May 18, 1882] 



NA TV RE 



69 



vol. xv. Part 3, p. 360) " On the Know ledge of 1 lisiance given 

 by Bi ocular Vision," in which he elaborated ilie idea that the 

 apparent position of the combined image produced by rays, from 



a pair of conjugate pictures, upon corresponding retinal points; 

 of the tv o eyes, is determined by the intersection of visual lines 

 passing through conjugate points. He deduced a formula and 

 constructed a table of apparent distances, thus determined, for 

 various values of the angle of convergence between the visual 

 lines. 



In 1S49 Brewster described his inventi >n of the lenticular 

 stereoscope (Phi!. Mag. 1852, p. 16) and of the binocular 

 camera, by which slightly dissimilar pictures of the same object 

 may be simultaneously obtained for examination in the stereo- 

 scope. Various modifications of the instruments already in use 

 were explained, and in all of I hern the apparent position of the 

 1 uage was referred to the point of convergence of the 

 visual lines, these being determined by the direction of rays on 

 entering the eyes after reflection or refraction in the stereoscope. 

 In 1S52 Wheatstone published a second piper [Phil. Mag. 

 1852, p. 504) on the Physiology of Vision, in which he discussed 

 the effects of varying 1 lie angle of convergence between the 

 visual lines, and also the distance of the pictures from the 

 mirrors of the reflecting stereoscope. He nuke- no reference to 

 divergence of visual lines, but, like Brewster, he subjoins "a 

 table of the inclinations of the optic axes, which correspond to 

 the different distances," which is abo applicable t 1 the binocular 

 camera. 



In direct binocular vision of a single point in front the inter- 

 ocular line is the base of an isosceles triangle, whose two sides 

 are the visual lines. Ilelmholtz ("Optique Physiologique," 

 p. 93) has shown that the latter are not coincident with the optic 

 axes, but practically they may be regarded as axial in relation to 

 the crystalline lens. For distinction it will be convenient to call 

 them visual axes, their intersection the optic vertex, and the 

 angle inclosed the optic angle, as has been customary. 

 Let < — interccular distance, 

 ,, a = op ic angle, 



,, D = distance of optic vertex from each eye, 

 Then 



D = .j. / cosec \ a. 



If = 0, D = co, and visual axes are parallel. 

 If o<o, D<0, and vi ual axes are divergent. 

 Wheatstone notices the exaggeraiion of perspective produced 

 when a pair of conjugate pictures, taken with a large angle 

 between the camera axes, are viewed in the stereoscope with the 

 visual axes nearly or quite parallel, lie mentions, as a remark- 

 able peculiarity [PAH. Mag. 1S52, p. 514), that "although the 

 optic axes are parallel, or nearly so, the image does not appear 

 to be referred to the distance we should from this circumstance 

 suppose it to be, but it is perceived to be much nearer. It 

 seems as if the dissimilarity of the projections, corresponding as 

 they do to a nearer distance than that which would be suggested 

 by the former circumstance alone, alters in some degree the 

 perception of distance." 



The last explanation is obviously inapplicable if two perfectly 

 similar pictures can be binocularly seen as one, with parallelism 

 or divergence of vi-ual axis. this cond !y imposed 



by placing before one eye a thin prism with its edge outward. 

 A single object in front is seen double un'il the visual axis 

 diverges enough to make the two images coincide in retinal posi- 

 tion. To test the strength of the external rectus mu-cles of the 

 eye-balls, this method has DOW been in use for many years by 

 oculists. The same effect may be attained by drawing a pair of 

 conjugate pictures apart until binocular fusion of their images 

 ceases to lie possible. Divergence of visual axes, to the extent 

 of S', has been thus obtained by Helmholtz ("Opt. Phys.," p. 

 616), and of 74° by 'he present writer, Since this point of 

 meeting is, in these cases, in the rear of the observer, the theory 

 of binocular prospective held by Wheatstone and Brewster is 

 incorrect. It is nevertheless given without qualification, either 

 directly or implicitly, in most, if not all, of our text-books of 

 physics. 



No analysis of the phenomena of binocular vision by axial 

 divergence has thus far been published, 



Helmholtz mentions the exaggeration of apparent distance 

 thus produced, and adds ("Opt. Phys. p. 828 ") that "in our 

 visual conceptions infinity is not presented as an impassable 

 limit." He accounts for this by stating that in abnormal vision 

 "all we can do is to compare the sensation produced with that 

 which it resembles most in normal vision." 



by examination of a largo number 1 f store 'graphs and lenti 

 cular stereoscopes, 1 have found [Am. Journ. of Science, No- 

 vember and December, 1SS1 J that in using them, slight axial 

 divergence is very frequently practised. It is neariy always 

 tnocu'ar fusion of images is obtained, in re- 

 garding ski \ luntanly diminishing the natural con- 

 vergence of visual axes without the aid of the stereoscope. The 

 n of axial convergence, as if in normal vision, is un- 

 necessary and misleading ; it should be entirely discarded in 

 explaining vision through the stereoscope. What is really 

 necessary is that the camera axes from corresponding points of 

 the stereograph, at the moment the picture is taken, shall con- 

 verge ; and that these points shall be imaged upon corresponding 

 points of the two retinas. The visual axis may then be either 

 convergent, parallel, or divergent. The visual effect will vary 

 with these conditions, but by no means in accordance with the 

 mathematical formula given above. I have described elsewhere 

 (Am. Journal of Science, November and December 18S1) a 

 determining approximately the apparent position of 

 the object regarded in the stereoscope, rejecting the hypothesis 

 that the visual axis must necessarily converge. It remains to 

 discuss the effect of making the optic angle alternately positive 

 and negative. Helmholtz's conclusion that the only resource, 

 when the visual axes diverge, is to compare the sensation pro- 

 duced with that which it resembles most, is unnecessary. No 

 such resource in the present case would have been needed, even 

 temporarily, h id not undue stress been laid upon the convergence 

 of visual lines. 



From the fact that a pair of similar images upon correspond- 

 ing retinal points produce the same impression, as if coming 

 from the same external point, there result two consequences of 

 fundamental importance in binocular vision, on which depends 

 tde explanation of all vision with axial divergence. One is 

 that both eyes are subjectively combined into a single central 

 binocular eye, composed of two eyes coincident in position, 

 each of them receiving its own image, which is wholly or partly 

 superpo-ed on that of the other. This observation is due to 

 Hering (Hering, "Beitrage zur Physiologie," 1S61, p. 35-64, 

 or Helmholtz, "Opt. Phys," p. "7"), and lias been extended and 

 appilied by Prof. Le Conte (Am. Journal of Science, S. III. 

 vol. i., p. 33, and vol. ii. p. 1, or "Sight," Appleton and Co., 

 New York, 1881, pp. 213-261). The two visual lines termi- 

 nating on corresponding retinal points are hence subjectively 

 combined into a single median line, to some point of which the 

 binocular image is referred. The apparent position of this 

 point of sight, how ever, is the result of .1 judgment, and not a 

 mathematical determination. In normal binocular vision the 

 judgment of distance may accord very nearly with what might 

 be determined by the intersection of visual lines, but there is no 

 necessary coincidence. 



The second consequence is that a point farther or nearer than 

 the point of sight is necessarily seen double, because imaged upon 

 retinal points that do not correspond. Conversely, if conjugate 

 points of a stereograph are imaged upon non-corresponding retina 1 

 points, fusion can be accomplished only by changing the relation 

 between the visual axes. To the binocular eye, therefore, such 

 point- will appear farther or nearer than the point of sight. On 

 these two principles depends, in large measure, the perception 

 of binocular relief. 



The perception of relative distance depends upon a variety of 

 conditions, which must be eliminated before binocular perspec- 

 tive is studied. There are then left still three elements to 

 consider : — 



1. The optic angle. 



2. The focal adjustment of the crystalline lens. 



3. The retinal magnitude of the binocular image. 



The import of the first of these depends upon the relative 

 degree of tension in the rectus muscles of the eyeballs ; of the 

 second on the tension of the ciliary muscle ; of the third on the 

 relation between the magnitude and distance of the object. The 

 judgment of distance. and size depends upon the acquired skill 

 of the observer in interpreting the sensations due to variation of 

 these elements. This variation is best accomplished with the 

 aid Of a modified Wheatstone stereoscope. 



Let the stereoscope be so arranged that the visual axi- may 

 successively inclose every possible angle between the limits 

 beyond which vision becomes impossible. On its arms let a pair 

 of conjugate pictures be kept at a fixed distance each from its 

 mirror. If the arms be so placed that the optic angle is that 

 of normal vision, the point of sight approximately coincides 



