of Edinburgh, Session 1881-82. 
359 
We have 
g— J a 2 + y 2 . 
d. log y y 
dy a 2 + y 2 ’ 
This is the curvature of a nearly horizontal ray at distance y from 
plane of minimum It vanishes for y = 0 and y — cc , and takes a 
maximum for y = a. Hence rays, which are nearly horizontal at dis- 
tance approximately a from the plane, will go on to meet rays whose 
distance from the plane is considerably greater than a. If a vessel 
with parallel glass sides be filled with a liquid in which this law 
holds it will behave like a cylindrical lens, with a section like this — 
the points of inflexion of the section being at distances a from the 
axis. The caustic will be something like a golf -club, and two tan- 
gents can be drawn to it from an eye in the position shown (by the 
small circle), one of which is the line of vision of a real and inverted 
image, and the other of an erect image. 
“ In tracing the analogy between a continuously varying medium 
and a lens, deviation in the case of the lens corresponds to curvature 
of ray in the case of the medium. The lens in the present case 
gives no deviation at the axis ; the deviation increases till we come 
to the point of inflexion, and then diminishes indefinitely as the 
sides tend to parallelism, which they would attain at an infinite 
distance. 
