The birth of Stereoscopy: Wheatstone on Binocular Vision 1838, original source

digitized by Alexander Klein and first published on, used with kind permission. Preface by Pascal Martiné.
Charles Wheat­stone

Today, it is com­mon­ly known (at least for those inter­est­ed in stere­oscopy) that our vision con­sists of two images. Our brain fus­es these two images into one and lets us per­ceive a sense of depth caused by slight dif­fer­ences between the two images.

Back in the 19th cen­tu­ry the con­cept of binoc­u­lar vision had not yet been explored or writ­ten about any­where. It was a sci­en­tist in his mid 30s who not only described the phe­nom­e­non lat­er called stere­op­sis but also con­struct­ed a device to view two flat images in 3D which he called a stere­o­scope. This is espe­cial­ly remark­able as pho­tog­ra­phy was not invent­ed until one year lat­er. Charles Wheat­stone’s obser­va­tions were based only on draw­ings. Most of these draw­ings are based on hor­i­zon­tal mir­ror­ing which is why we call them mir­ror stere­os today.

Wheat­stone’s paper, pre­sent­ed to the Roy­al Soci­ety of Lon­don on June 21st 1838, is orga­nized in 16 para­graphs and is there­fore quite exten­sive. But even if the improve­ments by Sir David Brew­ster replaced Wheat­stone’s stere­o­scope about ten years lat­er, his obser­va­tions can still be con­sid­ered as the birth of Stere­oscopy. There­fore, I want to give my full rec­om­men­da­tion to read this source entire­ly. Do you remem­ber your first time look­ing through a stere­o­scope? Well, put your­self into the mind­set that noth­ing about it is known. After a talk about binoc­u­lar vision that you fol­lowed with more or less inter­est, you are pre­sent­ed with a strange-look­ing opti­cal mir­ror toy and some hand draw­ings. But look­ing through it com­plete­ly blows your mind…

If you got more inter­est­ed in the the­o­ry of stere­oscopy after­wards, you might also want to read David Kuntz’ arti­cles about the base­line and the stereo win­dow or my arti­cle about hyper stere­os. I’ve also cre­at­ed an inter­ac­tive ver­sion of the graph­ic in para­graph 15 which can be accessed here.

§1 §2 §3 §4 §5 §6 §7 §8 §9 §10 §11 §12 §13 §14 §15 §16

Philo­soph­i­cal Trans­ac­tions of the Roy­al Soci­ety of Lon­don, Vol. 128, pp. 371 — 394

Contributions to the Physiology of Vision. — Part the First.
On some remarkable, and hitherto unobserved, Phenomena of Binocular Vision.

By CHARLES WHEATSTONE, F.R.S., Professor of Experimental Philosophy in King’s College, London.

Received and Read June 21, 1838.

§ 1.

WHEN an object is viewed at so great a dis­tance that the optic axes of both eyes are sen­si­bly par­al­lel when direct­ed towards it, the per­spec­tive pro­jec­tions of it, seen by each eye sep­a­rate­ly, are sim­i­lar, and the appear­ance to the two eyes is pre­cise­ly the same as when the object is seen by one eye only. There is, in such case, no dif­fer­ence between the visu­al appear­ance of an object in relief and its per­spec­tive pro­jec­tion on a plane sur­face; and hence pic­to­r­i­al rep­re­sen­ta­tions of dis­tant objects, when those cir­cum­stances which would pre­vent or dis­turb the illu­sion are care­ful­ly exclud­ed, may be ren­dered such per­fect resem­blances of the objects they are intend­ed to rep­re­sent as to be mis­tak­en for them; the Dio­ra­ma is an instance of this. But this sim­i­lar­i­ty no longer exists when the object is placed so near the eyes that to view it the optic axes must con­verge; under these con­di­tions a dif­fer­ent per­spec­tive pro­jec­tion of it is seen by each eye, and these per­spec­tives are more dis­sim­i­lar as the con­ver­gence of the optic axes becomes greater. This fact may be eas­i­ly ver­i­fied by plac­ing any fig­ure of three dimen­sions, an out­line cube for instance, at a mod­er­ate dis­tance before the eyes, and while the head is kept per­fect­ly steady, view­ing it with each eye suc­ces­sive­ly while the oth­er is closed. Plate XI. fig. 13. rep­re­sents the two per­spec­tive pro­jec­tions of a cube; is that seen by the right eye, and a that pre­sent­ed to the left eye; the fig­ure being sup­posed to be placed about sev­en inch­es imme­di­ate­ly before the spectator.

The appear­ances, which are by this sim­ple exper­i­ment ren­dered so obvi­ous, may be eas­i­ly inferred from the estab­lished laws of per­spec­tive; for the same object in relief is, when viewed by a dif­fer­ent eye, seen from two points of sight at a dis­tance from each oth­er equal to the line join­ing the two eyes. Yet they seem to have escaped the atten­tion of every philoso­pher and artist who has treat­ed of the sub­jects of vision and per­spec­tive. I can ascribe this inat­ten­tion to a phe­nom­e­non lead­ing to the impor­tant and curi­ous con­se­quences, which will form the sub­ject of the present com­mu­ni­ca­tion, only to this cir­cum­stance; that the results being con­trary to a prin­ci­ple which was very gen­er­al­ly main­tained by opti­cal writ­ers, viz. that objects can be seen sin­gle only when their images fall on cor­re­spond­ing points of the two ret­inæ, an hypoth­e­sis which will be here­after dis­cussed, if the con­sid­er­a­tion ever arose in their minds, it was hasti­ly dis­card­ed under the con­vic­tion, that if the pic­tures pre­sent­ed to the two eyes are under cer­tain cir­cum­stances dis­sim­i­lar, their dif­fer­ences must be so small that they need not be tak­en into account.

It will now be obvi­ous why it is impos­si­ble for the artist to give a faith­ful rep­re­sen­ta­tion of any near sol­id object, that is, to pro­duce a paint­ing which shall not be dis­tin­guished in the mind from the object itself. When the paint­ing and the object are seen with both eyes, in the case of the paint­ing two sim­i­lar pic­tures are pro­ject­ed on the ret­inæ, in the case of the sol­id object the pic­tures are dis­sim­i­lar; there is there­fore an essen­tial dif­fer­ence between the impres­sions on the organs of sen­sa­tion in the two cas­es, and con­se­quent­ly between the per­cep­tions formed in the mind; the paint­ing there­fore can­not be con­found­ed with the sol­id object.

After look­ing over the works of many authors who might be expect­ed to have made some remarks relat­ing to this sub­ject, I have been able to find but one, which is in the Trat­ta­to del­la Pit­tura of LEONARDO DA VINCI¹. This great artist and inge­nious philoso­pher observes, “that a paint­ing, though con­duct­ed with the great­est art and fin­ished to the last per­fec­tion, both with regard to its con­tours, its lights, its shad­ows and its colours, can nev­er show a relie­vo equal to that of the nat­ur­al objects, unless these be viewed at a dis­tance and with a sin­gle eye. For,” says he, “if an object C (Plate X. fig. 1.) be viewed by a sin­gle eye at A, all objects in the space behind it, includ­ed as it were in a shad­ow E C F cast by a can­dle at A, are invis­i­ble to the eye at A; but when the oth­er eye at B is opened, part of these objects become vis­i­ble to it; those only being hid from both eyes that are includ­ed, as it were, in the dou­ble shad­ow C D, cast by two lights at A and B, and ter­mi­nat­ed in D, the angu­lar space E D G beyond D being always vis­i­ble to both eyes. And the hid­den space C D is so much the short­er, as the object C is small­er and near­er to the eyes. Thus the object C seen with both eyes becomes, as it were, trans­par­ent, accord­ing to the usu­al def­i­n­i­tion of a trans­par­ent thing; name­ly, that which hides noth­ing beyond it. But this can­not hap­pen when an object, whose breadth is big­ger than that of the pupil, is viewed by a sin­gle eye. The truth of this obser­va­tion is there­fore evi­dent, because a paint­ed fig­ure inter­cepts all the space behind its appar­ent place, so as to pre­clude the eyes from the sight of every part of the imag­i­nary ground behind it.”

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§ 2.

It being thus estab­lished that the mind per­ceives an object of three dimen­sions by means of the two dis­sim­i­lar pic­tures pro­ject­ed by it on the two ret­inæ, the fol­low­ing ques­tion occurs: What would be the visu­al effect of simul­ta­ne­ous­ly pre­sent­ing to each eye, instead of the object itself, its pro­jec­tion on a plane sur­face as it appears to that eye? To pur­sue this inquiry it is nec­es­sary that means should be con­trived to make the two pic­tures, which must nec­es­sar­i­ly occu­py dif­fer­ent places, fall on sim­i­lar parts of both ret­inæ. Under the ordi­nary cir­cum­stances of vision the object is seen at the con­course of the optic axes, and its images con­se­quent­ly are pro­ject­ed on sim­i­lar parts of the two ret­inæ; but it is also evi­dent that two exact­ly sim­i­lar objects may be made to fall on sim­i­lar parts of the two ret­inæ, if they are placed one in the direc­tion of each optic axis, at equal dis­tances before or beyond their intersection.

Fig. 2. rep­re­sents the usu­al sit­u­a­tion of an object at the inter­sec­tion of the optic axes. In fig. 3. the sim­i­lar objects are placed in the direc­tion of the optic axes before their inter­sec­tion, and in fig. 4. beyond it. In all these three cas­es the mind per­ceives but a sin­gle object, and refers it to the place where the optic axes meet. It will be observed, that when the eyes con­verge beyond the objects, as in fig. 3., the right hand object is seen by the right eye, and the left hand object by the left eye; while when the axes con­verge near­er than the Objects, the right hand object is seen by the left eye, and con­verse­ly. As both of these modes of vision are forced and unnat­ur­al, eyes unac­cus­tomed to such exper­i­ments require some arti­fi­cial assistance. 

If the eyes are to con­verge beyond the objects, this may be afford­ed by a pair of tubes (fig. 5.) capa­ble of being inclined towards each oth­er at var­i­ous angles, so as to cor­re­spond with the dif­fer­ent con­ver­gences of the optic axes. If the eyes are to con­verge at a near­er dis­tance than that at which the objects are placed, a box (fig. 6.) may be con­ve­nient­ly employed; the objects a a’ are placed dis­tant from each oth­er, on a stand capa­ble of being moved near­er the eyes if required, and the optic axes being direct­ed towards them will cross at c, the aper­ture b b’ allow­ing the visu­al rays front the right hand object to reach the left eye, and those from the left hand object to fall on the right eye; the coin­ci­dence of the images may be facil­i­tat­ed by plac­ing the point of a nee­dle at the point of inter­sec­tion of the optic axes c, and fix­ing the eyes upon it. In both these instru­ments (figs. 5. and 6.) the lat­er­al images are hid­den from view, and much less dif­fi­cul­ty occurs in mak­ing the images unite than when the naked eyes are employed.

Now if, instead of plac­ing two exact­ly sim­i­lar objects to be viewed by the eyes in either of the modes above described, the two per­spec­tive pro­jec­tions of the same sol­id object be so dis­posed, the mind will still per­ceive the object to be sin­gle, but instead of a rep­re­sen­ta­tion on a plane sur­face, as each draw­ing appears to be when sep­a­rate­ly viewed by that eye which is direct­ed towards it, the observ­er will per­ceive a fig­ure of three dimen­sions, the exact coun­ter­part of the object from which the draw­ings were made. To make this mat­ter clear I will men­tion one or two of the most sim­ple cases.

If two ver­ti­cal lines near each oth­er, but at dif­fer­ent dis­tances from the spec­ta­tor, be regard­ed first with one eye and then with the oth­er, the dis­tance between them when referred to the same plane will appear dif­fer­ent; if the left hand line be near­er to the eyes the dis­tance as seen by the left eye will be less than the dis­tance as seen by the right eye; fig. 7. will ren­der this evi­dent; a a’ are ver­ti­cal sec­tions of the two orig­i­nal lines, and b b’ the plane to which their pro­jec­tions are referred. Now if the two lines be drawn on two pieces of card, at the respec­tive dis­tances at which they appear to each eye, and these cards be after­wards viewed by either of the means above direct­ed, the observ­er will no longer see two lines on a plane sur­face, as each card sep­a­rate­ly shows ; but two lines will appear, one near­er to him than the oth­er, pre­cise­ly as the orig­i­nal ver­ti­cal lines them­selves. Again, if a straight wire be held before the eyes in such a posi­tion that one of its ends shall be near­er to the observ­er than the oth­er is, each eye sep­a­rate­ly refer­ring it to a plane per­pen­dic­u­lar to the com­mon axis, will see a line dif­fer­ent­ly inclined ; and then if lines hav­ing the same appar­ent incli­na­tions be drawn on two pieces of card. and be pre­sent­ed to the eyes as before direct­ed, the real posi­tion of the orig­i­nal line will be cor­rect­ly per­ceived by the mind.

In the same man­ner the most com­plex fig­ures of three dimen­sions may be accu­rate­ly rep­re­sent­ed to the mind, by pre­sent­ing their two per­spec­tive pro­jec­tions to the two ret­inæ. But I shall defer these more per­fect exper­i­ments until I describe an instru­ment which will enable any per­son to observe all the phe­nom­e­na in ques­tion with the great­est ease and certainty.

In the instru­ments above described the optic axes con­verge to some point in a plane before or beyond that in which the objects to be seen are sit­u­at­ed. The adap­ta­tion of the eye, which enables us to see dis­tinct­ly at dif­fer­ent dis­tances, and which habit­u­al­ly accom­pa­nies every dif­fer­ent degree of con­ver­gence of the optic axes, does not imme­di­ate­ly adjust itself to tIme new and unusu­al con­di­tion ; and to per­sons not accus­tomed to exper­i­ments of this kind, the pic­tures will either not read­i­ly unite, or will appear dim and con­fused. Besides this, no object can be viewed accord­ing to either mode when the draw­ings exceed in breadth the dis­tance of the two points of the optic axes in which their cen­tres are placed.

These incon­ve­niences are removed by the instru­ment I am about to describe; the two pic­tures (or rather their reflect­ed images) are placed in it at the true con­course of the optic axes, the focal adap­ta­tion of the eye pre­serves its usu­al adjust­ment, the appear­ance of lat­er­al images is entire­ly avoid­ed, and a large field of view for each eye is obtained. The fre­quent ref­er­ence I shall have occa­sion to make to this instru­ment, will ren­der it con­ve­nient to give it a spe­cif­ic name, I there­fore pro­pose that it be called a stere­o­scope, to indi­cate its prop­er­ty of rep­re­sent­ing sol­id figures.

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§ 3.

The stere­o­scope is rep­re­sent­ed by figs. 8. and 9; the for­mer being a front view, and the lat­ter a plan of the instru­ment. A A’ are two plane mir­rors, about four inch­es square, insert­ed in frames, and so adjust­ed that their backs form an angle of 90° with each oth­er; these mir­rors are fixed by their com­mon edge against an upright B, or which was less easy to rep­re­sent in the draw­ing, against the mid­dle line of a ver­ti­cal board, cut away in such man­ner as to allow the eyes to be placed before the two mir­rors. C C’ are two slid­ing boards, to which are attached the upright boards D D’, which may thus be removed to dif­fer­ent dis­tances from the mir­rors. In most of the exper­i­ments here­after to be detailed, it is nec­es­sary that each upright board shall be at the same dis­tance from the mir­ror which is oppo­site to it. To facil­i­tate this dou­ble adjust­ment, I employ a right and a left-hand­ed wood­en screw, r l; the two ends of this com­pound screw pass through the nuts e e’, which are fixed to the low­er parts of the upright boards D D’, so that by turn­ing the screw pin p one way the two boards will approach, and by turn­ing it the oth­er they will recede from each oth­er, one always pre­serv­ing the same dis­tance as the oth­er from the mid­dle line f. E E’ are pan­nels, to which the pic­tures are fixed in such man­ner that their cor­re­spond­ing hor­i­zon­tal lines shall be on the same lev­el: these pan­nels are capa­ble of slid­ing back­wards and for­wards in grooves on the upright boards D D’. The appa­ra­tus hav­ing been described, it flow remains to explain the man­ner of using it. The observ­er must place his eyes as near as pos­si­ble to the mir­rors, the right eye before the right hand mir­ror, and the left eye before the left hand mir­ror, and he must move the slid­ing pan­nels E E’ to or from him until the two reflect­ed images coin­cide at the inter­sec­tion of the optic axes, and form an image of the same appar­ent mag­ni­tude as each of the com­po­nent pic­tures. The pic­tures will indeed coin­cide when the slid­ing pan­nels are in a vari­ety of dif­fer­ent posi­tions, and con­se­quent­ly when viewed under dif­fer­ent incli­na­tions of the optic axes; but there is only one posi­tion in which the binoc­u­lar image will be imme­di­ate­ly seen sin­gle, of its prop­er mag­ni­tude, and with­out fatigue to the eyes, because in this posi­tion only the ordi­nary rela­tions between the mag­ni­tude of the pic­tures on the reti­na, the incli­na­tion of the optic axes, and the adap­ta­tion of the eye to dis­tinct vision at dif­fer­ent dis­tances are pre­served. The alter­ation in the appar­ent mag­ni­tude of the binoc­u­lar images, when these usu­al rela­tions are dis­turbed, will be dis­cussed in anoth­er paper of this series, with a vari­ety of remark­able phe­nom­e­na depend­ing there­on. In all the exper­i­ments detailed in the present mem­oir I shall sup­pose these rela­tions to remain undis­turbed, and the optic axes to con­verge about six or eight inch­es before the eyes.

If the pic­tures are all drawn to be seen with the same incli­na­tion of the optic axes, the appa­ra­tus may be sim­pli­fied by omit­ting the screw r 1 and fix­ing the upright boards D D’ at the prop­er dis­tances. The slid­ing pan­nels may also be dis­pensed with, and the draw­ings them­selves be made to slide in the grooves.

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§ 4.

A few of out­line fig­ures, cal­cu­lat­ed to give rise to the per­cep­tion of objects of three dimen­sions when placed in the stere­o­scope in the man­ner described, are rep­re­sent­ed from figs. 10. to 20. They are one half the lin­ear size of the fig­ures actu­al­ly employed. As the draw­ings are reversed by reflec­tion in the mir­rors, I will sup­pose these fig­ures to be the reflect­ed images to which the eyes are direct­ed in the appa­ra­tus; those marked being seen by the right eye, and those marked a by the left eye. The draw­ings, it has been already explained, are two dif­fer­ent pro­jec­tions of the same object seen from two points of sight, the dis­tance between which is equal to the inter­val between the eyes of the observ­er; this inter­val is gen­er­al­ly about 2½ inches.

a and b, fig. 10. will, when viewed in the stere­o­scope, present to the mind a line in the ver­ti­cal plane, with its low­er end inclined towards the observ­er. If the two com­po­nent lines be caused to turn round their cen­tres equal­ly in oppo­site direc­tions, the resul­tant line will, while it appears to assume every degree of incli­na­tion to the ref­er­ent plane, still seem to remain in the same ver­ti­cal plane.

Fig. 11. A series of points all in the same hor­i­zon­tal plane, but each towards the right hand suc­ces­sive­ly near­er the observer.

Fig. 12. A curved line inter­sect­ing the ref­er­ent plane, and hav­ing its con­vex­i­ty towards the observer.

Fig. 13. A cube.

Fig. 14. A cone, hav­ing its axis per­pen­dic­u­lar to the ref­er­ent plane, and its ver­tex towards the observer.

Fig. 15. The frus­tum of a square pyra­mid; its axis per­pen­dic­u­lar to the ref­er­ent plane, and its base fur­thest from the eye.

Fig. 16. Two cir­cles at dif­fer­ent dis­tances from the eyes, their cen­tres in the same per­pen­dic­u­lar, form­ing the out­line of the frus­tum of a cone.

The oth­er fig­ures require no observation.

For the pur­pos­es of illus­tra­tion I have employed only out­line fig­ures, for had either shad­ing or colour­ing been intro­duced it might be sup­posed that the effect was whol­ly or in part due to these cir­cum­stances, where­as by leav­ing them out of con­sid­er­a­tion no room is left to doubt that the entire effect of relief is owing to the simul­ta­ne­ous per­cep­tion of the two monoc­u­lar pro­jec­tions, one on each reti­na. But if it be required to obtain the most faith­ful resem­blances of real objects, shad­ow­ing and colour­ing may prop­er­ly be employed to height­en the effects. Care­ful atten­tion would enable an artist to draw and paint the two com­po­nent pic­tures, so as to present to the mind of the observ­er, in the resul­tant per­cep­tion, per­fect iden­ti­ty with the object rep­re­sent­ed. Flow­ers, crys­tals, busts, vas­es, instru­ments of var­i­ous kinds, &c., might thus be rep­re­sent­ed so as not to be dis­tin­guished by sight from the real objects themselves.

It is wor­thy of remark, that the process by which we thus become acquaint­ed with the real forms of sol­id objects, is pre­cise­ly that which is employed in descrip­tive geom­e­try, an impor­tant sci­ence we owe to the genius of MONGE, but which is lit­tle stud­ied or known in this coun­try. In this sci­ence, the posi­tion of a point, a right line or a curve, and con­se­quent­ly of any fig­ure what­ev­er, is com­plete­ly deter­mined by assign­ing its pro­jec­tions on two fixed planes, the sit­u­a­tions of which are known, and which are not par­al­lel to each oth­er. In the prob­lems of descrip­tive geom­e­try the two ref­er­ent planes are gen­er­al­ly assumed to be at right angles to each oth­er, but in binoc­u­lar vision the incli­na­tion of these planes is less accord­ing as the angle made at the con­course of the optic axes is less ; thus the same sol­id object is rep­re­sent­ed to the mind by dif­fer­ent pairs of monoc­u­lar pic­tures, accord­ing as they are placed at a dif­fer­ent dis­tance before the eyes, and the per­cep­tion of these dif­fer­ences (though we seem to be uncon­scious of them) may assist in sug­gest­ing to the mind the dis­tance of the object. The more inclined to each oth­er the ref­er­ent planes are, with the greater accu­ra­cy are the var­i­ous points of the pro­jec­tions referred to their prop­er places; and it appears to be a use­ful pro­vi­sion that the real forms of those objects which are near­est to us are thus more deter­mi­nate­ly appre­hend­ed than those which are more distant.

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§ 5.

A very sin­gu­lar effect is pro­duced when the draw­ing orig­i­nal­ly intend­ed to be seen by the right eye is placed at the left hand sidle of the stere­o­scope, and that designed to be seen by the left eye is placed on its right hand side. A fig­ure of three dimen­sions, as bold in relief as before, is per­ceived, but it has a dif­fer­ent form from that which is seen when the draw­ings are in their prop­er places. There is a cer­tain rela­tion between the prop­er fig­ure and this, which I shall call its con­verse fig­ure. Those points which are near­est the observ­er in the prop­er fig­ure are the most remote from him in the con­verse fig­ure, and vice ver­sâ, so that the fig­ure is, as it were, invert­ed; but it is not an exact inver­sion, for the near parts of the con­verse fig­ure appear small­er, and the remote parts larg­er than the same parts before the inver­sion. Hence the draw­ings which, prop­er­ly placed, occa­sion a cube to be per­ceived, when changed in the man­ner described, rep­re­sent the frus­tum of a square pyra­mid with its base remote from the eye: the cause of this is easy to understand.

This con­ver­sion of relief may be shown by all the pairs of draw­ings from fig. 10. to 19. In the case of sim­ple fig­ures like these the con­verse fig­ure is as read­i­ly appre­hend­ed as the orig­i­nal one, because it is gen­er­al­ly a fig­ure of as fre­quent occur­rence; hut in the vase of a more com­pli­cat­ed fig­ure, an archi­tec­tur­al design, for instance, the mind, unac­cus­tomed to per­ceive its con­verse, because it nev­er occurs in nature, can find no mean­ing in it.

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§ 6.

The same image is depict­ed on the reti­na by an object of three dimen­sions as by its pro­jec­tion on a plane sur­face, pro­vid­ed the point of sight remain in both cas­es the same. There should be, there­fore, no dif­fer­ence in the binoc­u­lar appear­ance of two draw­ings, one pre­sent­ed to each eye, and of two real objects so pre­sent­ed to the two eyes that their pro­jec­tions on the reti­na shall be the same as those aris­ing from the draw­ings. The fol­low­ing exper­i­ments will prove the just­ness of this inference.

I pro­cured sev­er­al pairs of skele­ton fig­ures, i. e. out­line fig­ures of three dimen­sions, formed either of iron wire or of ebony bead­ing about one tenth of an inch in thick­ness. The pair I most fre­quent­ly employed con­sist­ed of two cubes, whose sides were three inch­es in length. When I placed these skele­ton fig­ures on stands before the two mir­rors of the stere­o­scope, the fol­low­ing effects were pro­duced, accord­ing as their rel­a­tive posi­tions were changed. 1st. When they were so placed that the pic­tures which their reflect­ed images pro­ject­ed on the two ret­inæ were pre­cise­ly the same as those which would have been pro­ject­ed by a cube placed at the con­course of the optic axes, a cube in relief appeared before the eyes. 2ndly. When they were so placed that their reflect­ed images pro­ject­ed exact­ly sim­i­lar pic­tures on the two ret­inæ, all effect of relief was destroyed, and the com­pound appear­ance was that of an out­line rep­re­sen­ta­tion on a plane sur­face. 3rdly. When the cubes were so placed that the reflect­ed image of one pro­ject­ed on the left reti­na the same pic­ture as in the first case was pro­ject­ed on the right reti­na, and con­verse­ly, the con­verse fig­ure in relief appeared.

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If a sym­met­ri­cal object, that is one whose right and left sides are exact­ly sim­i­lar to each oth­er but invert­ed, be placed so that any point in the plane which divides it into these two halves is equal­ly dis­tant from the two eyes, its two monoc­u­lar pro­jec­tions are, it is easy to see, invert­ed fac­sim­i­les of each oth­er. Thus fig. 15, a and b are sym­met­ri­cal monoc­u­lar pro­jec­tions of the frus­tum of a four-sided pyra­mid, and figs. 13. 14. 16. are cor­re­spond­ing pro­jec­tions of oth­er sym­met­ri­cal objects. This being kept in view, I will describe an exper­i­ment which, had it been casu­al­ly observed pre­vi­ous to the knowl­edge of the prin­ci­ples devel­oped in this paper, would have appeared an inex­plic­a­ble opti­cal illusion.

M and M’ (fig. 21.) are two mir­rors, inclined so that their faces form an angle of 90° with each oth­er. Between them in the bisect­ing plane is placed a plane out­line fig­ure, such as fig. 15 a, made of card all parts but the lines being cut away, or of wire. A reflect­ed image of this out­line, placed at A, will appear behind each mir­ror at B and B’, and one of these images will be the inver­sion of the oth­er. If the eyes be made to con­verge at C, it is obvi­ous that these two reflect­ed images will fall on cor­re­spond­ing parts of the two ret­inæ, and a fig­ure of three dimen­sions will be per­ceived; if the out­line placed in the bisect­ing plane be reversed, the con­verse skele­ton form will appear; in both these exper­i­ments we have the sin­gu­lar phe­nom­e­non of the con­ver­sion of a sin­gle plane out­line into a fig­ure of three dimen­sions. To ren­der the binoc­u­lar object more dis­tinct, con­cave lens­es may be applied to the eyes; and to pre­vent the two lat­er­al images from being seen, screens may be placed at D and D’.

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§ 8.

An effect of binoc­u­lar per­spec­tive may be remarked in a plate of met­al, the sur­face of which has been made smooth by turn­ing it in a lathe. When a sin­gle can­dle is brought near such a plate, a line of light appears stand­ing out from it, one half being above, and the oth­er half below the sur­face; the posi­tion and incli­na­tion of this line chances with the sit­u­a­tion of the light and of the observ­er, but it always pass­es through the cen­tre of the plate. On clos­ing the left eye the relief dis­ap­pears, and the lumi­nous line coin­cides with one of the diam­e­ters of the plate; on clos­ing the right eye the line appears equal­ly in the plane of the sur­face, but coin­cides with anoth­er diam­e­ter; on open­ing both eyes it instant­ly starts into relief². The case here is exact­ly anal­o­gous to the vision of two inclined lines (fig. 10.) when each is pre­sent­ed to a dif­fer­ent eye in the stere­o­scope. It is curi­ous, that an effect like this, which it must have been seen thou­sands of times, should nev­er have attract­ed suf­fi­cient atten­tion to have been made the sub­ject of philo­soph­ic obser­va­tion. It was one of the ear­li­est facts which drew my atten­tion to the sub­ject I am now treating.

Dr. SMITH³ was very much puz­zled by an effect of binoc­u­lar per­spec­tive which he observed, but was unable to explain. He opened a pair of com­pass­es, and while he held the joint in his hand, and the points out­wards and equidis­tant from his eyes, and some­what high­er than the joint, he looked at a more dis­tant point ; the com­pass­es appeared dou­ble. He then com­pressed the legs until the two inner points coin­cid­ed; hav­ing done this the two inner legs also entire­ly coin­cid­ed, and bisect­ed the angle formed by the out­ward ones, appear­ing longer and thick­er than they did, and reach­ing from the hand to the remotest object in view. The expla­na­tion offered by Dr. SMITH accounts only for the coin­ci­dence of the points of the com­pass­es, not for that of the entire leg. The effect in ques­tion is best seen by employ­ing a pair of straight wires, about a foot in length. A sim­i­lar obser­va­tion, made with two flat rulers, and after­wards with silk threads, induced Dr. WELLS to pro­pose a new the­o­ry of vis­i­ble direc­tion in order to explain it, so inex­plic­a­ble did it seem to him by any of the received theories.

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§ 9.

The pre­ced­ing exper­i­ments ren­der it evi­dent that there is an essen­tial dif­fer­ence in the appear­ance of objects when seen with two eyes, and when only one eye is employed, and that the most vivid belief of the solid­i­ty of an object of three dimen­sions aris­es from two dif­fer­ent per­spec­tive pro­jec­tions of it being simul­ta­ne­ous­ly pre­sent­ed to the mind. How hap­pens it then, it may be asked, that per­sons who see with only one eye form cor­rect notions of sol­id objects, and nev­er mis­take them for pic­tures? and how hap­pens it also, that a per­son hav­ing the per­fect use of both eyes, per­ceives no dif­fer­ence in objects around him when he shuts one of them? To explain these appar­ent dif­fi­cul­ties, it must be kept in mind, that although the simul­ta­ne­ous vision of two dis­sim­i­lar pic­tures sug­gests the relief of objects in the most vivid man­ner, yet there are oth­er signs which sug­gest the same ideas to the mind, which, though more ambigu­ous than the for­mer, become less liable to lead the judg­ment astray in pro­por­tion to the extent of our pre­vi­ous expe­ri­ence. The vivid­ness of relief aris­ing from the pro­jec­tion of two dis­sim­i­lar pic­tures, one on each reti­na, becomes less and less as the object is seen at a greater dis­tance before the eyes, and entire­ly ceas­es when it is so dis­tant that the optic axes are par­al­lel while regard­ing it. We see with both eyes all objects beyond this dis­tance pre­cise­ly as we see near objects with a sin­gle eye; for the pic­tures on the two ret­inæ are then exact­ly sim­i­lar, and the mind appre­ci­ates no dif­fer­ence whether two iden­ti­cal pic­tures fall on cor­re­spond­ing parts of the two ret­inæ, or whether one eye is impressed with only one of these pic­tures. A per­son deprived of the sight of one eye sees there­fore all exter­nal objects, near and remote, as a per­son with both eyes sees remote objects only, but that vivid effect aris­ing from the binoc­u­lar vision of near objects is not per­ceived by the for­mer; to sup­ply this defi­cien­cy he has recourse uncon­scious­ly to oth­er means of acquir­ing more accu­rate infor­ma­tion. The motion of the head is the prin­ci­pal means he employs. That the required knowl­edge may be thus obtained will be evi­dent from the fol­low­ing con­sid­er­a­tions. The mind asso­ciates with the idea of a sol­id object every dif­fer­ent pro­jec­tion of it which expe­ri­ence has hith­er­to afford­ed; a sin­gle pro­jec­tion may be ambigu­ous, from its being also one of the pro­jec­tions of a pic­ture, or of a dif­fer­ent sol­id object; but when dif­fer­ent pro­jec­tions of the same object are suc­ces­sive­ly pre­sent­ed, they can­not all belong to anoth­er object, and the form to which they belong is com­plete­ly char­ac­ter­ized. While the object remains fixed, at every move­ment of the head it is viewed from a dif­fer­ent point of sight, and the pic­ture on the reti­na con­se­quent­ly con­tin­u­al­ly changes.

Every one must be aware how great­ly the per­spec­tive effect of a pic­ture is enhanced by look­ing at it with only one eye, espe­cial­ly when a tube is employed to exclude the vision of adja­cent objects, whose pres­ence might dis­turb the illu­sion. Seen under such cir­cum­stances from the prop­er point of sight, the pic­ture projects the same lines, shades and colours on the reti­na, as the more dis­tant scene which it rep­re­sents would do were it sub­sti­tut­ed for it. The appear­ance which would make us cer­tain that it is a pic­ture is exclud­ed from the sight, and the imag­i­na­tion has room to be active. Sev­er­al of the old­er writ­ers erro­neous­ly attrib­uted this appar­ent supe­ri­or­i­ty of monoc­u­lar vision to the con­cen­tra­tion of the visu­al pow­er in a sin­gle eye⁴.

There is a well-known and very strik­ing illu­sion of per­spec­tive which deserves a pass­ing remark, because the rea­son of the effect does not appear to be gen­er­al­ly under­stood. When a per­spec­tive of a build­ing is pro­ject­ed on a hor­i­zon­tal plane, so that the point of sight is in a line great­ly inclined towards the plane, the build­ing appears to a sin­gle eye placed at the point of sight to be in bold relief, and the illu­sion is almost as per­fect as in the binoc­u­lar exper­i­ments described in §§ 2, 3, 4. This effect whol­ly aris­es from the unusu­al pro­jec­tion, which sug­gests to the mind more read­i­ly the object itself than the draw­ing of it; for we are accus­tomed to see real objects in almost every point of view, but per­spec­tive rep­re­sen­ta­tions being gen­er­al­ly made in a ver­ti­cal plane with the point of sight in a line per­pen­dic­u­lar to the plane of pro­jec­tion, we are less famil­iar with the appear­ance of oth­er pro­jec­tions. Any oth­er unusu­al pro­jec­tion will pro­duce the same effect.

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§ 10.

If we look with a sin­gle eye at the draw­ing of a sol­id geo­met­ri­cal fig­ure, it may be imag­ined to be the rep­re­sen­ta­tion of either of two dis­sim­i­lar sol­id fig­ures, the fig­ure intend­ed to be rep­re­sent­ed, or its con­verse fig­ure (§ 5.). If the for­mer is a very usu­al, and the lat­ter a very unusu­al fig­ure, the imag­i­na­tion will fix itself on the orig­i­nal with­out wan­der­ing to the con­verse fig­ure; but if both are of ordi­nary occur­rence, which is gen­er­al­ly the case with regard to sim­ple forms, a sin­gu­lar phe­nom­e­non takes place; it is per­ceived at one time dis­tinct­ly as one of these fig­ures, at anoth­er time as the oth­er, and while one fig­ure con­tin­ues it is not in the pow­er of the will to change it immediately.

The same phe­nom­e­non takes place, though less decid­ed­ly, when the draw­ing is seen with both eyes. Many of my read­ers will call to mind the puz­zling effect of some of the dia­grams annexed to the prob­lems of the eleventh book of Euclid; which, when they were atten­tive­ly looked at, changed in an arbi­trary man­ner from one sol­id fig­ure to anoth­er, and would obsti­nate­ly con­tin­ue to present the con­verse fig­ures when the real fig­ures alone were want­ed. This per­plex­ing illu­sion must be of coim­mon occur­rence, but I have only found one record­ed obser­va­tion relat­ing to the sub­ject. It is by Pro­fes­sor NECKER of Gene­va, and I shall quote it in his own words from the Philo­soph­i­cal Mag­a­zine, Third Series, vol. i. p. 337.

“The object I have now to call your atten­tion to is an obser­va­tion which has often occurred to me while exam­in­ing fig­ures and engraved plates of crys­talline forms; I mean a sud­den and invol­un­tary change in the appar­ent posi­tion of a crys­tal or sol­id rep­re­sent­ed in an engraved fig­ure. What I mean will be more eas­i­ly under­stood from the fig­ure annexed (fig. 22.). The rhom­boid A X is drawn so that the sol­id angle A should be seen the near­est to the spec­ta­tor, and the sol­id angle X the far­thest from him, and that the face A C D B should be the fore­most, while the face X D C is behind. But in look­ing repeat­ed­ly at the same fig­ure, you will per­ceive that at times the appar­ent posi­tion of the rhom­boid is so changed that the sol­id angle X will appear the near­est, and the sol­id angle A the far­thest; and that the face A C D B will recede behind the face X D C, which will come for­ward, which effect gives to the whole sol­id a quite con­trary appar­ent inclination.”

Pro­fes­sor NECKER attrib­ut­es this alter­ation of appear­ance, not to a men­tal oper­a­tion, but to an invol­un­tary change in the adjust­ment of the eye for obtain­ing dis­tinct vision. He sup­posed that when­ev­er the point of dis­tinct vision on the reti­na is direct­ed on the angle A, for instance, this angle seen more dis­tinct­ly than the oth­ers is nat­u­ral­ly sup­posed to be near­er and fore­most, while the oth­er angles seen indis­tinct­ly are sup­posed to be far­ther and behind, and that the reverse takes place when the point of dis­tinct vision is brought to bear on the angle X.

That this is not the true expla­na­tion, is evi­dent from three cir­cum­stances: in the first place, the two points A and X being both at the same dis­tance from the eyes, the same alter­ation of adjust­ment which would make one of them indis­tinct would make the oth­er so ; sec­ond­ly, the fig­ure will under­go the same changes whether the focal dis­tance of the eye be adjust­ed to a point before or beyond the plane in which the fig­ure is drawn; and third­ly, the change of fig­ure fre­quent­ly occurs while the eye con­tin­ues to look at the same angle. The effect seems entire­ly to depend on our men­tal con­tem­pla­tion of the fig­ure intend­ed to be rep­re­sent­ed, or of its con­verse. By fol­low­ing the lines with the eye with a clear idea of the sol­id fig­ure we are describ­ing, it may be fixed for any length of time; but it requires prac­tice to do this or to change the fig­ure at will. As I have before observed, these effects are far more obvi­ous when the fig­ures are regard­ed with one eye only.

No illu­sion of this kind can take place when an object of three dimen­sions is seen with both eyes while the optic axes make a sen­si­ble angle with each oth­er, because the appear­ance of the two dis­sim­i­lar images, one to each eye, pre­vents the pos­si­bil­i­ty of mis­take. But if we regard an object at such a dis­tance that its two pro­jec­tions are sen­si­bly iden­ti­cal, and if this pro­jec­tion be capa­ble of a dou­ble inter­pre­ta­tion, the illu­sion may occur. Thus a plac­ard on a pole car­ried in the streets, with one of its sides inclined towards the observ­er, will, when he is dis­tant from it, fre­quent­ly appear inclined in a con­trary direc­tion. Many anal­o­gous instances might be adduced, but this will suf­fice to call oth­ers to mind ; it must how­ev­er be observed, that when shad­ows, or oth­er means capa­ble of deter­min­ing the judge­ment are present, these fal­lac­i­es do not arise.

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§ 11.

The same inde­ter­mi­na­tion of judge­ment which caus­es a draw­ing to be per­ceived by the mind at dif­fer­ent times as two dif­fer­ent fig­ures, fre­quent­ly gives rise to a false per­cep­tion when objects in relief are regard­ed with a sin­gle eye. The appar­ent con­ver­sion of a cameo into an intaglio, and of an intaglio into a cameo, is a well-known instance of this fal­la­cy in vision; but the fact does not appear to me to have been cor­rect­ly explained, nor the con­di­tions under which it occurs to have been prop­er­ly stated.

This curi­ous illu­sion, which has been the sub­ject of much atten­tion, was first observed at one of the ear­ly meet­ings of the Roy­al Soci­ety⁵. Sev­er­al of the mem­bers look­ing through a com­pound micro­scope of a new con­struc­tion at a guinea, some of them imag­ined the image to be depressed, while oth­ers thought it to be embossed, as it real­ly was. Pro­fes­sor GMELIN, of Wurtem­burg, pub­lished a paper on the same sub­ject in the Philo­soph­i­cal Trans­ac­tions for 1745 ; his exper­i­ments were made with tele­scopes and com­pound micro­scopes which invert­ed the images; and he observed that the con­ver­sion of relief appeared in some cas­es and not in oth­ers, at some times and not at oth­ers, and to some eyes also and not to oth­ers. He endeav­oured to ascer­tain some of the con­di­tions of the two appear­ances; “but why these things should so hap­pen,” says he, “I do not pre­tend to determine.”

Sir DAVID BREWSTER accounts for the fal­la­cy in the fol­low­ing manner:⁶ — “A hol­low seal being illu­mi­nat­ed by a win­dow or a can­dle, its shad­ed side is of course on the same side with the light. If we now invert the seal with one or more lens­es, so that it may look in the oppo­site direc­tion, it will appear to the eye with the shad­ed side fur­thest from the win­dow. But as we know that the win­dow is still on our left hand, and as every body with its shad­ed side fur­thest from the light must nec­es­sar­i­ly be con­vex or pro­tu­ber­ant, we imme­di­ate­ly believe that the hol­low seal is now a cameo or bas-relief. The proof which the eye thus receives of the seal being raised, over­comes the evi­dence of its being hol­low, derived from our actu­al knowl­edge and from the sense of touch. In this exper­i­ment the decep­tion takes place from our know­ing the real direc­tion of the light which falls on the seal ; for if the place of the win­dow, with respect to the seal, had been invert­ed as well as the seal itself, the illu­sion could not have tak­en place. The illu­sion, there­fore, under our con­sid­er­a­tion is the result of an oper­a­tion of our own minds, where­by we judge of the forms of bod­ies by the knowl­edge we have acquired of light and shad­ow. Hence the illu­sion depends on the accu­ra­cy and extent of our knowl­edge on this sub­ject; and while some per­sons are under its influ­ence, oth­ers are entire­ly insen­si­ble to it.”

These con­sid­er­a­tions do not ful­ly explain the phe­nom­e­non, for they sup­pose that the image must be invert­ed, and that the light must fall in a par­tic­u­lar direc­tion but the con­ver­sion of relief will still take place when the object is viewed through an open tube with­out any lens­es to invert it, and also when it is equal­ly illu­mi­nat­ed in all parts. The true expla­na­tion I believe to be the fol­low­ing. If we sup­pose a cameo and an intaglio of the same object, the ele­va­tions of the one cor­re­spond­ing exact­ly to the depres­sions of the oth­er; it is easy to show that the pro­jec­tion of either on the reti­na is sen­si­bly the same. When the cameo or the intaglio is seen with both eyes, it is impos­si­ble to mis­take an ele­va­tion for a depres­sion, for rea­sons which have been already amply explained; but when either is seen with one eye only, the most cer­tain guide of our judge­ment, viz. the pre­sen­ta­tion of a dif­fer­ent pic­ture to each eye, is want­i­ng; the imag­i­na­tion there­fore sup­plies the defi­cien­cy, and we con­ceive the object to be raised or depressed accord­ing to the dic­tates of this fac­ul­ty. No doubt in such cas­es our judge­ment is in a great degree influ­enced by acces­so­ry cir­cum­stances, and the intaglio or the relief may some­times present itself accord­ing to our pre­vi­ous knowl­edge of the direc­tion in which the shad­ows ought to appear; but the real cause of the phe­nom­e­non is to be found in the inde­ter­mi­na­tion of the judge­ment aris­ing from our more per­fect means of judg­ing being absent.

Observers with the micro­scope must be par­tic­u­lar­ly on their guard against illu­sions of this kind. RASPAIL observes⁷ that the hol­low pyra­mi­dal arrange­ment of the crys­tals of muri­ate of soda appears, when seen through a micro­scope, like a stri­at­ed pyra­mid in relief. He rec­om­mends two modes of cor­rect­ing the illu­sion. The first is to bring suc­ces­sive­ly to the focus of the instru­ment the dif­fer­ent parts of the crys­tal; if the pyra­mid be in relief, the point will arrive at the focus soon­er than the base will; if the pyra­mid be hol­low, the con­trary will take place. The sec­ond mode is to project a strong light on the pyra­mid in the field of view of the micro­scope, and to observe which sides of the crys­tal are illu­mi­nat­ed, tak­ing how­ev­er the inver­sion of the image into con­sid­er­a­tion if a com­pound micro­scope be employed.

The inver­sion of relief is very strik­ing when a skele­ton cube is looked at with one eye, and the fol­low­ing sin­gu­lar results may in this case be observed. So long as the mind per­ceives the cube, how­ev­er the fig­ure be turned about, its var­i­ous appear­ances will be but dif­fer­ent rep­re­sen­ta­tions of the same object, and the same prim­i­tive form will be sug­gest­ed to the mind by all of them: but it is not so if the con­verse fig­ure fix­es the atten­tion; the series of suc­ces­sive pro­jec­tions can­not then be referred to any fig­ure to which they are all com­mon, and the skele­ton fig­ure will appear to be con­tin­u­al­ly under­go­ing a change of shape.

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§ 12.

I have giv­en ample proof that objects whose pic­tures do not fall on cor­re­spond­ing points of the two ret­inæ may still appear sin­gle. I will now adduce an exper­i­ment which proves that sim­i­lar pic­tures falling on cor­re­spond­ing points of the two ret­inæ may appear dou­ble and in dif­fer­ent places.

Present, in the stere­o­scope, to the right eye a ver­ti­cal line, and to the left eye a line inclined some degrees from the per­pen­dic­u­lar (fig. 23.); the observ­er will then per­ceive, as for­mer­ly explained, a line, the extrem­i­ties of which appear at dif­fer­ent dis­tances before the eyes. Draw on the left hand fig­ure a faint ver­ti­cal line exact­ly cor­re­spond­ing in posi­tion and length to that pre­sent­ed to the right eye; and let the two lines of this left hand fig­ure inter­sect each oth­er at their cen­tres. Look­ing now at these two draw­ings in the stere­o­scope, the two strong lines, each seen by a dif­fer­ent eye, will coin­cide, and the resul­tant per­spec­tive line will appear to occu­py the same place as before; but the faint line which now falls on a line of the left reti­na, which cor­re­sponds with the line of the might reti­na on which one of the coin­cid­ing strong lines, viz. the ver­ti­cal one, falls, appears in a dif­fer­ent place. The place this faint line appar­ent­ly occu­pies is the inter­sec­tion of that plane of visu­al direc­tion of the left eye in which it is sit­u­at­ed, with the plane of visu­al direc­tion of the right eye, which con­tains the strong ver­ti­cal line.

This exper­i­ment affords anoth­er proof that there is no nec­es­sary phys­i­o­log­i­cal con­nec­tion between the cor­re­spond­ing points of the two retinæ,—a doc­trine which has been main­tained by so many authors.

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§ 13. 

Binocular Vision of Images of different Magnitudes.

We will now inquire what effect results from pre­sent­ing sim­i­lar images, dif­fer­ing only in mag­ni­tude, to anal­o­gous parts of the two ret­inæ. For this pur­pose two squares or cir­cles, dif­fer­ing obvi­ous­ly but not extrav­a­gant­ly in size, may be drawn on two sep­a­rate pieces of paper, and placed in the stere­o­scope so that the reflect­ed image of each shall he equal­ly dis­tant from the eye by which it is regard­ed. It will then be seen that, notwith­stand­ing this dif­fer­ence, they coa­lesce and occa­sion a sin­gle resul­tant per­cep­tion. The lim­it of the dif­fer­ence of size with­in which the sin­gle appear­ance sub­sists may be ascer­tained by employ­ing two images of equal mag­ni­tude, and caus­ing one of them to recede from the eye while the oth­er remains at a con­stant dis­tance ; this is effect­ed mere­ly by pulling out the slid­ing board C (fig. 8.) while the oth­er C’ remains fixed, the screw hav­ing pre­vi­ous­ly been removed.

Though the sin­gle appear­ance of two images of dif­fer­ent size is by this exper­i­ment demon­strat­ed, the observ­er is unable to per­ceive what dif­fer­ence exists between the appar­ent mag­ni­tude of the binoc­u­lar image and that of the two monoc­u­lar images to deter­mine this point the stere­o­scope must be dis­pensed with, and the exper­i­ment so arranged that all three shall be simul­ta­ne­ous­ly seen ; which may be done in the fol­low­ing manner:—The two draw­ings being placed side by side on a plane before the eyes, the optic axes must be made to con­verge to a near­er point as at fig. 4., or to a more dis­tant one as at fig. 3., until the three images are seen at the same time, the binoc­u­lar image in the mid­dle, and the monoc­u­lar images at each side. It will thus be seen that the binoc­u­lar image is appar­ent­ly inter­me­di­ate in size between the two monoc­u­lar ones.

If the pic­tures be too unequal in mag­ni­tude, the binoc­u­lar coin­ci­dence does not take place. It appears that if the inequal­i­ty of the pic­tures be greater than the dif­fer­ence which exists between the two pro­jec­tions of the same object when seen in the most oblique posi­tion of the eyes (i. e. both turned to the extreme right or to the extreme left), ordi­nar­i­ly employed, they do not coa­lesce. Were it not for the binoc­u­lar coin­ci­dence of two images of dif­fer­ent mag­ni­tude, objects would appear sin­gle only when the optic axes con­verge imme­di­ate­ly for­wards; for it is only when the con­verg­ing visu­al lines form equal angles with the visu­al base (the line join­ing the cen­tres of the two eyes) as at fig. 2., that the two pic­tures can be of equal mag­ni­tude; but when they form dif­fer­ent angles with it, as at fig. 24., the dis­tance from the object to each eye is dif­fer­ent, and con­se­quent­ly the pic­ture pro­ject­ed on each reti­na has a dif­fer­ent mag­ni­tude. If a piece of mon­ey be held in the posi­tion a, (fig. 24.) while the optic axes con­verge to a near­er point c, it will appear dou­ble, and that seen by the left eye will be evi­dent­ly small­er than the other.

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§ 14. 

Phenomena which are observed when objects of different forms are simultaneously presented to corresponding parts of the two retinæ.

If we regard a pic­ture with the right eye alone for a con­sid­er­able length of time it will be con­stant­ly per­ceived; if we look at anoth­er and dis­sim­i­lar pic­ture with the left eye alone its effect will be equal­ly per­ma­nent; it might there­fore be expect­ed, that if each of these pic­tures were pre­sent­ed to its cor­re­spond­ing eye at the same time the two would appear per­ma­nent­ly super­posed on each oth­er. This, how­ev­er, con­trary to expec­ta­tion, is not the case.

If and (fig. 25.) are each pre­sent­ed at the same time to a dif­fer­ent eye, the com­mon bor­der will remain con­stant, while the let­ter with­in it will change alter­nate­ly from that which would be per­ceived by the right eye alone to that which would be per­ceived by the left eye alone. At the moment of change the let­ter which has just been seen breaks into frag­ments, while frag­ments of the let­ter which is about to appear min­gle with them, and are imme­di­ate­ly after replaced by the entire let­ter. It does not appear to be in the pow­er of the will to deter­mine the appear­ance of either of the let­ters, but the dura­tion of the appear­ance seems to depend on caus­es which are under our con­trol: thus if the two pic­tures be equal­ly illu­mi­nat­ed, the alter­na­tions appear in gen­er­al of equal dura­tion; but if one pic­ture be in ore illu­mi­nat­ed than the oth­er, that which is less so will be per­ceived dur­ing a short­er time. I have gen­er­al­ly made this exper­i­ment with the appa­ra­tus, fig. 6. When com­plex pic­tures are employed in the stere­o­scope, var­i­ous parts of them alter­nate differently.

There are some facts inti­mate­ly con­nect­ed with the sub­ject of the present arti­cle which have already been fre­quent­ly observed. I allude to the exper­i­ments, first made by DU TOUR, in which two dif­fer­ent colours are pre­sent­ed to cor­re­spond­ing parts of the two ret­inæ. If a blue disc be pre­sent­ed to the right eye and a yel­low disc to the cor­re­spond­ing part of the left eye, instead of a green disc which would appear if these two colours had min­gled before their arrival at a sin­gle eye, the mind will per­ceive the two colours dis­tinct­ly one or the oth­er alter­nate­ly pre­dom­i­nat­ing either par­tial­ly or whol­ly over the disc. In the same man­ner the mind per­ceives no trace of vio­let when red is pre­sent­ed to one eye and blue to the oth­er, nor any ves­tige of orange when red and yel­low are sep­a­rate­ly pre­sent­ed in a sim­i­lar man­ner. These exper­i­ments may be con­ve­nient­ly repeat­ed by plac­ing the coloured discs in the stere­o­scope, but they have been most usu­al­ly made by look­ing at a white object through dif­fer­ent­ly coloured glass­es, one applied to each eye.

In some authors we find it stat­ed, con­trary to fact, that if sim­i­lar objects of dif­fer­ent colour be pre­sent­ed one to each eye, the appear­ance will be that com­pound­ed of the two colours. Dr. REID⁸ and JANIN are among the writ­ers who have fall­en into this incon­sid­er­ate error, which arose no doubt from their decid­ing accord­ing to pre­vi­ous notions, instead of ascer­tain­ing by exper­i­ment what actu­al­ly does happen.

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§ 15.

No ques­tion relat­ing to vision has been so much debat­ed as the cause of the sin­gle appear­ance of objects seen by both eyes. I shall in the present sec­tion give a slight review of the var­i­ous the­o­ries which have been advanced by philoso­phers to account for this phe­nom­e­non, in order that the remarks I have to make in the suc­ceed­ing sec­tion may be prop­er­ly understood.

The law of vis­i­ble direc­tion for monoc­u­lar vision has been var­i­ous­ly stat­ed by dif­fer­ent opti­cal writ­ers. Some have main­tained with Dr’s. REID and PORTERFIELD, that every exter­nal point is seen in the direc­tion of a line pass­ing from its pic­ture on the reti­na through the cen­tre of the eye; while oth­ers have sup­posed with Dr. SMITH that the vis­i­ble direc­tion of an object coin­cides with the visu­al ray, or the prin­ci­pal ray of the pen­cil which flows from it to the eye. D’ALEMBERT, fur­nished with imper­fect data respect­ing the refrac­tive den­si­ties of the humours of the eye, cal­cu­lat­ed that the appar­ent mag­ni­tudes of objects would dif­fer wide­ly on the two sup­po­si­tions, and con­clud­ed that the vis­i­ble point of an object was not seen in either of these direc­tions, but sen­si­bly in the direc­tion of a line join­ing the point itself and its image on the reti­na; but he acknowl­edged that he could assign no rea­son for this law. Sir DAVID BREWSTER, pro­vid­ed with more accu­rate data, has shown that these three lines so near­ly coin­cide with each oth­er, that “at an incli­na­tion of 30°, a line per­pen­dic­u­lar to the point of impres­sion on the reti­na pass­es through the com­mon cen­tre, and does not devi­ate from the real line of vis­i­ble direc­tion more than half a degree, a quan­ti­ty too small to inter­fere with the pur­pos­es of vision.” We may, there­fore, assume in all our future rea­son­ings the truth of the fol­low­ing def­i­n­i­tion giv­en by this emi­nent philoso­pher :—“ As the inte­ri­or eye-ball is as near­ly as pos­si­ble a per­fect sphere, lines per­pen­dic­u­lar to the sur­face of the reti­na must all pass through one sin­gle point, name­ly the cen­tre of its spher­i­cal sur­face. This one point may be called the cen­tre of vis­i­ble direc­tion, because every point of a vis­i­ble object will be seen in the direc­tion of a line drawn from this cen­tre to the vis­i­ble point.”

It is obvi­ous, that the result of any attempt to explain the sin­gle appear­ance of objects to both eyes, or, in oth­er words, the law of vis­i­ble direc­tion for binoc­u­lar vision, ought to con­tain noth­ing incon­sis­tent with the law of vis­i­ble direc­tion for monoc­u­lar vision.

It was the opin­ion of AGUILONIUS, that all objects seen at the same glance with both eyes appear to be in the plane of the horopter. The horopter he defines to be a line drawn through the point of inter­sec­tion of the optic axes, and par­al­lel to the line join­ing the cen­tres of the two eyes; the plane of the horopter to be a plane pass­ing through this line at right angles to that of the optic axes. All objects which are in this plane, must, accord­ing to him, appear sin­gle because the lines of direc­tion in which any point of an object is seen coin­cide only in this plane and nowhere else; and as these lines can meet each oth­er only in one point, it fol­lows from the hypoth­e­sis, that all objects not in the plane of the horopter must appear dou­ble, because their lines of direc­tion inter­sect each oth­er, either before or after they pass through it. This opin­ion was also main­tained by DECHALES and PORTERFIELD. That it is erro­neous, I have giv­en, I think, suf­fi­cient proof, in show­ing that, when the optic axes con­verge to any point, objects before or beyond the plane of the horopter are under cer­tain cir­cum­stances equal­ly seen sin­gle as those in that plane.

Dr. WELLS’S “new the­o­ry of vis­i­ble direc­tion” was a mod­i­fi­ca­tion of the pre­ced­ing hypoth­e­sis. This acute writer held with AGUILONIUS, that objects are seen sin­gle only when they are in the plane of the horopter, and con­se­quent­ly that they appear dou­ble when they are either before or beyond it; but he attempt­ed to make this sin­gle appear­ance of objects only in the plane of the horopter to depend on oth­er prin­ci­ples, from which he deduced, con­trary to AGUILONIUS, that the objects which are dou­bled do not appear in the plane of the horopter, but in oth­er places which are deter­mined by these prin­ci­ples. Dr. WELLS was led to his new the­o­ry by a fact which he acci­den­tal­ly observed, and which he could not rec­on­cile with any exist­ing the­o­ry of vis­i­ble direc­tion ; this fact had, though he was unaware of it, been pre­vi­ous­ly noticed by Dr. SMITH; it is already men­tioned in § 8., and is the only instance of binoc­u­lar vision of relief which I have found record­ed pre­vi­ous to my own inves­ti­ga­tions. So lit­tle does Dr. WELLS’S the­o­ry appear to have been under­stood, that no sub­se­quent writer has attempt­ed either to con­firm or dis­prove his opin­ions. It would be use­less here to dis­cuss the prin­ci­ples of this the­o­ry, which was framed to account for an anom­alous indi­vid­ual fact, since it is incon­sis­tent with the gen­er­al rules on which that fact has been now shown to depend. Notwith­stand­ing these erro­neous views, the “essay upon sin­gle vision with two eyes” con­tains many valu­able exper­i­ments and remarks, the truth of which are inde­pen­dent of the the­o­ry they were intend­ed to illustrate.

The the­o­ry which has obtained great­est cur­ren­cy is that which assumes that an object is seen sin­gle because its pic­tures fall on cor­re­spond­ing points of the two ret­inæ, that is on points which are sim­i­lar­ly sit­u­at­ed with respect to the two cen­tres both in dis­tance and posi­tion. This the­o­ry sup­pos­es that the pic­tures pro­ject­ed on the ret­inæ are exact­ly sim­i­lar to each oth­er, cor­re­spond­ing points of the two pic­tures falling on cor­re­spond­ing points of the two ret­inæ. Authors who agree with regard to this prop­er­ty, dif­fer wide­ly in explain­ing why objects are seen in the same place, or sin­gle, accord­ing to this law. Dr. SMITH makes it to depend entire­ly on cus­tom, and explains why the eyes are habit­u­al­ly direct­ed towards an object so that its pic­tures fall on cor­re­spond­ing parts in the fol­low­ing man­ner:—“ When we view an object steadi­ly, we have acquired a habit of direct­ing the optic axes to the point in view; because its pic­tures falling upon the mid­dle points of the reti­nas, are then dis­tinc­ter than if they fell upon any oth­er places; and since the pic­tures of the whole object are equal to one anoth­er, and are both invert­ed with respect to the optic axes, it fol­lows that the pic­tures of any col­lat­er­al point are paint­ed upon cor­re­spond­ing points of the retinas.”

Dr. REID, after a long dis­ser­ta­tion on the sub­ject, con­cludes, “that by an orig­i­nal prop­er­ty of human eyes, objects paint­ed upon the cen­tres of the two ret­inæ, or upon points sim­i­lar­ly sit­u­at­ed with regard to the cen­tres, appear in the same vis­i­ble place; that the most plau­si­ble attempts to account for this prop­er­ty of the eyes have been unsuc­cess­ful ; and there­fore, that it must be either a pri­ma­ry law of our con­sti­tu­tion, or the con­se­quence of some more gen­er­al law which is not yet discovered.”

Oth­er writ­ers who have admit­ted this prin­ci­ple have regard­ed it as aris­ing from anatom­i­cal struc­ture and depen­dent on con­nex­ion of ner­vous fibres; among these stand the names of GALEN, Dr. BRIGGS, Sir ISAAC NEWTON, ROHAULT, Dr. HARTLEY, Dr. WOLLASTON and Pro­fes­sor MÜLLER.

Many of the sup­port­ers of the the­o­ry of cor­re­spond­ing points have thought, or rather have admit­ted, with­out think­ing, that it was not incon­sis­tent with the law of AGUILONIUS; but very lit­tle reflec­tion will show that both can­not be main­tained togeth­er; for cor­re­spond­ing lines of vis­i­ble direc­tion, that is, lines ter­mi­nat­ing in cor­re­spond­ing points of the two ret­inæ, can­not meet in the plane of the horopter unless the optic axes be par­al­lel, and the plane be at an infi­nite dis­tance before the eyes. Some of the mod­ern Ger­man writ­er­s⁹ have inquired what is the curve in which objects appear sin­gle while the optic axes are direct­ed to a giv­en point, on the hypoth­e­sis that objects are seen sin­gle only when they fall on cor­re­spond­ing points of the two ret­inæ. An ele­gant propo­si­tion has result­ed from their inves­ti­ga­tions, which I shall need no apol­o­gy for intro­duc­ing in this place, since it has not yet been men­tioned in any Eng­lish work.

R and L (fig. 26.) are the two eyes; C A, C’ A the optic axes con­verg­ing to the point A; and C A B C’ is a cir­cle drawn through the point of con­ver­gence A and the cen­tres of vis­i­ble direc­tion C C’. If any point be tak­en in the cir­cum­fer­ence of this cir­cle, and lines be drawn from it through the cen­tres of the two eyes C C’, these lines will fall on cor­re­spond­ing points of the two ret­inæ D D’; for the angles A C B, A C’ B being equal, the angles D C E, D C’ E are also equal; there­fore any point placed in the cir­cum­fer­ence of the cir­cle C A B C’ will, accord­ing to the hypoth­e­sis, appear sin­gle while the optic axes are direct­ed to A, or any oth­er part in it.

I will men­tion two oth­er prop­er­ties of this binoc­u­lar cir­cle: 1st. The arc sub­tend­ed by two points on its cir­cum­fer­ence con­tains dou­ble the num­ber of degrees of the arc sub­tend­ed by the pic­tures of these points on either reti­na, so that objects which occu­py 180° of the sup­posed cir­cle of sin­gle vision are paint­ed on a por­tion of the reti­na extend­ed over 90° only; for the angle D C E or D C’ E being at the cen­tre, and the angle B C A or B C’ A at the cir­cum­fer­ence of a cir­cle, this con­se­quence fol­lows. 2ndly. To what­ev­er point of the cir­cum­fer­ence of the cir­cle the optic axes be made to con­verge, they will form the same angle with each oth­er; for the angles C A C’, C B C are equal.

In the eye itself, the cen­tre of vis­i­ble direc­tion, or the point at which the prin­ci­pal rays cross each oth­er, is, accord­ing to Dr. YOUNG and oth­er emi­nent opti­cal writ­ers, at the same time the cen­tre of the spher­i­cal sur­face of the reti­na, and that of the less­er spher­i­cal sur­face of the cornea; in the dia­gram (fig. 26.), to sim­pli­fy the con­sid­er­a­tion of the prob­lem, R and L rep­re­sent only the cir­cle of cur­va­ture of the bot­tom of the reti­na, but the rea­son­ing is equal­ly true in both cases.

The same rea­sons, found­ed on the exper­i­ments in this mem­oir, which dis­prove the the­o­ry of AGUILONIUS, induce me to reject the law of cor­re­spond­ing points as an accu­rate expres­sion of the phe­nom­e­na of sin­gle vision. Accord­ing to the for­mer, objects can appear sin­gle only in the plane of the horopter; accord­ing to the lat­ter, only when they are in the cir­cle of sin­gle vision; both posi­tions are incon­sis­tent with the binoc­u­lar vision of objects in relief, the points of which they con­sist appear­ing sin­gle though they are at dif­fer­ent dis­tances before the eyes. I have already proved that the assump­tion made by all the main­tain­ers of the the­o­ry of cor­re­spond­ing points, name­ly that the two pic­tures pro­ject­ed by any object in the ret­inæ are exact­ly sim­i­lar, is quite con­trary to fact in every case except that in which the optic axes are parallel.

GASSENDUS, PORTA, TACQUET and GALL main­tained, that we see with only one eye at a time though both remain open, one accord­ing to them being relaxed and inat­ten­tive to objects while the oth­er is upon the stretch. It is a suf­fi­cient refu­ta­tion of this hypoth­e­sis, that we see an object dou­ble when one of the optic axes is dis­placed either by squint­ing or by pres­sure on the eye-ball with the fin­ger; if we saw with only one eye, one object only should under such cir­cum­stances be seen. Again, in many cas­es which I have already explained, the simul­ta­ne­ous affec­tion of the two ret­inæ excites a dif­fer­ent idea in the mind to that con­se­quent on either of the sin­gle impres­sions, the lat­ter giv­ing rise to the idea of a rep­re­sen­ta­tion on a plane sur­face, the for­mer to that of an object in relief; these things could not occur did we see with only one eye at a time.

Du TOUR¹⁰ held that though we might occa­sion­al­ly see at the same time with both eyes, yet the mind can­not be affect­ed simul­ta­ne­ous­ly by two cor­re­spond­ing points of the two images. He was led to this opin­ion by the curi­ous facts allud­ed to in § 14. It would be dif­fi­cult to dis­prove this con­jec­ture by exper­i­ment; but all that the exper­i­ments adduced in its favour, and oth­ers relat­ing to the dis­ap­pear­ance of objects to one eye real­ly proves, is, that the mind is inat­ten­tive to impres­sions made on one reti­na when it can­not com­bine the impres­sions on the two ret­inæ togeth­er so as to resem­ble the per­cep­tion of some exter­nal objects; but they afford no ground what­ev­er for sup­pos­ing that the mind can­not under any cir­cum­stances attend to impres­sions made simul­ta­ne­ous­ly on points of the two ret­inæ, when they har­mo­nize with each oth­er in sug­gest­ing to the mind the same idea.

A per­fect­ly orig­i­nal the­o­ry has been recent­ly advanced by M. LEHOT¹¹, who has endeav­oured to prove, that instead of pic­tures on the ret­inæ, images of three dimen­sions are formed in the vit­re­ous humour which we per­ceive by means of ner­vous fil­a­ments extend­ed thence from the reti­na. This the­o­ry would account for the sin­gle appear­ance to both eyes of objects in relief, but it would be quite insuf­fi­cient to explain why we per­ceive an object of three dimen­sions when two pic­tures of it are pre­sent­ed to the eyes; accord­ing to it, also, no dif­fer­ence should be per­ceived in the relief of objects when seen by one or both eyes, which is con­trary to what real­ly hap­pens. The proofs, besides, that we per­ceive exter­nal objects by means of pic­tures on the ret­inæ are so numer­ous and con­vinc­ing, that a con­trary con­jec­ture can­not be enter­tained for a moment. On this account it will suf­fice mere­ly to men­tion two oth­er the­o­ries which place the seat of vision in the vit­re­ous humour. VALLEE¹², with­out deny­ing the exis­tence of pic­tures on the reti­na, has advo­cat­ed that we see the relief of objects by means of ante­ri­or foci on the hyaloid mem­brane; and RASPAIL¹³ has devel­oped at con­sid­er­able length the strange hypoth­e­sis, that images are nei­ther formed in the vit­re­ous humour nor paint­ed on the reti­na, but are imme­di­ate­ly per­ceived at the focus of the lentic­u­lar sys­tem of which the eye is formed.

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§ 16.

It now remains to exam­ine why two dis­sim­i­lar pic­tures pro­ject­ed on the two reti­naæ give rise to the per­cep­tion of an object in relief. I will not attempt at present to give the com­plete solu­tion of this ques­tion, which is far from being so easy as at a first glance it may appear to be, and is indeed one of great com­plex­i­ty. I shall in this place mere­ly con­sid­er the most obvi­ous expla­na­tions which might be offered, and show their insuf­fi­cien­cy to explain the whole of the phenomena.

It may be sup­posed that we see but one point of an object dis­tinct­ly at the same instant, the one name­ly to which the optic axes are direct­ed, while all oth­er points are seen so indis­tinct­ly, that the mind does not rec­og­nize them to be either sin­gle or dou­ble, and that the fig­ure is appre­ci­at­ed by suc­ces­sive­ly direct­ing the point of con­ver­gence of the optic axes suc­ces­sive­ly to a suf­fi­cient num­ber of its points to enable us to judge accu­rate­ly of its form.

That there is a degree of indis­tinct­ness in those parts of the field of view to which the eyes are not imme­di­ate­ly direct­ed, and which increas­es with the dis­tance from that point, can­not be doubt­ed, and it is also true that the objects thus obscure­ly seen are fre­quent­ly dou­bled. It may be said, this indis­tinct­ness and duplic­i­ty is not attend­ed to, because the eyes shift­ing con­tin­u­al­ly from point to point, every part of the object is suc­ces­sive­ly ren­dered dis­tinct; and the per­cep­tion of the object is not the con­se­quence of a sin­gle glance, dur­ing which only a small part of it is seen dis­tinct­ly, but is formed from a com­par­i­son of all the pic­tures suc­ces­sive­ly seen while the eyes are chang­ing from one point of the object to another.

All this is in some degree true; but were it entire­ly so, no appear­ance of relief should present itself when the eyes remain intent­ly fixed on one point of a binoc­u­lar image in the stere­o­scope. But on per­form­ing the exper­i­ment care­ful­ly, it will be found, pro­vid­ed the pic­tures do not extend too far beyond the cen­tres of dis­tinct vision, that the image is still seen sin­gle and in relief when this con­di­tion is ful­filled. Were the the­o­ry of cor­re­spond­ing points true, the appear­ance should be that of the super­po­si­tion of the two draw­ings, to which, how­ev­er, it has not the slight­est simil­i­tude. The fol­low­ing exper­i­ment is equal­ly deci­sive against this theory.

Draw two lines inclined towards each oth­er, as in Plate XIX. fig. 10, on a sheet of paper, and hav­ing caused them to coin­cide by con­verg­ing the optic axes to a point near­er than the paper; look intent­ly on the upper end of the resul­tant line, with­out allow­ing the eyes to wan­der from it for a moment. The entire line will appear sin­gle and in its prop­er relief, and a pin or a piece of straight wire may with­out the least dif­fi­cul­ty be made to coin­cide exact­ly in posi­tion with it; or, if while the optic axes con­tin­ue to be direct­ed to the upper and near­er end, the point of a pin be made to coin­cide with the low­er and fur­ther end or with any inter­me­di­ate point of the resul­tant line, the coin­ci­dence will remain exact­ly the same when the optic axes are moved and meet there. The eyes some­times become fatigued, which caus­es the line to appear dou­ble at those parts to which the optic axes are not fixed, but in such case all appear­ance of relief van­ish­es.. The same exper­i­ment may be tried with more com­plex fig­ures, but the pic­tures should not extend too far beyond the cen­tres of the retinæ.

Anoth­er and a beau­ti­ful proof that the appear­ance of relief in binoc­u­lar vision is an effect inde­pen­dent of the motions of the eyes, may be obtained by impress­ing on the reti­nal ocu­lar spec­tra of the com­po­nent fig­ures. For this pur­pose the draw­ings should be formed of broad coloured lines on a ground of the com­ple­men­tary colour, for instance red lines on a green ground, and be viewed either in the stere­o­scope or in the appa­ra­tus, fig. 6, as the ordi­nary fig­ures are, tak­ing care, how­ev­er, to fix the eyes only to a sin­gle point of the com­pound fig­ure; the draw­ings must be strong­ly illu­mi­nat­ed, and after a suf­fi­cient time has elapsed to impress the spec­tra on the ret­inæ, the eyes must be care­ful­ly cov­ered to exclude all exter­nal light. A spec­trum of the object in relief will then appear before the closed eyes. It is well known that a spec­trum impressed on a sin­gle eye and seen in the dark, fre­quent­ly alter­nate­ly appears and dis­ap­pears: these alter­na­tions do not cor­re­spond in the spec­tra impressed on the two ret­inæ, and hence a curi­ous effect aris­es; some­times the right-eye spec­trum will be seen alone, some­times that of the left eye, and at those moments when the two appear togeth­er, the binoc­u­lar spec­trum will present itself in bold relief. As in this case the pic­tures can­not shift their places on the reti­na in what­ev­er man­ner the eyes be moved about, the optic axes can dur­ing the exper­i­ment only cor­re­spond with a sin­gle point of each.

When an object, or a part of an object, thus appears in relief while the optic axes are direct­ed to a sin­gle binoc­u­lar point, it is easy to see that each point of the fig­ure that appears sin­gle is seen at the inter­sec­tion of the two lines of vis­i­ble direc­tion in which it is seen by each eye sep­a­rate­ly, whether these lines of vis­i­ble direc­tion ter­mi­nate at cor­re­spond­ing points of the two ret­inæ or not.

But if we were to infer the con­verse of this, viz. that every point of an object in relief is seen by a sin­gle glance at the inter­sec­tion of the lines of vis­i­ble direc­tion in which it is seen by each eye singly, we should be in error. On this sup­po­si­tion, objects before or beyond the inter­sec­tion of the optic axes should nev­er appear dou­ble, and we have abun­dant evi­dence that they do. The deter­mi­na­tion of the points which shall appear sin­gle seems to depend in no small degree on pre­vi­ous knowl­edge of the form we are regard­ing. No doubt, some law or rule of vision may be dis­cov­ered which shall include all the cir­cum­stances under which sin­gle vision by means of non-cor­re­spond­ing points occurs and is lim­it­ed. I have made numer­ous exper­i­ments for the pur­pose of attain­ing this end, and have ascer­tained some of the con­di­tions on which sin­gle and dou­ble vision depend, the con­sid­er­a­tion of which, how­ev­er, must at present be deferred.

Suf­fi­cient, how­ev­er, has been shown to prove that the laws of binoc­u­lar vis­i­ble posi­tion hith­er­to laid down are too restrict­ed to be true. The law of Aguilo­nius assumes that objects in the plane of the horopter are alone seen sin­gle; and the law of cor­re­spond­ing points car­ried to its nec­es­sary con­se­quences, though these con­se­quences were unfore­seen by its first advo­cates, many of whom thought that it was con­sis­tent with the law of Aguilo­nius, leads to the con­clu­sion that no object appears sin­gle unless it is seen in a cir­cle pass­ing through the cen­tres of vis­i­ble direc­tion in each eye and the point of con­ver­gence of the optic axes. Both of these are incon­sis­tent with the sin­gle vision of objects whose points lie out of the plane in one case and the cir­cle in the oth­er; and that objects do appear sin­gle under cir­cum­stances that can­not be explained by these laws, has, I think, been placed beyond doubt by the exper­i­ments I have brought for­ward. Should it be here­after proved, that all points in the plane or in the cir­cle above men­tioned are seen sin­gle, and from the great indis­tinct­ness of lat­er­al images it will be dif­fi­cult to give this proof, the law must be qual­i­fied by the admis­sion that points out of them do not always appear double. 

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  1. See also a Trea­tise of Paint­ing, p. 178. Lon­don, 1721; and Dr. SMITH’S Com­plete Sys­tem of Optics, vol. ii. r. 244, where the pas­sage is quot­ed.
  2. The lumi­nous line seen by a sin­gle eye aris­es from the reflec­tion of the light from each of the con­cen­tric cir­cles pro­duced in the oper­a­tion of turn­ing; when the plate is not large the arrange­ment of these suc­ces­sive reflec­tions does not dif­fer from a straight line.
  3. Sys­tem of Optics, vol. ii. p. 388. and r. 526.
  4. “We see more exquis­ite­ly with one eye shut than with both, because the vital spir­its thus unite them­selves the more, and become the stronger: for we may find by look­ing in a glass whilst we shut one eye, that the pupil of the oth­er dilates.” — Lord BACON’S Works, Syl­va Syl­varum, art. Vision.
  5. BIRCH’S His­to­ry, vol. ii. p. 348.
  6. Nat­ur­al Mag­ic, p. 100.
  7. Nou­veau Sys­tème de Chimie Organique, 2me edit. t. 1. p. 333.
  8. Enquiry, Sect. xiii.
  9. Tor­tu­al, die Sinne des Men­schen. Mün­ster, 1827. Bar­tels, Beitrage zur Phys­i­olo­gie der Gesichtssinnes. Berlin, 1834.
  10. Act. Par. 1743. M. p. 334.
  11. Nou­velle Théorie de la Vision, Par. 1823.
  12. Traité de la Sci­ence du Des­sein, Par. 1821, p. 270.
  13. Nou­veau Sys­tème de Chimie Organique, t. 2. p. 329.
Sir Charles Wheatstone (London, UK)

Charles Wheat­stone was born in 1802 and was a sci­en­tist and inven­tor dur­ing the Vic­to­ri­an Era. Besides his efforts in the field of stere­oscopy, he is also known for inven­tions like the Eng­lish con­certi­na musi­cal instru­ment, the Play­fair cipher encryp­tion method and the Wheat­stone bridge to mea­sure elec­tri­cal resis­tance. In 1868 he was knight­ed soon after he com­plet­ed his auto­mat­ed tele­graph.

It’s said that he was talk­a­tive and live­ly on pri­vate occa­sions but rather reserved in pub­lic. He died of pneu­mo­nia in 1875 dur­ing a vis­it in Paris.

Wikipedia: Charles Wheat­stone