]8 Mr. C. J. Monro on a case of Stereoscopic Illusion. 



and without comparison of estimated with calculated results, 

 which it would be very hard to conduct satisfactorily, I think I 

 may give this phenomenon as a confirmation of Sir David Brew- 

 ster's view, subject to the qualification above stated, which he 

 applies himself in a particular class of cases at pages 209, 210, 

 and 217. 



That such a surface is given by the theory is evident. The 

 visual rays approach without limit to parallelism as you run 

 your eyes away along the wall : they are parallel also when the 

 four quantities following are proportional, the distances of the 

 eyes and of the points to be combined from the intersection of 

 the wall by the line through the eyes. When these are propor- 

 tional to one another, they are proportional to their differences. 

 So the direction of the second asymptote is that of the base of a 

 triangle whose sides are in direction and magnitude the distances 

 between the eyes and between the points to be combined. The 

 latter distance is in these patterns constant in magnitude, and 

 must be positive if the stereoscopic combination is direct, and 

 negative if converse, provided that the directions containing the 

 acute angle are taken to be of the same sign. The surface is 

 cylindrical, because the points to be combined in any part of the 

 pattern, and therefore the lines through them from fixed points, 

 and the intersection of these, all have for orthogonal projections 

 points and lines answering the same description in the horizontal 

 plane. 



For further details, let us confine our attention to this plane. 

 Take for axes the line through the eyes and the trace of the 

 wall; and, with the above convention as to signs, let the dis- 

 tances of the eyes and of the two other points from the origin 

 be a, a ! , b, b 1 . Then, if it is remembered that a, a 1 and jb — b' 

 are constant, the coordinates of the point of intersection of the 

 visual rays will be given by the equations 



x y x y 



aba' b' 



whence 



a — — a 

 x 2 + r — jj-xy — (a + a!)x + aa ! = 0, 



the equation of an hyperbola of whose asymptotes the equa- 

 tions are 



~ x y a + a! 



a— a! b—b' a— a' 



The line given by the last equation cuts the line through the 

 eyes as far on one side of the mid-point between them as the 

 trace of the wall cuts it on the other, and makes with these lines 



