100 J. LeConte — Phenomena of Binocular Vision. 



crossing each other at small angles as shown above. Let us fix 

 our thoughts on the middle one only. In natural vision, the 

 two images of this line a will cross one another at small angle 

 at the point of sight as already explained. Bat in making the 

 phantom-images the lines bb or cc or dd or ee, etc., are brought 

 together in the middle and viewed as the middle line. But it is 

 evident that the angle of perspective convergence and therefore 

 the angle of crossing one another where they come together is 

 greater and greater as they are brought from greater distances 

 right and left. In other words: the perspective angle is added to 

 the binocular angle and all credited to the binocular angle because 

 viewed as a middle line which ought to have no perspective 

 angle. But we have already seen that crossing of binocular 

 images at greater angles means a nearer approach to the plane 

 of sight — a looking niore "end on." In other words, it means 

 in this case a lifting of the hither end of the plane. As more 

 and more separated, figures bb, cc, dd, ee, etc., are successively 

 brought forward and united in front, the angle of crossing of 

 the lines and therefore the inclination of the phantom-plane be- 

 comes greater, until if we could bring together from infinite 

 distance, the phantom plane would coincide with the plane of 

 sight, i. e., would slope at an angle of 45°. 



So much for the explanation of the inclination of the plane; 

 now for that of the elongation of the figures. 



As already seen, the projection — or what amounts to the 

 same thing the retinal image — of a horizontal line in the median 

 plane is shortened, or the vertical angle subtended at the eye 

 is lessened in proportion as the line is brought nearer to the 

 plane of sight by. lifting the nearer end. Therefore, in order to 

 subtend the same angle under these conditions it would require 

 a longer line. Now in the phantom-image the subtending angle 

 remains constant. Therefore in proportion as the phantom 

 plane is apparently lifted toward the plane of sight, the plane 

 and all its figures must appear to elongate in the direction of 

 the slope. The elongation is greater in proportion as the phan- 

 tom plane approaches the plane of sight and therefore without 

 limit except the power of the eyes to combine more and more 

 distant points right and left. 



Experiment 2. In the case of the floor, the body of the obser- 

 ver prevents the viewing of the phantom in the other direction, 

 i. e., by looking obliquely backward, unless indeed the observer 

 could place himsef horizontally above the floor face downward. 

 We therefore take next a vertical wall, such as a regularly 

 figured wall papering of small pattern or a coarse wire-netting. 

 The windows of the basement of one of the university build- 

 ings are protected by a coarse wire netting with lozenge-shaped 

 meshes about 2£ inches in their shorter or horizontal diameter. 



