J. LeConte — Phenomena of Binocular Vision. 105 



distinctly saddle-shaped. It will be also remembered that the 

 same fore and aft curvature was observed in experiment 3. In 

 fig. 4, the phantom is not only concave from side to side, but 

 convex fore and aft. The explanation of this fore arid aft 

 curvature I am not yet able to give. 



The concavity and convexity of concentric circles, drawn on 

 two planes inclined toward, or away from each other and 

 viewed by binocular combination — one of the most beautiful 

 phenomena brought out by Prof. Stevens — must be explained, 

 partly at least in a different way. This has been done very 

 perfectly by him. We only mention it to avoid confusion. 

 Figures of other forms do not appear curved in two directions 

 alike, as concentric circles do, but on the contrary, often as 

 already said, in opposite directions. 



Some general remarks suggested by the above. 



(1.) I believe, indeed am quite sure, that the phenomenon of 

 transverse curvature of the phantom surfaces described above 

 is a necessary result of the " horopteric circle of Midler ; v for this 

 circle is the necessary consequence of the concavity of the 

 retina together with the law of corresponding points. 



Supposing, for the moment, that the eyes in convergence 

 moved on vertical axes, i. e., without rotation on the optic axis,* 

 then it may be shown that with the point of sight fixed, other 

 objects right and left of that point, in order that their retinal 

 images should fall on corresponding points, must lie, not in a 

 plane, but in a circle passing through the point of sight and the 

 nodal points. This is called the horopteric circle of M filler. 

 The images of objects or points on a. plane passing through the 

 point of sight would not fall on corresponding points but on 

 points nearer together than such points, and therefore a plane 

 surface ought to appear convex, like the surface of a cylinder 

 with reverse curvature equal to that of the horopteric circle. 

 We do not ordinarily observe this because in planes at the usual 

 distance the curvature is too small to be detected near the point 

 of sight, and at a distance from that point, right or left, vision 

 is too indistinct for accurate observation. The form of any 

 surface is practically always gotten by sweeping the point of 

 sight over the surface and gathering up the result in memory, 

 the distance of that point being always truly estimated. But 

 in the case of phantom images in proportion as the point of 

 sight comes nearer, the curvature (by definition of horopteric 

 circle) becomes greater until it becomes quite distinct. 



Now if a plane is seen as a horopteric curve reversed, it is 

 evident that a horopteric curve ought to be seen as a plane, and 



*This is not exactly true, especially in strong convergence. This Jour., vol 

 xlvii, p. 153, 1869. 



