Physiological Perspective. • 315 



E'. The binocular image of the horizontal diameters must 

 hence be perceived as a curve, convex toward the observer. 



Each circle, obliquely viewed, must be seen approximately 

 as an ellipse, the ratio of whose axes is readily calculable if 

 the angle of inclination be known. But the retinal ellipses 

 are no longer concentric (figs. 3 and 4), the extent of retinal 

 displacement depending on the extent of minor axis in 

 each. If the successive vertices be connected, we have two 

 curved lines, ACB and A'C'B 7 . If these be binocularly 

 combined and externally projected, since C'C is less than A 7 A 

 and B'B, optic divergence becomes necessary in transferring 

 the attention from C and C to A and A.' or B and B 7 . The 

 binocular image of the vertical diameters must hence be per- 

 ceived as a curve convex toward the observer. 



Let F and Gr (fig. 3) be points symmetrically situated 

 with regard to the vertical diameter, and hence equidistant 

 from D and E respectively. When the card is revolved, as in 

 fig. 2, the distance OE exceeds OD, and hence the visual angle 

 subtended by E G is less than that subtended by D F. Every 

 ellipse therefore is distorted ; but since the distortion is equal 

 and opposite on the two retinas, it is perfectly corrected in 

 the binocular combination of each pair of curves. To each 

 eye separately the effect is the same as if every major axis 

 were bent, and every point of each curve, above and below 

 the horizontal axis, were correspondingly displaced : F and 

 G 7 are elevated, F 7 and Gr depressed ; hence F and F 7 differ 

 in retinal latitude as well as longitude, but are nevertheless 

 binocularly combined. This confirms the views of Wheatstone 

 in opposition to those of Brewster. 



If a pair of small circles whose vertical diameters are a b 

 and a'V be viewed above the large circles, the visual lines 

 directed to their centres are similarly oblique to their vertical 

 diameters. They are therefore retinally projected as approxi- 

 mate ellipses ; and when these are thence externally projected, 

 their upper vertices are further apart, and their lower vertices 

 nearer together, than their centres. The binocular combi- 

 nation is hence an ellipse whose plane is oblique, the upper 

 vertex being further from, and the lower vertex nearer to, the 

 observer. A pair of small circles below the large ones are 

 binocularly combined with opposite obliquity. 



So explanation is now needed to show that if the planes of 

 the cards be revolved into the positions P 77 Q 77 and P 7// Q' 7/ 

 (fig. 2), the binocular combination of the concentric circles 

 must present a concave surface, and the obliquity of the plane 

 of each pair of conjugate small circles, when binocularly 

 viewed, must be reversed in sense. 



