Brewster's Theory of Binocular Perspective. 439 



corresponding points on the stereograph. The relative posi- 

 tions of the different parts of the externally projected binocular 

 image is determined mainly by the stereoscopic displacement 

 in the pair of pictures viewed. This in turn is determined 

 by the degree of convergence of the camera axes ; while the 

 relation between the visual lines of the observer in the stereo- 

 scope may be either convergence, parallelism, or divergence. 

 It is not, however, a matter of indifference which of these 

 relations is assumed. Theoretically the visual lines should 

 meet at an angle the same as that between the camera axes, 

 when a given point is examined; practically this is rarely ever 

 the case. The distance between corresponding stereograph 

 points is adjusted to secure, if possible, comfort to an average 

 pair of eyes in viewing the picture; and the same stereograph 

 may necessitate convergence of visual lines for one observer, 

 divergence for another, in order that binocular fusion be 

 attained. 



In studying the effect of varying the optic angle while a 

 given stereograph is examined, I have found a modification of 

 Wheatstone's reflecting stereoscope to be valuable. The arms 

 were made to glide under a divided circle in such manner that, 

 from a given point on either of the conjugate pictures, the angle 

 of incidence at the surface of each mirror could be varied from 

 0° to 60°. When its value is 45° the visual lines must be 

 parallel, if the image is seen binocularly ; if less than 45°, they 

 must converge; if greater, they must diverge. Calling angles 

 of convergence positive, I was able to vary the optic angle 

 from — 7^°to +80°, though clear and steady vision was not 

 possible through so wide a range. Placing the conjugate 

 pictures each at a fixed distance, such as 50 centim., this 

 being the sum of the lengths of the incident and reflected 

 rays, the apparent distance of the binocular image should be 

 50 centim. when the arms of the instrument are so disposed 

 as to make the optic angle about equal to 7° 20'. The effect 

 upon the combined image may then be noted for any change 

 in the relation between the visual lines. 



Helmholtz * has shown that the visual lines are not coinci- 

 dent with the true optic axes of the eyeballs ; but since each 

 is practically axial in its relation to the crystalline lens, it will 

 involve no confusion to call them visual axes, while the angle, 

 ct, between them is still called the optic angle. If an isosceles 

 triangle be constructed whose base, a, is the interocular line, 

 then for the distance, D, of its vertex from either optic centre, 

 we have 



D = ^ a cosec ^ a. 

 * Opt. Phys. p. 93 (edit. 1867). 



