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purely on convergence, but on convergence disparity and we write 
(12) ray) 
where it is convenient to choose y, as the maximum value of y in the stimulus 
so that y - y, is non-negative for all visible points. The function f is the same 
for all binocularly equivalent stimuli, that is, for all stimuli which can be trans- 
formed into each other by the rule of (1l. We cannot conclude, a priori, that f is 
a universal function for a given observer and takes on the same values for stimuli 
which are not binocularly equivalent. Fortunately, our present experimental informa- 
tion on this point does indicate that for any given observer the function f is universal 
and does not particularly depend on the stimulus, | S]. 
It is not sufficient to know that the circles r = constant, (p - constant of the 
polar coordinate grid in visual space correspond to the loci y = constant, ()- constant 
of physical space: we must describe the correspondence by a precise numerical trans- 
formation. Even accepting the relations, 
refly Vo) 
929 
we cannot determine the function f without knowing the intrinsic geometry of the per- 
(13) 
ceptual space. There are a number of experiments which show that the perceptual 
geometry is not euclidean [5], [1], and which determine the type of geometry involved. 
Most observers give experimental results which can be explained consistently only on 
the hypothesis that the visual geometry is the so-called hyperbolic non-Euclidean 
geometry of Lobachevski. In this geometry the distance D between two points with 
sensory polar coordinates (ry, ®, and (r,, Pa) is given by 
(14) cosh d » cosh r, cosh r, - sinh r, sinh r, cos (9, -9) 
Equation (14) is the hyperbolic analog of the Euclidean law of cosines and is used in 
much the same way. With (13) and (14) it is possible to design experiments to deter- 
mine the function f(y - y9) and a number of such experimental determinations have 
been made. Once the numerical values of the function f have been determined there 
is no longer any difficulty in calculating the perceptual effect of stereoscopic presen- 
tations. 
For the purpose of seeing how this knowledge may be applied, let us take the 
example of the preceding section. We take as our object of regard in real space, an 
open rectangular chamber symmetric with respect to the median, with its farther 
wall in the background plane, 4 meters wide and 5 meters deep (Fig. 9). We shall 
-Al-