360 
Proceedings of the Royal Society 
“ In my arrangement (suggested by Maxwell) of three liquids, 
the corresponding lens would be of this shape — 
and gives triple images seen in the three lines of vision shown. 
The middle one comes through the convex portion and gives a real 
inverted image ; the other two come through concave portions and 
give erect images. 
“ The medium 
/ot = \J sec 2 - - c 2 , 
is an unnatural monster, giving infinite curvature of rays, as veil as 
infinite values of ^u. 
“ The equation of a ray in the medium 
according to the value of c for the ray in question ; this quantity c 
being the value of fi cos 6 for the ray. The second equation is what 
we get when c = a. 
“ Your 1 locus of vertices’ belongs, I presume, to the curves repre- 
sented by the first of these equations, but the tracing of it by 
points would take more time than I have at my disposal. Your 
result obtained from the ‘locus of vertices’ seems to agree with 
mine obtained by the foregoing methods, except that you profess to 
get three images, and I only get two. 
may be any one of the three 
