6o 



SCIENCE. 



[Vol. XI. No. 261 



•calling these ' corresponding ' halves, we mean that they have the 

 same function of localization ; that is, that they are constructed for 

 seeing the same object, at the same point in space, at the same 

 time, assuming a given state of fixation and the proper position of 

 the object. Thus one image of an object falling upon a in the left 

 eye, L, and the other upon a' in the right eye ; or upon b in the left, 

 and b' in the right eye ; and so on, — will make the object to appear 

 ■single and in the same place. Hence they are called ' correspond- 

 ing ' points. But if one of the images falls upon a, and the other 

 upon b' or any point between that and a\ which may happen ac- 



■cording to the position of the external object, there will appear to 

 be two objects. This is because all other points than a ' are ' dis- 

 parate ' in relation to a. So with b and c' , or c and d'. Thus, 

 while every point in a temporal half is a ' corresponding ' point to 

 -a given point in the nasal half of the other eye, it is ' disparate ' to 

 all other points. This is the binocular use of the term. But since 

 the temporal halves of the two eyes are non-corresponding halves, 

 the points a, b, d', and e' are also ' disparate.' Now, inthemonocu- 

 Jar retina all the points are ' disparate ' in relation to each other ; 

 that is, combination never takes place. Hence a, b, c, d, and e, or 

 jz', b', c' , d', and e' axe. respectively ' disparate ' in relation to each 

 other monocularly considered. Then, since the temporal half of the 

 right eye corresponds to the nasal half of the left eye, and the two 

 -are thus identical in visual functions, a and d', or b and e', are ' dis- 

 parate ' in relation to each other in precisely the same sense as a 

 and d, or b and e, in monocular vision. This is the monocular use 

 of the term. Now, since fusion of images never takes place in 

 monocular vision (say, when separate images fall upon a and b, b 

 and c, or a and d, and so on), it can never take place when the two 

 images fall upon non-corresponding halves of the retina (say, both 

 upon the temporal, or both upon the nasal halves ; that is, upon b 

 and d', a and d', or b and e'), any more than they would upon b and 

 d, a and d, or b and e, and so on. The reason for this is plain. 

 Each eye forms binocularly only half an eye, so that the temporal 

 half of one is identical in function with the nasal half of the other. 

 This being the case, the non-corresponding halves of the binocular 

 eye form a monocular eye. Experiment will show this to be the 

 case. Hence stereoscopic images falling both of them in the tem- 

 poral, or both of them in the nasal halves of the binocular eye, will 

 appear precisely as if one of them fell in the nasal and the other in 

 the temporal half of the monocular eye, or as if both fell upon sep- 

 arate points in any one half of the monocular eye. Thus the 

 images in the temporal halves a, b, and d', e', can no more combine 

 than if they were a, b, and d, e'. Hence a, b, d', e' , are monocular- 

 ■ly ' disparate ; ' so also d, e, a', b'. Now, since monocular combi- 

 nation of ' disparate ' images never takes place, we can demonstrate 

 that it can never take place in stereoscopic combination ; at least, 

 where the figures to be combined are such as Wheatstone's original 

 illustration represented : namely, two lines which indicate opposite 

 inclinations to the median plane. This is shown in the following 

 lines, where A and B, the upper ends of the lines, will fall upon 

 temporal halves of the retina when C and D fall upon the fovea, 

 and yet fusion is as apparent as if it were real. The lower ends 

 fall upon the nasal halves, and fusion is also apparent ; the total re- 

 ■sultant being a line with the upper end nearer the observer than 

 the lower, and apparently upright or at an inclination to the plane 

 of the paper. But it is effected by non-corresponding halves of the 

 eye. 



To illustrate this, take Fig. 4, R and L representing the two 

 -eyes. Let^ and B represent two figures farther from the median 

 line EF\.\\a.n Cand D. A and B may represent the upper ends of 

 ■the lines in Fig. 3, and C and D the centres ; both together forming 



a plane geometrical outline for a stereoscopic figure such as Wheat- 

 stone employed. Take E for the point of fixation before combina- 

 tion, so that we may suppose A, B, C, and D to lie in the horopter. 

 c and c' are the fovea: centrales ; and when the eyes are fixated 

 for an object at E, its two images will fall, one upon c and the 

 other upon c' ; while those of A will fall upon e and e', of 7? upon a 

 and a', of C upon rfand d' , and of D upon b and b'. Now, a and 

 a', b and b', <rand c', rfand d', e and e', being corresponding points, 

 the several objects will be seen single while they are in the horop- 

 ter ; but the position of their images upon the retina must be no- 

 ticed before indicating the effect of stereoscopic combination. The 

 images of each object fall upon corresponding halves of the retina; 

 but the images of A and B compared, also of C and D compared, 

 fall upon non-corresponding halves of the retina. Now, in stereo- 

 scopic combination the object is to make A and B, or C and D, ap- 

 pear to coincide respectively ; that is, appear upon the fovea. This 

 may be done by converging or by diverging the eyes. But this can 

 be effected only by fusing one image ol A or C in the one eye with 

 the image oi B ox D respectively in the non-corresponding half of 

 the other eye. By convergence the fusion will be of images at 

 present in the temporal halves ; by divergence, of images in the 

 nasal halves : that is, by the former combination, must be of extra- 

 foveal, and by the latter of intra-foveal, images, a and b, and d' and 

 e', are extra-foveal, because they lie in the temporal halves : d and e, 

 and a ' and 1^' , are intra-foveal, because they lie in the nasal halves of 

 the eyes. Now, if we converge the eyes so as to bring the image of C 

 and Dm\.o the fovea, it is evident that the combination takes place 

 only by what are extra-foveal images when the point of fixation is 

 E. Convergence to produce combination of C and D requires a 

 new point of fixation in the median line at the intersection of the 

 lines which represent the course of light from C to d', and from D 

 to b. When this is effected, the foves c and c' are shifted, the 

 former to b and the latter to d', to receive the images at those 

 points. But thus, while the images of C and D are fused in the 



fovea, those of A and B still fall upon extra-foveal points as far 

 from the new position of c and d 2lS a \s from b, and e' from d'. 

 But being both extra-foveal, they fall in temporal and therefore 

 non-corresponding halves of the retina. In Wheatstone's experi- 

 ment. Fig. I, these would represent the larger squares, and the ap- 

 parent combination represented in the base of a visibly solid figure 

 thus perceived is explained by ' fusion upon disparate points.' But 

 being extra-foveal, and in the temporal or non-corresponding 

 halves of the retina, these points are not binocularly, but monocu- 

 larly ' disparate,' and hence the fusion claimed for them is as im- 

 possible as if it were claimed for the points a and b, or a and e, or 



