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THE INTERNATIONAL SCIEWIFI 
 
 SIG- 
 
 AN EXPOSITION OF THE PRINCIPLES 
 
 OF 
 
 MONOCULAR AND BINOCULAR VISION. 
 
 BY 
 
 JOSEPH LE CONTE, LL. D., 
 
 ==^" 
 
 ACTH.OR OF "ELEMENTS OF GEOLOGY," "RELIGION AND SCIENCE," AND PROPES:OE OP 
 GEOLOGY AND NATtfKAL HISTORY IN THE UNIVERSITY OF CALIFORNIA. 
 
 WITH NUMEROUS ILLUSTRATIONS. 
 
 NEW YORK: 
 
 D. APPLETON AND COMPANY, 
 1, 3, AND 5 BOND STREET. 
 
 1881. 
 
COPYRIGHT BY 
 
 D. APPLETON AND COMPANY. 
 
 1881. 
 

 PKEFACE. 
 
 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. Vision 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 whiqji 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, out of one hun- 
 dred and thirty illustrations, only about twelve have 
 
 361 
 
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 musc]e, 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 II. 
 
 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. 
 
 PAGE 
 
 DEFECTS OF THE EYE AS AN INSTRUMENT . . .46 
 
 Emrnetropy, 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 1 compared with other senses, 
 65 ; illustrations of this property, 66 ; phosphenes, 67 ; muscse 
 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 retinas, 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, 103 ; experiments illustrating, 108-109 ; Case 
 
ANALYTICAL TABLE OF CONTENTS. 
 
 2. Similar objects, 112 ; experiments illustrating, 112-113 ; 
 Case3. 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, 1 60 ; outline form, 160 ; 
 solid form, 160 ; gradation of judgments, 160 ; retrospect, 162. 
 
 PART III. 
 ON SOME DISPUTED POINTS IN JBINOCULAK 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 convci'gent motion contrasted, 189. 
 
8 ANALYTICAL TABLE OF CONTENTS. 
 
 CHAPTER II. 
 
 PAGE 
 
 THE HOROPTER . . . . . .192 
 
 Defined, 192 ; difference of opinion as to its nature, 193 ; Muller'.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 DlA- 
 
 GRAMMATIO 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. 
 
 INTKODUCTOKY. 
 
 RELATION OF GENERAL SENSIBILITY TO SPECIAL 
 
 SENSE. 
 
 SENSOEY 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 nerve-system, and the blood-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. H 
 
 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-vohmtary ', or sensori- 
 molor, 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 
 mon sensation as a jarring. When the vibrations 
 so rapid that there are sixteen complete movem 
 back and forth in a second, an entirely different sensa- 
 
 v 
 
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. 
 
 UNMOlDiriED 
 
 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 smelly 
 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. We 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. We 
 distinctly perceive the sensation as in the nose, and yet 
 by experience we 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 j the sound does not seem to be in the 
 ear, 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 1 " 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 skin, or outer integument of 
 the face, for the skin which covers the lids turns over the 
 edge (Fig. 2, 1 1) 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. 
 
 MUSCLE? OF THE EYEBALL. #, optic nerve; 5, supe- 
 rior oblique muscle ; c, pulley ; d. inferior oblique. 
 The other four are the recti. 
 
 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, J) 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 \k& inferior Tectus 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 ((7, 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. 
 
 FIG. 4. 
 
 SECTION OF Tire EYE. 0, optic nerve; S. sclerotic ; Ch, choroid ; R, retina; v, vitre- 
 ous body ; (7m, ciliary muscle ; Cj, conjunctiva ; C, cornea ; /, iris ; Z, lens ; 
 *, aqueous humor ; **, ciliary body or zonule 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 <?, 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. (J.) 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 Lens. 
 Immediately behind the 
 iris, and in contact with it, 
 is found the crystalline. It 
 is a flattened ellipsoid, or 
 double convex leas, as clear 
 as finest glass, about one 
 third of an inch in diameter, 
 and one sixth of an inch in SECTI * OF EYE.-, sclerotic ; &, cor- 
 
 nea; c, conjunctiva; <?, iris ;, lens ; 
 
 thlCKneSS, firm enOUgh tO / ciliary muscle behind the dark 
 handle easily, but elastic and ciliary processes ; g retina; h, optic 
 ' 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. 
 
 (J.) 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. 
 
 (0.) 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 wiU 
 he a fac-simile 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, 5, Fig. 6, A, 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 
 J', 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! 1}' c', 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, J5), 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, J, are 
 
28 MONOCULAR VISION. 
 
 bent so as to come together again at the point b f . Of 
 the divergent pencil, I 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 f . 
 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 1 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 #' $', the rays have not yet come 
 together ; if too far, at S ff /$", 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 HIE 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 of 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, and we 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 
 
 FIG. 9. 
 
 r-i\ spectrum : r, red; o, orange; y, yellow; g, green; 6, blue; i, indigo; , violet. 
 
 straight beam, a 5, 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. JSTow 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 plae 
 
 FIG. 10. 
 
 FIG. 11. 
 
 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- 
 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 S 8, between these ; but even there the 
 image would not be sharp. In such a lens there is no 
 
 * Helmholtz, " Popular Lsctures," 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- SECTION ~ OW1HO TIIE 
 ness of vision is wholly conditioned on STRUCTURE OF THB 
 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 eye requires a proper regulation 
 
 * "Archives des Sciences," vol. kiii, p. 66. 18*75. 
 
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 w T e 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. 
 
 PIG. 14. 
 
 FIG. 15. 
 
 HITMAN EYE, ENLARGED, WITH PART OF CORNEA AND 
 SCLEROTIC REMOVED. a, sclerotic; >, cornea; c, 
 choroid ; d, iris ; , pupil ; /, ciliary muscle. (Af- 
 ter Cleland.) 
 
 SHOWING STRUCTURE 
 OF IRIS. 
 
 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 
 
THE 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 opsn 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 01 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 dimmish 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 ' S f 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 S* S ff , 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, S S. 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 w r ays 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 
 
 Fia. IT. 
 
 c(r 
 
 A, eye observed ; B, eye of observer ; c, section of -candle flame ; /, a distant point of 
 eight, 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, <7, 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, fy ; 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 
 
 FIG. 18. 
 
 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, y, 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 protrude a little 
 
 FIG. 19. 
 
 F) lens adjusted to _di4ant objects ; W, to nejtf 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, N, is adapted to near objects ; the left, F, 
 to distant objects, 
 
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. 47 
 
 
 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. ^Kow in the 
 passive state of the eye, as for instance in^gakii^oh^^ ;. 
 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, 
 8 
 
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 AS" /S v/ , 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 a functional 
 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 
 ^ artner 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 $' /#', 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 mate 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 liypermetropic eye may 
 be compared to a camera which, when entirely pushed 
 up, is too short for the imaging of any objects what- 
 ever. 33y 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 eve, 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 w r onderful 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. 
 
 A VIEW OF THE Two EYES, WITH OPTIO NERVES. ch, optic chiasm ; r r', nerve- 
 roots ; n and ', right and left optic nerves. (After Helmholtz.) 
 
 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 RETINA, ETC. 0, optic nerve; S, sclerotic; ch, choroid; X, 
 retina; ft, bacillary layer; g, granular and cellular layer; /, fibrous layer; V, vitre- 
 ous humor ; c, central spot. 
 
 in contact with the vitreous humor, F, is composed 
 wholly of fine interlaced fibers of the optic nerve. This 
 nerve, 0, 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, cA, 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 KETINA (after Schultze). A, general view ; .5, nervous ele- 
 ments ; a, bacillary layer ; c, external nuclear layer ; d, external granular layer ; e, 
 internal nuclear layer; /, internal granular layer; 0, 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, <?, 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, A, 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 <?, 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 ^-J-^ inch in length and 
 
58 MONOCULAR VISION. 
 
 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 TTr foir i nc ^ ^ n diameter. In this 
 spot, therefore, there are probably no less than one mil- 
 lion cones in a square Y 1 ^ inch. 
 
 FIG. 23. 
 
 BACILLART LAYER, VIEWED FROM THE OUTSIDE SURFACE. A, appearance of usual 
 surface ; E, 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, Ms 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 
 ]ayer 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 Hack 
 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 ; 
 
 * Ilcring, " Zur Lchrc von Licht-Sinnc," 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 w T ith 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. 
 
 Yery 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 Bering'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 extremes! 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-Hue. A pure 
 green appears simple gray a yellow-green, yellow mixed 
 with gray i. e., brown / and a blue green, slate-Hue. 
 
 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 ^ 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, 
 we 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 bo 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 spate. 
 
 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 mew. 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 w r ing. 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. Muscce 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 muscce voli- 
 tantes, or flying gnats. What are they ? They are specks 
 or imperfections in the transparency of the vitreous 
 
68 MONOCULAR VISION. 
 
 humor. As fishes or other objects floating in mid water 
 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- Purkinjds 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- 
 
 FIG. 21. ,-, ,, ,, 
 
 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, 
 
 INTERNAL VIEW OF THE RETINA, l ea fl e gg tree Qr }{^Q a 
 showing the retinal vessels rami- 
 
 fying over the surface, but avoid- bodileSS Spider with many 
 
 cie Jfd 6 ) C6ntral SPOt ' (After Branching legs. What is it ? 
 It is an exact but enlarged 
 
 image of the blood-vessels of the retina (Fig. 21). 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 
 
FUNCTION OF THE RETINA. 09 
 
 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 Spectra. 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 eye is first green, then blue, then 
 purple, and so gradually fades away. The spectrum is 
 equally seen w r hen 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 prof ounder 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. f 1 
 
 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. When 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 h'eld is ineradicable. If we shut our eyes, still 
 the field is there, and still it represents the state of tho 
 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, tho 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, ea3h 
 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, by 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 
 field, 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. 
 
 it is evident that these lines must 
 In other words, the lines forming coi 
 in space and on the retina cross each other m" 
 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. 
 
 'l. 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 (5) 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 YTj-for ^ an mcn m 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- 
 
Y6 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 i to f inch; on the palm, about J 
 inch ; on the finger-tips, about -^ or -fa inch ; and 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, land 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 TTF Vo (which i s the diameter 
 given by some), the smallest distance between two 
 points which ought to be visible at five inches dis- 
 tance is Y^Vo" ^ an i ncn - 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 
 
 while looking steadily with the right eye at the left 
 object, Ay 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. 
 
 FIG. 25. 
 
 B 
 
 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 , in the axis A c, 
 and the blind spot by 0, where 
 the optic nerve enters. It is 
 obvious that the image a of the 
 object A will be always on <?, 
 and the place of the image of 
 B is on the intersection J of 
 the line B ft with the retina. 
 Now, as the eye approaches the objects A and B, it is 
 seen that the image I 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, E"^ it is upon it. 
 
80 MONOCULAR VISION. 
 
 At the fourth position, 7?'", 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 4- 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 Yen us 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, I 
 measure the latter by the former. I have made many \ 
 experiments to determine the size of the invisible spot. 
 At the distance of 3J feet (42 inches) I find the invisi- 
 ble spot 12 inches from the point of sight, and 3J inches 
 in diameter ; i. e., a circle of 3J 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 -fa 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 4f . 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 f 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 jy p 
 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 darkness 
 is the outward projection of' the unstim.ulated 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 
 the left eye shut, bring the pin-head 
 
 very near to the open eye, so that it 
 touches the lashes, and in the line of 
 sight : a perfect inverted image of 
 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 
 
 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 ; 
 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 3. 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 1871. See 
 "Philosophical Magazine," vol. Ixi, 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, Z') 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, 5 $, 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 1 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. With 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 
 
 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 retinae. 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 f , 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 tw T o 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 AXD 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 Tight-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-drained. 
 
 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 
 
SIXGLE 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- 
 
 5 
 
 FIG. 80. 
 
96 
 
 BINOCULAR VISION. 
 
 tion, that we always see tilings 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 w T hat are called corresponding points (or some- 
 times identical points) of the two retinae. 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'* 
 
 Fo. 81. 
 
 in the centers of the bottom, will represent the position 
 of the central spots. If now we draw vertical lines 
 (vertical meridians), a J, a' ', 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 5 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 J, aJ 5', 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 VISIOX. 
 
 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 Z, two eyes ; 0, center of rotation of ball, or optic center ; ce, point of crossing 1 
 of ray-lines nodal point ; A, point of sight; Z>, some other point in the horoptoric 
 circle A O 0' ; c c', 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, 
 It 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 L 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, ', 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 horopterio 
 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, It and Z, are fixed upon A, 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., J 5', 
 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 retinse, 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 portion of the dou- 
 
100 
 
 BINOCULAR VISION. 
 
 ble images will be correctly represented by c c', bb f . 
 It is seen at a glance that the images c c' of C are het- 
 eronymous, while the images & $' of B are homony- 
 mous. Generally, all the field of view within the lines 
 
 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 
 while those formed by impressions on 
 .halves are heteroriymous. ' 
 
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 O' 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', ths nasal halves, and 1 1', 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. 1Q3 
 
 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 W . \ 
 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 nativistic, 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. 
 
CHAPTER II. 
 
 SUPERPOSITION OF EXTERNAL 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 tw r o 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. Xow 
 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. 
 
 O - O 
 
 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, It, is 
 directed toward the object B, and the left eye, Z, to- 
 
 FIG. 35 
 
 In both figures the letters are the same. R and Z, the two eyes ; A and B, two ob- 
 jects ; '&, Fig. 35, and aft', 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 &', are seen to the right 
 and left. Their position in the plane of sight, and as 
 
SUPERPOSITION OF EXTERNAL IMAGES. HI 
 
 determined by the law of direction, is given by con- 
 necting the points R A and L 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, aV, 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 L A to the 
 plane of sight. It is evident that in this case the two 
 objects A 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 p p 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 will 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 &', 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. 
 
 113 
 
 bined images, like a real opaque object, will be seen at 
 the point of sight ab f , and the two shadowy monocular 
 images right and left, as before, only they are now het- 
 eronymous. 
 
 FIG. 37. 
 
 FIG. 
 
 ii> 
 
 Iii 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, SG, sc f , 
 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, &/, will hide the left piece E 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 f 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 (2J inches), then it 
 is possible also to unite the figures beyond the real plane 
 i.e., on the plane P 1 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 ail 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 iind 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. 
 
CHAPTEK III. 
 
 BINOCULA R 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 #', the nearer, b and ', will not have come 
 together yet, and will therefore be heteronymously 
 
 FIG. 43. 
 
 FIG. 42. 
 
 u 
 
 R 
 
 II 
 
 double, as in Fig. 43, I ; when by greater convergence 
 we combine the images b and b f 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. 
 
 ]S r ow, 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 J a being the nearer 
 and ~b the farther end. If we shut the right eye and 
 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 /\ . If, on the contrary, we look at the 
 
 a/ \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 \/ . 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 V . Or, to put it differently, the 
 
 external images of the two eyes are like these lines 
 
 / and \ : if these two be brought together so 
 
 as to unite the farther ends 5 ~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 fa . 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 IB. 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 
 
 H. 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 (pi. If we look at the nearer part or back, 
 then this is seen single, but the farther edge is now 
 double, thus n. 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. 
 
 STEREOSCOPV. 
 
 "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 w r e 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 Fi ^ 44 
 
 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- 
 S3Opic 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. Seleet 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 card; 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. 
 
 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 w T e 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 J3 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 Z> 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 diagrammatical!) 7 
 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 ; 
 It and Z, the right and left eyes. 
 On the plane of the paper p p, a FlG - 46 - 
 
 and a' represent identical points in 
 the foreground, viz., the centers of 
 the small circles in the diagram Fig. 
 45 ; and b and If 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. ISTow when b and b f 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 f 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 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 A> 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. 
 
 FIG. 48. 
 
 identical points of the foreground, and b and I' of the 
 background ; and sc and ?', 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 5 
 and 5', 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 b f 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 J?, 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 VISIOX. 
 
 For example, I now take up a stereoscopic card ^pre- 
 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 away 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. 
 
 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. Monocular 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. ISTow, 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 
 point. 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 IY. 
 
 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 
 
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-per.ception. 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. 14.7 
 
 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. 
 
 Briicke'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). 
 
14:8 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 -g-j-^-g- 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, w r hich according to Arago lasts only -j-oW?* and 
 according to Rood -^-J^f f a second. It is inconceiva- 
 
 * Arago, " CEuvrcs Completes," tome iv, p. 70. 
 
 f Rood, "American Journal of Science and Arts," vol. i, 1870, p. 15. 
 
THEORIES OF BINOCULAR PERSPECTIVE. 149 
 
 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 ^- ^oir P art ^ a secon d- 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 Briicke'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 Leyden 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 eyes 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^griicke, Brewster, and others. 
 
 two rival theories, therefore, the case 
 r^hkatstone is right in so far as he asserts 
 
 B- 
 
THEOEIES OF BINOCULAR PERSPECTIVE. 
 
 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 \)j less 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 
 f "American Journal of Science and Arts," vol. ii, 1871, p. 425. 
 
152 BINOCULAR VISION. 
 
 Tims, 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 develop 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 form 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 two essential because found every- 
 where between human and natural mechanism : In the 
 one case we 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 world, 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 Y. 
 
 JUDGMENT OF DISTANCE, SIZE, AND FORM. 
 
 WE are now 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. 
 
 Yery 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 ait 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 conies solid form, which, as we have seen, 
 
JUDGMENT OF DISTANCE, SIZE, AND FORM. 
 
 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. 
 
 IS r ow, 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. 
 
: 3 
 
 PAET III. 
 
 ON SOME DISPUTED POINTS IN 
 BINOCULAR VISION. 
 
 CHAPTER I. 
 
 LAWS OF OCULAR MOTION. 
 SECTION I. LAWS OF PARALLEL MOTION. LISTING'S LAW. 
 
 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 tlie 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 V ; 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 ( x \ x ), 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. 
 
 DlAJBAM SHOWING THE INCLINATION OF VERTICAL AND HORIZONTAL IMAGES FOB 
 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 4- Make a rectangular cross-slit in the 
 window, gaze steadily upon it until the spectral impres- 
 
168 DISPUTED POINTS IN BINOCULAR VISIOX. 
 
 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 -r~^ . Looking upward and to the left, it is 
 
 \ 
 
 seen thus ""V*-* Oblique motion downward and to 
 the right makes it appear thus ^W , and to the left 
 
 thus ^. 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, loth 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 
 
 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 -\ ^ 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 everywhsre 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. 56. 
 
 DIAGRAM SHOWING THE PROJECTION OF A SYSTEM OF SPHERICAL COSRDINATES 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 we 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 low r er to the 
 left, and the left lower to the right, and 
 we have the precise phenomena repre- 
 sented 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 TRUE TORSION OF TOE EYE FOR VARIOUS POSITIONS OF 
 THE POIMT 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." * 
 
 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 Physiologique," p. 602. 
 
1T6 
 
 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 
 
 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 Vto the left. It will be 
 seen that V Fis no longer vertical, norJIII horizontal ; 
 but some other line x x is vertical, and y y horizontal. 
 In other words, the whole disk seems to have rotated 
 to 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 game, 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- FlG - co - 
 
 tal line exactly the height **( 
 of the root of the nose. \ 
 
 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 
 
180 
 
 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. 
 
 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 f . 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, w T hich 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, 
 
 r\ll 
 
 but make a small angle, thus U ; and ako 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 r is the experimental plane. 
 The arrows show the direc- 
 tion of rotation of the images 
 of the plane and of the eyes. 
 Experiment 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 
 
 r \l l 
 together, not parallel, but -as a sharp V, thus \ I , 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 horizontally 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 W ; 
 
 looking horizontal, parallel, thus . But on account 
 of rotation, looking horizontal brings them together 
 
 r\ll ry il 
 
 thus y ; downward, at higher angle, thus W 
 
 Looking upward more and more, the angle decreases 
 till it becomes (i. e., the jambs parallel), and then in- 
 verted. I find that in the previous experiment, stand- 
 ing from the 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 \\. 
 
 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 1J, 
 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", HOKIZONTALS 6". 
 
 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 
 
 \/ r 
 other, thus V , 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. 
 
 a closed window. I now turn about, and, keeping the 
 left eye Z, 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 P, 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 L s ' . 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 Meet 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 theso 
 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 bs 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 Hi, 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. 
 
 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. 
 
CHAPTEE 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 retinae, 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 homonyrnously, 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 
 
THE 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' is the line 
 between the optic centers, n n f the nodal points or 
 points of ray-crossing, A the point of sight, and B an 
 
 FIG. 66. 
 
 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 f . It is seen also that the images of B 
 fall at & 5', at equal distances from the central spots 
 c c f , one on the nasal half and one on the temporal half, 
 and therefore on corresponding points. The Jioropteric 
 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 
 
 FIG. 67. 
 
 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 f , Fig. 67, and the ho- 
 ropteric circle, A O', 
 and in addition is fur- 
 ther characterized by 
 the fact that the inter- 
 section with it of every 
 plane passing through 
 the optic centers 0' 
 upward as B 0' or 
 downward as B' 0' is 
 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 which 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 w r e stand which 
 is equally distant from the two eyes, the horopter is not 
 a plane, but the straight line w r hich 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 w r hich pegs may be set. The 
 
THE HOROPTER. 197 
 
 eyes look horizontally over tlie 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 demarcation, 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 
 1J, and therefore with one another in the two eyes of 
 2J. The horizontal meridians of the eyes, both real 
 and apparent, coincide completely. Therefore, if the 
 two eyes were 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 
 
 l \r 
 
 each other at the central spot thus V , making 
 
 r/\l 
 
 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 1J 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 1J 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 w r ith 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 
 
THE HOROrTER. 
 
 199 
 
 true ; for, with an interocular distance of 2 inches, two 
 lines drawn through the optic centers, each inclined 1 J 
 with the vertical and therefore 2J 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 retinse, 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 1J 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 
 v fiQ other, so that the real vertical meridians 
 
 Jr IG. by. 
 
 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|. ~Now the 
 tw r o rods 2 inches apart at the height 
 of the eyes, and meeting below at the 
 THE BETING SUPERPOSED, feet, or the rod lying along the ground 
 
 -r r, line of demarka- t i n fi n i te distance, WOuld OCCUpV with 
 tion of right eye ; II, * 
 
 line of demarkation of their images only the upper half of 
 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 we 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 we 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- 
 ticality 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 
 
 ~~ 
 
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 1J. 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. dt., p. 914. 
 
 f Meissner, "Physiologic 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 
 
 r \l l 
 at the point of sight thus V , r r being the right- 
 
 l'!\r' 
 
 eye image, and I I' 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, 
 
 r \ I 1 
 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 / 
 
 FIG. 70. 
 
 so that the vertical lines of demarkation, C 7), C' D' , 
 Fig. TO, no longer coincide perfectly with the vertical 
 
THE HOROPTER. 205 
 
 meridians A B, A' B' , nor the horizontal lines of de- 
 markation G H, G ' H' with the horizontal meridians 
 E F, E' F', as they do when the eyes are parallel, hut 
 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. 
 
 FIG. 71. 
 
 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 rny 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, w r ere 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 1J 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 L represent the right and left eyes respectively, 
 
 FIG. 72. 
 
 H 
 
 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 H 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' H, 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 4J inches in the first to 1J 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 retinoe. 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 the 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 j, 
 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. 
 
 trarj, 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 j 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 
 E A Z, R B L. 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 & 
 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 SOME FUNDAMENTAL PHENOMENA. 217 
 
 other by a space exactly equal 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 cyclopienne), 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, with 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 retinas 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, 7? 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 eve (mil cyclopi- 
 enne) ; n and n', the two images of the nose belonging 
 to the right and left eyes respectively ; F", the combined 
 or binocular visual line, looking between the double im- 
 ages a and a! of the object A; while r f 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 A and B are before the eyes in the visual 
 lines v v and Fig. 83 is the visual result, in which a! 
 and 5 are the monocular images, one belonging to the 
 left and the other to the right eye, AE 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 ^i, 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 L 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 f , a a! of fig. 85 ; while the two eyes, R and Z, 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 V, 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 
 two images we look out on the combined pictures. 
 
 Experiment 4- 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 on.e 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. We 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, we 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 cydopienne 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 brow, and ch of the cheek of 
 the right- eye field ; &/, 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 tke 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. FIG. 88. 
 
 225 
 
 the rod, together with nose and finger-point, will be 
 doubled heteronymously and become two parallel rods, 
 
 FIG. 89. 
 
 Fro. 90. 
 
226 DISPUTED POINTS IN BINOCULAR VISION. 
 
 between which, the binocular eye will 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. We will observe 
 that the double images of the rod represented in the 
 visual result, Fig. 88, approach at their farther end, car- 
 
 Fio. 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 5 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- 
 rnously. 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 (7, 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 r , 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 IX 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, hornony- 
 mously in the former case and heteronymously in the 
 latter, about the optic center of the binocular eye (mil 
 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 ceil 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 ; (&) 
 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 #-&', or c-e', is exactly the 
 interocular distance i. e., the dis- 
 tance between the central points 
 of the central spots of the two 
 retinoe. 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 ml cydopienne 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 L 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 L 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 
 
OX 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 Fi as if coming from a single bin- 
 ocular eye K 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 would 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. 
 
 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, with 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 fr ', Fig. 104, unite to 
 form B, Fig. 103, and v E, v f 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 It and L on the experimental 
 board, Fig. 98, 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. PIG. 105. 
 
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 J?, let the 
 dotted lines to E be stronger to represent visual lines ; 
 
 FIG. 106. FIG. 10T. 
 
 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, 
 Fig. 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. 1 07. 
 
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- 
 Fro m ging the eyes slowly, the two 
 
 images of Fig. 106 shown in 
 Fig. 108 are seen to rotate on 
 E until the points b V and the 
 dotted lines b E^ V 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. 111. 
 
 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. 
 
 Experiment. 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. 
 
 FIG. 112. 
 
 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 
 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 w r ill unite into a bin- 
 
 FIG. 113. 
 
 FIG. 114. 
 
 a. 
 
 o 
 
 ft' 
 
 o 
 
 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 ; in s, the median screen, which cuts off the super- 
 numerary monocular images ; a a, identical points in 
 the foreground of the pictures, and b J, in the back- 
 ground. The two eyes and the nose are represented 
 as before by It, Z, and n ; and a 7?, a L, 1> 7?, 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 .7?, 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 5, then b 7?, 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 of b b 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 5, 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 JB, 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 b', 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 with 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- 
 
244 
 
 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, J &. 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 tlie 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. Now, 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 V. 
 
 If stereoscopic pictures mounted in the usual w r ay 
 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 o b f will become heteronymous, and 
 therefore referred to the nearer point. 
 
 Some curious Phenomena 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, 
 
246 
 
 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 object 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 L 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 outlino is traced with the poncil P. This 
 
 FIG. 121. 
 
 FIG. 122. 
 
 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. 94.7 
 
 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 with 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 f 
 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 
 
 d 
 
 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 way. 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. F is 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. 
 
 ts 
 
 its 
 
 ms 
 
 r 
 
 n 
 
 the visual line of the right eye pierces the transverse 
 screen, viz., at /", 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 4- 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 2|- 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 lino 
 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. 120. 
 
CHAPTEE IY. 
 
 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 
 ba 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 w r as 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 heieronymows. 
 But convergence produces homonymous images, while 
 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 2J- 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," MuUcr, " 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 well-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 hoinony- 
 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 1J. 
 
 Experiment 4- But by mechanical force we 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 unit3. 
 
 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 ; I ~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 J b are brought together and 
 superposed at B ; the median line is doubled and ro- 
 
 Fis. 12T. 
 
 A 
 
 I b 
 
 m \r 
 
 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 
 
258 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. 120 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 IX OCULAR DIVERGENCE. 259 
 
 pletely reversed. It may indeed be said that the case 
 of a a seen in front may be reconciled with the law of 
 direction. For, if the combined images be referred to 
 
 FIG. 129. 
 M 
 
 a., 
 
 '' 
 
 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 
 
 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 f of the object J/, 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- 
 
 FIG. 181. FIG. 132. 
 
 / 
 
 (n 
 
 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 Y. 
 
 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. Whether 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 t 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, w r ith 
 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 w T ider 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 110 
 longer 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. 265 
 
 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 w r e find in the eyes, and which 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 (1878); "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. We 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 bj 
 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 eyes 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 . . . 81 
 
 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 
 
 Bacillary layer 55, 86 
 
 Back of the hand, to see through 250 
 
 Binocular combinations, by the stereo- 
 scope 134 
 
 field 91 
 
 perspective 120, 143, 144 
 
 perspective, experiments illus- 
 trating 120-124 
 
 perspective, theories of 145 
 
 perspective, Wheatstone's theo- 
 ries of 145-147 
 
 perspective, Briicke's theory of. . 147 
 
 perspective, experiment illustrat- 
 ing Briicke's theory 147 
 
 perspective, Dove's experiment. . 145 
 
 perspective, Helmholtz's, the true 
 
 theory of. 151 
 
 perspective, judgment by means 
 
 of 156 
 
 vision 90 
 
 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.. 73-81 
 spot, size of 81 
 
 spot, representative in the visual 
 field of the 82 
 
 Book, to see through 250 
 
 Brief statement of laws 229 
 
 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 
 
 Chore-id coat 22 
 
 Chromatism, correction of 31 
 
 correction of, hint for 35 
 
 Ciliary processes '. 22 
 
 Colors, perception of 59 
 
272 
 
 INDEX. 
 
 Colors, primary 
 
 r Brewster's view of 
 
 - Young's view of 
 
 - Bering's view of 
 
 PAGE 
 
 60 
 
 60 
 60 
 60 
 
 Color blindness ..................... 62 
 
 - blindness, theory of. ............ C3 
 
 Combination of images of different ob- 
 
 jects .............................. 10S 
 
 -- 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 ............. 118 
 
 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 tho retinae, relation of 
 the optic chiasm to the law of ..... 101 
 
 - points of the retinae, cause of law 
 
 of ................................ 262 
 
 Crystalline lens ..................... 23 
 
 Daltonism 62 
 
 Deal board, to see through a 250 
 
 Dcxtrality 94 
 
 Dispersion 32 
 
 Divergence of eye-sockets 2C3 
 
 of eye-sockets, extreme 263, 2C4 
 
 Double images 92 
 
 images, experiments illustrating 
 
 92, S3 
 E 
 
 Ectoderm 11 
 
 Emmetropy 46 
 
 Endoderm 11 
 
 Erect vision 63 
 
 Experience, inherited 104 
 
 Experiments illustrating ihe combina- 
 tion of images of dissimilar objects, 
 
 103-112 
 
 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 
 
 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 
 
 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 ofthe 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 169,202 
 
 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 of the 20c-2 1 
 
 conclusions in regard to the 210 
 
 difference between the author's 
 
 and Meissner's view of the 211 
 
 Horopteric circle of Miiller 99, 194 
 
 Human eye, general structure of IT 
 
 muscles of the 18 
 
 Humor, aqueous ... 24 
 
 vitreous 24 
 
 Hypermetropy 51 
 
 Identical points 98 
 
 Image, light 152, 158 
 
 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 
 
 Judgments of distance 156 
 
 of size , 157 
 
 of size, experiments illustrating 
 
 157-159 
 
 of form 160 
 
 gradations of 160 
 
 visual 161 
 
 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 
 
 of Listing 164,174,191, 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 28 
 
 capsule of 23 
 
 opacity of 24 
 
 property 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, C4 
 
 Muscse 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 delect 50 
 
 N 
 
 Nativistic theory 262 
 
 Near-sightedness 46 
 
 Nerves, olfactive 10 
 
 optic 10 
 
 auditive 10 
 
 gustati ve 10 
 
 Nodal point . 29 
 
 Ocular divergence, binocular visual 
 
 phenomena in 252 
 
 divergence, other modes of pro- 
 ducing 255 
 
 spectrae 69 
 
 (Eil cyclopienne 222, 229, 231 
 
 Old-sightedness 48 
 
 Opposition of law of direction to law 
 
 of corresponding points 258 
 
 of law of direction to law of cor- 
 responding points, explanation of 
 
 253-2(50 
 
 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 
 
 Parallel motion, laws of 164 
 
 motion, laws of, experiments il- 
 lustrating 164-172 
 
 motion, statement of the laws of 
 
 173, 174 
 
 motion, Ilelmholtz's contrary 
 
 statement of the laws of 1 75 
 
 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, 16 
 
 PAGE 
 
 Phosphenes 67 
 
 Point of sight 192 
 
 Presbyopy , 43 
 
 a functional defect 50 
 
 Primary visual plane defined ... 179 
 
 Properties of central spot 73 
 
 Pupil 21 
 
 Purkinje's figures 63 
 
 E 
 
 Kate of transmission of nerve impres- 
 sions 9 
 
 Relation of general sensibility to spe- 
 cial sense 9 
 
 Eetina 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 1S8 
 
 experiments illustrating 188 
 
 cause of the 189 
 
 Meissncr's experiments on 189 
 
 Sclerotic coat 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 12S 
 
 pictures, combination with the 
 
 naked eye of 128 
 
INDEX. 
 
 275 
 
 PAGE 
 
 Stereoscopic pictures, experiments 
 illustrating combination with the 
 naked eye of. 129-133 
 
 phenomena, application of new 
 
 mode of representation to 238 
 
 Sub-systems, conscio-voluntary 11 
 
 sensori-motor 11 
 
 reflex 
 
 ganglionic 
 
 Superposition of external images . 
 
 System, nutritive 
 
 nerve 
 
 blood... 
 
 11 
 11 
 107 
 10 
 10 
 10 
 
 Theories of the origin of the law of 
 
 corresponding points 102-104 
 
 Theory, adjustment 44 
 
 PAGE 
 
 Theory, nativistic 1C3 
 
 empiristic 103 
 
 of color perception 61 
 
 of color perception, Young's 61 
 
 of color perception, Stanly HalPs 61 
 
 Torsion 177 
 
 Transmission of nerve impressions, 
 
 rate of 9, 12, 13 
 
 Two eyes, a single instrument 90 
 
 View of Briicke 103 
 
 of Giraud-Teulon 103 
 
 of Helmholtz. 103 
 
 ofMuller 103 
 
 of Pictet 103 
 
 of Prevost 103 
 
 Vitreous humor 24 
 
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UNIVERSITY OF CALIFORNIA MEDICAL SCHOOL LIBRARY 
 
 THIS BOOK IS DUE ON THE LAST DATE 
 STAMPED BELOW 
 
 
 
,,P475 Le 
 
 L4t 
 
 1881 
 
 Qonte, 
 ight-. 
 
 361 
 
 
 361