690 



Prof. Horace Lamb on the 



circles of the spherical field. In particular, if we consider a 

 plane perpendicular to OA, the lines in question which lie in 

 this plane are a doubly infinite system of hyperbolic arcs *. 

 The annexed diagram (fig. 4), which is similar to the one given 



Fis. 4. 



r~T:> 



by Helmholtz, shows two sets of such curves, the boundary 

 corresponding to an angular distance of 45° from OA. If a 

 strong after-image be formed of a short horizontal line at A, 

 the directions assumed by it as the eye is directed to various 

 points of the plane are indicated by one set of these curves. 

 The after-imnge of a short vertical line at A is in its 

 various positions tangential in like manner to the other setf. 

 The fact that linos which are really straight, but do not 

 meet OA, appear to be concave towards A is an immediate 

 consequence. 



This completes the mathematical theory. The physio- 

 logical basis of Listing's law is a more abstruse question. 



* Their equations are of the form 



x-+if— (lx+myy + ( 2a{lv+my) = Q. 

 t We have here (in principle) one method of testing- Listing's law. 



