SCIENCE. 



547 



removed to Mi and M 2 respectively, while the convergence 

 of visual lines remains unchanged, the images still appear 

 at A and B. Wheatstone seems to have been the first 

 to show experimentally that the illusion of apparent 

 solidity can be obtained in this manner from a pair of 

 projections representing the same object from slightly 

 different points of view. If the eyes be properly trained, 

 the visual lines may be directed to points whose distance 

 is greater or less than that of the objects regarded at the 

 same moment, and Brewster described many striking 

 illusions thus obtained without the aid of the stereoscope. 

 The principle applied by him, as described in the paper 

 to which reference has been made, may be briefly given, 

 and his results can be easily tested by anyone who is 

 accustomed to analyzing his own visual sensations. 

 Upon a uniform horizontal surface (Fig. 2) let two lines, 

 AC and BC, be drawn, forming a small angle, ft, with 

 its vertex toward the observer. Let the eyes, R and L, 

 be placed above this. If they be directed to the point, 

 C, this appears in its true position. If the right eye be 

 directed to B and the left to A, the axes meet at P; this 

 point Brewster calls the binocular centre ; and since the 

 retinal images of B and A correspond, the visual effect is 

 that of the union of these two external points at the 

 binocular centre. Sweeping the glance toward C, the 

 two lines appear united in the air, and PC is the apparent 

 position of the combination, intermediate in direction be- 

 tween two monocular images, which may be disregarded 

 or hidden from view with screens. If the convergence 

 of visual lines be now diminished, the binocular image is 

 lost until the right eye becomes directed to A and the 

 left to B. The two points appear united at P , and the 

 line P C now appears in the air on the further side of the 

 surface. If the convergence be increased till P is again 

 the binocular centre, and the face be lowered and with- 

 drawn till the eyes are at R" and L", then C P" becomes 

 the position of the variable external image. And if low- 

 ered until R "L" coincides with the surface, C P" vanishes 

 at the moment of becoming coincident with the prolon- 

 gation of G C, the median of the triangle A C B. 



i 



ft 



Fig. 2. 



Brewster's formula for determining the distance 

 of the binocular centre from G is easily deduced and 

 applied. 



Let i = interocular distance, R L. 

 " a = interval between the corresponding points, 

 A and B. 



Let b = distance, G E, between card and observer. 

 " x = distance G P, or G P', which is positive when 

 measured toward the observer, negative in the direction 

 opposite. Then, observing the usual rule of signs, we 

 have, by Geometry, 



a b 



x = ± . 



1 ± a 



Applying this formula, Brewster constructed a table of 

 distances for the binocular centre. For negative values 

 it is seen that x becomes infinite when the visual lines 

 become parallel ; and, if they be slightly divergent, the 

 binocular centre is far in the rear of the observer. 

 Either of these conditions would make binocular vision 

 impossible if the theory be correct. In testing the ex- 

 periment with trained eyes, it is found quite possible to 

 secure binocular fusion of the images of A and B when 

 the interval between these points equals or slightly ex- 

 ceeds the interocular distance. It is also found that fu- 

 sion of the images of the whole line at any given instant 

 is impossible, especially when the angle ft is large, or the 

 lines are viewed very obliquely, as from R" and L". If 

 the images of A and B fall on corresponding retinal 

 points, the resulting sensation is binocular fusion, whether 

 the visual lines be convergent, parallel or divergent ; and 

 the images of any two points nearer or farther apart can- 

 not fall on corresponding retinal points at the same mo- 

 ment with those of A and B. though small differences are 

 easily neglected. Whatever may be the importance there- 

 fore of optic convergence, as a factor ordinarily in de- 

 termining the binocular judgment of distance, it has no 

 such exclusive and measurable value as that attributed 

 in Brewster's experiments ; and the apparent distance cf 

 objects viewed through the stereoscope is obviously not 

 determined by intersection of visual lines, if condiiions 

 are such as to render these parallel or divergent. The 

 visual effects of optic divergence can be more conveni- 

 ently studied by using stereographs than by the method 

 already described, and a modification of Wheatstone's 

 reflecting stereoscope affords the best means of measur- 

 ing variations of the optic angle. As the lenticular ster- 

 eoscope, however, is now almost universally employed, it 

 is important that this instrument, as found in the market, 

 be examined first. 



By diminishing the natural convergence of visual lines, 

 the stereoscopic effect of binocular relief can be quite easily 

 obtained, while gazing upon a stereograph, without any 

 instrument, when the interval between corresponding 

 points of the two pictures does not exceed that between the 

 observer's optic centres. This distance does not often 

 differ very much from 64 mm., which may be taken as an 

 average value. In Fig. 3 the distance between the two 

 central dots is 50 mm. If the reader will fix his gaze 

 upon a point ten feet off, just visible below the edge of 

 the page, and then suddenly raise the visual lines to the 

 figure without changing their convergence, he will see 

 three circles instead of two; the central one moreover 

 will appear as the base of a cone whose vertex is pointed 

 toward him, but capped with a small circle. A little at- 

 tention then will reveal the fact that when the dots are 

 seen distinctly and singly, the small circle is double and 

 slightly indis'inct, and vice versa. 



On stereographs, however, the interval between cor- 

 responding points is always greater than 50 mm. As the 

 result of measurement made upon the foreground inter- 

 vals of it6 cards, European and American, taken at 

 random, the mean value I have found to be 72.9 mm., the 

 maximum being 95 mm. If binocular combination is se- 

 cured without the stereoscope, therefore, optic divergence 

 is nearly always necessary. To ascertain the extent to 

 which this is counteracted by the semi-lenses of our best 

 stereoscopes, 30 pairs of these were kindly loaned me by 

 Mr. H. T. Anthony, of New York. With very slight va- 

 riation, their focal length was found to be 18.3 cm., and 

 their deviating power not sufficient to prevent the neces- 



