J. LeConte — Phenomena of Binocular Vision. 



99 



In addition to the slope of the phantom-plaue, another phe- 

 nomenon is plainly perceived ; the figures change their shape, 

 being all elongated in the direction of the slope, the degree of 

 elongation being also proportioned to the angle of the slope and 

 therefore to the degree of ocular convergence. If for example, 

 the figures are regular squares looked at from the direction of 

 the diagonals, then they become greatly elongated rhombs. 



Explanation. — Principles. If a slender rod a b c be held in a 

 horizontal position in the median plane but a little below the 

 horizontal plane passing through the two eyes, so that the eyes 

 shall look down upon it at small angle, the perspective projec- 

 tion of the rod as seen by the two ,\C 

 eyes will be according as we look j/\^ 

 at the farther end or the nearer end 

 or the middle point. In accord- el \a va 



ance with the mode of representation used in all my previous 

 papers, capitals indicate objects or points seen single by binocular 

 combination at the point of sight, small letters show right-eye- 

 images and the same primed left-eye-images. In all cases, it is 

 seen, the right and left-eye-images meet each other at the point 

 of sight making small angles. 



If, now, the rod instead of being held horizontally, be in- 

 clined by lifting the nearer end toward the plane of vision,* the 

 angle of meeting or crossing of the two images becomes greater 

 but the vertical length of the projection 

 less, thus: until, when the rod is in the 

 plane of sight, the angle between the two 

 images becomes 180° and the subtended 

 vertical line of projection becomes 0°. In other words the pro- 

 jection becomes a continuous horizontal straight line. Of 

 course, to the binocular observer it does not seem like a hori- 

 zontal straight line, because he introduces the element of depth 

 of space by binocular perspective. To him it will look like a 

 v or an x looked at end on. 



Application of principles. — The figures of a regularly tessella- 

 ted plane must of course lie in parallel lines. We will suppose 

 these parallels to run from the observer. By geometric or 

 monocular perspective such 

 lines on a horizontal floor 

 converge to vanishing point 

 on the horizon. Fig. 1 repre- 

 sents a projection of such 

 parallels. This is as seen 

 with one eye. As seen with 

 two eyes there are, of course, 

 two images of all these lines 



* The plane passing through the optic centers and the point of sight or through 

 the two visual lines. 



% 



st. I vy. 



