SOME ASPECTS OF STEREOPSIS 101 



cues, say the horizontal disparities which are unaffected by the lens. 

 A quantitative analysis bears out the hypothesis just outlined 

 (Householder, 1943). If we take for the nodal points, C L and C R , the 

 coordinates (± 1, 0), with the positive y-axis extending forward 

 from the observer, and if the magnification is, as before, 



M = 1 + u , 



so that the increment of magnification in the vertical direction is 

 100 u % , then the locus of points in the horizontal plane whose retinal 

 images are equal in the vertical direction is the circle 



/ M 2 + IV / 2 M \ 2 



{*-jF=V +v ° = {m^1)- (1) 



or, very nearly, 



if we set 



/ 1 + u\ 2 /1 + uV 



(2) 



u 



1 = , (3) 



2(1 + u) 



then the tangent of the angle of rotation of the medial plane is, for 

 a fixed distance y of the fixation-point, 



x/y = Xy(l + Py 2 + 21 i y i ---), 



and for smajl angles this is equal to the angle itself. This is approxi- 

 mately proportional to the increment of magnification, to the distance 

 of the point of fixation, and also to the interocular distance since half 

 of this distance is the unit employed. The figure shows a comparison 

 of theory and experiment with two subjects, both left and right eyes. 

 It is especially to be noted that all parameters are determinable, 

 these being only the interocular distance and the magnification. The 

 breakdown of the effect occurs before the equality of the images be- 

 comes impossible at increments of about 6 or 8%. When a spherical 

 size-lens is employed the two conflicting effects of horizontal and ver- 

 tical disparities neutralize one another for small magnifications also 

 up to about 6 or 8%, while for larger magnifications the horizontal 

 disparities provide the effective cue and the effect of the vertical dis- 

 parities gradually dies out. 



