necessary,
indeed, to  have two  cameras; for the  pictures,  being
permanent and not evanescent like retinal images, may
be retained and  combined at any time.   The object  or
scene  is often photographed  from  one position, and
then the camera  is moved a little, and the same object
or scene is again  photographed from the new position.
The two slightly dissimilar pictures thus taken are then
mounted in such wise that the right-hand  picture shall
be  that taken by the  right camera, and the left-hand
picture that taken by the left camera.  In other words,
they are mounted  so  that the right picture shall be
similar (except inverted)  to  the retinal image  of the
object  or scene in the right eye,  and the  left picture
to the  retinal image  in the left eye.  The marvelous
distinctness of the  perception of  depth of space, and
therefore the marvelous resemblance to an actual object
or scene, produced by binocular combination of such
pictures properly taken and properly mounted,  is well
known.
   It is easy to test whether  stereoscopic  pictures are
properly mounted or not.   Select some point or object
in the  foreground; measure accurately  with  a pair of 
128
BINOCULAR VISION.
dividers the distance between it and the same point or
object  in the other picture ; compare this with the dis-
tance between identical points in the extreme back-
ground of the two pictures.  The distance in the latter
case ought  to  be  greater than in the former.   This  is
the proper mounting for viewing pictures in a stereo-
scope.   If they are to be combined with the naked eye,
then the reverse mounting is better.
    Combination of Stereoscopic Pictures.—Stereoscopic
pictures may be easily combined by the use of  the ste-
reoscope or with the naked eyes.  For inexperienced
persons, however, the latter is more difficult  and the
illusion less complete, unless with special precautions.
Nevertheless,  it will be best to begin with this method,
because the principles  involved are thus most easily
explained.
    Combination with the Naked Eyes.—In  combining
stereoscopic pictures with the naked eyes, there  are two
difficulties  in  the way of obtaining the  best  results.
First, it is evident that  such pictures, as usually mount-
ed, were intended to be combined beyond  the plane of
the cardi for it  is only thus that the object or  scene
can be seen in natural perspective, and of natural size,
and at natural distance.   But in thus combining, the
eyes are of course looking at a distant object, and con-
sequently parallel or nearly so.   The eyes are therefore
focally adjusted for a distant  object, but the light comes
from a very near  object, viz., the card-pictures.   Hence,
although the  pictures  unite  perfectly, the combined
image or scene is indistinct.   Myopic eyes will not ex-
perience this  difficulty, and in normal eyes it  may be
remedied by the  use of slightly convex glasses.  Such
glasses supplement the lenses of the  eye,  and make
clear vision  of a  near object when the eyes are really 
BINOCULAR PERSPECTIVE.
129
looking far away; or, in other words,  make a clear
image of a near object on the retina of the unadjusted
eye.
    Another difficulty is, that the pictures are usually so
mounted that identical points are farther apart than the
interocular distance, and therefore, even with the optic
axes parallel—i. e., looking at  an infinite distance—the
pictures do not combine.   This  difficulty is  easily re-
moved  by cutting down the inner edges of the two pic-
tures, in order to bring them a little nearer together, so
that identical points in the background shall  be equal
to or a  little less than  the interocular distance.*
    With this explanation we  now proceed  to give ex.
amples of naked-eye combination.
    Fig. 45  represents a projection of a skeleton trun-
cated cone made of wire, as seen from  two positions a
little separated from each other ; in other words, as they

                        Fig. 45.





  &                   ®
         B                                  A
would be taken by two cameras for a stereoscopic card ;
or, again, as they would  be taken on the retinae of two
eyes looking at  such a skeleton truncated cone with the
smaller end toward the observer.
    Experiment.—If we now place a median screen 10
inches or a foot long midway between these two figures,
   * In a subsequent chapter we give the method of determining with
accuracy  the interocular distance. 
130
BINOCULAR VISION.
A and B, and place the nose and  middle of forehead
against the other edge of the screen, so that the  right
eye can only see A and  the left eye B—assisting the
eye with slightly convex glasses if necessary—and then
gaze as it were at  a distant  object beyond the plane of
the picture, the two  figures will be  seen to approach
and finally to unite in one, and appear as a real skeleton
truncated cone of a considerable height.   If we are able
to analyze our visual impressions, we shall find further
that, when we look steadily at the larger circle or base,
the smaller cone or summit  is slightly double, and when
we look steadily at the smaller circle or  summit this be-
comes single, but now the larger circle or base is double;
further, that it requires a  greater convergence,  as in
looking at a nearer object, to unite the smaller circles,
and a  less convergence, as in looking at a more distant
object, to unite the larger circles; and still further, that
the lines a a' and  b b' behave exactly like the lines de-
scribed on page 122, forming a V, an inverted V,  or an
X, according  to the distance of the point of sight;  or,
in other words, behave exactly like the two images of
a  rod held  in  the median  plane with  one end nearer
than  the other.   In a single word, the  phenomena are
exactly those produced by looking at an actual skeleton
cone  made of wires.   Thus, as in the case of an actual
object, the eyes by greater and  less convergence run
their point  of  sight  back and forth, uniting different
parts, and thus acquire a distinct perception of depth
of space between the smaller and larger circles.
    The same is true of all  pictures constructed on this
principle, and all objects or  scenes on stereoscopic cards.
In these, it will be remembered, identical points in the
foreground  are always nearer together than identical
points in the background; therefore,  when the  back- 
STEREOSCOPY.
131
 ground is united the  foreground is  double, and vice
 versa.  We may represent these facts diagrammatically
 by Fig. 46, in which p p is the plane of the pictures;
 ms, the median screen resting on the root of the nose, n •
 R and  Z, the  right  and  left eyes.
 On the  plane  of the paper p p, a
 and  a' represent identical  points in
 the foreground, viz., the centers of
 the small circles in the diagram Fig.
 45 ; and  b and b' identical  points in
 the background (centers of the  larger
 circles in Fig.  45).  Now when the
 eyes  are  directed toward  b and  b',
 the two visual lines will pass through
 these points, and the images of these
 two points will fall  on corresponding
 points of the retinae, viz., on the cen-
 tral spots, and will be united and seen
 single.    But where ?  Manifestly at
 the point  of optic convergence or point
 of sight B.  Now when  b and  V fall
 on corresponding points and are seen
 single, evidently a and  a' must fall on
 non-corresponding points, viz.,  the two temporal por-
 tions of  the  retinae, and are  therefore seen double.
 When, on the other hand, by greater  convergence the
 optic axes are  turned  on  a and a', then the images
 of these fall  on the central  spots,  and are seen  single
 at the nearer point of  sight A  • but now b  and b' are
 seen  double, because they fall on non-corresponding
 points, viz., the two  nasal halves of the retinae.   Inter-
 mediate points between  the background and foreground
 will be seen at  intermediate points between B and
A.  Thus the point  of  sight runs back and forth from
 
132              BINOCULAR VISION.
background B  to  foreground  A, and we acquire a
distinct perception of  depth of space between these
two points.
    But, for those at all practiced in binocular experi-
ments, by far  the most perfect  naked-eye combination
is obtained  by crossing the eyes; i. e., by combining
on the nearer instead of the farther side of the pictures.
For this  purpose,  however, it  is  necessary  that  the
mounting be reversed;  i. e., the right-hand  picture
must  be put  on the left  side,  and the  left-hand  pic-
ture on the  right side  of  the card.   By this reversal it
is evident that identical  points in the background of
the two pictures are nearer together than  identical
points in the foreground.
    If, now,  holding such a card before us  at any  con-
venient distance, say 18 inches or 2 feet, we converge
the optic axes so that  the right eye shall  look across
directly toward the  left picture, and the left eye toward
the right picture, then  the two pictures will unite at the
point of crossing of the optic axes (point of sight),  and
will be seen there in exquisite miniature, but with  per-
fect perspective.  The effect is really marvelously beau-
tiful.   For persons of slightly presbyopic eyes there  will
be no difficulty in getting the combined image perfectly
clear.  In normal eyes, as already explained (page 117),
there  must be dissociation between the axial and focal
adjustments before the  combined image is perfectly
clear.   For those who  can not make this dissociation it
may be necessary to use  very slightly concave  glasses.
Again, if the observer is  annoyed  by the existence of
the monocular uncombined  images to the right  and
left, it will be best to  use two side screens, as  already
explained (page 114), instead of the median screen used
in combining beyond the plane of the picture. 
BINOCULAR PERSPECTIVE.           133
   Experiment.—I draw (Fig. 47) two projections of a
skeleton truncated cone precisely like those represented
on page 129, but reversed.   It is seen, for example, that
the centers of  the small  circles are  in  this case  farther
Fig. 47.
apart than  the centers of the large circles.   If, now,
holding  these about 18 inches distant, I combine them
by crossing the optic axes, the impression of a skeleton
truncated cone with the  smaller end toward me is  as
complete as possible.   The singleness of the impression
at first seems perfect,  but by observing attentively the
lines a and a' it will  be  seen that they unite only  in
points and not throughout—that they come together as
a  v, thus—V, or an inverted v—f\, or an x—x? according
to the distance of the point of sight.   In other words,
when by greater  convergence the small circle is sin-
gle, the  larger circle  is double; and when  by less
convergence the larger circle is single, then the small-
er circle  is double.  And thus the eyes run the  point
of  sight back and  forth, uniting  first  the one and
then the  other, and in this way acquire a clear concep-
tion of depth of space between the smaller and larger
circles.
    These facts are illustrated by the diagram  Fig. 48,
in which, as before, R and Z are  the two eyes; n, the
root of nose ; P P, the plane of the pictures ; a and a', 
134
BINOCULAR VISION.
identical points of the foreground, and b and V of the
background; and sc and sc', the two side-screens to cut off
                          monocular  images.   When
                          the eyes are directed toward
                          a and a',  these unite and
                          are  seen at  the  point  of
                          sight as a single object A.
                          When the eyes by less con-
                          vergence are directed  to  b
                          and b', then these are  seen
                          single at  the point of sight
                          B.  The point of sight runs
                          back and forth  from A  to
                          B, and we  thus acquire dis-
                          tinct perception  of depth of
                          space between.
                             Of  course,  any  stereo-
                          scopic pictures may be com-
                          bined in  this way if we re-
                          verse the mounting; and I
am quite sure that any one who will try it  will be de-
lighted with the beautiful miniature effect and the per-
fection of the perspective.
   Combination by the Use of the Stereoscope.—The stere-
oscope is an instrument for facilitating binocular combi-
nations beyond the plane of the pictures.  By means of
lenses also it supplements the  lenses  of the  eyes, and
thus makes on the retinae perfect images of a near ob-
ject, although the eyes are looking  at  a distant object,
and are  therefore unadjusted for a near one.  The lenses
also enlarge the images, acting  like a perspective glass,
and  thus complete the illusion of a  natural scene or
object.
   It is difficult to  convince many persons that there
 
BINOCULAR PERSPECTIVE.
135
is in the stereoscope any doubling of points in the fore-
ground when the background is regarded, and vice versa.
But  such  is  really always  the fact; and if we  do not
observe it, it is because we have not carefully analyzed
our visual impressions.  It is  best observed in skeleton
diagrams of geometrical figures, such as  are commonly
used to explain the principles of stereoscopy.  In or-
dinary stereoscopic pictures it is also easily observed in
those cases  where points  in  the  extreme  foreground
and background are in the  same range ; as, for example,
when a column far in front is  projected against a build-
ing.   In such a case, when we look at the building the
column is distinctly double, and  vice versa.  For my-
self, I  never look at a stereoscopic  card, whether in a
sterescope or by  naked-eye combination, without dis-
tinctly observing this doubling.  For example: I now
combine in a stereoscope the  stereoscopic pictures of a
skeleton polyhedron.  The illusion of a polyhedral space
inclosed by white lines is perfect.  Now, when I look at
the farther inclosing lines I see the nearer ones  double,
and vice versa.  Moreover, I perceive that this doubling
is absolutely necessary  to the stereoscopic effect, for  it
is exactly like what would  take place if  I were looking
at an actual skeleton polyhedron.
   Inverse Perspective.—I  have  heard  a  few persons
declare that  they saw  no  superiority of a stereoscope
over an ordinary enlarging or perspective glass; that
they saw just as well while looking through the stereo-
scope if they  shut one eye  as with both eyes open.
Such persons evidently do not combine properly the
two  pictures, and they lose a real enjoyment.  That the
binocular is  a real perspective, entirely different from
other kinds, may  be  clearly demonstrated by the phe-
nomena of inverse perspective  now about  to be described. 
136
BINOCULAR VISION.
   If stereoscopic diagrams suitably mounted for view-
ing in a stereoscope be combined with the naked eye
by squinting (crossing  the optic axes),  as  in Fig. 48
(page 134), or if  such  diagrams properly mounted for 
BINOCULAR  PERSPECTIVE.           137
combination by squinting be viewed in the stereoscope,
the perspective is completely reversed, the background
becoming the foreground, and vice versa.  For example,
Fig. 49  represents a stereoscopic card.  When the two 
138              BINOCULAR VISION.
pictures  are combined with  a  stereoscope, the result is
a jelly-mold with the small end  toward the observer;
but if the same be  combined with the naked eye by
squinting,  we  have  now beautifully  shown the same
jelly-mold  reversed,  and we are looking into the hol-
low.  If there should  be other  forms of perspective
strongly  marked  in  the pictures, these  may even be
overborne  by the inverse binocular perspective.  For
example, in the stereoscopic picture Fig. 50, represent-
ing the interior of a  bridgeway, the diminishing size of
the arches  and the converging lines, even without  the
stereoscope, at once  by mathematical  perspective sug-
gest the  interior of a long archway.   This  impression
is greatly strengthened by viewing it in the stereoscope;
for the binocular perspective and the mathematical per-
spective strengthen each other, and the illusion is com-
plete.  But if we  combine  these with the naked eyes
by  squinting,  we see with  perfect distinctness, not a
long hollow archway, the small arch  representing  the
farther end, but a short conical  solid, with  the small
end toward the observer.  Thus the binocular perspec-
tive entirely overbears the mathematical.
   The cause of this reversal of the natural perspective
is  shown in the following  diagrams.  In Fig.  51  the
mounting is reversed, as seen by the fact that the points
b and V in  the background are nearer together than the
points a and a' in the foreground.   By combining these
in  a stereoscope, the  background  is seen nearer the ob-
server at  B, and the foreground  thrown farther back
to  A.  In  Fig. 52 the  pictures are mounted suitably
for viewing in the  stereoscope, but are combined by
the naked eye.  Here also the perspective is reversed,
for the background is seen at a nearer point B, and the
foreground at a farther point A. 
               BINOCULAR PERSPECTIVE.            139

   This  inverse perspective is easily brought out, not
only in stereoscopic  diagrams, but in nearly all stereo-
scopic pictures, even  in those representing extensive and

         Fig. 51.                          Fig. 52.
complex views.  In these,  of course, when viewed  in
the stereoscope, the binocular is in harmony with other
forms  of perspective, and each enhances  the  effect  of
the other.   But if we combine with  the naked eyes by
squinting, or if we reverse the mounting and view again
with the stereoscope, there  is in either case a complete
discordance between the  binocular and other  forms  of
perspective.  In some cases the ordinary perspective is
too strong for the binocular, and the only result is a
kind of confusion of the view; but in others the binoc-
ular completely overbears all  opposition  and reverses
the perspective, often producing  the strangest effects.
 
140
BINOCULAR VISION.
Fig. 53.
For example, I now take up a stereoscopic card repre-
senting a building with extensive grounds in front.  I
view it in a stereoscope. The natural perspective comes
out beautifully—the fine building in the background,
the sloping lawn in the middle, and a piece of statuary
and a fountain in the  foreground.  I  now combine the
same  with the naked eyes by squinting.  As  soon  as
the combination is perfect  and the vision distinct, the
                          house  is seen in front, and
                          through a space in the wall
                          the statue and fountain are
                          seen   behind.   Observing
                          more closely, all  the parts
                          of the house, the slope  of
                          the  roof, and the slope  of
                          the  lawn are also reversed.
                          In Fig. 53, A and B show
                          the natural and the inverted
                          perspective in section, and
the arrows the direction in which the observer is look-
ing.  In the one case the roof and the lawn slope down-
ward  and toward the observer;  in the other, downward
and awray from the observer.  In the one case the build-
ing is a solid object; in the other it is an inverted shell,
and we are looking at the interior of the shell.
    In nearly all stereoscopic views  I can thus invert
the perspective by naked-eye combination.   Almost
the only exceptions are views looking up the streets of
cities.  Here the mathematical perspective is too strong
to be  overborne.  Stereoscopic pictures of the full moon
are quite common.  If these be viewed in a stereoscope,
we have the natural perspective, viz., the appearance of
a globe ; if combined  with the naked eyes by squinting,
we have a hollow hemisphere.   If the mounting  be
 
              BINOCULAR PERSPECTIVE,           141

reversed, then the hollow is seen in the stereoscope and
the solid globe with the naked eyes.  We will give one
more example.  I have now a stereoscopic view of the
city of  Paris, but not looking up the streets.  When
viewed  in the stereoscope, the perspective  is natural
and perfect;  the large houses are in the foreground
and below, and the others gradually smaller and higher,
until the dimmest and smallest are on the uppermost
part and  form the distant  background.   I am looking
on the upper surface of a receding rising plane full of
houses.   I now combine the same pictures  with the
naked eyes by  squinting.  As  soon as  the combined
image comes out clear, 1 see the smallest and dimmest
houses on the upper part of  the scene, but  nearest  to
me.  I  am looking  on the under side  of a receding
declining plane, on which the houses grow larger and
larger in the distance, until they become largest at the
lowest and farthest margin of the plane.  If the mount-
ing of the  pictures  be reversed, then  the  natural per-
spective will be seen with  the naked eyes, and the in-
verse perspective just  described will be  seen  in the
stereoscope.
    The extreme accuracy of our judgment of relative
distance  by binocular perspective is well shown by the
combination, either by the naked eyes or by the stereo-
scope, of  apparently  identical figures  on a  flat plane.
For example, in combining  with the naked eyes the
figures of  a regularly figured wall-paper or  tessellated
pavement, the least  want of perfect regularity in the
size or position of the figures is at once  detected by
an  appearance of gentle undulations  or more  abrupt
changes of level.  This fact  is made use of in  detect-
ing  counterfeit  notes.   If two  notes from the same
plate be put  into a  stereoscope and identical figures 
142              BINOCULAR VISION.
 combined, the combination is absolute and the plane of
 the combined images is perfectly flat; but if the notes
 be not from the same plate, but copied, slight variations
 are unavoidable, and such variations will show them-
 selves in a gently wavy surface.
    Different Forms of Perspective.—In order  to bring
 out in stronger relief the distinctive character of binoc-
 ular perspective, it is necessary to mention briefly the
 several  different forms of perspective.  There are many
 ways in which we judge  of  the relative distance of ob-
 jects in the field of  view, all  of which may be called
 modes of perspective.
    1. Aerial Perspective.—The atmosphere is neither
 perfectly transparent nor  perfectly colorless.  More and
 more distant  objects, being  seen through greater and
 greater depths of this medium, become therefore  dim-
 mer and dimmer and bluer and bluer.  We judge of
 distance in this way ;  and if the air be more than usually
 clear or more than usually obscure, we may misjudge.
    2.  Mathematical  Perspective. — Objects  become
 smaller and smaller in appearance, and nearer and near-
 er together, the farther away they are.  Thus streets ap-
 pear narrower and narrower, and the houses lower and
 lower, with distance.  Parallel lines of all kinds, such
 as railway stringers, bridge timbers, etc., converge more
 and more to a vanishing point.
   3. Monocidar or Focal Perspective.—Objects at the
 distance of  the point of  sight  are distinct,  the  lenses
 being focally adjusted for that distance; but all objects
 beyond  or within this distance  are dim.  Now, we are
 aware of a greater or less effort of adjustment  to make
 a distinct  image, according to  the nearness or  the dis-
 tance of the object looked at.   This  is also a means of
judging of the distance especially of near objects. 
BINOCULAR PERSPECTIVE.
143
   These three forms may all be called monocular ; for
they would  equally exist, and we could judge of  dis-
tance, so far as these modes are concerned, equally well,
if we had but one eye.  But there is still another, viz.:
   4. Binocular Perspective.—In order to combine the
images of objects near at hand, we converge the optic
axes strongly; for more distant  objects, less  and  less
according to their distance.   By this  constant change
of axial adjustment necessary for single vision, the point
of optic convergence is run rapidly back and forth ;  and
thus, by a kind of rapid and almost unconscious trian-
gulation, we estimate the relative distance of objects in
the field of view.  The man with only one eye can not
judge  by this method, and thus often  misjudges the
distance of near objects.   In rapidly dipping a pen into
an  inkstand, or  putting a stopper into a decanter, the
one-eyed man can not  judge  so accurately as  the  two-
eyed man.   If we shut one eye and attempt to plunge
the  finger  rapidly into the open mouth of a bottle, we
are very apt to overreach or fall short.
    As clearness  of vision is  confined to a small area
about  the point  of sight, and rapidly fades away with
increasing  distance in any direction on the same plane,
so clearness and singleness of  vision are confined to the
distance of  the point of sight, and images become dim
and double in passing beyond or to this side of that
paint.   Again, as we  sweep  the point of sight  about
laterally over a wide  field  of view, and gather up all
the  distinct  impressions into  one mental image, so we
run the point of optic convergence back  and forth, and
gather up  a mental  picture of the relative distance of
objects,  in a deep field.
    These different forms of perspective operate for very
different distances.  The focal adjustment becomes im- 
144
BINOCULAR VISION.
perceptible for  distances greater than about  20 feet.
Judgments based on this, therefore, are limited within
that distance.  Binocular perspective operates percep-
tibly for much greater distance, perhaps several hundred
yards; but beyond this it becomes imperceptible.  The
other two forms, the mathematical  and aerial, operate
without limit.
   Now the  painter can imitate the aerial perspective.
He skillfully diminishes the brightness, dulls the sharp-
ness of outline, and blues the  tinge of all  objects, in
proportion  to their supposed distance, so as to produce
the effect of  depth of air.  He can  also and still  more
perfectly imitate the mathematical  perspective, by  di-
minishing the size of objects and the distance between
them as he  passes from his  foreground  to  his  back-
ground.  But he can not imitate the focal perspective,
and still less can he imitate the binocular perspective.
This is artificially given  only in the  stereoscope, and is
the glory of  this little instrument.   Focal perspective
is unimportant  to the painter, because imperceptible at
the distance  at which pictures are usually viewed; but
the want of binocular perspective in paintings interferes
seriously with the completeness of the illusion.  There-
fore the illusion is more complete and the perspective
comes  out more distinctly when we look with only one
eye.  In a  natural scene it is  exactly the opposite :  the
perspective is far more  perfect with both eyes  open,
because then all the forms cooperate. 
CHAPTER  IV.
      THEORIES OF BINOCULAR PERSPECTIVE.

   Wheatstone's Theory.—To Wheatstone  is due the
credit of having discovered  the fact that two slightly
dissimilar pictures—dissimilar in the  same way as the
two retinal images of a solid object or of a scene—when
united, produce a visual effect similar  to that produced
by an actual solid  object or an actual  scene.  He also
invented the stereoscope to  facilitate the combination
of such pictures.   His theory  of  these effects was  as
follows : In viewing  a solid object  or a scene,  two
slightly dissimilar images are formed  in the two eyes,
as already  explained;  but the mind completely unites
or fuses them  into one.  Whenever there  occurs such
complete mental fusion of images really dissimilar  in
this particular  way, and therefore  incapable of mathe-
matical  coincidence, the result is a perception of depth
of space, or solidity, or relief.  In the stereoscope, there-
fore, he supposes that the two slightly dissimilar pictures
are mentally fused  into one,  and hence  the appearance
of depth of space follows as the necessary result of this
mental fusion.
   This theory is still widely held by  even the most
recent and best physiologists; but it is evidently the
result of imperfect  analysis  of  visual  impressions.  In
stereoscopic diagrams it is always possible to detect the 
146
BINOCULAR VISION.
doubling on which the perception of depth of  space is
based.   It  is a little more difficult in ordinary stereo-
scopic pictures, and in natural scenes; but practice and
close observation will always detect it in these also.   It
is most  difficult of all to detect it in the case of single
solid objects;  but this is mainly because the doubling
of the edges of such objects is usually out of the line
of sight.  Even where we can not detect the doubling,
and yet binocularly perceive depth of space, such per-
ception must be regarded as an example of  unconscious
cerebration. We actually ground our judgments upon im-
pressions which do not emerge into clear consciousness.
   Observe the degrees of this unconsciousness.  Even
the doubling of the forefinger, when held up before the
eyes while we gaze at the wall, is  undetected by some
persons.  To such the binocular perspective here seems
to be  a simple  primary sense-perception.  But the
slightest scientific observation is  sufficient to separate
this apparently simple impression into its  component
elements, and  thus to show that it is a judgment based
on simpler elements.  Next, the doubling of objects  in
the foreground of a scene or stereoscopic picture, when
the background is regarded, fails to appear in conscious-
ness.  But analysis again shows that the perception  of
depth here also is not simple, but decomposable into
simpler  elements.  Close observation again detects the
elements on  which judgment is  based.   Therefore,
where  we  can not detect the simpler  elements, we
must believe that they still exist  and that  judgments
are based upon them.   Nothing  can be more certain
than that complete fusion never takes place; and if it
seems so to us. it is only  because we do not  observe
and analyze with sufficient care.
   Wheatstone's  theory  therefore seems true  only  to 
        THEORIES  OF BINOCULAR PERSPECTIVE.     147

the unpracticed and unobservant.  It makes that simple
and primary which is capable of analysis into simpler
elements.   It is therefore a  popular, not  a scientific
theory.   It cuts, but does not loose, the Gordian knot.
   Brucke's Theory.—Briicke and Brewster and Prevost,
by more refined observation and more careful analysis,
easily perceived that there  was in reality no  mental
fusion of two dissimilar  images.   Their  view,  most
completely  expressed by Briicke,*  is that which has
been assumed in the foregoing account and  explanation
of binocular phenomena.  It  is, that in  regarding a
solid  object or a natural scene, or two stereoscopic pic-
tures in a stereoscope, the eyes are in incessant uncon-
scious motion,  and the  observer, by alternately  greater
and less convergence of  the axes, combines successively
the different parts of the two  pictures as seen by the
two eyes, and thus by running  the point of sight back
and forth reaches by  trial  a  distinct perception of bin-
ocular perspective or binocular relief, or depth of space
between foreground and background.
   That double images are really necessary to binocular
perspective,  as maintained by  Briicke, is  abundantly
proved  by the experiments already given on that sub-
ject.   But  one additional experiment may  be given
here to  complete the  proof.
   Experiment.—As I  look  out of my window, I see
the clothes-lines of a  neighboring family, about 40 feet
distant.  Two  of these  are parallel, but one about 5 or
6 feet beyond the other.  The lines being horizontal,
no double images are visible when the head is  erect.
In this position I am unable to tell which line is the
farther  off.   But when I turn the head to one side, so
that  the interocular line is at right angles to the cords,
        * "Archives des Scisnces," tome iii, p. 142 (1858). 
148
BINOCULAR VISION.
immediately their relative distance comes out with great
distinctness.
    This theory is  a great advance on the preceding.
It is really a scientific  theory, since it  is based on an
analysis of our visual judgments.   It is also in part a
true theory, and for this reason, in anticipation of what
we believe to be a more perfect theory, we have used
it in the explanation of many visual phenomena in the
preceding  pages.   But it is evidently not the whole
truth, as we now proceed to  show.
    1. If we place  one object  before  another in  the
median plane of sight,  even  when we look steadily and
without change of  optic convergence at the one or the
other, we distinctly perceive  the depth of space between
them.   Evidently no trial combination, no  running of
the point of sight back and  forth, and successive union
and disunion of the images, are necessary for the per-
ception of  binocular relief.  But if it be said that change
of optic convergence does indeed take place, only rapidly
and unconsciously, I proceed to prove that such is not
the case.
    2. Dove^s Experiment.—The instantaneous percep-
tion of binocular relief is demonstrated by the now cele-
brated  experiment  of Dove.  If a  natural  object, or a
scene, or two  stereoscopic pictures, -be  viewed by  the
light of an electric spark or a succession  of electric
sparks,  the perspective is  perfect, even  though  the
duration of such  a spark is  only j-^^q-q of a second of
time.  On  a dark night the  relative distance of objects
is perfectly perceived by the light  of  a flash  of light-
ning, which according  to Arago  lasts  only y^oif* an(^
according to Rood y^f of a second.  It is  inconceiva-
   * Arago, " (Euvrcs Completes," tome iv, p. 10.
   f Rood, "American Journal of Science and Arts," vol. i, 18*70, p. 15, 
        THEORIES  OF BINOCULAR PERSPECTIVE.     H9

ble that  there  should be any change  of  optic conver-
gence, any running of the point of sight back and forth,
in the space of ^T^oir part of  a second.  Evidently,
therefore, binocular perspective may be perceived with-
out such change of convergence.   This point is certainly
one of capital importance.  The instantaneous percep-
tion of relief is fatal to Brucke's theory in its pure un-
modified form.  I have therefore repeated Dove's ex-
periment with  care, varying it  in every  possibly way,
so as to guard against every source  of  error.   These
experiments completely confirm  Dove's result, and es-
tablish beyond doubt the instantaneous  perception of
binocular relief.   From a large number of experiments
I select  a few of  the most conclusive and most easily
repeated.  The spark apparatus used was  a Ritchie's
Ruhmkorff capable of producing sparks 12 inches long.
A Ley den jar was  introduced into the circuit to increase
the brilliancy of the sparks.
   Experiment 1.—I select  stereoscopic pictures in
which other forms of perspective are wanting, or near-
ly so ; skeleton geometric diagrams are the best.   Stand-
ing in a perfectly dark room, and viewing  these in a
stereoscope by the light  of a succession  of sparks, the
perspective  is perfectly distinct  with two eyes, but not
at all with one  eye.
   Experiment 2.—I select a stereoscopic card like the
last,  except that mathematical perspective is also  strong
—such, for example,  as  a view of the  interior of a
bridgeway.  Of course, as in the last case, the natural
perspective  is  instantly  perceived in  the stereoscope;
but this  might be attributed to  the mathematical  per-
spective.  But  now hold the card in the hand and unite
the pictures with  the naked eves by squinting: the in-
verse perspective described on page 135 will be brought 
150
BINOCULAR VISION.
out with perfect clearness with two eyes, but  the nat-
ural perspective  (mathematical) returns when we shut
one eye.  This experiment is conclusive, being removed
from even the suspicion of the effect  being the result
of other forms of perspective;  for in  this case the bin-
ocular is opposed to all other forms of perspective, over-
bears them, and reverses the perspective.
    So  much for combination of stereoscopic pictures,
whether beyond the plane of the card, as in the stereo-
scope, or on this side the plane of the card, as in naked-
eye combination by squinting.  We will next try the
viewing of natural  objects, eliminating as before as
much as possible other forms of perspective.
    Experiment 3.—Let two objects, as two brass balls,
of the same size, be hung by invisible threads, one about
5 or 6  feet  distant, and the other about 1 foot farther.
At this distance focal adjustment is practically the same
for the  two balls, and thus this mode of judging of rel-
ative distance is eliminated.  Let the balls be placed in
the median plane of sight, or nearly so, in such wise
that their relative distance may be easily detected with
two eyes, but not with one.  In the  latter case—i. e.,
with one eye—they look like two balls side  by  side, the
one a trifle  larger than the other.   Now, after darken-
ing the room, try the experiment by the instantaneous
flash of electric sparks.  It will be found that  under
these conditions also the relative distance  is perceived
with perfect clearness with two eyes, but not with one.
   It is certain, then, that binocular perspective  is per-
ceived  instantly, and therefore without the trial com-
binations of different parts of the two images, as main-
tained by Briicke, Brewster, and others.
   Between the  two rival  theories, therefore,  the case
stands thus: Wheatstone is right in  so far as he asserts 
        THEORIES OF  BINOCULAR PERSPECTIVE.     151

immediate  or instantaneous  perception of  relief, but
wrong in supposing that there is a complete mental fu-
sion of the two images.  Briicke  is right in asserting
that binocular perspective is a judgment  based on the
perception  of double images, but  wrong  in  supposing
change of optic convergence and successive  trial com-
binations of different parts of the two  images to be a
necessary part of the evidence on which judgment is
based.
    My own View is  an  attempt to bring  together and
reconcile what  is true in  both of the preceding views.
This, which I conceive to be the only true  and complete
theory, is hinted at, but  not distinctly "formulated, by
Helmholtz.*   I have strongly insisted upon it  in all
my papers on this subject.  I quote from one of them : f
"■ All objects or points of objects, either beyond  or
nearer than the point of  sight, are doubled, but differ-
ently—the former homonymously, the  latter heterony-
mously.   The  double images  in  the  former case are
united by leas convergence, in the  latter case by greater
convergence,  of the optic axes.   Now,  the observer
knows instinctively  and  without  trial, in any case of
double images, whether they will  be united  by greater
or  less optic  convergence, and therefore never  makes a
mistake, or attempts to  unite by making a wrong move-
ment of  the optic axes.   In other  words,  the eye {or the
mind) instinctively  distinguishes homonymous from
heteronymous images, referring the former to objects
beyond, and  the latter to objects this side of the point
of sight."  Or again: In case of double images, " each
eye, as it were, knows  its own image," although such
knowledge does not  emerge into distinct  consciousness.
    * " Optique Physiologique," p. 939 d seq.
    f "American Journal of Science and Arts," vol. ii, 1871, p. 425. 
152
BINOCULAR VISION.
   Thus, then, I conclude that the mind perceives re-
lief instantly, but not immediately;  for  it does so by
means of double images, as just explained.   This is all
that is absolutely necessary for the perception of relief;
but it is probable—nay, it is certain—that the relief is
made clearer by a ranging of the point of sight back
and forth, and a successive combination of the different
parts  of the object or scene or pictures, as  maintained
by Briicke.
   Return to the Comparison of the Eye and  the Camera.
—It is time now to return to, and to continue, our com-
parison  of  the eye and the photographic  camera.   We
have seen that both the camera and the eye are equally
optical instruments contrived for the purpose of making
an image ; but we have also seen that in both this image
is  only a means by which to  attain a  higher end, viz.,
to make a photographic  picture in the one case, and to
accomplish distinct vision in the other.   In both also,
in order to accomplish its higher purpose, there  must
be a  sensitive receiving plate, viz., the iodized silver
plate  in the one, and the living retina in the other.  In
both, finally, there are wonderful changes, chemical or
molecular, or both, in the sensitive plate.   Let us then
continue the comparison.
   1. In the photographic camera when accomplishing
its work there are three images which may be mentally
separated and described.  First, the light-image.  This
is what we see on the ground-glass plate.  It comes and
goes with the object in front.  It is the facsimile in
form and color of the  object, but diminished in size
and  inverted in position.  Second, the invisible image.
When the  ground-glass plate  is withdrawn and  the
sensitive plate substituted,  the light-image falling on
this plate determines in it wonderful molecular changes, 
        THEORIES OF BINOCULAR PERSPECTIVE.      153

which are  graduated in intensity exactly according to
the intensity and kind of light in the light-image: the
aggregate effect  is therefore  rightly called  an image,
though it  is  invisible.  Third, the  visible  image, or
picture.  The operator then  takes the plate with the
invisible image to a  dark  room, and applies  certain
chemicals which decelop the image—i. e., which de-
termine certain permanent chemical changes, which in
intensity and  kind  are exactly proportioned to the an-
tecedent molecular changes,  and  therefore  graduated
over  the surface exactly  as the molecular changes of
the invisible  image were graduated, and  hence  also
exactly as the light of the light-image was graduated.
This  is the permanent photographic  picture—the  fac-
simile in form of the object which produced it.
    So also in  the work of the  eye, vision, we may men-
tally  separate and  may describe  three corresponding
images.  First, there is the light-image, which is formed
in the dead as well as the living eye.  Second, the in-
visible image.   The light-image, falling on the sensitive
living retina,  determines  in  its  substance  molecular
changes which are graduated  in intensity and kind ex-
actly  as the light of the light-image is graduated in in-
tensity and color, and  may therefore be rightly called
an  image, even though it be  invisible, and the nature
of the  molecular changes  be  inscrutable.  Third,  the
external visible image.   The invisible image,  or  the
molecular changes which constitute  it, is transmitted
to the brain, and  by the brain  or the mind is projected
outward into space, and hangs there as a visible exter-
nal image, the sign and facsimile in forni and  color of
the object which produced it.
    2.  Again, as there  are certain effects which  can not
be produced by one camera—as  two cameras from two 
154              BINOCULAR  VISION.
positions take two slightly different pictures of the same
object or the same scene, which when combined in the
stereoscope produce  the  clear perception of depth of
space—even so the two eyes act as a double camera in
taking and a stereoscope in combining  two slightly dif-
ferent images of every object or scene, so as to give a
clear perception of binocular perspective.
   We have thus carried the comparison as far as com-
parison  is possible.  But there is this essential differ-
ence between  the twro—essential because found every-
where between human and natural mechanism :  In the
one case wTe trace mechanism and physics and chemistry
throughout.   In the other  we also trace  mechanism,
exquisite mechanism, but only to a certain point, be-
yond  which we  discover  something  higher than mere
mechanism.   We trace physics and chemistry to a cer-
tain point, but as we pursue the investigation we  find
something superphysical and  superchemical, or else a
physics  and a  chemistry far higher than  any  we yet
know.  At  a  certain  point molecular  and chemical
change is replaced by sensation, perception, judgment,
thought, emotion.  We pass suddenly into another and
wholly different wrorld, where  reigns an entirely differ-
ent order of  phenomena.   The connection between
these  two orders of phenomena, the material and the
mental, although it is right here in the phenomena of
the senses, and although we bring to bear upon it the
microscopic eye of science, is absolutely incomprehen-
sible,  and must in  the very nature of things always
remain so.   Certain vibrations of the molecules of the
brain, certain oxidations, with the formation of carbonic
acid, water, and urea, on the one side, and there appear
on the other sensations, consciousness, thoughts, desires,
volitions.  There are, as it were, two sheets of blotting 
        THEORIES OF  BINOCULAR PERSPECTIVE.     155

paper pasted together;  the one  is the brain, the other
is the mind.  Certain ink-scratches and ink-blotchings,
utterly meaningless, on  the one, soak through and ap-
pear on  the other  as intelligible  writing.   But how
or why  we know not, and  can never hope even to
guess. 
CHAPTER  V.
     JUDGMENT OF DISTANCE, SIZE, AND FORM.

   We are nowT prepared to understand the modes of
estimating distance, size, and form/  for these modes
are founded partly on monocular and partly on binoc-
ular vision.
   As  already  stated,  the direct and simple sense-im-
pressions given by the optic nerve are light, its inten-
sity, its color,  and its  direction.   These  can not  be
analyzed into simpler  elements, but distance, size, and
form are judgments based upon these.
   Distance.—We  judge of distance  by means of  the
different forms of perspective  already described  on
page 142: 1. By focal adjustment, or monocular per-
spective.  The  eye adjusts itself for distinct vision for
all distances from  infinite distance to five inches.   By
experience we know distance from the amount of effort
necessary to  adjust for  perfect image,  and therefore
distinct vision.   Judgments based  on this are tolerably
accurate from 5 inches to several yards.  Beyond  20
feet it  is too small to .be  appreciable.   2. By axial
adjustment, or  binocular perspective.  The greater or
less amount of  optic convergence necessary  to  produce
single vision is  a far more accurate mode of judging of
distance than the last.  It is reliable from near  the root 
       JUDGMENT OF DISTANCE, SIZE, AND FORM.    157

of the nose to the distance of two or three hundred
yards.   Beyond this it also becomes inappreciable, for
the doubling of objects is only equal to the interocular
distance.  3. By mathematical perspective.  By dimi-
nution of the  apparent size of known objects and the
convergence of parallel lines we judge of distance with
great accuracy and almost without limit.  4. By aerial
perspective.   Change of color and  brightness of all ob-
jects, in proportion to the depth of air looked through,
is still  another mode of judging  of  distance, which,
though far  less accurate than the  last, like it extends
without limit.   Estimates of distance, being judgments,
are liable to error.  Such errors are often called decep-
tions of sense, but they are not so.  They are errors of
judgment based upon  true deliverances of sense.
    Size.—The size of  an unknown object is judged by
its angular  diameter,  or the size of its retinal image

                        Fig. 54.
multiplied by its estimated  distance.   For example, an
image a, Fig. 54, occupies a certain space on the retina.
Now, evidently,  precisely the same  image  would  be
made by a small object at A, or a  proportionally larger
similar object  at A', or a still larger similar one at A".
Therefore the estimated size of the object which pro-
duced  the image will depend upon  the  distance we
imagine the object to be from us, this distance being of
course  estimated  by the different  forms of perspective 
158
BINOCULAR  VISION.
given above.  Thus, estimates of size and distance are
very closely related to each  other, and an error in the
one will involve an error in the other.  If we misjudge
the distance of an unknown  object, we will to the same
degree and in the same direction misjudge  its size:  if
our estimate of distance be too great, our judgment  of
size will  also and to the same extent be too great;  if
our estimate of distance be too small, so also will be our
judgment of size.  Contrarily, if we make a mistake  as
to the size of a known object—as, for example, if we
mistake a boy for a man—we will also to the same ex-
tent misjudge the distance.
   Very many illustrations  may be given of this  gen-
eral  principle, but by far  the most perfect are the ex-
periments on combination of the regular figures given
on pages 114 and 115.   In combining by squinting,  in
proportion as the point of  optic convergence, and there-
fore the imagined  place of the pattern, becomes nearer
and  nearer, the figures of the pattern  become smaller.
On the other hand, when we combine beyond the plane
of the pattern, so  that the more distant point of  optic
convergence  makes the imagined place of the pattern
farther off than its real place, then the figures are magni-
fied in the same proportion.   So also stereoscopic scenes
are larger or smaller than the actual picture, according
as we combine beyond  or on this side the plane of the
picture.
   Illustrations  like the  above are  most  conclusive,
because the relation of  size  and distance is seen to be
mathematically proportioned; but many familiar  illus-
trations may be given.
   1. While intently regarding  the  paper on which I
am writing, or the page which I am reading, a fly  or
gnat passes across  the extreme margin of the field  of 
       JUDGMENT OF DISTANCE, SIZE, AND  FORM.    159

view toward the open window.  I mistake it for a large
bird like a hawk flying  at some distance in  the open
air.  The reason is, that under these conditions we have
no means of judging either of form or of  distance ;  the
size and distance of an object are therefore left wholly to
the suggestions of the imagination.   If we look around
so as to see the form distinctly, and to bring binocular
or other forms of perspective to bear on the subject,
we quickly detect our error and correct our judgment.
   2. Where there are no means of  judging of distance,
we can not estimate size, and different  persons will
estimate differently.  Thus, the sun or moon  seems to
some persons  the size of a saucer, to some that of  a
dinner-plate, and to some that of the head of a barrel.
But  under peculiar conditions we imagine them much
larger.  For example, a pine-tree stands on the western
horizon about a mile distant.  I am accustomed to judge
of the size and distance of trees.  This one seems to me
at least 20 feet across the branches.  The evening  sun
slowly descends and  sets behind the tree.  It fills and
much  more than fills  its branches.   Again,  here in
Berkeley, on a clear day, the Farallone Islands, 40 miles
distant, are  distinctly seen through the Golden Gate.
I think no one would say that the larger one seems  less
than 100 feet across.  At certain seasons  in spring and
autumn the sun sets behind  the  Farallones, and these
islands are  projected in clear outline as black spots on
his disk.
   3. Illustrations meet us on every side.  In fog, ob-
jects look larger, because, through excess of aerial per-
spective, we overestimate distance.   On the high Sierra,
or the Colorado mountains, or anywhere  on  the high
interior plateau, the clearness of the air and consequent
distinctness of distant objects are such, that we imagine 
160
BINOCULAR VISION.
objects  to  be nearer  and therefore smaller than they
really are.
   Form.—Outline form is a combination of directions
of component radiants.  In a ring of stars, the direction
of each star is given immediately; the combination of
these several directions gives the ring.   This is so sim-
ple and immediate a  judgment, that it may almost  be
called a direct sense-perception.   It is apparently a  di-
rect perception of the form of the retinal image.  It is
so sure and immediate that it is not liable to error; yet
it is capable of analysis into simpler elements, as shown
above.
   Solid form is a  far more complex judgment, and
therefore  liable  to error.   We judge of  solid form
partly  by binocular  perspective and partly by shades
of light.  The roundness of a column is perceived part-
ly by the greater  optic convergence necessary to see dis-
tinctly the nearer central parts than the farther marginal
parts, and partly by the shading of light on the different
parts.   The latter effect can be perfectly  imitated  by
the painter, but  not  the  former.   Hence  the illusion
produced by the  painter  is most perfect at a distance
where  binocular  perspective is very small,  but  is de-
stroyed  by near approach.  Hence also the roundness
of a  painted column is most perfect when looking with
one eye, but of a natural column when looking with
two eyes.
   Gradation of Judgments.—Intensity, color,  and  di-
rection of light are simple impressions which can  not
be further analyzed.  Next come  outline form and
surface contents,  which may indeed  be analyzed into
combination of directions, but yet the perception is so
direct and  so certain  that it may well be called imme-
diate.   Next comes solid form, which, as we have seen, 
       JUDGMENT OF DISTANCE, SIZE,  AND FORM.    161

is a more complex judgment based on simple elements,
and therefore may be deceived.  Next come the closely
related and still more complex judgments of size  and
distance, which  are therefore still more liable to error.
These latter judgments  become more and  more com-
plex  as the objects in the field of view become more
numerous  and more complex  in form and varied in
position; as, for example, the  judgments of form,  size,
and distance of  all the objects in an extended natural
scene.  All these seem to the uninstructed as immedi-
ate instinctive perceptions, and mistakes are supposed
to be the result of deceptions of sense instead of errors
of judgment, as they really are.  Judgments like these,
which are so quickly made that the process has largely
dropped out of  consciousness, I shall call visual judg-
ments.   But  these higher and more complex visual
judgments pass, by almost insensible degrees, into still
higher and more complex intellectual judgments. Thus
from simple sense-impressions we pass without break
through  the various grades of visual judgments to the
lower intellectual judgments, and  from these again
through various  grades  of complexity to  the highest
efforts of the cultured mind.
    Now, as visual judgments  seem to  the uninstructed
primary, immediate, and simple perceptions, so  also
among intellectual judgments many seem to  those unin-
structed in psychology and unskilled in mental analysis
as primary, immediate, instinctive, or innate, and there-
fore certain.  But, as the  study of  visual  phenomena
teaches that these visual judgments  are capable of an-
alysis  into  simpler elements,  and  therefore  liable to
error, so also  the study of psychology should teach us
that many of the so.-called instinctive judgments, pri-
mary intuitions, etc., may also be capable  of analysis, 
162
BINOCULAR VISION.
and  therefore liable to error.   Further, it  is evident
that  the so-called facts of consciousness, in the one field
as in the other, can not be considered reliable until sub-
jected to rigid analysis.   The study of visual  (especially
binocular visual) phenomena is peculiarly valuable :  first,
in teaching us that so called immediate intuitions are in
many cases only judgments, the processes of which have
dropped  out of consciousness; and, second, in teaching
us the habit of analysis of such apparently  simple in-
tuitions.
                     RETROSPECT.

   We have now given in clear outline the most im-
portant phenomena of vision and their explanation.  It
will  not be amiss, before proceeding further, to look
back over what we have  passed, and justify its logical
order.
   There are three essentially  different modes  of  re-
garding the eye, which must be combined in a complete
account of this organ.  We have taken up these suc-
cessively.   First,  we treated of the eye as an optical
instrument  contrived to  form a perfect image, every
focal  point  of which shall correspond with  a radiant
point in the object.  This is a purely physical  inves-
tigation.  Second, we treated of  the  structure of  the
retina, especially its  bacillary layer, and showed how
from  this structure resulted the wonderful property of
corresponding points  retinal and  spatial, and the  ex-
change between  these  by impression and  perceptive
projection, and how the  law of direction and all the
phenomena of monocular vision flow out of  this prop-
erty.   Third, we  treated  of  the still  more  wonderful 
RETROSPECT.
163
correspondence of  the two retince point for point, and
therefore of their spatial representatives point for point;
and considered how by ocular motion the two images of
the same object are made to fall on corresponding points
of the two retinae, and their spatial representatives are
thereby made to coincide and become  one; and  how,
finally, all the phenomena of binocular vision flow from
this property.
    We have therefore apparently covered the ground
originally laid out.  But there  are  still a number of
questions on  binocular vision, somewhat more abstruse
and more disputed than the preceding,  but of so high
interest that  they  must not  be wholly neglected.   The
remaining chapters will be devoted to these. 
PAET  III.
ON  SOME  DISPUTED  POINTS  IN
        BINOCULAR  VISION.
                  CHAPTER  I.

             LAWS OF OCULAR MOTION.

SECTION I.—LAWS OF PARALLEL MOTION.—LISTING'S LAW.

   We have already (page 69) spoken of spectral  im-
ages produced by strong impressions on the retina.   It
is  evident  that these, being the result of impressions
branded upon the retina and remaining there for some
time, must  while they remain follow all the motions of
the eye with the greatest exactness.  They are specially
adapted, therefore,  for detecting motions  of the eyes,
such as slight torsions or  rotations on the optic axes,
which could not be detected in any other way.
   Experiment 1.—Let the experimental room be dark-
ened by closing the shutters, but allow light to enter
through a vertical slit  between the shutters of one win-
dow.   Standing before the window with head erect,
gaze steadily at the slit until a  strong  impression is
branded in upon the  vertical meridian of the retina.
If we now  turn about  to the blank wall, we  see a very 
LAWS OF PARALLEL MOTION.          165
distinct colored vertical  spectral image of  the slit.
Placing now the eyes in the  primary position—i.  e.,
with face perpendicular and  eyes looking horizontally
—if, without changing the  position of the head, we
turn the eyes to the right or left horizontally, the im-
age remains vertical.  Also if we turn the eyes upward
or downward by elevating or depressing the visual plane,
the image remains vertical.   But if, with the visual
plane elevated extremely,  say 40°, we cause  the eyes to
travel  to  the right or left, say also 40°, or  if we  turn
the eyes from their original primary position obliquely
upward and to one side  to  the same point, the image
is no longer vertical, but leans decidedly to the same
side;  i. e., in going to the right, the image leans to the

right, thus— / ;  in going to  the left, it leans to the

left, thus— \ .  If, on the contrary,  the visual  plane

be depressed, then motion of the eyes to the right causes

the image to lean to  the  left, thus— \ ; while motion

to the  left causes it to lean to the right, thus—

    Experiment 2.—If, instead of a vertical, we  use a
horizontal slit in the window,  and thus obtain a  hori-
zontal  image and throw it on the wall as before, then,
if the  image has  been made with the eyes  in the pri-
mary position,  it will be seen on the  wall perfectly
horizontal.  Furthermore, if  the  eyes  travel right and
left in the primary visual plane,  or upward  and down-
ward  by elevating or depressing the visual plane, the
image  retains  its perfect horizontality.  But  if,  with
the visual plane elevated,  we cause the point of sight
/• 
166     DISPUTED POINTS IN BINOCULAR  VISION.

to travel to the one side or the other, the image is seen
to turn  to the opposite side; i. e., when the eyes turn
to the right, the image turns to the left, thus—^^;
when they turn to the left, the image rotates to the
right, thus—"~-\^.  If  the visual plane be depressed,
then motion to the right causes the image to rotate to
the right (N^), and motion to the  left causes  it to
rotate to the left (^^).
   These rotations of the image depend wholly on the
oblique  position of the eyes, and it makes no difference
how that oblique position is reached—whether by mo-
tion along rectangular coordinates, as in the experiments,
or by oblique motion from the primary position.  Fur-
thermore, the amount of rotation of the image increases
with the amount of elevation or depression of the visual
plane, and the amount of lateral motion of the  eyes.
   Experiment 3.—The  fact of rotation or torsion of
the images, and the direction of that torsion, are easily
determined by the somewhat rough methods  detailed
above; but if we desire to measure the amount of tor-
sion, the wall  or other  experimental plane  must be
covered with rectangular coordinates, vertical and hori-
zontal.  By experimenting in this way, I find that for
extreme oblique  positions the  torsion of the vertical
image on  the vertical lines of the experimental plane
is about 15°, but the torsion of the horizontal image on
the horizontal lines is only about 5°.   The reason of
this difference will be explained farther on.
   Putting  now  all these results  together,  the fol-
lowing  diagram  (Fig. 55) gives the position of the
vertical and  horizontal  images  when projected  on  a
vertical plane for all positions of the point of sight.
Simple  inspection of the  diagram is sufficient to show 
             LAWS OF PARALLEL MOTION.          167

that the inclination or torsion of the vertical image on
the true verticals, and that of the horizontal image on the
true horizontals, are  in opposite directions.   If torsion

                        Fig. 55.
dla .ham 6how1ng the inclination op vertical and horizontal images for
              all Positions of the Point of Sight.
of the images show torsion of the eye, there must be a
fallacy  somewhere.   The  one or the  other must  be
wrong; for when one indicates torsion to the right, the
other indicates torsion to the  left, and  vice versa.   To
show this contradictory testimony more clearly, and thus
to prove that there is a fallacy here, we  make another
experiment.
   Experiment Jf.—Make a rectangular cross-slit in the
window, gaze steadily upon it until the spectral impres-
             8 
168     DISPUTED POINTS IN BINOCULAR VISION.

sion is made on the retina, and then cast the image on the
wall.   In the primary position of the eyes it is of course
a. perfect rectangular cross.  Now turn the eyes to the
extreme upper right-hand corner of the wall.  The cross,
by opposite rotations of the two parts, is seen distorted

thus-----/""""•   Looking upward and  to the left, it is

             \
seen thus—   V--.   Oblique motion downward and to


the right makes it appear  thus— ~"V-», and to the left


thus— -7  •  It will be observed that this is exactly the

manner in which the lines cross in the diagram,  and we
have placed crosses in the corners to indicate that fact.
   Evidently  the cause of the  contradictory evidence
of the two images is projection on a plane  inclined at
various angles to the line of sight.   The diagram is a
correct  representation of  the phenomena as seen pro-
jected on a vertical plane, but is not a correct represen-
tation of the torsions  of  the eyes.  To eliminate this
source of fallacy and get the true  torsion of the eyes,
we must project the cross-image on a plane in every
case perpendicular to the line of sight.
   Experiment  5.—Prepare an  experimental plane a
yard square, make a  rectangular cross in the center, and
set up  a perfectly perpendicular rod at the point of
crossing.  Fix  the plane in a position inclined 30° to
40° with the vertical, and obliquely to  the right side
and above, so that, when sitting before the experimen-
tal window and turning the eyes extremely upward and 
LAWS OF PARALLEL MOTION.
169
to the right, the observer looks directly on the top of
the rod, and this latter is projected against the plane as
a round spot.   We thus  know that the line of sight is
perpendicular to the  plane.   Now, after gazing at the
cross-slit in the window until the spectral impression is
made on the retina, without moving the head, cast the
image on the  center of  the plane by turning the eyes
obliquely upward and to the right.   The  rectangular
cross-image rotates, both  parts alike, so as to retain per-
fectly its rectangular symmetry, to  the right, thus—

"">-,  showing unmistakably a torsion of the eyes in the

same direction.  If the plane be arranged similarly on

the left side, the cross turns to the left, thus— --V'.  If

the plane  be  arranged below and to the right, so that
the eyes turned obliquely downward  and to  the right
shall  look  perpendicularly upon it, the cross will turn

to the left, thus—^V"'.   If similarly arranged on the

left side, the  cross will  turn  to  the right, thus—

In all cases the rectangular symmetry is perfectly pre-
served, a sure sign that  there is no error by projection,
and that they truly represent  the torsion of the eyes.
    Experiment 6.—In  order  to neglect no  means of
testing the truth  of  this conclusion, we will  make one
more  experiment, using the sky as  the -plane upon
which to project the image.  This spatial concave is of
course everywhere at right angles  to  the line of  sight,
and therefore is free from any suspicion of error from
projection.  Standing in the open air before a vertical 
170     DISPUTED POINTS IN BINOCULAR VISION.

flag-staff, I gaze upon it steadily until its image is, as it
were, burned into the vertical meridian of the retina.
Now, without moving  the head, I turn the eyes ob-
liquely upward and  to  the right, and  the  image leans
decidedly to the right; and turning to the left, the image
leans to the left.  In this position of the head, of course,
the ground  prevents us from making  the same experi-
ment with  the  visual  plane depressed.   I therefore
vary  the experiment  slightly.   Sitting  directly  in
front of the college building, with the morning  sun
shining obliquely on its face, the light-colored perpen-
dicular  pilasters gleam in the sunshine, and  contrast
strongly with the shadows which border their northern
margin.   Gazing steadily at the building, I easily get a
strong spectral image of the whole structure,  with its
vertical and its horizontal lines.  Now throwing myself
flat on my back, I see the image  perfectly erect on the
zenith.   Turning the eyes upward toward the brows
and  to  the right and left, then downward toward the
feet  and to the right and left, the  whole image of the
building rotates precisely as indicated  in my previous
experiments.
   Evidently, then, in the diagram Fig. 55,  the verticals
give true results, but the horizontals  deceptive results
by projection.  Why this is so is easily explained.  Sup-
pose an observer to  stand in a room  before a vertical
wall; suppose him further to be surrounded by a spher-
ical wire cage constructed of rectangular spherical co-
ordinates, or meridians and  parallels, with the eye in
the center and the pole in the zenith.   Evidently, the
surface of this spherical concave is  everywhere perpen-
dicular to the line of sight, and therefore, like the sky,
is the proper surface of projection.  Evidently, also, the
meridians and parallels everywhere at right angles to 
*
             LAWS OF PARALLEL MOTION.          171

each other are the true coordinates wherewith  to com-
pare the images,  vertical  and horizontal,  in order  to
determine  the direction and amount  of their rotation.
Now the simple question is, "How do these true rec-
tangular coordinates project themselves on the wall  to
an eye placed in the center, or how would their shad-

                        Fig. 5C.
Diagram showing thb PROJFCTfON of a System of Spherical Coordinates on
                    a Vertical Plane.
ows be cast by a light in the center?"   It is evident
that the meridians would project as straight  verticals,
but the parallels not as straight lines, but as hyperbolic
curves,  increasing  in  curvature as  wTe go upward or
downward.   The  diagram  Fig. 56  shows   how  the 
172    DISPUTED POINTS IN BINOCULAR VISION.
spherical  coordinates would  project on a vertical wall.
By calculation or by careful  plotting it may be shown
that at an angle of elevation or depression of 40°, and
a lateral  angle of the same amount, the inclination of
the hyperbolic curve on the horizontals of  the wall will
be  about  20°.  Now a rectangular cross-image, if un-
rotated, would project as the crosses in the corners;  i. e.,
the vertical arm would project vertically, but the hori-
zontal arm would be inclined 20° with the horizontal,
so that the angles of the cross would be about 70° and
             110°.   Now rotate  these crosses  15°, the
      ' *"     right upper one to  the right, the left up-
       /      per one to the left,  the right  lower to the
     J^^l  left, and the  left lower to  the right,  and
^/        we  have the precise phenomena  repre-
    /        eentcd  by the diagram Fig. 55; i. e., the
    /         verticals are  turned 15°  right or left as
   / |       the  case may be, and the horizontals in
             the opposite  direction, but  only 5°.  Fig.
57  illustrates this in the case of  the right-hand upper
cross-image—the heavy cross representing the cross un-
rotated, and the lighter one the same rotated 15° to the
right by extreme obliquity  of the line of sight.
  .  Therefore, the diagram which truly  represents the
torsion of the eye in various positions,  or the torsion of
the cross-image when referred to a spherical  concave
perpendicular to  the line of  sight  in every position, is
represented  in  Fig. 58.  Simple  inspection of this fig-
ure shows the  real  direction and  amount of  rotation
both of the vertical and the horizontal image for every
position of the line  of sight.   The crosses in  the cor-
ners show that there is no distortion by projection.
    We are justified  therefore in formulating the laws
of parallel motion of the eyes thus: 
             LAWS  OF PARALLEL MOTION.           173

   1. When the eyes move together in the primary plane
to the one side or the other, or in a  vertical plane up
or down, there is no rotation on  the  optic axes, or  tor-
sion.
                         Fig. 58.
Diagram showing the Trfe Torsion of the Eyb for Various Positions of
                    the Point of Sight.
    2.  When the visual plane is elevated  and the eyes
move to the right, they rotate to the right; when they
move to the left, they rotate to the left.
    3.  When the visual plane is depressed, motion  of
the eyes to the right is accompanied with rotation to  the
left, and motion to the left with rotation to the right.
    4.  These laws may be all generalized into one, viz.:
 When  the  vertical and  lateral angles have the same 
174    DISPUTED POINTS IN BINOCULAR VISION.

sign* the rotation is positive {to the right)/  when  they
have contrary signs, the rotation is negative {to the left).
    The law now announced as the result of experiment
is evidently  identical with  the law of listing, which
has been formulated by Listing himself thus:
    " When the  line of sight passes from  the primary
position to any other position, the angle of torsion of
the eye in its second position is the same as if the eye
had come to  this second position by  turning about a
fixed axis perpendicular both to the first and the second
position of the line of sight." f
    Now an axis which satisfies these conditions can be
none other than an equatorial axis, or at least an axis
in a plane perpendicular to the polar axis.   In turning
from  side  to side in the primary  plane, it is a vertical
equatorial  axis.   In turning up  and  down vertically,
it is a  horizontal equatorial axis.  In turning obliquely,
as in the experiments on torsion, it is  an oblique equa-
torial axis.  Now take a globe, and, placing the equator
in a vertical  plane, make  a distinct vertical and  hori-
zontal  mark  across the pole.  Then turn the globe on
an  oblique equatorial axis, so  that the pole shall look
upward and to the right.  It will be seen that the polar
cross is no longer vertical and horizontal, but is rotated
to the right.   If the globe be turned upward and to the
left, the polar cross will rotate to the left; if downward
and to the right, it will rotate to the left; and if to the
left, it will rotate to the right.  In a word, the rotation
in every case  is  the  same as given in the above laws
determined by experiment.

  * In  reference to a vertical line, positions to the right are positive
and  to the left negative; in reference to a horizontal line, above is posi-
tive and below negative.
   f Helmholtz, " Optiquc Physiologique," p. 606. 
LAWS OF PARALLEL MOTION.          175
   Contrary Statement by Helmholtz.—We have  given
these laws and their experimental proof in some detail,
and have  taken some pains  to  show that they are in
complete accord with  Listing's law, because Helmholtz
in his great work on " Physiological Optics " has given
these  laws of  ocular motion  the very reverse of  mine.
I quote from the French edition of  1867, which  is not
only the latest but also  the  most  authoritative edition
of the work:
   " When the plane of sight is  directed upward, lateral
displacements to the right make  the eye turn to the left,
and displacements to the left make it turn to the right.
   " When the plane of sight is depressed, lateral dis-
placements to the right are  accompanied with torsion
to the right, and vice versa.
   " In other words,  when the  vertical and lateral an-
gles are both of the same sign, the torsion is negative;
when they  are  of  contrary  signs, the torsion is posi-
tive:1 *
   We have  demonstrated  the very reverse  of  every
one of these propositions, and we  have also shown that
they are inconsistent  with Listing's law as quoted by
Helmholtz himself.  The experiments by which Helm-
holtz seeks to  determine the  torsions of the eye are the
same as those already described under experiments 1 and
2, page 165.   The results which he reaches are also the
same as those  reached by myself, except that he makes
the inclination of the vertical image on the verticals of
the wall, and of the horizontal image on the horizontals
of the wall, equal  to  each other, while I  make the in-
clination of the verticals much greater.  The diagram by
which he embodies all these results is also similar to my
diagram, Fig.  55, except that in his the horizontal and
              * " Optique Fhysiologique," p. 602. 
176     DISPUTED POINTS IN  BINOCULAR  VISION.

vertical curves are exactly similar, while in mine the
curves of the verticals are  much greater.  He also, like
myself, admits that there is a fallacy by  projection.
But  unaccountably he imagines that  the inclination of
the horizontal image on the true  horizontal gives true
results, and the inclination of the vertical image on the
true  vertical deceptive results by projection;  therefore
he imagines the eye to turn exactly the reverse of the
reality.  Experiments  5 and 6, under conditions  elim-
inating errors by projection, prove the  falseness of his
results.  The reader who desires to follow up this sub-
ject  will find it discussed in an article by the writer re-
ferred to below.*
   The Rotation only Apparent.—There can be no doubt,
then, that when the eye passes from its primary position
to an oblique position, the vertical meridian of the ret-
ina is no longer vertical, but inclined.  If we observed
            Fig. 59.              the  iris  of another per-
                               son, we  should see that
                               it had turned as a wheel.
                               In  deference  to  the
                               usage  of other writers
                               and to the appearance,
                               I have spoken of this as
                               a rotation on  the  optic
                               axis, but it is so in ap-
                               pearance only,  and not
                               in reality; for the mo-
                               tion of  the  eye, being
                               always on an  axis  in a
plane  perpendicular to the polar or optic axis, can not
be resolved into a rotation about  that axis.   A simple
experiment will show  the kind  of rotation which  takes
   * "American Journal of Science and Arts," III, vol. xx, 1880, p. 83.
 
            LAWS OF CONVERGENT MOTION.         177

place in bringing the eye to an oblique position.  Take
a circular card, Fig. 59, and make on it a rectangular
cross which shall represent the vertical ( V V) and hori-
zontal {H H) meridians of the retina.   A small central
circle p  represents the pupil.  Now take  hold of the
disk with the thumb and  finger of  the right hand at
the points V V, and  place this line in a vertical  plane.
Then tip the disk up so that the pupil p shall look up-
ward 45° or more, but  the line V V still remaining in
the vertical  plane.  Finally, with the finger of the left
hand turn the disk on the axis V Fto the left.   It will be
seen that V  V is no longer vertical, nor IIH horizontal;
but some other line x x is vertical, and y y horizontal.
In other words, the whole disk seems to have rotated
ro the left.  But this is evidently no true rotation on a
polar axis, but only  an apparent rotation consequent
upon reference to a new vertical meridian of space.  It
does not take place in the primary plane, because there
all the  spatial meridians  are parallel, but  only in an
elevated or  depressed plane, because the spatial merid-
ians  are  there convergent.   I shall therefore  hereafter
call  this apparent rotation on the optic axis torsion.
This is the  more  important, because there is a real ro-
tation on the optic axis, which we shall speak of under
the next head.
      SECTION II.—LAWS OF  CONVERGENT MOTION.

   We have thus far confined  ourselves to explanation
of the laws which govern the eyes when they move in
the same direction with axes parallel, as in looking from
side to side or up and down. I have called this the law
of parallel motion.  We now come to speak of the laws 
178     DISPUTED POINTS IN BINOCULAR VISION.

which govern the eyes when they move in opposite di-
rections, as in convergence.   These I will call the laws
of convergent motion.
   In convergence there is not merely  an apparent
rotation or torsion, but a real  rotation of the  eyes on
the optic  axes; and since the  motions are  in  opposite
directions, the rotations are  also opposite.   But, except
in very strong convergence, the rotation  is small and
difficult to observe, and therefore has been  either over-
looked or denied by many observers.   As the existence
or non-existence of  this rotation has an important bear-
ing on  the much-vexed question of  the horopter, it is
important  that proof  should be accumulated  even to
demonstration.
   The first difficulty which meets us in experimenting
on this subject is, that spectral images, which  are such
delicate indicators of ocular motion, are almost useless
here.   In parallel motion of the eyes these  images fol-
low every movement with the utmost exactness, but in
convergent motion  they do not.   Suppose, for example,
with the eyes parallel  or nearly so, a spectral image is
branded on the vertical meridians  of both eyes.  In
convergence each eye may move through 45° or more,
but the place of the spectral  image is the same, viz.,
directly in front.   The eye also in extreme conver-
gence may rotate on the optic axis 10°, but  the vertical
image remains still perfectly vertical.  The reason of
this is, that the two retinal images are on corresponding
points, and therefore by the  law of corresponding points
their external representatives are indissolubly united.
In moving the eyes in opposite directions,  it is impos-
sible that the images should move except by  separating;
but separation, either complete or partial, is impossible
without violating the  law of corresponding points—a 
LAWS OF CONVERGENT  MOTION.         179
law which is never  violated under any circumstances
whatsoever.  Actual objects therefore, not spectral im-
ages, must be used in these experiments.
   As the experiments about to be described are among
the most difficult in the whole field of  binocular vision,
and as in many of them it is  absolutely necessary that
the primary visual plane should be perfectly horizontal,
I must first define what we mean by the primary visual
plane, and show how it may be made  perfectly hori-
zontal.
   Take a thin  plate, like a cardboard;  place its edge
on the root of the nose and the card at  right angles to
the line of the face, in such wise that  the plane of the
card shall cut through the center of the two pupils, and
you  can see  only its edge.  The card  is then in the
primary visual plane.  Keeping the position of the card
fixed in relation to the face, the face may be elevated
or depressed, and the card will be also elevated or de-
pressed, but will remain in the  primary visual plane.
But if the card be elevated or depressed so as to make
a different angle with the line of  the face, then  the vis-
ual plane is elevated or depressed above or below the
primary position.  When the head  is erect and the line
of the face vertical, the primary visual plane  is hori-
zontal. Suppose we wish now to look  at a vertical wall
in such wise that the primary visual plane shall  be per-
fectly  horizontal.  We first
mark on the wall a horizon-            Fl°"co'
tai  line exactly the  height    »L______________\n;
of the root  of  the nose.      V                /
Standing  then  say  6 feet
off, and shutting first one eye  and then the other, we
bring  the image of  the lowest part of the root of the
nose directly across the line.   The  primary plane is 
DISPUTED POINTS IN  BINOCULAR VISION.
then perfectly horizontal.   In Fig. 60, n and n' are the
curves of the outline of the root of the nose as seen by
the right and left eye respectively, and n n' is the hori-
zontal line on the wall.  We are now prepared to make
our experiments.
    Experiment 1.—Prepare a plane 2 feet long and 1
foot wide.  Dividing this  by a  middle line  into  two
equal squares, let  one of  the halves  be painted black
and the other white.  Let  the whole be covered with
rectangular  coordinates, vertical and horizontal, on the
black half the lines being white and on the white half
Fig. 61.
ismiiu n
■■»■■■■
wmmmmmm
w^muam ^
wmmammm ^

■■■■■■■
black, as in Fig. 61.  Near the middle of the two square
halves, and at the crossing of a vertical and  horizontal
line, make two small circles, c c'.  Set up this plane on
the table  in a perfectly vertical position, and at a dis-
tance of 2 or 3 feet.  Rest  the chin on the table im-
mediately in  front of  the plane, with a book or other
support under the chin, so that the root of the nose
shall be exactly the same height as the circles, which in
this case is about 6 inches.   Now, shutting alternately 
LAWS OF CONVERGENT  MOTION.         181
one eye and the other, bring the image of the lowest
part of the root of the nose coincident with the hori--
zontal line running through the circles.   The primary
plane is now perfectly horizontal, and therefore at right
angles  to the  experimental plane.   Now, finally, con-
verge the eyes until the right eye looks directly at  the
left circle, and the left  eye at  the right circle, and of
course  the two circles combine.  If  one is practiced in
such experiments,  and  observes closely, he will see that
the vertical lines  of the two squares (which can  be
readily distinguished, because those of the one are white
and of the other black), as they approach and pass over
one  another  successively, are not  perfectly parallel,

but make a small angle, thus—  1/ ; and  also that  the
angle increases as the convergence is pushed farther
and farther, so that lines even beyond the circles  are
brought successively together.  Similarly also the hori-
zontals cut each other at a small angle, but this fact is
not so easy to  observe as in the case of the verticals.
   Such are the phenomena; now for the interpretation.
Tt must  be remembered that images  of objects differ
wholly from spectral images in this, viz.: that spectral
images, being fixed impressions on the retina, follow
the motions of the eye with perfect exactness; while,
images of objects  being  movable on  the  retina, their
external  representatives in convergence seem to move
in a direction  contrary to the motions of the eye (page
107).   This is true of all motions, whether by  transfer
of the point of sight or by rotation about the optic
axes.  Now, in the  above experiment, the images of
the two squares with all their lines seem to rotate about
the point of sight  outward—i. e., the right-hand square
to the right, and the left-hand square to the left.   At 
182
DISPUTED POINTS IN BINOCULAR  VISION.
Fig. 62.
 first sight this might seem to indicate a contrary rota-
tion of the eyes, viz., inward.   But not so ; for, observe,
 the  field  of view of the right eye is the left or black
 square, and the field of view of the left eye is the right or
                        white square.   The right-eye
                        field turns to the left, showing
                        a rotation of the right eye to
                        the right;  while  the left-eye
                        field turns to the right, show-
                        ing a rotation of the left eye
                        to the left.   Thus the  two
                        eyes in convergence rotate out-
                        ward.  This is shown in the
                        diagram  Fig.  62,  in  which
                        c c' is the experimental plane.
                        The arrows show the direc-
                        tion of rotation of  the images
                        of the plane and of the eyes.
    Experifnent 2.—When one becomes accustomed to
 experiments of this kind, he can make them in many
 ways. I find the following, one of the easiest and most
 convenient:  Measure the exact height of the root of the
 nose upon the sash  of  the open window, and mark  it.
 Stand with head erect about 3 or  4  feet from the win-
 dow.  Using the cross-bars of the  sash-frame as hori-
 zontal lines, arrange the head so  that the two images
 of the root of  the nose  shall be exactly the same height
 as the mark.  The primary plane  is now horizontal.
 Now converge the eyes until the  dark outer jambs or
 sides of  the  frame of  the sash  approach each other.
 This will be very distinct on account of the bright light
 between  them.  It  will be seen that the frames come
together, not parallel, but as a sharp V, thus— \| , r and 
LAWS OF CONVERGENT MOTION.        183
I being the  right- and left-eye images respectively.   I
find  that when I  stand at  a distance  from the window
equal to the width of  the sash, the angle between the
two  jambs as they come together is about 15°,  showing
a rotation of each eye outward 7° 30'.  When standing
still  nearer, so that  the convergence is extreme, the
angle is 20° or more, showing a rotation of  each eye of
10° or more.
   In  all these experiments the extremest care is neces-
sary to insure the perfect horizontality of the visual
plane.   The  slightest upward or downward looking
vitiates the result by introducing mathematical perspec-
tive.   If there were  no rotation, then looking upward
and  converging  would bring the jambs  together  by

perspective, thus— A ; looking downward, thus— y  ;

looking horizontal, parallel, thus—  .  But on account
of rotation, looking horizontal brings  them  together

thus— y ;  downward, at higher  angle, thus—  \J .

Looking upward more and more, the angle decreases
till it becomes 0 (i. e.,  the jambs parallel), and then in-
verted.  I find that in the previous experiment, stand-
ing  from tiie window the  distance of its width, I  must
elevate the plane of vision about 6°—i.  e., I must look
about 8 or 9 inches above the mark—to make the jambs
parallel. This is therefore a good method of measuring
amount of rotation.
   Experiment 3.—A  far more accurate mode of  mea-
suring  the  amount  of rotation is  by constructing dia-
grams on a plane similar to the one used in experiment
1, but in which  the verticals and horizontals are  both
inclined on  the true verticals and true horizontals in a 
184     DISPUTED POINTS IN BINOCULAR VISION.

direction contrary to the rotation of the eyes—i. e., in-
ward—and then determining the degree of convergence
necessary to make them come together perfectly par-
allel.  I find  that for my eyes, when the verticals are
thus inclined in each square 1 J° with  the true vertical,
and  therefore make an angle of 2|-° with each other
(Fig. 63), they come together  parallel when  the point
of sight  is 7 inches  from the root of the nose.   When
the  angle of inclination in each is 2^° with the  true
vertical,  and therefore 5° with each other, the point of
                        Fig. 63.
Verticals and Horizontals inclined 1J°.
sight must be 4 inches off.  When the inclination with
the  true  vertical is 5°, and  therefore  10° with each
other, the point of sight is 2-2 inches.  Finally, when
the inclination with the true vertical is 10° or 20° with
each other, then they can be brought together  parallel
only by the extremest convergence, the point of sight
being then  only a quarter of  an inch in front  of  the
root of the  nose.   In the diagram Fig. 63 the lines,
both vertical and  horizontal, are inclined inward  1\°,
and  therefore the verticals of the two squares make an 
LAWS OF CONVERGENT MOTION.         185
angle with each other of 2£°.  It is therefore a reduced
facsimile of the plane used. The coordinate lines coincide
when the point of sight is 7  inches from the root of the
nose.
   In the cases  of extreme  convergence  mentioned
above, I find  that for perfect  coincidence of both ver-
ticals  and horizontals it is necessary that the inclination
of- the verticals with the true vertical must be greater
than that of the horizontals with the true horizontal; so
that the little squares are not perfect squares.  Thus,when
                        Fig.  64.
Verticals inclined 10', Horizontals 5°.
the verticals incline 5°, the horizontals must incline only
3|° ; when the verticals  incline 10°, the horizontals in-
cline only 5°.   Fig. 64 is a reduced facsimile of this last
case of extreme convergence.   I can not account for this,
except by a distortion of the ocular globe  by the unu-
sual and unnatural strain on the muscles, especially the
oblique muscles of the eyes.   It  may be that other eyes
are more rigid  than mine, and suffer less distortion.
   The above  is  by far the most refined method of
proving  rotation,  and of measuring its amount.  But 
 186    DISPUTED POINTS IN BINOCULAR VISION.

 so  difficult are these experiments, and  so delusive  the
 phenomena, that it  is necessary to  prove it  in  many
 ways.  Another method is by means of ocular spectra.
 We have already shown that  these are not  so well
 adapted to experiments in convergent  motion as they
 are in parallel motion.   For example, two brands on
 the vertical  meridians of the two retinae produce spec-
 tral images which are perfectly  united (p. 178).  Now
 in strong  convergence, when the two  eyes rotate out-
 ward, the two  images will  not  separate or cross each

 other, thus—   Y  , as we might at first expect;  for

this is forbidden by  the law of corresponding points.
But we  may use a spectral  image of one eye  to  show
rotation of that eye.
    Experiment 4-—The manner in which  I  conduct
the experiment is as follows: I make a vertical spectral
image in the manner already explained (page  164), by
gazing with  one eye (say the right) on a vertical slit in
                       Fig. 65.
y		ff. R t~\	
	8	> St	r/
<:----	i>	A	u.
a closed window.   I  now turn about, and, keeping the
left eye I, Fig. 65, still shut, I look across the root of
the nose n with the right eye R at a perfectly vertical
line w on the wall.  I see the vertical  image perfectly
parallel and nearly coincident with the vertical line on
the wall.  Then, while the right eye still continues to
look along the line R s, I turn the shut left eye L from 
            LAWS OF CONVERGENT  MOTION.         187

its previous position L s through an angle of 90°, until
its line of sight is Is'.   In other words, I  run the
point of sight or point of convergence from the distant
point of the wall w along the line R s to the point a
near the root of the nose.  When I do so, I see the

spectral image incline to the right, thus— /, indicating

(since the image is spectral) a rotation of the eye in the
same direction.  This experiment is very difficult, but
it is  conclusive.
   Experiment  5.—I shut one eye, say the left, and
look across the  root of  the nose at a distant object, as
in Fig. 63.   An assistant now observes attentively my
iris,  and notes with  care the  position of  the radiating
lines.  Now, without changing at  all the direction of
the line of sight, I change the point of sight to an ob-
ject  or  point very near  the root of the nose, as  in Fig.
63, by turning the optic axis  of the shut eye through
90°.   I again relax the  convergence so as to make the
optic axes parallel, and  again converge upon the near
point; and so on alternately.  With every convergence
the iris is seen to rotate like a wheel outward.   I have
subjected my eyes to the observation of five different
persons, and they all made the same  statement  in re-
gard to the direction of rotation.
   There can be no longer any doubt that my eyes in
convergence rotate on the optic  axes  outward, the de-
gree of rotation  increasing with  the degree of conver-
gence.  To generalize this as  a law of ocular motion I
have found extremely difficult, because there are so few
persons who  are able to verify the results,  on account
of imperfect voluntary control  of  the ocular muscles,
and especially the difficulty or even impossibility which
most persons find in  observing intelligently  images 
188    DISPUTED POINTS IN BINOCULAR VISION.

which  are not  at the point of sight.   Nevertheless, I
have found  several persons who  by considerable prac-
tice have been able to confirm nearly all these experi-
ments.  I have also made observations  directly on  the
eyes of other persons in the manner described in  the
fifth experiment,  and  noted the rotation  of the  iris
in strong convergence.  I  think, therefore,  I am justi-
fied in announcing the  outward rotation of  the eyes in
convergence as a general law.
   The Effect of Elevation and Depression of the Visual
Plane on  Rotation.—The question  next  occurs, What is
the effect, on this rotation,  of elevation or depression of
the visual plane ?  I  have also made many experiments
to determine this point.
   Experiment 6.—In making experiments of this kind,
all that  is necessary is that the experimental  plane
shall  be  exactly perpendicular  to  the visual plane.
This  may be insured either  by keeping the face in its
former position and  changing the  inclination  of  the
plane, or else,  more  conveniently, by fixing the  plane
in its vertical  position and changing  the  inclination
of  the face.   If  we choose the latter method, then,
for experiments with the  visual plane elevated,  the
head  or  face  is turned downward and  the eyes look
upward toward the brows upon the experimental plane
—care being taken that the eyes in their new position
shall  be  on a level with the center of  the  plane.  By
experiments of this kind I find that the outward rota-
tion in convergence, especially in strong convergence,
increases decidedly for the same degree of convergence
with the elevation of the visual plane.
    Experiment 7.—For experiments on rotation with
the visual plane depressed, the face must be turned up-
ward (taking care as before that  the eyes in their new 
LAWS OF CONVERGENT  MOTION.         189
position are on a level with the center of the plane),
and then the eyes look downward  toward the point of
the  nose upon the experimental plane.  In  this case I
find that for the same degree of convergence  the rota-
tion decreases steadily, until it becomes zero for all  de-
grees of convergence when the visual plane is depressed
45° below its primary position—i. e., when the eyes look
toward the  point of the nose.  Below this angle the ro-
tation seems to be inverse—i. e., inward—although it is
impossible to try this with strong convergence, because
the nose is in the way.
   Cause  of the Rotation.—It is probable that  the rota-
tion is produced by the action  of  the inferior oblique
muscles.  If so,  we  can  understand  why it increases
with elevation of the visual plane, and  decreases with
its depression; for  in the first case  the tension  on these
muscles would be increased, while  in the latter case it
would be decreased.
   Previous Researches on this Subject.—The only writer
who has to my knowledge made  experiments on rotation
of the eyes  in convergence is Meissner.*  The results he
arrives at are substantially the  same as my own;  but
he arrives at them indirectly, while investigating the
question of  the horopter, and by methods far less exact
than those employed  by myself.   My results, therefore,
must be regarded as a confirmation and a demonstration
of his.  Meissner's method will  be spoken of under the
head of the  horopter.
   Laws of  Parallel and of Convergent Motion Compared.
—We  will now formulate the laws of convergent mo-
tion, and at  the same time contrast  them with  those of
parallel motion.
   1. When the eyes move in the primary plane in the
        * "Archives des Sciences," tome iii, 1858, p. 160. 
190    DISPUTED  POINTS IN BINOCULAR VISION.

same direction (parallel motion), there is no torsion ; but
when they move in that plane in opposite directions, as
in convergence, they rotate outward.
    2. When the visual plane is  elevated and the eyes
move in  the  same direction by parallel motion, then
lateral motion to the right produces torsion to the right,
and to the left, torsion to the  left; but when, on the
contrary,  they move in opposite directions, as  in con-
vergence, then  as  the right eye moves to  the left, i. e.,
toward  the nose, it rotates to the right, and  as the  left
eye moves toward the nose, i. e.,  to the right, it rotates
to the left.  If Listing's law operated at all in this case,
as  it acts in the  opposite direction, it would  tend to
neutralize the effects of convergent  rotation; but such
is not the fact.  On  the contrary, as we have seen, the
outward rotation  increases with  elevation of the visual
plane.
    3. When the visual plane is depressed, and the eyes
move from side to side by parallel motion, then lateral
motion to the right is attended with torsion to the left,
and motion to the left  with torsion to  the right. Also
when the eyes move by convergent motion in opposite
directions, they rotate in the same  direction as in  the
case of parallel  motion; but there  is this great differ-
ence : that while in parallel motion the torsion increases
with the angle of depression, in  convergent motion  it
decreases to zero at 45°.  If Listing's law operated at
all  in this case, it would  cooperate  with and increase
the effect of convergent motion; but  the very  reverse
is the  fact, the  rotation decreasing with the angle of
depression.
    4. We have  already shown that the so-called torsion
of parallel motion is not  a true rotation on the optic
axes, but only an apparent rotation, the result of refer- 
            LAWS  OF CONVERGENT MOTION.        191

ence to a new spatial meridian not parallel with  the
primary meridian.   On the contrary, the rotation pro-
duced  by convergent motion is a  true rotation  on  the
optic axes, as  shown by the fact that  one eye without
change of position  will rotate  in sympathy with  the
convergent  motion  of  the other  eye (experiments  4
and 5).
   It  is evident, then, that when  the eyes move in the
same  direction parallel to  each other, as in ordinary
vision  of distant objects, then all their motions are gov-
erned by Listing's  law; but when, on the contrary, they
move in opposite directions, as in convergence, then the
law of Listing is  wholly abrogated,  or  else overborne,
and another law reigns in its place.
              9 
CHAPTER  II.
               THE  HOROPTER.

   If we look at  any point, the  two visual lines con-
verge and meet at that point.  Its two images therefore
fall on corresponding  points of the two retinse, viz., on
their central spots.  A small  object at  this point of
convergence is seen absolutely  single.  We have called
this point " the point of sight."  All objects beyond or
on this side the point of  sight are seen double—in the
one case homonymously, in the  other heteronymously
—because their images do  not  fall  on corresponding
points of the two retinae.  But objects below or above,
or to one side or the other  side  of the point of sight,
may possibly be seen  single also.  The sum of all the
points which are  seen single  while the point of sight
remains unchanged is called the horopter.
   Or it  may be otherwise  expressed thus: Each eye
projects its own retinal images outward into space, and
therefore has its own field of view crowded with its own
images.  When we look at any  object, we bring the
two external images of that  object together, and super-
pose them at the  point  of  sight. Now the point of
sight, together with the images of all other objects or
points which coalesce at that moment, lie in the horop-
ter.  The images of all  objects  lying in the horopter 
TD.E  HOROPTER.
193
fall on corresponding  points, and are seen single; and
conversely, the horopter is the surface (if it be a surface)   »
of single vision.
    Is the horopter a surface, or is it only a line f  In
either case, what are its form and position ? These ques-
tions have tasked the ingenuity of physicists, mathemati-
cians, and physiologists.   If the position of correspond-
ing points were certainly known, and invariable in ref-
erence to a given spatial meridian, then the question of
the horopter would be a purely mathematical one.  But
the position of corresponding  points  may  change in
ocular motions.  It is evident,  then, that it is only on
an experimental basis that a true theory of the horopter
can be constructed.   And yet the experimental deter-
mination, as usually  attempted, is very  unsatisfactory
on account of the indistinctness  of perception of objects
except very near the point of sight.  Therefore experi-
ments  determining  the  laws  of ocular motion,  and
mathematical  reasoning based upon these laws, seem to
be the only sure method.
    The most  diverse views have therefore been held as
to the nature and form of the horopter. Aguilonius, the
inventor of the name, believed  it to be a plane passing
through  the point of sight and perpendicular  to the
median line of sight.   Others have believed it to be the
surface of a sphere passing through the optic  centers
and the  point of  sight;  others, a torus  generated by
the revolution of a circle  passing through the optic
centers and the point of sight, about a  line joining the
optic centers.   The subject has  been investigated with
great acuteness by Prevost, Miiller, Meissner, Claparede,
and finally by Helmholtz.  Prevost and  Miiller deter-
mine in it, as  they think, the circumference of a circle
passing through the optic centers and  the point of sight. 
194     DISPUTED POINTS IN BINOCULAR  VISION.

(the  horopteric circle), and a  line passing through the
point of sight and  perpendicular to  the plane of the
circle (horopteric vertical).   The  horopteric  circle  of
Miiller  is shown  in  Fig. 66, in which 0 0'  is the line
between the optic  centers, n n' the nodal points  or
points of ray-crossing, A  the  point of sight, and B  an

                        Fig. 66.
                       ___A
 object to  the left and situated  in  the circumference
 of the circle.   Of course, the images of A  fall on the
 central spots c c'.   It is seen also that  the images of B
 fall  at b b', at equal distances from the  central spots
 c c', one on the nasal half and one on the temporal half,
 and  therefore on corresponding points.   The horopteric
 vertical of Miiller passes through A  and perpendicular
 to the plane of the circle (i. e., of the diagram).
   Claparede makes the horopter a  surface, of such a
 form that it contains a straight line passing through the
point of sight and perpendicular to the visual plane, and 
                    THE HOROPTER.                195

also such that every plane passing through the optic cen-
ters makes by intersection with this surface the circum-
ference of a circle.   In other words, he thinks that the
horopter   is  a  surface
which contains the  ho-
ropteric vertical, B  A
B', Fig. 67, and the ho-
ropteric circle, O A 0',
and in addition is fur-
ther  characterized  by
the fact that the inter-
section with it of every
plane  passing  through
the optic  centers  O 0'
upward  as 0 B 0' or
downward as O B' O' \z
also a circle.   It is evi-
dent  that,  as these cir-
cles increase in size up-
ward  and  downward,
the horopter according
to  Claparede is a  surface  of  singular and complex
form.
    Helmholtz arrives at results entirely different.   Ac-
cording to  him, the horopter varies  according to the
position  of the point of  sight, and is therefore  very
complex.   He sums up his conclusions thus :  *
    " 1. Generally the horopter is  a line of double cur-
vature produced by the  intersection  of two hyperbo-
loids, which in some exceptional cases may be changed
into a combination of two plane curves.
    " 2. For example, where the point of convergence
   * Croonian Lecture, in " Proceedings of the Royal Society," xiii (1864),
p. 197; also "Optique Physiologique," p. 901 et seq.
 
  196    DISPUTED POINTS IN BINOCULAR VISION.

  (point of  sight) is situated in the median  plane of the
  head, the horopter is composed of a straight line drawn
  through the point  of  convergence, and a conic section
  going through the  optic centers  and intersecting the
  straight line.    >
     " 3. When the  point of convergence is situated in
  the plane wThich contains the primary directions of both
  visual lines (primary visual plane), the horopter is com-
  posed of a circle going through that  point and through
  the optic centers (horopteric circle), and a straight line
  intersecting the circle.
     " 4. When the point of convergence is situated both
  in the middle plane of the head and in the primary
.  visual plane, the horopter is composed of the horopteric
  circle  and of a straight line going through that point.
     " 5. There is only one  case in  which the horopter is
  a plane, namely:  when the point of  convergence is sit-
  uated in the middle plane  of the head and at an infinite
  distance.   Then the horopter  is a plane parallel to the
  visual  lines, and  situated  beneath them at a distance
  which is nearly as great as the distance of the feet of
  the observer from his eyes when he is standing.  There-
  fore, when we look straight forward at a point on the
  horizon, the horopter is a horizontal plane going through
  our feet; it is the ground  on which we stand.
     " 6. When we look not at an infinite distance, but
  at  any point  on the ground on which we stand which
  is equally distant from the two  eyes, the horopter  is not
  a plane, but the straight line which  is one of its parts
  coincides with the ground."
     Some  attempts  have  been made to establish the
  existence of the horopteric circle of Miiller by means
  of experiments.  A plane  is prepared and pierced with
  a multitude of holes into which pegs may be set.   The 
THE HOROPTER.
197
eyes look horizontally over the plane on one peg, and
the others are arranged  in  such wise  that they appear
single.  It is found that they must  be arranged in a
circle.  I have tried repeatedly, but in vain, to verify
this result.  The difficulty is the extreme indistinctness
of perception at any appreciable distance from the point
of sight.  But, as a general fact, the results reached by
the observers thus far mentioned have been reached by
the most refined  mathematical calculations,  based on
certain premises concerning the position of correspond-
ing points and on the laws of ocular motion.   We will
examine only those of Helmholtz, as being the latest
and most authoritative.
   Helmholtz's results are based upon the law of Lis-
ting as governing all the motions of the eye, and  upon
his own peculiar  views concerning the relation between
what he  calls the apparent and the real vertical me-
ridian of  the retina.  The real vertical meridian of the
eye  is the line  traced  on the retina by the image of a
really vertical linear object when the median plane of
the head is vertical and the eye in the primary position.
The  apparent vertical meridian of the eye is the line
traced by the  image of an apparently vertical  linear
object in the same position of the eye.  This is also
called the vertical line of demarkation, because it di-
vides the retina into two halves which correspond each
to each  and point for point.  Now, according to Helm-
holtz, the apparent vertical  meridian or vertical line
of demarkation does not coincide with the real vertical
meridian, but makes with it in each eye an  angle of
1^°, and  therefore with  one another in the two eyes of
2.i°.  The horizontal meridians of the eyes, both real
and  apparent, coincide completely.   Therefore,  if  the
two eyes  wrere brought together in such wise that their 
198     DISPUTED POINTS IN BINOCULAR VISION.

real vertical and horizontal meridians should coincide,
their  apparent horizontal  meridians would also  coin-
cide ;  but the apparent vertical meridians would  cross
                                       i
each  other  at the central spot thus—
                                       r
an angle  of 2£°.  For this reason a perfectly  vertical
line  will  appear to  the right eye not  vertical, but in-
clined to the left, and to  the left  eye inclined to the
right.  In order  that a line shall appear perfectly ver-
tical  to one eye, it must incline for the right  eye 1J°
to the right, and for  the  left 1J0 to the left.   But a
horizontal line appears truly horizontal.  Therefore an
upright rectangular cross will appear to  the right eye

thus-----—, and  to  the  left eye thus-----1—.   The

inclination of these lines is, however, exaggerated.  If,
therefore, according to Helmholtz, we make a diagram
of which one  half is composed of black lines on white
ground, and  the other of white lines on black ground,
like  those already used, but in which, while the hori-
zontals run straight across  horizontally, the verticals on
the right  half are inclined 1£° to the right, and on the
left half the same amount to the left (Fig. 68), then, on
combining these by gazing beyond the plane of  the dia-
gram (i. e., with parallel eyes), either  with the naked
eye or with the stereoscope, the verticals will be seen
to come together parallel and unite perfectly.
   Now Helmholtz's views of the form of the horopter
are based wholly on this supposed  relation of  real and
apparent vertical.  Take for  example  his case of the
eyes  fixed on a distant point  on the horizon.   In this
case, he says, " the horopter is the ground on which we
stand."   This is true if the relation above mentioned is
making 
THE HOROPTER.                199

true; for, with an interocular distance of 2| inches, two
lines drawn through the optic centers, each inclined 1J°
with the  vertical and  therefore 2£° with  each other, 
200     DISPUTED POINTS IN BINOCULAR VISION.
would in fact meet about  5 feet below—i. e., about the
feet.  If, therefore, we place  two actual  rods together
on the ground between the feet, and the upper ends be-
fore the pupils, the eyes being parallel, it is evident that
the image of the right rod on the right retina and that
of the left rod on the left  retina would fall exactly on
Helmholtz's apparent vertical meridian, and, if Helm-
holtz's views be  correct, on the vertical lines of  demar-
kation and on corresponding  points of the retinae, and
thus would be bin ocularly combined and seen as a single
line lying along the ground to infinite distance.  And
conversely, with the eyes parallel and  the lines of de-
markation inclined 1£° with the vertical, a rod lying on
the ground to infinite distance would cast its images on
these  lines, and therefore be seen single throughout.
    There are several curious questions which force them-
selves on our attention here if  Helmholtz's view be true.
    1. If we suppose the two eyes to be placed one on the
                  other, so that the real vertical meridians
                  coincide, we have  already  seen that
                  Helmholtz's apparent verticals or lines
                  of demarkation will cross each  other
                  like  an X, as in Fig. 69, making with
                  each other an angle of 2-J0.  Now the
                  two rods 2^  inches apart at the height
                  of the eyes,  and meeting below at the
the eetinje superposed, feet, or the rod lying along the ground
  -r r, line of demarka- ^ infinite distance, WOuld OCCUpy with
  tion of right eye; 11,                  '           -r«/
  line of demarkation of their images only the upper  half of
  lett eye'           the X.  But suppose the two rods, in-
stead  of stopping opposite the eyes, to continue upward
to the limits of the field of view.  Obviously this upper
half would cast images on  the lower half of  the X, and
therefore would  be seen single also.  Where shall  we
 
THE HOROPTER.
201
refer them ?  Or, to express it differently, the horopter
with the eyes looking at a distant horizon, according to
Helmholtz, is the ground wTe stand on; but this is evi-
dently pictured on the upper  halves  only of the two
retinae.   Where is  the other half of the horopter cor-
responding to the lower halves of the retinae %
    2. Again: According to Helmholtz, in looking at
a distance the horopter is the ground we stand on, and
he  gives this  as the  reason  why distance  along the
ground is more  clearly  perceived than in  other  posi-
tions.*   On the contrary, it seems to me that it would
have  just the reverse effect.  If the horopter were the
ground Ave stand  on, then relative distances on the
ground could not  be  perceived by binocular perspec-
tive at  all; for this is wholly dependent on  the exist-
ence of double images, which  could not occur in this
case by the definition of the  horopter.  It would  be
therefore only by  other forms  of  perspective that we
could  distinguish relative distance along the ground.
But that we do perceive  perspective of the ground
binocularly—i. e., by double images—is proved by the
fact that the perspective of  the receding ground is very
perfect  in stereoscopic pictures, where  the  images of
nearer  points  are  necessarily double;  for the  camera
has no such distinction between real and apparent ver-
tically as Helmholtz attributes to the eye.
    But  it is useless to argue the point any further, for
I  am  quite sure that the  property which  Helmholtz
finds in his eye is not general, and therefore not nor-
mal.   We have seen that in convergence the eyes  ro-
tate outward, so as to bring about the  very condition of
things  temporarily which Helmholtz finds  permanent
in  his  eyes.   I have  therefore thought it  possible, or
                    * Op. cit., p. 923. 
202     DISPUTED POINTS IN BINOCULAR VISION.

even probable, that the same habits in early life which,
by constant adapting of the eyes  to vision of near ob-
jects, finally  produce myopy,  may  also, by  constant
slight rotation of the eyes outward  and  distortion in
convergence on near objects, finally bring about a per-
manent condition of slight distortion  and outward rota-
tion of 1^°.  Helmholtz is slightly myopic*
   However this may be, I am sure there is no such
relation between real and apparent vertical meridian in
my eyes as that spoken of by Helmholtz.   All the ex-
periments supposed to prove such relation fail complete-
ly with me.   A vertical rectangular cross appears rectan-
gular to  either eye.  The lines of Helmholtz's diagram,
Fig. 66,  when combined beyond the plane of the dia-
gram, either by the naked eyes or by a stereoscope, do
not come together parallel, but with a decided  angle,
viz., 1J°.  But when I turn the diagram upside down,
and combine by squinting, then the vertical lines, being
inclined  the other way, as in my diagram, Fig. 61, com-
bine perfectly by outward rotation of the  eyes.  I have
constructed other diagrams with less and less inclination
of the verticals, until the inclination was only 10', and
still I detected the want of  parallelism when combined
beyond  the plane of the diagram.  Beyond this limit
I could  not detect it, but I believe  only because the
limit of  perception was passed; for when the lines are
made perfectly vertical, they  come together  perfectly
parallel and unite absolutely.   It  is certain, therefore,
that  in  my eyes the vertical line  of demarkation coin-
cides completely with the true vertical meridian.
   Meissnerf alone,  of  all writers with whom I am
   * Op. cit., p. 914.
   f Meissner, " Physiologie des Sehorgans"; also " Archives des Sci-
ences," vol. iii (1858), p. 160. 
THE HOROPTER.                203
acquainted, attempts to determine the horopter by ex-
periment.  According  to him, if  a stretched thread be
held in the median plane at right  angles to the primary
visual plane, about 6 to 8 inches distant, and the point
of sight be directed on the middle, the thread will not
appear single, but the two images will cross each other

                           T\ll
at the point of sight thus—  V  ,»•/ being the right-

eye  image, and  I V  the  left-eye  image.  Now, as the
images are heteronymous at the upper end and homo-
nymous at the lower end, it is evident that they will
unite at some farther point above and some nearer point
below.  By inclining  the thread in the manner indi-
cated—i. e.,  by carrying the upper  end farther  and
bringing the lower end  nearer—the two images come
together more and more, until at a certain angle of in-
clination, varying with the distance of the point of sight,
they unite perfectly. The thread is now in the horopter.
    Experiment.—I find  that the best way  to succeed
with Meissner's  experiment  is  as follows: Hold a
stretched black thread parallel with the surface of 'the
glass of an open window, and  within  half an inch of
it.   Now, with the eyes  in  the primary position, look,
not  at the thread,  but at some spot  on the glass.  It
will be seen that the double images of the  thread  are
not parallel, but make a small angle with each  other,

thus—  \ / .  Now bring the lower end nearer the ob-

server very gradually.  It will be seen that  the double
images  become  more  and more  nearly parallel,  until
at a certain angle of inclination  the parallelism is per-
fect.  I have made several experiments  with a view
to measuring the  angle of inclination for different dis- 
204    DISPUTED POINTS IN BINOCULAR VISION.

tances of the point of  sight.  I find that for 8 inches
the inclination is  about 7° or  8°;  for  4 inches, about
8° or 9°.   It seems to  increase as the point of sight is
nearer.  But of this  increase  subsequent experiments
make me doubtful.
   Meissner's results may be summarized thus:
   1. With the eyes in the primary position and  the
point of sight at  infinite  distance, the  horopter  is a
plane perpendicular to the median line of sight (plane
of Aguilonius).
   2. For  every nearer point of sight in the primary
plane, the  horopter is not  a surface at all, but a  line
inclined  to the visual  plane and dipping toward  the
observer, the inclination increasing with  the nearness
of the point of sight or degree of convergence.
   3. In turning the  plane of vision upward, the in-
clination of the horopteric line increases.  In  turning
the  plane  of vision downward, the inclination of  the
horopteric line decreases, until it becomes zero at  45°,
and  the horopteric line expands  into  a  plane  passing
through  the point of  sight and perpendicular to  the
median visual line.
   Furthermore, Meissner attributes these results to a
rotation of the eyes on the  optic or visual axes outward;
so that  the vertical lines of demarkation,  C D, C D',
Fig. 70, no longer coincide perfectly with the vertical 
THE HOROPTER.
205
meridians A B, A' B', nor the horizontal  lines of  de-
markation G II. G' II' with the horizontal meridians
E F,  E' F', as they do when the eyes are parallel, but
cross  them at a small angle.  With eyes  parallel, the
images of a vertical line will fall on the vertical lines of
demarkation  (for these then coincide with  the vertical
meridians) and be seen single.  But if the eyes rotate
outward in convergence, then the images of a vertical
line will no longer fall on the vertical lines of demar-
kation, and  therefore will be seen double except at the
point of sight.  In order that the image of a line shall
fall on  the vertical lines  of demarkation and  be seen
single, with  the eyes  in this rotated condition, the line
must  not be vertical, but  inclined with the upper end
farther away and  the lower end nearer to the observer.
It is  evident also that under these circumstances the
horopter can not be a surface, but is restricted to a line.
This requires some explanation.
   If the eyes be converged on a vertical line,  and then
rotated  on their  optic axes, as we  have seen, the line
will  be  doubled  except  at the point  of sight.  This
doubling is the result of horizontal displacement of the
two images  in opposite directions at the two ends—the
upper ends  heteronymously, the  lower ends  homony-
mously.   Now, since  heteronymous images unite by car-
rying the object farther away and homonymous images
by bringing it nearer, it is evident that if the line be in-
clined by carrying the upper end farther and bringing the
lower end nearer, the two  images will unite completely,
and thus form a horopteric line.  But all points to the
right  or left of this horopteric line will also double by
rotation  of the eyes; but this  doubling is by vertical
displacement, as shown in Fig. 70.  Now doubling by
vertical displacement can not be remedied by increasing 
206     DISPUTED POINTS IN BINOCULAR VISION.
or decreasing distance, because the eyes are separated
horizontally.  It is therefore irremediable.   Hence no
form  of surface  can  satisfy the conditions of single
vision  right  and left  of the horopteric line.  Hence,
also, the restriction of the horopter to a line, and the
inclination of that line on the plane of vision, are ne-
cessary consequences of the  rotation of the eyes  on
their viusal axes.  This rotation I have already proved
in the  most conclusive manner by experiments detailed
in the  last chapter.
   It will  be seen by reference to the preceding chap-
ter that my results coincide perfectly  with those of
Meissner, although I  was ignorant of  Meissner's  re-
searches when I  commenced  my experiments  many
                  years ago.   The end in view in the
                  two cases,  and  also  the methods
                  used, were different.   Meissner was
                  investigating  the question of  the
                  horopter, and outward  rotation of
                  the eyes was  the logical inference
                  from the position  of the horopter
                  discovered by him.   I was investi-
                  gating the laws of convergent mo-
                  tion, and the nature of the horopter
                  was a logical consequence of the out-
                  ward rotation  which  I  discovered.
                  Meissner's method is, however, far
                  less refined and exact than mine.
                      I  have also proved the inclina-
                  tion of the horopteric line by direct
                  experiments by my method.
   Experiment  1.—If two lines, one black on  white
and the other white  on black, be drawn with an  in-
clination of  1£°  with the vertical,  and therefore 2£°
 
THE HOROPTER.
207
with each other, and the eyes be brought so near to any
points a a, Fig. 71 (taking care that the visual plane
shall  be perpendicular to  the plane of the diagram),
that these shall unite beyond the plane of the diagram
at the distance of 7 inches, the two lines will coincide
perfectly.  If then the diagram be turned upside down,
and the lines be again united by  squinting—the dia-
gram being in this case a  little farther off,  so that  the
point of sight shall again be 7 inches—the coincidence
of the  lines will be again  perfect.   Fig. 72—in which
R and I represent the right and left eyes respectively,
a H and  a' II the lines to be combined  in these two
positions,  and A the point of sight—will explain how
the combination takes place.   The line H A II is the
horopteric line.
    This experiment is difficult to make, but I am quite
confident  of  the reliability of the results reached.   I
made many experiments with different degrees of in-
clination  of  the lines a H,  a' II, and therefore  with
different degrees of convergence, and many calculations
based on these experiments, to determine the inclination
of the horopteric line  for different degrees of conver-
gence.  But  the experiments are so difficult that, while 
208     DISPUTED POINTS IN BINOCULAR VISION.
in every case the inclination of the horopteric line was
proved, the  exact angle could not be  made out with
certainty.   It seemed to me about 7° for all  degrees of
convergence, and  therefore for all  distances.  It cer-
tainly does not seem to increase with the degree of con-
vergence,  as maintained by Meissner.
   Experiment 2.—I next adopted another and I think
a better method.  I used a  plane and diagram covered
with true verticals only, as  in Fig. 73.   I placed this,
instead of vertical as in previous experiments, inclined

                        Fig. 73.
7°, and therefore in the supposed position of the horop-
ter.  Placing the face in a vertical position and the
plane of vision horizontal—i. e., my eyes at the same
height as the little  circles—I combined these succes-
sively, and watched how the lines came  together.  I
found  that when inclined 7° all the lines, even the far-
thest apart—viz.,  30 inches—came together perfectly
parallel.  I then tried the plane inclined  8°; the par-
allelism was  still  complete  for  all degrees  of conver-
gence.   But  when the plane was  inclined  9°, the in-
clination of the lines in coming together successively 
THE  HOROPTER.
209
was  distinctly  perceptible.  I am sure therefore that
the true inclination is about 7° or 8°.
   Such are the phenomena; now for the interpretation.
It will be observed that when the plane represented by
the diagram fig. 73 is  inclined to the visual plane, all
the vertical lines converge by perspective; the conver-
gence increasing with the distance from the central line,
as in Fig. 74, which represents such an inclined plane
referred  to a plane  perpendicular to  the  visual plane.
By calculation  and careful plotting, I  find that at the
Fig. 74.
                Projection of Plane inclined 8°.

distance of 15  inches  the convergence of the first two
lines, 6  inches  apart,  for a plane inclined  8°, is each
about 1° 31', or to each other 3° 2';  of the second pair,
12  inches apart, 3°  3' each, or 6° 6'  to each other; of
the third pair, 18 inches apart, 4°  35' each, or  9° 10'
to each other;  of the fourth pair, 24 inches  apart, 6° 7'
each, or 12° 14' to each other; of the fifth pair, 30 inches
apart, 7° 40' each, or 15°  20' to each  other.  Therefore,
an increasing rotation  of  the eyes outward is necessary
to bring these  together parallel.  The distance of the
point of sight  measured from the optic centers  varied 
 210    DISPUTED  POINTS IN  BINOCULAR  VISION.

 from 4| inches in the first to 1\ inch in the last case;
 but the inclination of the horopteric line was the same
 in every case.  This is probably the most accurate means
 of determining by direct experiment both the horopter
 and the degree of rotation of the eyes for every degree
 of convergence of the optic axes.
    Experiment  3.—I next  tried the same experiment
 with the visual  plane depressed 45°, but yet perfectly
 horizontal.  In this position, on combining the vertical
 lines, I find that they retain perfectly their natural per-
 spective convergence.   On decreasing  the  inclination
 of  the diagram the  perspective convergence  becomes
 less and less, until when the plane of the diagram  is
 vertical the lines come  together again  parallel for all
 degrees of convergence,  as already found in the  previ-
 ous experiment.   I conclude therefore that in turning
 the visual plane downward the inclination of the horop-
 teric line becomes less and  less, until when the visual
 plane is depressed 45° it becomes perpendicular to that
 plane, and at the same time expands to a surface.
    In turning the visual plane  upward, I find,  espe-
 cially for high degrees of convergence, that I must in-
 cline the plane of the diagram more than 8° (viz., about
 10°) in order that  the lines shall come together parallel.
 From this I conclude a higher degree of rotation  of the
 eyes and a higher inclination of the horopteric line.
    The points on which  I do not confirm Meissner are:
 1. The increasing inclination of the horopteric line with
 increasing nearness of the point of sight.   I  make  it
 constant.  2.  I think it  probable also that  Meissner  is
 wrong in supposing that the horopter, when the visual
 plane is depressed 45°, is a plane.  It is certainly a sur-
face, but not a plane ; for it  is geometrically clear  that
points  in a perpendicular plane to the right or left of 
THE HOROPTER.
211
the point of sight can not fall on corresponding points of
the two retinae.  The horopter in this case is evidently
a curved surface.  I do not  undertake to determine its
nature by mathematical calculation, and the experimen-
tal investigation is unsatisfactory for the reason already
given, viz., the extreme indistinctness of  perception of
points situated any considerable distance from the point
of sight in any direction.
   In regard  to the horopter I consider  the  following
points to be well established:
   1.  As a necessary consequence of the outward rota-
tion of the eyes  in convergence, for all distances in the
primary visual plane the horopter is a line inclined to
the  visual plane, the  lower end  nearer  tne observer.
But  whether the inclination is constant, or increases or
decreases  with distance, I have not been able to deter-
mine with certainty.   It is probably constant.
   2.  In  depressing the visual plane, the inclination of
the  horopteric line  becomes less and  less, until when
the visual plane is inclined 45° below the primary posi-
tion the horopteric line becomes  perpendicular to  the
visual plane, and at the same time expands into a sur-
face.  The exact nature of that surface I have not at-
tempted to investigate, for  reasons already explained;
but it is evidently a curved surface.
   3.  In  elevating  the visual plane, especially with
strong convergence, the  inclination of the horopteric
line  increases.
   Finally, the question naturally occurs: Of what ad-
vantage is this outward  rotation of the eyes,  and  the
consequent  limitation  of  the horopter to a line ?  Or is
it not rather a defect ?   Should the law of Listing be re-
garded as the ideal  of  ocular motion under all  circum-
stances, and should  the departure from this law in the 
212     DISPUTED  POINTS IN BINOCULAR VISION.

case of convergence be  regarded as abnormal ?   Or  is
there some useful purpose subserved by the rotation of
the eyes on their optic axes?   I  feel quite sure that
there is a useful purpose subserved; for there are spe-
cial  muscles adapted to  produce this rotation, and the
action of these muscles is consensual with  the  adjust-
ments, axial and focal, and with the contraction of the
pupil.  This purpose I explain as follows:
   A general view of objects in a wide field is a neces-
sary condition of animal life in its  higher phases; but
an equal distinctness of  all objects in this field would
be fatal to that thoughtful attention which  is necessary
to the development of the higher faculties of the human
mind.  Therefore the human eye is so constructed and
moved as to restrict as much as possible the conditions
both  of distinct vision and of single vision.  Thus, as
in monocular vision the  more elaborate structure of the
central spot restricts distinct vision to the visual line,
and focal adjustment still further restricts it to a single
point in that line, the point of  sight, so also in binocu-
lar vision axial  adjustment restricts single vision to the
horopter, while rotation on the optic axes restricts  the
horopter to  a single line. 
                  CHAPTER  III.

 ON SOME FUNDAMENTAL PHENOMENA OF BINOCULAR
    VISION USUALLY OVERLOOKED, AND  ON A  NEW
    MODE OF DIAGRAMMATIC REPRESENTATION FOUND-
    ED THEREON.

    In all that I have said thus far,  I have made use of
 the ordinary mode of representing binocular visual phe-
 nomena.  I have done so because I
 could thus make myself more easily
 understood.  But it is evident on a
 little reflection that the usual dia-
 grams do not  in any case represent
 the real visual facts—i. e., the facts
 as they really seem to the binocular
 observer.
    Thus, for example, if a, B, and
 c, Fig. 75, be three objects in the
 median plane, but at different dis-
 tances, and the two eyes, R and L,
 be  converged  on B, as  already ex-
 plained, a and c will be both seen
 double—the former heteronymous-
 ly,  the  latter  homonymously.   It
 will be observed that in the dia-
gram the double images of both  a and c are referred to
the plane of sight P P.  Now every one who has ever
tried the experiment knows that the double images are
not thus referred in  natural vision; but, on the con-
 
214     DISPUTED POINTS IN BINOCULAR VISION.

trary, they are seen at their real distance, though not in
their natural position.  Indeed, it is only by virtue of this
fact that we have perception  of binocular perspective.
The diagram therefore, although it truly represents the
parallactic position of the double images, does not rep-
resent truly their apparent distance.   If, on the  other
hand, we attempt in the  diagram to refer the  double
images to their real distance (observing the law of di-
rection), then they unite and form one, which is equally
untrue.  Thus, if we represent truly the visual position,
we misrepresent  the visual distance; if,  on the con-
trary, we try to represent  the visual  distance, We mis-
represent the visual position.   It is  evident therefore
that  the  usual diagrams,  while they  represent  truly
many important visual  phenomena, wholly fail  to rep-
resent truly many others, especially  the facts  of bin-
ocular perspective.
   The falseness of the usual mode of representation
becomes much  more conspicuous  if, instead of  two or
more  objects, we  substitute a continuous  rod  or line.
In this case the absurdity of  projecting the double im-
ages on the plane of sight  is so evident that it is never
attempted.  The  mode universally used for represent-
ing the visual result when a rod is placed in the median
plane  is shown  in Figs. 76-79, of which Fig. 76 repre-
sents the actual position of the rod in  the median plane,
and the actual position of the visual lines when the eyes
are fixed on the nearer end A  ;  Fig. 77, the same when
the eyes are fixed on the farther end  B; and Figs. 78
and 79, the visual results  in the two cases  respectively.
Now it will be observed that  in both these figures rep-
resenting visual results (Figs. 78 and 79) the image of
the rod belonging to  each eye is coincident with the
visual line of the other eye,  and therefore makes an 
ON SOME FUNDAMENTAL PHENOMENA.
215
angle with its own visual line equal to the visual angle
R A I, R B I.  But this is not true, for Figs. 76 and
77 show that it ought to make but half that angle.  If
these figures therefore truly represent the position of
the double images  (as indeed  they do), then they do
not represent the visual  or apparent position of the
visual lines.   The truth is, in natural vision the visual
             10 
216
DISPUTED POINTS IN  BINOCULAR VISION.
lines are shifted, as well as the images of all objects not
situated at the point of sight, and to the same degree,
so that the position of such objects relative to the visual
lines is perfectly maintained in the visual result.
   It is evident  then that  figures constructed  on the
usual plan, while they give correctly the place and dis-
tance of  objects seen single, fail  utterly to give the
place of  double  images.  They are well  adapted to
express  binocular combination of  similar objects or
similar figures on the plane of sight,  but are  wholly
inadequate to the expression of the facts of  binocular
perspective, whether in natural objects or scenes or in
stereoscopic pictures.
    In an article published in  January,  1871,* I  pro-
posed, therefore, a new and I am convinced a far  truer
mode of diagrammatic representation of the phenomena
of binocular vision,  applicable alike to  all cases.  I am
satisfied that if this method had always  been used, much
of the confusion and many of the mistakes to be found
in the writings  on  binocular vision would  have been
avoided.   But it is evident  that such  a new and  truer
method must be founded upon some fundamental bin-
ocular  phenomena  usually overlooked.   I  must  first
therefore enforce these.  They may be compendiously
stated in the form  of two fundamental laws.  It will
be best, however, before formulating them, to give some
familiar experiments, and then to give the laws  as an
induction from the facts thus brought out.
    Experiment 1.—If a single  object,  as for example a
finger, be held before the eyes in the median plane, and
the eyes be directed to a distant point so that their axes
are parallel, the  object will of course  be seen  double,
the  heteronymous images  being separated from  each
      * "American Journal of Science," Series III, vol. i, p. 33. 
         ON  POME FUNDAMENTAL  PHENOMENA.      217

other by a space exactly eq ual to the interocular space.
Now, the nose is no exception to this law.  The nose is
always seen double and bounding the common field  of
view on either side.
    Experiment  2.—If two similar objects be placed
before the eyes in the horizontal plane of sight, and
separated  by a  space  exactly equal to  the interocular
space, and the eyes be directed to a distant point so that
their axes  are parallel and the two visual lines  shall
pass through the two objects, then both objects will  be
doubled, the  double images of  each  being separated
by an interocular space; and therefore two of the four
images—viz., the right-eye  image of the right object,
and the left-eye image of  the left object—will combine
to  form a single binocular image in the middle ; while
the right-eye image of the left  object will be seen to
the left, and the left-eye  image of the right object  to
the right.   Thus there will be  three  images  seen—a
middle  binocular image,  and two monocular  images,
one on each  side, that on the right side belonging  to
the left eye alone, and that on  the left to the right
eye alone.   Now, the eyes themselves are no exception to
this law.  In binocular vision the eyes themselves seem
each to double—two of the images combining  to form
a  binocular eye in the middle {ceil eyelopienne), while
the other  two are  beyond the two images of  the nose
on either side.  Each  eye seems  to itself to occupy a
central position, while it sees (or would see if the nose
were not in the way) its fellow on the other side of the
double images of the nose.
    In other words, in  binocular vision,  when the optic
axes are parallel, as  in gazing on a  distant object, the
whole field  of view, wTith all its  objects, including the
parts of the face, is shifted by the  right eye a half inter- 
218     DISPUTED POINTS  IN  BINOCULAR  VISION.

ocular space to the left, and by the left eye a half inter-
ocular space  to the right, without  altering the relative
position of parts.  It is evident that, by this shifting in
opposite directions, the two  eyes with their visual lines
are brought together in perfect coincidence, so that cor-
responding points in the two retinae seem to be perfectly
united.
Fig. 80.            Fig, 81.
    The facts as thus far stated—both the actual condi-
tion of things as we know them, and  the visual results
as they seem to the binocular observer—are represented
in the following diagrams.  Fig.  80 shows the actual
condition of things, and Fig. 81 the visual result, in the
first experiment; Fig. 82 the actual condition of things,
and  Fig.  83 the binocular visual result, in  the second
experiment.  To explain further:  In Fig. 80, R and L
are the right and left eyes; N, the nose; A, the object 
         ON SOME FUNDAMENTAL  PHENOMENA.      219

in the median plane;  the dotted lines v v, the direction
of the visual lines.  Fig. 81 represents the visual results;
E being the combined or binocular eye {mil cyclopi-
enne); n and n', the two images  of the nose belonging
to the right and left eyes respectively;  V, the combined
or binocular visual line, looking between the double im-
ages a and a' of the object A; while r' is the position
Fig. 82.            Fig. 83.
of the right eye as it would be seen by the left eye, and
I of the left eye as it would be seen by the right, if the
nose were not in the way, and v and v' are the positions
of their visual lines if they were visible lines.  Fig. 82
represents the actual condition of things when two sim-
ilar objects .1 and B are before the eyes in the visual
lines v v ; and Fig.  83  is the visual result, in which a'
and  b are the monocular images, one belonging to the
left  and the other to the right eye, AB the combined 
220     DISPUTED POINTS IN BINOCULAR VISION.

or binocular image, and the other letters  representing
the same as before.
   Experiment  3.—These facts  are  brought out  still
more clearly if, instead of an object like A, Fig. 80. we
use a continuous line or rod, as in Fig. 76.  We have
seen above that, with the optic axes parallel, any object
placed in the median line of sight, at whatever distance,
is separated into two images an interocular space apart.
Fig. 84.                  Fig. 85.
Evidently, therefore, the median line of sight itself is
doubled, and becomes  two lines, which, resting on  the
nose on each side, run  out  parallel  to each other indefi-
nitely.  Between  these  two  lines  the binocular  eye
(combined eyes)  looks out along the combined visual
line at a  distant  object.  If the median line be occu-
pied by a real  visible  line or a  rod, we shall see two
parallel lines or  rods.   If the median plane be  occu- 
ON SOME FUNDAMENTAL PHENOMENA.
221
pied by a real plane, we shall  see two parallel planes
bounding the binocular field of view on each side, be-
tween which we look.
   These facts are represented  by the  diagrams Figs.
84 and 85.   In  Fig. 84, B represents a rod resting on
the root of the nose n, and held in place  by the point
of the finger A ; R and I are the two eyes,  and v and
v the two visual lines in a parallel position.   Such is
the actual condition of things.  Now Fig.  85  represents
the visual results.  It is seen that the nose  n, the rod B,
and the finger-point A of fig. 84 are all doubled, as n n',
b b', a a' of fig. 85 ; while the two eyes, R and I, and
the two visual lines, v and v, of fig. 84, are combined in
the middle as the binocular eye E, which looks out along
the combined visual line V between the  parallel rods
b b', of fig 85.
   As already stated, if instead of a rod we use a plane
coincident with the median  plane, then  the plane is
doubled, and  we  look  between  the doubled  images.
This is the case  in using the  stereoscope.  The median
plane of  the stereoscope is doubled, and between its
twro images we look out on the combined pictures.
   Experiment 1^.—An excellent illustration of the fun-
damental fact, that in binocular vision the two eyes are
moved to the middle  and  combined  into a binocular
eye, must be familiar to every one who has ever worn
spectacles.   If  the spectacles are properly  chosen, so
that the distance between the centers of the two glasses
is exactly equal to the interocular space, then we  see
but one glass exactly in the middle, through which the
binocular eye seems to look.   We would see two other
glasses, monocular images, right and left, if  these were
not hidden by the nose.  AVe do indeed see two others
in these  positions if we remove the spectacles  to such 
222     DISPUTED POINTS IN BINOCULAR VISION.

distance that the nose no longer conceals them, while we
still look through the middle glass at a distant  object.
   Many other familiar illustrations may be given.  If
we put our face against a mirror, so that forehead and
nose shall touch the glass, and then  gaze  on  vacancy,
there will be of course four images of the  two eyes in
the mirror.  Two of these, viz., the right-eye  image of
the right eye and the left-eye image of the  left eye,
will  unite to form a central binocular eye, an  image of
our own  central binocular eye, and into which  our own
seems to gaze.  The nose will be  seen double and on
each side of the central eye, and beyond the double im-
ages of the nose on either side will be seen monocular
images of the  eyes.  In other words, wTe actually see
exactly what  I have expressed in  the diagrams (Figs.
83 and 85) representing visual results.
   If, in place of the reflection  of our own face in a
mirror, we make use in this experiment of  the face of
another person, placing forehead against forehead, nose
against nose, and the eyes exactly  opposite  each other,
and gaze on vacancy, the same visual result  will follow.
Our own central binocular eye looks  between  our two
noses into another central binocular eye, situated also
between  two noses.   Other monocular eyes  are seen
beyond the noses, right and left.
   The fields of view of the two eyes are bordered by
the nose, the brows, and  the  cheeks.  Its  form there-
fore varies in different persons. It has no definite limit
on the outside.   I  reproduce  as Fig. 86 the  diagram
already used on page  91,  representing rudely  the gen-
eral  character of the field of view of  the binocular ob-
server.   I have introduced the ceil cyclopienne and the
two  monocular  images of the eyes;  and,  in  order to
make it more comprehensible, I have supposed the ob- 
         ON SOME FUNDAMENTAL PHENOMENA.      223

server to wear glasses.   In this diagram, n n is an out-
line of the nose, br of the browr, and ch of the cheek of
the right-eye field; br', n' n', and ch', the outline of the
left-eye field.   The middle space where they  overlap,
bounded on each side by the outline of the nose, n n,
n' n', is the common or binocular field occupied by the
central binocular eye E, surrounded by the single ellipse
                        Fig. 86.
of the combined spectacle-glasses.  I have  also intro-
duced in dotted outline the left  eye I and the spectacle-
rim s s as they would be seen by the right eye, and the
right eye r'  and spectacle-rim s'  s' as they would be
seen by the left eye, if the nose  were not in the way.
   First Law.—We are now in position to formulate
the first law\  I would express it thus: In binocular
vision, with the optic axes parallel, as in looking at a
distant  object, the whole field of view and  all objects
in the field, including the visible  parts of the face,  are
shifted  by the right eye a half  interocular space to  the
left, and by the left eye the  same distance to the right,
without altering the relative positions of parts; so that
the two eyes with their two visual lines seem to unite
to form a single  middle  binocular eye, and  a single 
224     DISPUTED POINTS IN BINOCULAR VISION.

middle visual line, along which  the eye seems to look.
It follows  that  any line, rod, or plane in the median
line, as also the nose itself, is doubled  heteronymously,
and  becomes two lines, rods, or planes, parallel to each
other, and  separated by a space exactly  equal  to the
interocular space.  Between the two noses, and between
the two parallel lines, rods, or planes, the  binocular eye
seems to look out along the middle visual  line upon the
distant  object.   Of course, by this shifting  of the two
fields in opposite directions, all  objects in the field are
similarly doubled.
   Thus in binocular vision the two eyes seem actually
to be brought together and superposed, and correspond-
ing points of the two retinae to coincide.   The two eyes
become actually  one instrument.  And conversely, this
apparent combination of two eyes and  their visual lines
is a  necessary consequence of  the law of corresponding
points.  For images on corresponding points are seen
single;  all objects on the two  visual  lines must impress
corresponding points, viz., the central spots; therefore
the  visual  lines  themselves, if they were visible  lines,
would be seen  single.  But where could they be seen
single except in  the middle ?   Therefore the two visual
lines must combine to form a single middle visual line.
    We will next give  experiments leading up to the
second  law. For this purpose  let us recur to  the ex-
periment  with the rod represented by Fig. 84.  We
reproduce  this as Fig.  87, in  order to compare  with  it
the  results of  subsequent experiments.  As  already ex-
plained, if the rod B be placed in the  median  plane
with the nearer end resting on the nose-root n, and the
farther end held in place by  the point of the finger A,
the eyes looking at a distant object,  as shown  in Fig.
 87, which  represents the actual condition of things, then 
ON SOME  FUNDAMENTAL PHENOMENA.

   Fig. 87.             Tm.
225
the rod,  together with nose and finger-point,  will be
doubled heteronymously and become two parallel rods,
Fig. 90.
 
226     DISPUTED TOINTS  IN  BINOCULAR VISION.

between which  the  binocular eye wTill look out  along
the binocular visual line at the distant object, as shown
in Fig. 88, which represents the visual result.
   Experiment  1.—Now, while we hold the rod in the
position represented by Fig. 87, instead of looking at a
distant object with  eyes  parallel, let  the eyes  be con-
verged on the finger-point F, so that Fig. 89  shall rep-
resent the actual condition of things.   AVe will observe
that the  double images of the rod represented in  the
visual result, Fig. 88, approach at their farther end, car-
Fig. 91.             Fig. 92.
rying all objects in the field with them, until they unite
at the point of sight F, and we have  the visual result
represented in Fig. 90.
   Experiment  2.—If by greater convergence we next
look at some nearer point B  on the rod, as  in Fig. 91,
which represents the actual relation of  parts, then Fig.
92 represents the visual result.  By comparing this with 
         ON SOME FUNDAMENTAL  PHENOMENA.      227

the previous visual results, Figs.  88 and 90, it will be
seen that the double images b V approach each other
until they unite at the point of sight, and the two im-
ages of the rod cross each other at this point, and there-
fore become again double beyond, but now homony-
mously.   If by still greater  convergence we look at  a
still nearer  point  C, Fig. 93, then  the double images
of the median rod, Figs. 87, 89, 91, will cross at the point
of sight C, and give the visual result shown in Fig. 94.
Fig. 93.                      Fig. 94.
Finally, if the point  of  sight by extreme convergence
be brought to the root of the nose, then the double im-
ages of the nose n n', Figs. 92, 94, will be brought in con-
tact, and the common or binocular field will be obliter-
ated.   In all cases it will be observed that the combined
eyes look along the combined visual lines through the
point of sight, and onward to infinite distance.
    It is evident, then, that in optic convergence, as the
two real  eyes turn in opposite directions on their optic 
228     DISPUTED POINTS IN BINOCULAR VISION.

centers, the two fields of view turn also on the center
of the binocular eye in directions opposite to the real
eyes, and therefore to each other.
   It will  be observed that in speaking of visual phe-
nomena I have used much the same language as other
writers on  this subject, and used also a somewhat simi-
lar mode of representation ; only I have substituted eyes
in the place of the nose, and put noses in  the position
of the eyes,  I have made median lines cross each other
at the point of sight, instead of visual lines, and visual
lines combine in the middle  as a true median visual
line.   In other words, I  have used the true language
of binocular vision.   I have  expressed  what we see,
rather than what we know—the  language of simple
appearance, rather than that mixture of appearance and
reality which forms  the  usual language of writers on
this subject.
   Second  Law.—The  second law  may therefore  be
stated  thus: In turning the eyes in different directions
without altering  their convergence, objects seem  sta-
tionary, and the visual lines seem  to move and sweep
over them; but when we turn the eyes  in  opposite
directions, as in increasing or decreasing their conver-
gence, then the visual lines  seem stationary (i. e., we
seem  to look in the same  direction straight forward),
and all objects, or rather their  images, seem  to move
in directions contrary to the actual motion  of the eyes.
The whole fields of view of both  eyes  seem to rotate
about a middle optic center, in a direction contrary to
the motion of  the corresponding eyes, and  therefore to
each other.  This is  plainly seen by  voluntarily, and
strongly converging the eyes on an imaginary very near
point, as for example the root of the nose, and at  the
same time watching the motion of the images of more 
         ON SOME FUNDAMENTAL PHENOMENA.      229

distant objects.   The whole field of view of the right
eye, carrying all  its  images with it, seems to rotate to
the right, and of the left eye to the left—i. e., homony-
mously.  The images of all objects, as they are swept
successively by the two visual lines, are  brought from
opposite  directions to  the  front and superposed.  As
we relax the convergence,  and the eyes move back to
a parallel condition, the two  fields with  their images
are seen to rotate in  the other  direction—i. e, heterony-
mously.  If we could  turn the eyes outward, the  two
fields and  their images would continue  to rotate  het-
eronymously.   This, which we can  not  do by  volun-
tary effort  of  the ocular  muscles,  may be done by
pressing the fingers  in the  external corners of the  two
eyes.   By pressing in the internal corners, on the  con-
trary, the eyes are made to converge, and homonymous
rotation of the fields of view is produced.
   Or the  law may  be more  briefly formulated thus:
In convergence  and divergence of  the  eyes, the  two
fields  of view rotate  in opposite directions, homony-
mously in  the former  case and heteronymously in the
latter,  about the  optic  center of the binocular eye  {ceil
cyclopienne), while the middle or binocular visual line
maintains always its position in the median plane.
   Thus, then, there are two apparent movements of
the visual fields accomplished in binocular vision. First,
there is a shifting of each  field heteronymously a  half
interocular  space.   This is involuntary and  habitual,
and would of itself double all objects heteronymously,
separating  their  images exactly  an interocular space.
Second, in convergence, there is a rotation of each  field
about  the optic center of the  ml cyclopienne (or about
an axis passing through that  center and normal to the
visual  plane), homonymously.   The necessary conse- 
230     DISPUTED POINTS IN BINOCULAR VISION.

quences of these movements are:  {a)  that the  images
of an object  at  the  point of sight are superposed and
the object is seen single, while objects on this side of
the point of sight are doubled heteronymously, and
those beyond the point of sight  homonymously;  {b)
that all objects (different objects) lying in the direction
of the two visual lines, whether nearer than  or beyond
the point of sight,  have their images  (one of each)
brought to the front and superposed;  so that the two
visual lines are under all circumstances brought together
and combined to form a single binocular visual line,
passing from the middle  binocular eye  through the
point of sight and onward to infinity.
   In all  the experiments which follow on this subject
it  is necessary to get the interocular space with exact-
ness.   This may be  done very easily  in  the  following
manner:
   Experiment.—Take a pair of dividers  and hold it
at arm's  length  against the sky or a bright cloud, and,
                   while gazing steadily at  the sky or
                   cloud, separate the points until two
                   of the four double images of the
                   points  shall unite perfectly, as  in
                   Fig. 95.   The distance between
                   the points of the dividers, equal to
                   a-a', or b-b', or c-c', is exactly the
                   interocular distance—i. e., the dis-
                   tance between the central points
                   of  the  central spots  of the two
retinae.  The only difficulty in  the way  of perfect ex-
actness in  this experiment is the want of  fine definition
of the points when the  eyes are  adjusted for  distant
vision.  This may be obviated by using slightly convex
spectacles.  The accuracy of the determination may  be
 
         ON SOME  FUNDAMENTAL PHENOMENA.      231

verified thus:  Measure the distance just determined ac-
curately on a card, and pierce the card at the two points
with small pin-holes.  Now place  the card against the
forehead and  nose, with the holes exactly in  front of
the two eyes, and  gaze through them at a distant hori-
zon or cloud.  If the measurement is  exact, the two
pin-holes will  appear as one; their coincidence will be
perfect.   As  thus determined, I  find my  interocular
space almost exactly 2\ inches (63.5 mm.).  It will be
seen that this method  is founded upon  the opposite
shifting  of the two fields of view half an interocular
space each, spoken of in the first  law.  The  two pin-
holes are seen as  one exactly in the middle, which is
looked  through by the ceil  cyclopienne; and this is
therefore one  of the very best
illustrations of such shifting
of the two eyes and their vis-
ual lines to the middle.
    We will now give some ad-
ditional  experiments illustrat-
ing: and enforcing these two
laws, and showing the absolute
necessity of   using  this  new
mode of diagrammatic repre-
sentation in all cases in which
binocular  perspective  is  in-
volved.   For this purpose  I
find it most convenient to use
a small rectangular blackboard
about 18 inches long and 10
inches wide,  Fig. 96.  Mark
two points R and I at one  end, with a space between
exactly equal to the interocular space, and  in the middle
between these points make a notch n in the edge of the
 
232.    DISPUTED POINTS IN BINOCULAR VISION.

board to fit over the bridge of the nose.   Such a board
is admirably fitted for all experiments on binocular per-
spective.
    Experiment  1.—Draw a line through the middle of
the board from the notch n, Fig. 96.  This will  be the
visible representative of the median line; and  as the
median line is used in all the experiments, this may be
made permanent.  On this line place two  pins at A and
B.   Draw also from the points I  and R dotted lines
Fig. 97.                   Fig. 98.
parallel to the median line  and to each other, as the
visible representatives of the visual lines when the optic
axes are  parallel, as when looking  at a distant object.
Now fit  the plane over the  bridge of the nose, and
place it  in a horizontal position a little below the pri-
mary plane  of vision, say half an  inch or an inch,  so
that the  whole surface is distinctly seen, and then look 
         ON SOME FUNDAMENTAL PHENOMENA.      233

beyond at a distant  object.   Leaving out the board in
the representations,  the  actual position of the lines is
shown in Fig. 97 and the visual result in Fig. 98.   Re-
membering that in all  our figures capitals represent
combined  or binocular images, simple italics right-eye
images, and primed italics left-eye images,  it will be
seen that the whole board, with all the lines and objects
on  it and  the parts of the face, has been shifted  left
and right  by the two eyes, so that the nose  and  the
median line are seen as two noses and two parallel lines
with  their pins, separated by a space  exactly equal to
the  interocular  space, and  the  two  visual lines  are
brought together and united in  the middle  to form a
common visual line  V, as if  coming from a single bin-
ocular eye E  If two small circles be drawn or a  pin
be set at the end of the dotted visual  lines in  Fig. 97,
these will be united  in the result Fig. 98, at the end of
the combined visual  line V.  There will  also of course
be seen to  the extreme right  and  left monocular images
of the dotted representatives of the visual lines, and of
the circles or pins at their farther end.  I  have  con-
nected  by vincula the images of the whole drawing,
the primed vinculum being  the image of the left  eye,
the other of the right.
   Experiment 2.—If we now erase the  parallel visual
lines v v on the  board, and draw them convergent on
the pin A, so that Fig. 99 shall represent the actual
condition, and then adjust the board again to the nose
and look at the pin A, the visual result, or what we shall
see, is given in Fig. 100.  By comparing this result with
the actual condition of things—i.  e., by comparing Fig.
100 with Fig. 99—it w^ould seem as if  the whole draw-
ing on the  board, including the eyes and nose, had been
turned  about the point of sight A  by the two eyes in 
234     DISPUTED POINTS IN  BINOCULAR VISION.

opposite directions, the right carrying  it to the position
I A E, the left eye to the position r' A E, shown by
the unprimed and the primed vinculum respectively.
           Fig. 99.                Fig. 100.
vi fatyWy

The real nature of the rotation, however, is shown by
comparing the appearance of the drawing when the
eyes are parallel with  its appearance when the eyes are
converged on A.  Fig. 101 represents the visual result
when the same drawing is viewed with the eyes  par-
allel.  By comparing  this  figure with the visual result
when the eyes converge on A (Fig. 100), it is seen that
the two  images of the whole  drawing  rotate on the
optic center of the binocular eye E, until the pins a a'
and the visual lines v v' of Fig. 101 unite to form the
binocular image A and  the binocular visual line V of
Fig. 100.   If  the eyes be converged  very gradually,
the slow approach of the points a a', carrying with them
the dotted lines v v', as if  turning on the center of the
binocular eye E, can be distinctly seen. 
ON SOME FUNDAMENTAL  PHENOMENA.      235
   Experiment 3.—If we again erase the dotted repre-
sentatives of the visual lines and draw them converging
and crossing at the nearer pin B,
as in Fig. 102, then Fig. 103 gives
the visual result.  It is as if the
whole diagram, Fig. 102, had been
rotated on the point of sight B in
two directions, viz., a right-handed
rotation  by the right eye and  a
left-handed  rotation  by the left
eye.   But  what  actually  takes
place is seen by first gazing at a
distant object and comparing the
visual result thus obtained, shown
in Fig. 104, wdth that obtained by
converging  the eyes on B, shown
in Fig.  103.  It is seen that the
double images of  the whole dia-
gram turn on the center E until b b', Fig. 104, unite to
form  B, Fig.  103, and v E, v' Eto form V E; and of
course the other lines, a a', v v', cross over and become
homonymous.  When the eyes converge as  in  this last
experiment, the points R and L on the experimental
board, Fig. 96, must be a little less than an interocular
space apart.
   Let  us now return to  the original  experiment with
three points or objects in the median line given on page
213.   We reproduce here the figure (Fig. 105) usually
used to illustrate the visual  result.  We have already
shown how impossible it  is to represent all  the visual
results in this way.   If we are bent on representing the
parallactic position of the double images, then we must
refer  them all to the same  plane, as in Fig. 105; but
this is false.  If, on  the  other  hand, we try to place
 
236     DISPUTED POINTS IN BINOCULAR VISION.

           Fig. 102.                  Fig. 103.
them at the distances at which we actually see them,
observing the law of direction, then the double images
unite, which is also false.
Fig. 104.

Fig. 105.
b      w
V\  '<V   lh'\\l/'

 
         ON SOME FUNDAMENTAL PHENOMENA.     237

   Experiment 4.—Now try the same experiment by
the use of the board, and the true mode of representa-
tion  becomes manifest.   On the median line, Fig. 106,
place three pins, and draw dotted lines to each of them
from the position of  the eyes, which  shall be the vis-
ible  representatives of either visual lines  or ray-lines.
As in  the  experiment the eyes will look at B, let the
dotted lines to B be stronger to represent  visual lines;
Fig. 106.                    Fig. 107.
then the  others  will  represent only  ray-lines.  Now
when this diagram is observed with the point of sight
at B, Fig. 106, then  the  visual result—i. e., what we
actually see on the board—will be Fig. 107.   It is seen
that the whole diagram Fig. 106 is rotated in opposite
directions about the point of sight B to make the result,
Fip;, 107.   But the real nature of the rotation is shown
by comparing the result with the eyes parallel, Fig. 108,
with the result with the eyes converged on B, Fig. 107. 
238     DISPUTED POINTS IN BINOCULAR VISION.
With the eyes parallel, the whole diagram is simply
doubled heteronymously by each eye shifting it half an
interocular space in opposite directions.  Now conver-
        fig. io9.          sinstbe eyes  slowbT>  the two
                       imajres of  Fig. 106 shown in
                       Fig. 108 are  seen to rotate on
                       E until the points b b' and the
                       dotted lines b E, b' E  unite to
                       form  B E, Fig. 107.   In do-
                       ing so,  c  c' have approached,
                       but not united; they are there-
                       fore still heteronymous, while
                       a a' have met  and passed each
                       other,  and  become homony-
                       mously double.
                          Therefore  Fig.  107  truly
                       represents all  the visual facts.
                       It gives both  the  parallactic
                       position of the points  in rela-
tion to the observer, their relative position in regard
to each  other, and their relative distance.  Or, if we
leave out in the original diagram, as complicating the
figure, all except the  necessary median line and pins,
as in Fig. 109, then the visual  result is given in Fig.
110.   Or, adding  in the visual result  only the visual
line and the most necessary ray-lines,  viz., those going
to the binocular eye, we  have Fig. 111.  This last fig-
ure we shall hereafter use to represent the phenomena
of binocular perspective.
    Application  to  Stereoscopic  Phenomena.—We wish
now to apply this new method of representation to the
phenomena of  the stereoscope.  We  reproduce here as
Fig. 112 the diagram used on page 131.  It is  seen that
while  the different distances, A and B, at which  the
 
ON SOME FUNDAMENTAL PHENOMENA.
239
foreground  and background are seen, are truly repre-
sented, no attempt  is made to represent  the double im-
ages of the foreground  when  the background is  re-
garded, or vice versa.  It is  impossible by  this usual
method to represent these double images without refer-
Fig. 109.             Fig. 110.             Fig. ill.
ring them to the same plane; but this would of course
destroy the perspective, which it is the very object of
the diagram to illustrate.  The new method,  on the
contrary, represents  the true distance of the point of
sight, and the true positions and distances of the double
images, and therefore the  true  binocular perspective.
In  other  words, it  represents truly all the  binocular
visual  phenomena.   It  will be best to preface this ex-
planation by an additional experiment.
    Experimott.—If a rectangular card, like an ordinary
stereoscopic card, or a  letter envelope, be held before
the face at any convenient distance while the  eyes gaze
on vacancy, i.  e., with the optic  axes parallel, the  two
            11 
240     DISPUTED POINTS IN BINOCULAR VISION.
images of the card will be seen to slide over each other
heteronymously, each a distance equal to a  half inter-
ocular space, and therefore relatively to each other ex-
actly an  interocular space.  If the card be longer than
                an  interocular space, there will be a
    Fin. 112.                      XT   I
                part where the two images will overlap.
                    This is represented in the accom-
                panying diagrams, of which Fig. 113
                represents the  card  when  looked  at,
                and Fig. 114 the visual  result when
                the eyes are parallel.  In  this visual
                result c c is  the right-eye image of
                the card, c' c' the left-eye image, and
                d d the  binocular overlapping.  This
                overlapped part will be opaque, be-
                cause nothing can be seen behind it
                by  either eye.   But  right and left of
                this are two transparent spaces.  That
                on  the left belongs to the image of the
                right eye, but not to that of  the left,
                and therefore the left eye sees objects
                 beyond  it.  That on the right belongs
to the left eye, but the right eye sees objects beyond it.
    If two circles, a a, be drawn on the card, Fig. 113,
an  interocular space apart, they will  unite  into a bin-
r	Fig.	113	
			fli mam
Fig. 114.
ocular circle A  in the center of the opaque part, Fig.
114, while two  monocular circles a a' will occupy the
transparent borders. 
         ON  SOME FUNDAMENTAL  PHENOMENA.      241

    By the law of  alternation spoken  of on page  93,
sometimes the right eye will prevail, the right-hand trans-
parent border  will disappear, and the whole right-eye
image c c will appear opaque.  Then the left eye pre-
vails, and the left-hand border will  disappear, and  the
whole left-eye  image c' c' will  appear  opaque.   Some-
times both borders disappear, and only the binocular
overlapping is  seen.  Sometimes  the whole double  im-
age, including both borders, becomes opaque.  But the
true  normal  binocular  appearance or visual result is
given in Fig. 114—i. e., opaque center and transparent
borders, these borders being "exactly equal to the inter-
ocular space.
    We are  now  prepared  to show how stereoscopic
phenomena may be represented  by our  new method.
In  Fig. 115, c  c represents a stereoscopic card in posi-
tion ; m s, the median screen, which cuts off the super-
numerary monocular images; a a, identical points  in
the  foreground of the  pictures, and b b, in the  back-
ground.  The  two eyes and the  nose are represented
as before by  R, L, and  n ; and a R, a I, b R,b L are
ray-lines.   Leaving  out the dotted lines  beyond  the
card, this diagram represents the actual condition  of
things.   The dotted lines beyond  the picture show the
mode of representation usually adopted.   When  the
eyes are directed to a a, then a R, a L  become visual
lines, and a a are united and seen at the point of sight
A.   When the eyes are directed  to b b, then b R,b L
become visual  lines, and b and b  are united and seen
single at the point of sight B.
   The defect of this mode of representation is, that it
takes no cognizance of the double images oi bb when
A is regarded,  or of a a when B  is regarded.  The at-
tempt to represent these would destroy the perspective. 
242    DISPUTED POINTS IN BINOCULAR VISION.
   By our new method, on the contrary, all the phe-
nomena are  represented.   In Fig. 116  is shown the
visual result when the eyes are fixed on the background;
in Fig. 117,  the visual result when the eyes are fixed
on the foreground.  In  Fig. 116 we see that the nose
n n' and  the median screen ms m's are  doubled heter-
onymously, and the space between the two is the com-
mon  and only field of view (for the  monocular fields 
         ON SOME FUNDAMENTAL PHENOMENA.      243

are cut off by the screen).  In the middle between these
is the binocular eye E, looking straight forward.  This
is  manifestly exactly  what we  see in the stereoscope.
Again, we  see that the two images  of the  card have
slidden over each other, in such wise  that b b, Fig. 115,
are brought together in the middle, united, and seen
single in Fig. 116.  But where \  at what distance ?  Evi-
dently this  can only be at the  point of  sight, which,
as I  have already explained, is,  in diagrammatic repre-
sentations of visual phenomena, where the common vis-
ual line and the two median lines meet one another at
the point B, Fig. 116.  Meanwhile  a a,  Fig. 115, will
have crossed over and become heteronymous, and their
double images a a', Fig. 116, will  be seen just  where
their ray-lines E a and E a' cut  the median planes, viz.,
at a a,'.  In Fig. 117, which is the visual result when
the eyes are fixed on the foreground, the shifting or
sliding of the two images of the card is not quite so
great as  before.   It is only enough  to bring together
the nearer  points a a, Fig. 115, but not b b.   These
latter, therefore, are homonymously double.  The united
images of a a are seen single on  the common visual line,
and at the distance A where the double images of the
median line cross each other;  while b b  are seen ho-
monymously double,  and at b  V, the intersection of
their ray-lines with the continuation of the median lines
after crossing; for homonymous images are  always re-
ferred beyond the point of sight.
   The mode of representing  combinations writh the
naked eyes  by squinting is similar.  Of course the place
of the combined  picture will in this case be between
the eyes and the card. I reproduce (Fig.  118), for the
sake of comparison, the usual mode of representation
from page 139.  In order to make the  perspective nat- 
DISPUTED POINTS IN BINOCULAR VISION.
ural, it is necessary, as already explained, to reverse the
mounting.  In Fig. 118 the mounting is thus reversed,
as seen by the fact that points  in the foreground, a a,
are  farther apart  than  in  the  background, b b.  The
usual mode of representation is shown in this figure.
The true visual result  is shown  in Figs. 119 and 120,
of which Fig. 119 represents the result when the ob-
server is regarding the  background, and Fig. 120 when
he is regarding the  foreground.  It  is seen that not 
         ON SOME FUNDAMENTAL PHENOMENA.      245

only does the diagram give truly the place and distance
of the combined  image, but also of the double images
by means of which perspective is perceived.
   It will be remembered that double  images may be
nearer or farther off than the point of  sight, but that
in the former case they are heteronymous, in the latter
homonymous.   In this way we at once perceive their
distance in relation to point of sight.  Nowt, in the new
mode of  representation, this fact  is also indicated.   In
both of the  figures 119 and  120 there are two places
where the ray-lines cut the median lines, and therefore
where double images may be formed; but in  the  one
case the  images  are heteronymous,  and therefore we
refer  them to the nearer points a a,';  in  the other case
they are  homonymous, and therefore we refer them to
the farther points b b'.
   If  stereoscopic pictures mounted in  the usual way
be combined with the naked eyes by squinting, or pic-
tures  with reverse mounting be combined in the stereo-
scope, the perspective  will be inverted.  In this case
the diagrammatic representation  is exactly the same,
except that  the double images of points in the fore-
ground a a' will now be homonymous, and therefore
referred  to the other possible  point of  reference, viz.,
beyond the point  of sight;  and double images of points
in the background b b' will become  heteronymous, and
therefore referred to the nearer point.

Some curious Plienomcna illustrating the heteronymous
         Shifting of the two Fields  of View.
   Experiment 1.—To trace a picture where it is not.
Take  a postage stamp, or a piece of coin, or a medallion,
or a small object or picture of any kind; place it on a
sheet of white paper.  Take then a thin  opaque screen, 
DISPUTED POINTS IN BINOCULAR VISION.
like a  pamphlet, or thin book, or piece  of  cardboard,
and set it  upright on the right  side of  the object or
picture, and bring down the face  upon the top edge of
the screen,  in such wise that the latter shall occupy the
median plane.  If we now gaze with the eyes parallel—
i. e., on vacancy—the median card will double and be-
come  two  parallel cards,  and in  the middle between
them will be seen the  objeet or picture.   With a pencil
in the  right hand we may now trace the outline of the
object  or picture, by means of its image, on the right
side of the screen, although the actual object or picture
is on the left side of the same.
   The  accompanying diagrams  illustrate and explain
the phenomena.  In  Fig. 121, R and I are the  two
eyes looking down on the paper sheet sh; ms is the
median screen, and c the coin on its left side ; a, the
spot where the outline is traced with the pencil P.  This
Sfc
Fia. 121.
0i-wQ"
Fig. 122.
vYw
7/7 IS
ms
fy
S7i  ac'  S7i  &' s7l/'
figure therefore gives  the  actual condition  of  things.
The visual  result,  and therefore the explanation,  is
given in Fig. 122.   By careful inspection it is seen that
the screen is doubled heteronymously, and becomes two
parallel  screens ms, m's;  that the two  images  of the 
         ON  SOME FUNDAMENTAL PHENOMENA.      247

paper sheet are slidden over each other, so that the left
eye, its visual line, and its image of  the  coin c are all
brought to the middle, while the right eye, its visual
line, and its  image of  the pencil and  of the point a are
also brought to the middle  from the  other side,  and
superposed.  We  therefore see the  image of the coin
and trace  its outline exactly an interocular space  dis-
tant from  its real position.   If  it were not  for  the
screen,  there would be another (right-eye) image of  the
coin and another  (left-eye) image of  the pencil  and of
the point a.  These I  have indicated in dotted outline.
    Experiment 2.—If we make the  experiment with-
out the use of the median screen, then the cause of the
phenomenon becomes obvious.   If we lay a piece of
money  on a sheet  of paper, and then gaze in the direc-
tion of the coin,  but  with the eyes  parallel—i. e., on
vacancy—the money of course separates into  two images
an interocular space apart.  If we approach  this with a
pencil for  the purpose of  tracing the outline, we  will
see the pencil also doubled.   If we  now bring corre-
sponding images in contact—i. e., right-eye  image (left
in position) of the pencil wTith the right-eye image (left
in position)  of the coin—we touch the coin with  the
pencil.   But if, on the contrary, we bring the right-eye
image (left in position) of the pencil to the left-eye im-
age  (right  in position) of  the coin, we may trace  the
outlines of the piece an interocular space  distant from
its  true position.   This  is shown in Fig.  123, which
gives the visual result of such an experiment—c and c'
being the  right- and left-eye images of the coin,  and
P and P' of  the pencil. If, while the operation is going
on,  we  observe carefully, we will  see to the right  the
left-eye image of the pencil,  P', engaged  in making  a
tracing.  But there is no  tracing in this place; it is 
248     DISPUTED POINTS IN BINOCULAR  VISION.

only the left eye image of the real tracing being made
by the other pencil, P.  In the previous experiment the
screen cuts off all the images except the right-eye image
                       Fig. 123.
of the pencil and the left-eye image of the coin, which
are brought together in the middle.
    Tolerably good tracings of a picture  may be made
in this wTay.  The only difficulty in making them really
accurate is the unsteadiness of the optic axes, and there-
fore of the place of the image.   I  have, however, used
this method in making outline  tracings of  microscopic
objects,  which  may  be filled out  afterward.   For this
purpose a card  is placed on the  right side of the micro-
scope, and the microscopic object is viewed with the left
eye, while the right eye is used  for guiding the pencil.
Precisely as in the experiment with the coin (Fig. 123),
the left-eye image of the object  and the right-eye image
of the pencil and of a  certain spot on the card  are
brought together in the middle.
    Experiment 3.—To trace the outlines of a light on
an opaque screen.  The same experiment may be mod-
ified in an interesting way thus: Set a light in front of
you on a table.  Place a median screen of cardboard or
of tin between the eyes, so  that the light  can be seen
with both eyes.  Now bend the screen to the right so
as to make a right angle at the distance of 6 or 8 inches
from the eyes.  This part will  cut off the  view of the 
         ON SOME  FUNDAMENTAL PHENOMENA.      249

candle-flame from the right  eye.  Nevertheless, while
gazing steadily at  the flame,  a really correct outline of
it  may be drawn  on the opaque transverse screen,
precisely as if it were transparent.  This is illustrated
and  explained  by the accompanying  diagrams.   Fig.
124 is the actual condition of things,   Fis the flame;
ms, the median screen, resting on the nose n; ts,  the
transverse  portion  of the screen.   Now, just  where

           Fig. 124.                Fig. 125.

          r                          i^
:  -?n

s
the visual line of the right eye pierces the transverse
screen, viz., at f we may draw the picture of the flame
F,  precisely  as if it were transparent.  The explana-
tion is  found  by examining the  visual result,  Fig.
125.  By the heteronymous doubling of the  median
and transverse screens, the left-eye image of the flame
and the right-eye image of the transverse screen ts are
brought together, and the flame may be seen as it were 
250     DISPUTED POINTS IN BINOCULAR  VISION.

through the opaque screen as a transparency, and drawn
at f.   In order to show that the flame  is seen only by
one eye, I have stopped  one  of the combined visual
lines at the screen.  The apparent transparency of an
opaque screen in this case is precisely the same as the
transparent borders of an opaque screen  mentioned and
explained on  page  240.
   Experiment 1±.—To see through a book, a deal board,
or the back of the hand, or even if necessary through a
millstone.  Roll up a thin pamphlet into a hard tube a
            half or  three quarters of an inch  in diam-
            eter, and hold it with the left hand be-
            tween the thumb and hand, as shown in
            Fig. 126.  Place the right  eye to the end
            of the tube and look  through the tube at
            the opposite wall, or still better at a map
            or picture hanging  on the wall, while the
            back of  the hand  conceals the map or pic-
            ture from the left eye. A circular spot on
            the wall or map will  be seen through the
center of the hand (Fig. 126), precisely as if there were
a circular hole in  the hand.   Of course a book or an
opaque  plate of any kind may be  substituted for the
hand in this experiment.
   The explanation  is as follows: The  visual line of
the right eye passes  through  the axis of the tube and
pierces  the center of the  circular  visible area of the
object regarded, while the visual  line of the  left eye
pierces the back of the hand or the book at a point dis-
tant from the axis  of the tube just an interocular space,
or about 21- inches.  By the right and left shifting of
the fields of view already explained, the two visual lines
are brought together in the middle ; and therefore the
center of the area regarded by the right eye and the
 
         ON  SOME FUNDAMENTAL PHENOMENA.      251

spot on the hand or book pierced by the left visual line
are also brought together and superposed.
    One thing more to complete the explanation:  The
impression on the right eye prevails over  that on the
left — the  impression of the circular  area obliterates
that of the corresponding area on the hand or book for
two reasons: first, because the circular area is strongly
differentiated from  the rest  of  the right-eye field  of
view (i. e., the dark  interior of the tube), while the cor-
responding or coincident area of the left-eye field (the
hand or  book) is not thus differentiated;  and second,
because both eyes are focally adjusted  for  the distance
of the object seen by the right eye only.  Thus it  hap-
pens that the right  eye sees only the circular area, the
rest of its field being very dark ; while the  left eye sees
all its  field except the spot corresponding to and cover-
ing the circular area.  Thus the binocular observer sees
the  general field of the left eye (the hand  or book),  in
the  middle of which he also sees the  circular area  of
the right-eye field.   But if an ink-spot be made on the
back of the hand or  book just where the left visual line
pierces it, the impression of  this will be strong enough
to resist obliteration ; the strongly differentiated  ink-
spot will be seen in the center of the circular area,
as shown in Fig. 126. 
CHAPTER  IV.
    VISUAL PHENOMENA IN OCULAR  DIVERGENCE.

    The only normal condition of the optic axes is either
parallelism or convergence.  We  can not voluntarily
make the optic axes divergent, because there is no use-
ful purpose subserved  by such a position; there would
be no meeting of the optic axes, and therefore no point
of sight.  All  the advantages of  binocular vision are
conditioned on convergence  only.  Divergence would
only  confuse  by  giving  false information.  But, al-
though the power of  divergence  could be of no use
and has therefore never been acquired, yet under cer-
tain circumstances divergence does occur, and the curi-
ous phenomena which then follow are an  admirable
illustration of the principles of binocular vision already
set forth.  We will give a few of these phenomena.
    1.  In  Drowsiness.—It is well known that in extreme
drowsiness, when we lose control  over the ocular mus-
cles, we see double images.  It is universally believed
and taught by physiologists that this is the result of con-
vergence of the optic axes in sleep.  I know of no ob-
servations purporting to prove  this.   It is probably an
inference  from the  contracted state  of  the pupils  in
sleep, and the  fact  that contraction  of the pupils is 
     VISUAL PHENOMENA IN OCULAR  DIVERGENCE.  253

usually consensual with optic convergence.*  This view
is certainly false.  Double images in sleepiness are cer-
tainly  due to divergence, not convergence, of  the optic
axes.
    In  extreme  drowsiness I have often  observed  the
object  which I was regarding  (it might be the head of
a dull  speaker) divide into two images, which  then sep-
arated  more and more,  until at a distance of 30 feet
they were 10 to 15 feet apart.   Even under  these con-
ditions I  have found it possible  to make a scientific ex-
periment.  Often,  control over  the ocular muscles is
lost even while consciousness and control  over mental
acts is still perfect.   Often, although by effort I could
retain  control over  the eyes, I have chosen to abandon
it in order to make the following experiments.
    Experiment 1.—As soon as the images are well sep-
arated, I wink  the  right  eye :  immediately the left  im-
age disappears.  The images are therefore heteronymous.
But convergence produces homonymous images, wThile
parallelism and, a fortiori, divergence produce heterony-
mous  images.   In  this case the heteronymous images
can not be produced by  mere  parallelism, because this
state separates  the  images only an  interocular space, or
about  2£ inches, whereas the images may be separated
many feet: therefore they are produced by divergence.
The amount of divergence is easily calculated.  At a
distance of 30 feet a separation of the double images of
10 feet would require an angular  divergence of the optic
axes of nearly 19° ; a separation  of 15 feet would indi-
cate an angular divergence of 28°.

  * " In sleep and in sleepiness both eyes are turned inward and  up-
ward."  "The contracted state of the  irides in sleep is a consensual
motion dependent on the position of the eyes, which are turned inward
and  upward."—Miiller, " Physiology," Am. ed., pp. 810 and 535. 
254    DISPUTED POINTS IN BINOCULAR  VISION.

    In every such experiment the consciousness is quick-
ly and completely aroused, and the double images are
speedily reunited, though  not  so speedily but that the
result is unmistakable.  But, lest some may regard the
speedy union of the images as an objection to this ex-
periment, we will take another.
    Experiment  2.—While lying abed in the  morning,
if one gazes on  vacancy, objects near at hand (say the
bedpost) are doubled heteronymously, the images being
2\  inches apart.   If, while thus gazing  and observing
the heteronymous images, one should be overtaken by
drowsiness and  consequent loss  of  control  over  the
ocular muscles, he will see that the  already heterony-
mous images separate  more and  more.   Now,  if this
were  due to convergence, the heteronymous images
would approach, unite, cross over, and become homony-
mous.
    It is certain,  then, that in myself, in  extreme drow-
siness, when control over the ocular muscles is lost, and
therefore presumably in sleep, the eyes diverge.  I have
also satisfied myself that my case is not exceptional in
this respect, for my results  have been verified by several
other persons.   I think, therefore, I may assume  it as
a general law.
    Double vision is also a wrell-known phenomenon of
extreme intoxication.  The unnatural appearance of the
eyes in  such cases is due to want of parallelism of the
optic axes.   I  have on several occasions examined the
eyes of  those  in this sad  condition, and have  always
found the axes  divergent.  This seems to arise from
partial paralysis  of the ocular muscles.
    If we  examine the eye-sockets of a human skull,
we  find that their axes diverge about 25°-30°.   This
is about the extreme divergence of  the optic axes in 
     VISUAL PHENOMENA IN OCULAR DIVERGENCE.   255

drowsiness.   It is probable, therefore, that in a state of
perfect relaxation or paralysis of the ocular muscles the
optic  axes coincide  with the axes of the conical  eye-
sockets, and  that it  requires some degree of muscular
contraction to bring the optic axes to a state of parallel-
ism, and still more  to one of convergence, as in every
voluntary act of sight.  In  the human eye,  therefore,
and also in that of the highest animals, there are three
conditions of the optic axes : first, convergence, as when
we look at  a near object; second, parallelism, as when
we look at  a distant object or gaze on vacancy; third,
divergence, when we lose control  over the ocular mus-
cles, as  in drowsiness, in  drunkenness, in sleep, and in
death.  The first requires a distinct voluntary contrac-
tion of  the  ocular muscles; in the second there is no
voluntary action, but only that involuntary  tonic  con-
traction  characteristic of  the healthy  waking  state; in
the third the relaxation is complete.  The first  is the
active state of the eye, the second the waking passive
state, the third the absolutely passive state.
    2. Other  Modes of producing  Divergence.—But the
divergence  of the optic axes may be effected in other
ways.   In most normal eyes the passive state is one of
parallelism.  It  is easy therefore to double  homony-
mously  the images of an object at any distance by con-
vergence, but most  persons would find it  impossible
voluntarily to double the  images of a very distant ob-
ject, as for example a star, heteronymously—i. e., by
divergence.   Yet under certain conditions a slight di-
vergence is possible.   For example, I find I can  (and
I believe most persons can) combine with the naked eyes
and with natural perspective (i. e., beyond the plane of
the card) stereoscopic pictures in which identical points
are farther apart than the interocular distance.  I can 
256     DISPUTED POINTS IN BINOCULAR VISION.

not always succeed, being able to do so only when  my
mind is in an exceptionally passive state.
   Experiment 3.—I take now a skeleton stereoscopic
diagram, identical points  in the background of which
are separated by a space greater by an eighth of an inch
than  my interocular  space.   By holding it  at  arm's
length so as to make the divergence as small as  possi-
ble, I succeed  in combining.   After the combination
is stable, I  can bring the card nearer and nearer until
it is within 5 inches of my eyes, and yet the combina-
ation is retained.   But this corresponds to a divergence
of only 1£°.
   Experiment Jp.—But by mechanical force wTe may
make the eyes diverge 40° or 50°.  This is done by pres-
sure  in the  external corner of the eye.   By thrusting a
finger of each hand into the external corners of the eyes
I can make the two images of an object  directly in  front
separate 50°, or the images of  two objects situated 25°
to the right and left of the median line, and therefore
50° apart from each other, come to the  front and unite.
   The following diagrams represent  and explain the
visual phenomena in divergence of the optic axes.
   In Fig. 127, which represents the actual relation of
parts, m is the median line; v v, the visual lines or optic
axes  produced; A, an object on the median  line; b b,
two similar objects in the direction of  the diverging
visual lines; and r r, ray-lines from the object A.  Fig.
128 shows the visual result if the lines in Fig. 127 were
visible lines drawn on the plane described on  page 231.
It will be seen that by heteronymous shifting and then
heteronymous  rotation the whole diagram represented
by Fig. 127 has been carried and rotated by the right
eye to the  position of the lines connected by the un-
primed  vinculum, and by the  left eye to the position 
     VISUAL PHENOMENA IN OCULAR DIVERGENCE.   257

of the lines  connected  by the  primed vinculum.  By
this means the two visual lines v v are brought together
and combined as the common visual line V, and two of
the images of the objects b b are brought  together and
superposed at B;  the median  line is doubled and ro-
Fig. 127.                      Fig. 128.
tated heteronymously to the positions m m', carrying
with them the double images of the median object A
as a a'.  The above  diagram correctly represents  the
position and the distance of the double images a a', and
the position  of the combined image B, but can not
represent the distance of the combined image, because
there is no point of  sight.  For the point of sight is
really the point of optic convergence or meeting of vis-
ual lines ; in diagrams representing visual results, it is
the point of crossing of the doubled median lines ; but
this point, by both definitions, would be in this case be-
hind the head.   The diagram therefore correctly repre-
sents all the visual facts ; for, there being in divergence 
DISPUTED POINTS IN BINOCULAR VISION.
no point of sight, the distance of objects in the visual
line is indeterminate as represented.   It is impossible
by the usual  method to correctly represent any of the
visual facts.
   3.  If the Law of Direction be opposed to the  Law of
Corresponding Points, the  Latter will prevail.—These
two most fundamental laws of  vision  are sometimes
in discordance with each  other.    The  reason  of this
may be thus  explained:  The  law of direction is the
fundamental  law of monocular vision,  as  the  law of
corresponding points is of binocular vision.  Now, for
each eye, and therefore for the monocular observer,
direction is determined by reference  to  the optic axis,
but for the binocular observer  by reference to the me-
dian line.  On account of this difference of line of ref-
erence, while objects seen  single  are seen in their  true
positions, double images are always  seen in positions
different, and in some cases widely different, from the
object which they represent.  The difference may even
amount to 45°.   For example: The binocular  field of
view in my own case is 100° in a horizontal direction.
By strong  convergence I  can nearly bring the double
images of the root of my nose together, and thus oblit-
erate the common field.  I am sure therefore that I can
make the optic axes of my two eyes cross each other at
right angles.   In such  a case, of course, objects directly
in front are doubled and  their images separated  90°
from each  other, while objects lying to the right  and
left 90° from each  other are brought to the front and
their  images superposed.   Here  the images  are 45°
from the true position of  the objects which they repre-
sent.   Thus, Fig. 129  represents the actual relation of
things in this case, and Fig. 130 the visual result, show-
ing that the positions of the objects M and a a are com- 
     VISUAL PHENOMENA IN OCULAR DIVERGENCE.  259

pletely reversed.   It may indeed be said  that the case
oi a a seen  in front may be reconciled with the law of
direction.  For, if the combined images be referred to

                       Fig. 129.
the point of optic convergence A, as indeed they often
are, then each eye sees its own object in its true direc-
tion, but only mistakes its distance.  To this I would

                      Fig. 130.
answer that each eye does indeed give the true direction,
as is quickly shown  by shutting  one of them, but  the
two eyes  together do not.  Each sees its own object in 
260     DISPUTED POINTS IN BINOCULAR VISION.
the true direction, but the binocular observer sees their
combination in a wrong direction.  In the case of  the
double images m and m! of the object 31, it is still more
difficult to  explain their apparent position by the law
of direction.
   A curious Corollary.—It is seen  that, under all  cir-
cumstances, whatever  be the position of the optic axes,
objects  in the visual lines are moved to the front and
seen there.   Now the same would be true if our eyes
were  turned directly  outward right and  left.   There
can be no doubt that if we could turn our  eyes directly
outward, or if our eyes,  retaining their present  organi-
zation and properties in regard to corresponding points,
were  transferred  to the sides of  the head with their
axes  straight right  and left—i. e., making an angle of
180° with each other—images of objects in  the direction
of these axes, and therefore directly right and left, would
be moved round  90° each, and combined  and seen  di-
a--
Fig. 131.
///
O    Off---*'— « -^
Fig. 132.
 o-.a
y

ML
rectly in  front.  This  seems an  extraordinary result,
but it is a necessary consequence of the law of corre-
sponding points.  The retinal images of the two objects
are on corresponding points, viz., on the central spots; 
     VISUAL PHENOMENA IN OCULAR DIVERGENCE.   261

therefore, by  the  law  of  corresponding  points, they
must  be seen as one.  But where else can  this take
place but in front ?   The accompanying figures are a
diagrammatic  representation of these facts,  Fig.  131
being the supposed  condition of things, and Fig. 132
the visual result.  After the frequent explanations of
similar figures, a bare inspection will be sufficient. 
CHAPTER  V.
  COMPARATIVE PHYSIOLOGY OF BINOCULAR  VISION.

   The cause of the remarkable law of corresponding
points, on which all the phenomena of binocular vision
depend, has not been traced with certainty to anatomical
structure.   It is probably in  some way connected with
the existence of an optic chiasm and the crossing of the
fibers of the two optic nerves there, but  in what way
is not understood.  We have  already (page 102) alluded
to a hypothesis, " the nativistic theory," which  supposes
that  fibers from corresponding points unite  into one
fiber or end  in one brain-cell; but even if this be true,
it is  undiscoverable.  The optic  chiasm doubtless is a
sign of  some kind of sympathetic relation between the
two eyes;  but whether  this necessarily reaches the de-
gree which produces corresponding points is uncertain.
   The chiasm exists in nearly all vertebrates, but not
in invertebrates.  In vertebrates sometimes the fibers of
the two nerve-roots (optic tracts) simply cross each other
without uniting; this is the  case in fishes.  In others
the fibers of the roots  partly cross and partly do not,
so that each  nerve is made up of fibers from both roots;
this is the case in mammals and birds, and  probably to
some extent in reptiles.  It seems certain then that in-
vertebrates do not enjoy binocular vision.   It  is proba- 
          PHYSIOLOGY OF BINOCULAR VISION.       263

ble also, from anatomical structure alone,  that osseous
fishes do not enjoy this faculty.   AVhether in some still
higher animals the sympathetic relation which certainly
exists between the two eyes reaches the point necessary
for their  successful  use of the two  eyes as one instru-
ment is also, I believe, very doubtful.  I proceed to give
some reasons for this belief, derived from  the  position
of the two eyes.
    In man the axes of the conical eye-sockets diverge
about 25°, or each makes with the median line an angle
of  a little more than 12°.  In these slightly diverging
conical sockets the eyeballs are so placed, and the mus-
cles so adjusted, that in the waking  passive state their
axes are parallel; and from this passive parallel condi-
tion they  may be easily converged even upon very near
objects.  In  man,  then,  though the  eye-sockets still
diverge considerably, the eyes  are  set in front with
axes  naturally parallel.  This is evidently the position
most suitable for binocular vision;  for the eye-sockets
could not be brought any nearer to parallelism without
diminishing too much the interocular space, and  thus
the accuracy of binocular judgment of distance.
    In monkeys  the position of the eyes  is much the
same as in  man.  They are  placed well in front, with
their axes apparently parallel in the passive state, and
therefore  well adapted  for  binocular  convergence on
near objects.  But as we go down the vertebrate scale,
the eyes are placed  wider and wider apart, then moved
more and more  to the side of the head; the axes of the
eye-sockets are therefore more and more divergent, and
the difficulty of  convergence on a near point  becomes
greater and greater,  until in  some mammals, as cetacea,
in many birds, and  in all fishes, the eyes are placed no
lono-er in  front, but  on the sides  of the head, with their
              12 
264     DISPUTED POINTS IN BINOCULAR VISION.

optic axes inclined nearly or quite 180° with each other.
It is evident that animals with eyes so placed can not
converge the optic  axes on a  single point, especially a
near point.  In fact, it is. well known that those birds
which have their eyes placed well on the side of the
head, when they wish to look attentively, turn the head
and look with one eye.  It seems impossible that animals
like  the whale and fishes,  in which the eyes are fairly
on the side of the head, can enjoy a true binocular vision
with its consensual movements of the two eyes, with its
double and combined images, its stereoscopic effects,
and  its complex  but accurate visual  judgments based
on these effects.  It seems impossible that,  for  such
animals, the law of corresponding points could have
been developed, or can now exist;  for if it did, it could
only, as we have seen (page  260), lead to false judg-
ments as to  the direction of objects.  They see with two
eyes, but these do not act  together as one instrument,
as a  single binocular eye; they are independent, and see
each for itself.   I have watched the motions of the eyes
of fishes swimming in an  aquarium,  and they seem to
me to move independently of each other.   The same
is true of all other senses, even in man : however much
their organs may be multiplied, each organ  perceives
for itself.  The property of corresponding points, from
which all the phenomena of binocular vision are de-
rived, is something  peculiar to the  eye of  the higher
animals.  Nothing analogous exists in the other senses.
Binocular vision  in  its perfection, as it exists in man
and  the higher animals,  is  the last result of the gradual
improvement of  that most refined of all the  sense-or-
gans, the eye, specially adapting it to meet the wants
of the higher faculties of the mind.
   There are,  it  is true,  consensual movements and 
PHYSIOLOGY OF BINOCULAR VISION.
 sympathetic relations  in the double  organs of other
 senses—e. g., the consensual movements of the hands.
 There is even a kind of binaural audition* by means
 of which we judge  imperfectly of direction of sound.
 But  these are not only infinitely inferior  in degree of
 perfection to, but they are essentially different in kind
 from, that consensual  movement and that sympathetic
 relation which we find in the eyes, and Avhich slowly
 in the process of evolution gave rise to the wonderful
 property of corresponding points and  the phenomena
 of binocular vision.
    Binocular vision, then, is certainly wanting in  in-
 vertebrates, for the eyes in these are either immovably
 fixed, as in insects and  many crustaceans, or, if movable,
 as in snails, etc., their  movements  are  not consensual.
 The  most perfect eyes among invertebrates are found
 in cephalopods.   These  have true recti  muscles for
 turning  them about, but  from their position they can
 not move consensually.  There  is also no  optic chiasm
 in any invertebrate.
    Teleost fishes do not enjoy  binocular vision,  for
 there is in them no optic chiasm,  and  the position of
 their eyes makes it  impossible  for them  to converge
 their axes on objects, especially near objects.   The
 movements of their eyes also seem to be  independent.
 Sharks and selachians  generally have an optic chiasm,
 and therefore  probably more sympathetic connection
 between  the eyes than osseous fishes.   It is  possible
 that  binocular effects  begin  first  to  be developed  in
 these.  Yet not only in these, but even in reptiles and
some birds, binocular seems to be at least subordinate

   * Thompson, "Philosophical Magazine," vol. iv,  p.  274 (1877); vol.
vi, p. 383 (18*78); "American  Journal of Science and Arts," vol. xix, p.
145 (1880); Steinhauser, " Philosophical Magazine," vol. vii, p. 261 (1879). 
266     DISPUTED POINTS IN BINOCULAR VISION.

to monocular  two-eyed  vision (if I may be allowed the
expression).  The carnivorous birds  and all  mammals
except cetacea seem to enjoy binocular vision very much
as man does, though I believe in a less perfect degree.
   There is another peculiarity of the human eye, prob-
ably closely connected with the highest effects of  bin-
ocular vision, which still more quickly disappears as we
go down the vertebrate scale.  I refer to the existence
of the central spot of  the retina.  We have already seen
that  this spot, situated exactly in the center of the ret-
inal  concave, and therefore just where the visual  line
pierces  the retina, is the  most highly organized  and
sensitive portion of the retina.  It is not more  than a
millimetre in diameter.  Now every spot of the retina
has its representative in the field of view.  The repre-
sentative of this is the  point of sight and  a very small
area  about that point, viz.,  the area of very clear vision.
At the ordinary reading distance of 12 inches, this  area
is not more than three quarters of an inch in  diameter.
If, while gazing steadily and attentively at one point, we
observe the relative distinctness of points in other  por-
tions of the field of view, we shall find that these be-
come rapidly less and less distinct as the point is more
distant  from the line of sight.  In other words, there
is a regular gradation of distinctness, from the point of
sight, where it is greatest, to the  extreme margins  of
the field of view, where it is least.  Now, as the retina
corresponds to the field of view point for  point, it fol-
lows that there is a regular gradation in keenness and
definiteness of perception, and  therefore in fineness of
organization, from the central spot, where it is greatest,
to the anterior margin  of  the retina, where it  is least.
This  superior  fineness  of  organization has  not been
demonstrated  except for the central spot; but the gra- 
PHYSIOLOGY OF BINOCULAR VISION.       267
dation of distinctness of vision is its representative, and
therefore its sign, in the field of view.
    Now, as we  go down the vertebrate scale, the cen-
tral spot is found only in the higher monkeys.  After
a total absence in all other mammals and all birds, it is
said to reappear in some lizards, especially the chame-
leon.   But whether in  these the  organization of this
spot is similar to that  in man—whether it is really a
central spot in  the same sense, and has the same sig-
nificance in vision or not—may be still a question.  It
seems  fair to conclude, therefore,  that the  graduation
of  distinctness toward the point of sight, and the limi-
tation  of the greatest distinctness to that  point, which
we find in man, do not exist, at least to the same  de-
gree, in most of the lower animals.
    The importance of a central spot in the highest ani-
mals, and especially in man, is very evident.  The lim-
itation of the greatest distinctness to the point of sight
is absolutely necessary to the concentration and limita-
tion of the most  thoughtful attention to that point.  If
all  portions of the retina were similarly organized, and
therefore all points in the field of view equally distinct,
it would be impossible  to fix  the attention steadily and
thoughtfully on any one  point to the exclusion of oth-
ers.  AVe  might  see  equally well, and over a wider
area;  but  we could not  look attentively at anything;
we could not observe thoughtfully.  But in the lower
animals, especially those,  as the ruminants, which are
preyed upon by  others, it is far more important  to see
well in  every direction,  than to  fix attention  exclu-
sively on one point; therefore the advantages  of ex-
quisite  microscopic distinctness of the  center of the
field is sacrificed for the much greater advantages of
moderate distinctness over a very wide field.  The most 
268
DISPUTED POINTS IN BINOCULAR VISION.
important thing for them is a very wide field and the
equal distribution of attention over every part.  Hence
their eyes are prominent, set wide apart on the margins
of a broad front, and destitute of central spot; so that
they sweep the whole horizon, and see  all parts with
nearly equal distinctness.
   It may be said that the sight  of  these animals  is
equal  or even superior to that of man, and therefore the
organization of their retina is  probably  as fine as that
of our central spot.   I answer that there  are two things
to be  considered in this connection.  The one is sensi-
tiveness to light, and therefore perception of  the pres-
ence of objects ; the other is distinctness of the percep-
tion of form.  The one gives us notice of the  existence
of objects, the  other gives us distinct knowledge con-
cerning these objects.   It is this  latter which depends
on the  fineness of organization of the bacillary layer.
Other portions of the human retina are even more sen-
sitive  to light than the central  spot, as is shown by the
well-known  fact that we see a faint star by looking  a
little way from it, when we can not see it  by looking
directly at it.  But distinctness  of form is perceived
only by the central  spot.  It seems probable, therefore,
that animals destitute of a  central  spot,  although they
may have a more delicate  perception  of the  existence
of objects in the field of view  than we, yet do not see
the form of objects regarded as distinctly as we do. For
this reason they are more apt  to mistake the  nature of
objects, and therefore more  easily frightened by trifling
causes.
   Again, it is well to  observe that the chameleon, in
which  the central spot  seems  to reappear, is an animal
whose habits and mode of taking its food require the
most fixed and undivided attention. 
          PHYSIOLOGY OF BINOCULAR VISION.       269

    The close connection of  the central spot with  bin-
ocular vision is also quite evident.   The central spot,
more than all other portions of the retina,  is endowed
with  the  properties of corresponding points;  and the
somewhat complex binocular judgments expressed by
the term  '" stereoscopic perspective" are accurate  and
reliable only at and in the vicinity of the point  of sight.
This fact  constitutes  the great difficulty in the way of
the experimental determination of the horopter, as al-
ready explained (page 197).  It is therefore, to say the
least, doubtful if animals whose eyes "want the central
spots are able to judge as accurately of the relative dis-
tance and the solid forms of  near objects as we do.
    The following, then, are the general changes in the
vertebrate eye as we go up the  scale : 1. A gradual
change of the position of the eves  from the sides to the
front of the head, and a consequent change of the angle
of inclination of the  optic axes from 180°  to  parallel-
ism ;  2. A regularly increasing graduation  in the fine-
ness of the  bacillary  layer of the  retina, and therefore
in the accuracy of the  perception of  form, from  the
anterior margins toward the  central parts, so as finally
to form in monkeys and in  man a specially organized
central spot;  3. A gradually increasing power of con-
verging the optic axes on  a  single near point, so that
the images of that  point may fall on the central spots
of both eyes; 4.  The  gradual evolution of  the proper-
ties of corresponding points, and  therefore of all  the
distinctive phenomena of binocular vision.
   These  changes seem all intimately connected with
each other and with  the development  of  the higher
faculties of the mind. 
 
INDEX.
                                  PAGE
                   A
Aberration.........................   31
----reduction of...................   36
Accommodation.....................   41
----experiment illustrating.........   42
Adjustment for light................   37
----for distance....................   40
----loss of........................   50
----theory of.......................   44
Analogues of double images  in other
  senses............................   95
Aqueous humor.....................   24
Astigmatism........................   52
Auditive nerve......................  12

                   B
Bacillary layer.................... 55, 86
Back of the hand, to see through.....  250
Binocular combinations, by the stereo-
  scope.............................  134
----field...........................  9!
----perspective............ 120,143,144
----perspective,  experiments  illus-
  trating........................ 120-124
----perspective, theories of..........  145
----perspective, Wheatstone's  theo-
  ries of........................ 145-147
----perspective, Brucke's theory of..  147
----perspective, experiment illustrat-
  ing Brucke's theory...............  147
----perspective, Dove's experiment..  145
----perspective, Helmholtz's, the true
  theory of..........................  151
---perspective, judgment by means
  of................................  15C
----vision..........................  •"•
----vision, disputed points in........164
____vision, fundamental phenomena
   usually overlooked in............  213
                                  PAGE
Binocular vision, usual mode of repre-
  senting untrue.................... 214
----vision, experiments illustrating
  the false mode of representing..... 215
----vision, comparative physiology of 262
----vision, extreme divergence of eye-
  sockets incompatible with.........264
----vision first developed  in  sharks
  and selachians.................... 265
----visual phenomena  in  ocular di-
  vergence.......................... 252
----visual phenomena in drowsiness. 252
----visual phenomena in intoxication. 254
Blind spot.........................59,78
----spot, experiments illustrating..73-S1
----spot, size of....................   81
----spot, representative in the visual
  field of the.......................   S2
Book, to see through................ 250
Brief statement of laws............. 229
                   C
Central spot of the retina, properties
  of................................   73
----spot of the retina, function of the.   74
---spot of the retina...............266
----spot of the retina found in mon-
  keys..............................  267
____spot of the retina, absence in mam-
  mals and birds....................  267
----spot of the retina in lizards......  267
----spot of the retina, importance of.  267
----spot of the retina, size of........266
Cephalopods, eyes of................  265
Choroid coat........................   22
Chromatism, correction of...........  31
----correction of, hint  for...........  35
Ciliary processes....................  22
Colors, perception of................  59 
272
INDEX.
                                 PAGE
Colors, primary.....................  60
----Brewster's view of..............  60
----Young's view of................  60
----Hering's view of...............  60
Color blindness.....................  62
----blindness, theory of.............  €3
Combination of images of different ob-
  jects.............................. 103
----of images of dissimilar objects... 108
----of images of similar objects..... 112
----of images of many similar objects 115
Conjunctiva.........................  18
Consensual adjustments............. 104
----adjustments, dissociation of.___117
----adjustments, dissociation of, ex-
  periments illustrating............. IIS
Convergent motion, laws of.......... 177
----motion, difficulty in experiment-
  ing on............................ 178
----motion, experiments showing ro-
  tation on optic axis in......... 180-187
Cornea...........................  21,22
Corresponding points of the two reti-
  na?............................. 72,96
---points of the two retinae, law  of
                                97,105
----points of the retinae,  relation  of
  the optic chiasm to the law of.....101
----points of the retinae, cause of law
  of................................ 262
Crystalline lens.....................  23

                  D
Daltonism..........................  62
Deal board, to see through a......... 250
Dcxtrality..........................  94
Dispersion..........................  32
Divergence of eye-sockets........... 2€3
----of eye-sockets, extreme.....263,2C4
Double images......................  92
---images, experiments illustrating
                                 92, 93
                   E
Ectoderm.......................  11
Emmetropy.........................  46
Endoderm.  .......................  11
Erect vision........................  83
Experience, inherited................ 104
Experiments illustrating the combina-
  tion of images of dissimilar objects,
                               108-112
                                  PAGE
Experiments illustrating the combina-
  tion of images of similar objects 112-115
----illustrating the  combination of
  images of many similar objects reg-
  ularly arranged................  115-117
Eye, an optical instrument....... 30,162
----defects as an  optical  instrument
  ofthe.............................  46
----muscles ofthe..................  18
----comparison of the camera with
  the............................ 30,152
----adjustment of the............... 50
----ball............................  20
----ball, contents of................  23

                   F
Form.............................  160
----outline......................... 160
----solid...........................  160
Formation of the image.............  24
----conditions of perfect image......  25
----experiment.....................  27
----illustrations....................  27
----diagram  showing formation of
  image.............................  28
Fovea centralis................... 57, 73
Function of the retina..............  64

                  G
General changes in the eye as we as-
  cend the vertebrate  scale..........  269
----conclusions....................  118
----sensibility related to special sense
                                   9-15
----structure of human eye.........  17
Gradation among senses...........   11
----in kind of contact...............  13
----in distance of perception........  13
----in refinement of organ..........  14

                  H
Helmholtz's view as to the relation of
  apparent and real vertical meridian 197
----views, experiments testing..  197-202
Heteronymous  shifting of the two
  fields of view...................... 216
----shifting of the two fields of view,
  experiments illustrating........  216-222
----shifting of the two fields of view,
  statement of the law of............ 223
---■ shifting of the two fields of view,
  cuiious phenomena resulting from. 245 
INDEX.
273
                                  PAGE
Homonymous  rotation  of  the  two
  fields.............................  224
----rotation of the two fields, experi-
  ments illustrating............. 224-227
---- rotation of the  two fields, state-
  ment of the law of.................  228
Horopter, definition of........... 101,193
----Meissner's  investigations  with
  the........................... 189,202
----different opinions as to the nature
  ofthe.............................  193
----Claparede's view ofthe..........  194
----Helmholtz's conclusions  regard-
  ing the............................  195
----confirmation  by the  author of
  Meissner's views ofthe........ 206-210
----conclusions in regard to the.....  210
----difference  between the  author's
  and Meissner's view of the.........  211
Horopteric circle of M iiller........ 99, 194
Human eye, general structure of.....   17
----muscles of the..................   18
Humor, aqueous...  ................   24
----vitreous........................   24
Hypermetropy......................   51

                    I
Identical points......................   98
Image, light.................... 152,153
----invisible................... 152,153
----visible.........................  153
----formation of....................   24
----conditions of a perfect..........   25
Images, heteronymous.......  95,100, 151
----homonymous...........  95,100, 151
Interocular space, determination of..  230
Inverse perspective..................  135
----perspective, experiments illustrat-
  ing........................... 136-141
Iris..................................   21

                   J

Judgments of distance...............  It6
----of size.........................  157
----of size, experiments illustrating
                                157-159
----of form........................  10°
----gradations of...................  100
----visual..........................  101
----intellectual.....................  161
                                  PAGE
                  L
Law of differentiation...............   10
----of fatigue......................   70
----of direction.................  85,105
----of direction, illustrations of the 86-S9
----of direction, opposed to the law
  of corresponding points............  258
----of outward projection of retinal
  impressions.......................   64
---of outward projection of retinal
  impressions, illustrations of........   66
----ofListing......... 164, 171,191, 197
Laws of ocular motion...............  164
----of parallel motion.......... 164,177
----of convergent motion...........  177
----brief statement of two..........  229
----experiments illustrating new 231-237
----of parallel and convergent motion
  compared..................... 189,190
Layers of the retina.................   55
----of the retina, functions  of.......   58
Lens, crystalline....................   23
----capsule of......................   23
----opacity of......................   24
----pioperty of a...................   27
----achromatic.....................   34
----plano-convex...................   34
Linings.............................   22
Listing's law............164, 174, 191, 197

                  M
Macula centralis....................   73
----lutea...........................   74
Meissner's investigations with the ho-
  ropter............................  202
----results with the horopter........  204
Mesoderm..........................   11
Millstone, to see through a..........  250
Minimum visibile...................   76
----tactile..........................   77
Monocular vision....................   17
----vision, explanation of phenomena
  of..............................  53, 64
Muscip volitantes....................   67
Muscles, straight....................   18
----superior........................   18
----inferior........................   18
----external........................   18
----internal  rectus.................   18
----oblique.........................   19
----illustrations of actions of........   19 
274
INDEX.
                                   PAGE
 Myopy..............................  46
 ----a structural defect..............  50

                   N
 Nativistic theory.................... 262
 Near-sightedness....................  46
 Nerves, olfactive....................  10
 ----optic...........................  10
 ----auditive........................  10
 ----gustative.......................  10
 Nodal point.........................  29

                   O
 Ocular  divergence,  binocular  visual
  phenomena in..................... 252
 ----divergence, other modes of pro-
  ducing............................ 255
 ----spectra?........................  69
 Q3il cyclopienne............  222, 229, 231
 Old-sightedness.....................  43
 Opposition of law of direction to law
  of corresponding points........... 258
 ----of law of direction to law of cor-
  responding points, explanation  of
                                25S-260
 Optic chiasm.......................  54
 ----chiasm related to corresponding
  points............................ 101
 ----chiasm in  lower animals........ 262
 ----chiasm not found in invertebrates
                                262, 265
 ----chiasm found in sharks and sela-
  chians ...............»............ 265
 ----nerve...............,..........  13
 Outline of a picture, to trace___..... 245
 ----of a candle-flame, to trace...... 243
                   P
 Parallel motion, laws of............. 164
 ----motion, laws  of, experiments il-
  lustrating........,............ 164-172
 ----motion, statement of the laws of
                                173,174
---- motion, Helmholtz's   contrary
  statement ofthe laws of........... 175
Perception of color..................  59
Periscopism.........................  37
Perspective, different forms of....... 142
----aerial..................  142, 144,157
----mathematical..........  142, 144,157
----monocular................. 142,144
----focal...................  142, 144, 156
            »                      PAGE
Phosphenes........................  67
Point of sight...................... 192
Presbyopy.......,..................  48
----a functional defect..............  50
Primary visual plane defined___.....179
Properties of central spot............  73
Pupil...............................  21
Purkinje's figures...................  63

                   K
Rate of transmission of nerve impres-
  sions ...i.........................   9
Relation of general  sensibility to spe-
  cial sense.........................   9
Retina.............................  22
----structure of.................  53, 162
----cut, showing section of.......  55, 56
----rods and cones of...............  57
----function of.....................  64
----central spot of the.............. 226
Retinal and  spatial  corresponding
  points.........................  72,162
----impressions,  law of outward pro-
  jection of.........................  64
Retrospect......................... 162
Rotation, only apparent............. 176
----on the optic axis................ 176
----real............................ 178
----effect of elevation and depression
  of the visual plane on............. 188
----experiments  illustrating......... 188
----cause of the.................... 189
----Meissner's experiments on...... 189
Sclerotic cdat.......................  20
Sensation, general...................   9
Sense»organ.........................  14
Senses, gradation of.................  11
Sensory nerve-fibers.................   9
Sight compared with other senses..  65, 84
Simple sensations...................  15
Single vision........................  95
----vision, conditions of...........  97,98
Squinting...........................  20
Stereoscopy......................... 125
Stereoscopic pictures................ 126
----pictures, method of taking...... 127
----pictures, combination of......... 123
---- pictures, combination  with the
  naked eye of........  ............. 128 
INDEX.
275
                                 PAGE
Stereoscopic  pictures,  experiments
  illustrating combination  with the
  naked eye of..................12S-133
---- phenomena, application of new
  mode of representation to.........  238
Sub-systems, conscio-voluntary......  11
----sensori-motor..................  11
----reflex..........................  11
----ganglionic......................  11
Superposition of external images.....107
System, nutritive....................  10
---nerve..........................  10
----blood..........................  10

                   T
Theories of  the  origin of the law of
  corresponding points..........  102-104
Theory, adjustment.................  44
                                 PAGE
Theory, nativistic...................  103
----empiristic......................  103
----of color perception..............   61
----of color perception, Young's___   61
----of color perception, Stanly Hall's  61
Torsion.............................  177
Transmission of nerve impressions,
  rate of.......................9,12,13
Two eyes, a single instrument.......  90

                  V
View of Briicke.................... 103
----of Giraud-Teulon............... 103
----of Helmholtz................... 103
— ofMiiller...................... 103
----ofPictet....................... 103
----of Prevost...................... 103
Vitreous humor.....................  24
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and help to that study, greater perhaps than any book yet published.  It is a
cyclopaedia of Social Science, but a cyclopaedia edited by the greatest of sociolo-
gists."—G. W. Smallet.
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             D. APPLETON &> CO., Publishers, New York. 
MODERN   SCIENTISTS,
HERBERT  SPENCER'S WORKS.   H vols.,  12mo.   Cloth, $25.25.
First Principles.................$2 00
Hkincipi.es of Biology.  2 vols... 4 00
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Principles of Sociology.  Vol. I.
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Ceremonial Institutions. Being
  Part IV. of the Principles of Soci-
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Data of Ethics.................. 1 25
Study of Sociology. (International
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Education........................ 1 25
Discussions in Science, Philoso-
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Universal Progress............. 2 0U
Essays: Moral, Political, and ^Es-
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Social Statics.................... 2 00
            Philosophy of Style.  12mo.  Flexible cloth, 50 cents.
Descriptive Sociology. To Subscribers, for the whole work, per part, $3.50; single
   part, $4.00.  Published in folio, with Tables.  Six Parts now ready, namely; 1.
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  CHARLES DARWIN'S  WORKS.

Origin of Species................$2-00
IVscent of Man................. 3 00
Journal of Researches.......... 2 00
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11 vols.,  12mo.   Cloth, $24.00.

 Insectivorous Plants............$2 00
 Climbing Plants................. 1 25
 Orchids fertilized by  Insects... 1 75
 Fertilization in the Vegetable
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 Forms of Flowers............... 1 50
 THOMAS H.  HUXLEY'S  WORKS.

Man's Place in Nature.........$1 25
On the Origin of Species........ 1 00
More Criticisms on Darwin, and
  Administrative Nihilism.......   50
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A Manual of the Anatomy of In-
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Lay Sermons, Addresses, and Re-
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11 vols.,  12mo.   Cloth, $18.00.

Critiques  and Addresses........$1 50
American  Addresses............. 1 25
Physiography..................... 2 50
Elements of Physiology and Hy-
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  J. Youmans..................... 1 50
The CRAYFisn: An Introduction to
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JOHN  TYNDALL'S  WORKS.   10 vols.,  12mo.   Cloth, $19.75.
Heat as a Mode of Motion.....$2 00
On Sound........................ 2 CO
Fragments of Science........... 2 50
Light and Electricity........... 1 25
Lessons in Electricity........... 1 00
Hours of Exercise in the Alps.$2 00
Faraday as a Discoverer....... 1 00
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Banquet at. Delmonico's, paper, 50 cents; Belfast Address, paper, 50 cents.
D. APPLETON & CO.. Publishers, 1, 8, & 5 Bond Street, New York.
1882 
 
 
 
 
 
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