SCIENCE. 6n 



Fig. 3, and 50 mm. in Fig. 4. An average lenticular 

 stereoscope will fail to produce axial convergence when 

 Fig. 3 is viewed by a pair of eyes whose centres are 64 

 mm. apart. These variations in visual effect can be 

 rendered still more striking by using the reflecting stere- 

 oscope, after cutting apart the right and left halves of 

 the stereograph. 



It must be remarked that although the perception of 

 binocular relief is intensified by alternate examination 

 of foreground, and background it is quite possible to at- 

 tain it by momentary illumination with the electric spark, 

 at least with convergence of visual axes, as has been 

 done by Dove (") and others. During such brief illu- 

 mination, no variation of convergence is possible, and, 

 if the foreground be distinctly focalized, the background 

 must be slightly doubled homonymously. The position 

 of the point of sight is found thus to be almost 

 as nearly determinate as when the illumination is pro- 

 longed. Whether binocular relief, and the position of 

 the binocular image, be perceptible with equal distinct- 

 ness when the visual lines diverge, has not thus far been 

 ascertained by experiment, so lar as I am aware. I 

 hope to test this, and to study certain other points of in- 

 terest connected with it, at some future time. 



Since the apparent distance of the point of sight con- 

 tinues to increase in a positive direction after axial paral- 

 lelism passes into divergence, it becomes necessary to 

 investigate the physiological conditions that interfere 

 with the results of the mathematical theory hitherto gen- 

 erally applied. 



In looking at any picture constructed in accordance 

 with the rules of perspective applied by all artists, the ' 

 illusion of distance is quickly attained by forming aeon- | 

 ception of the reality in space to which the different parts 

 of the picture are supposed to correspond, or of the object I 

 as the observer has been accustomed to view things of its [ 

 kind. With the same degree of axial convergence a 

 mountain and a piece of statuary will never be judged | 

 equally distant. It is unnecessary here to enumerate the 

 elements that combine to produce the illusion. If these 

 be excluded to the utmost, as in mere skeleton diagrams, 

 there will still be left three to consider in judging the 

 distance, size, and form of what is represented. These 

 are — 



I. The optic angle between the observer's visual axes. 



[I. The focal adjustment of the crystalline lens. 



III. The visual angle subtended by the picture. 



Of these the first is the only one usually considered as 

 distinctive of binocular vision. It can never be dissoci- 

 ated entirely from the others, and its effect may be so 

 overpowered by them, when distance is to be estimated, 

 that calculations based upon its value, like those of 

 Brewster, lose all claim even as approximations to the 

 truth. Its true importance is dependent upon the extent 



to which the individual, in natural binocular vision, has 

 been accustomed to associate the sensation of muscular 

 contraction in the rectus muscles of the eyeballs with the 

 true distance of objects as learned by other means. 

 Doubtless this varies with different individuals. -For 

 distances of more than 240 m. the optic angle becomes 

 inappreciable, and hence theoretically valueless ; its im- 

 portance is greatest near the lower limit of distinct vis- 

 ion. In every case its effect is appreciated mainly through 

 the muscular sense and through the retinal perception of 

 double images from objects farther or nearer than the 

 point upon which attention is fixed. We are safe in 

 disregarding the mere fact that a pair of imaginary lines 

 would make a measurable angle with each other if con- 

 structed, though the use of this angle may be convenient 

 in analyzing the phenomena of vision. It is well to re- 

 member, however, that its variations imply simply 

 changes of muscular tension, and these constitute the 

 most appreciable effects that influence the estimate of 

 limited distance. 



The judgment due to fecal adjustment is also an in- 

 terpretation, based upon personal experience, and sug- 

 gested by the sense of contraction in the ciliary muscle, 

 while adapting the crystalline lens to produce a distinct 

 image. Variations in this are hence inappreciable for 

 distances of more than 6 m., and are most noticeable 

 near the lower limit of distinct vision. It is near this 

 limit that the stereograph is held in most cases when 

 regarded. 



The visual angle is important as chiefly determining 

 the size of the binocular retinal image. Since two eyes 

 receive more of the light reflected from a given surface 

 than either eye alone, the binocular image appears 

 brighter than one that is monocular ; and this is apt to 

 produce the illusion of slight decrease of distance, if the 

 focalization is perfect. But variation due to this cause is 

 not important in comparison with that due to change in 

 the visual angle. 



The relative importance attached to the separate ele- 

 ments enumerated depends most frequently upon the 

 unconscious experience of the individual. The results 

 which they combine to produce cannot be referred to 

 any one mathematical formula until the physiology of 

 sensation is completely brought within the domain of 

 mathematical law. 



In testing the effects of these elements it will be best 

 to apply a formula for the distance of the optic vertex 

 from each eye, in terms of the interocular distance, i, and 

 optic angle, a. Assuming the optic triangle to be isos- 

 celes, and calling D the required distance, we have, as 

 the formula to be tested by experiment, 

 D = y 2 i cosec. y z a. 



Considering angles of convergence positive, the possible 

 values of a, between which I find myself limited, are + 80° 



