256 
SUMMARY OF CURRENT RESEARCHES RELATING TO 
bull’s-eye when in its best position is 1*16^, viz. more than double 
Jb 
that of the equiconvex lens mirror. 
Now, if we consider carefully the action of the plano-convex lens 
mirror, we see that we have the aberration of the concave mirror plus 
that of the plane surface, these aberrations being positive, or the same 
as those of converging lenses ; it is evident that if we wish the system 
Fig 22.. 
to be aplanatic we must neutralize these positive aberrations by intro- 
ducing the negative aberration of some concave surface. Suppose we 
make the first surface concave, and of a radius equal to the focus of the 
system. It is obvious, in the first place, that there will be no aberration 
on the emergence of the rays, because they will be normal to the surface, 
and, further, the aberration of the first curve for the incident parallel 
rays will be of an opposite kind to that of the concave mirror. We may 
therefore conclude, without entering into any mathematical calculation, 
that the total aberration of such a system will be greatly reduced, and 
also we may infer that aplanatism is a possible condition. Hence the 
problem in the determination of the ratio of the curvatures of the inci- 
dent and silvered surfaces. Following out the argument above, if we 
put F = — r in equation (iii.) we shall find that - = — ; as both are 
8 o 
negative, the lens will be a diverging meniscus. We have therefore 
arrived at the following conclusions : — (1) That aplanatism is possible. 
(2) The form of the lens will be a diverging meniscus. (3) That the 
ratio of the curvature is about -. Further than this by mere inspection 
o 
we cannot go ; but, as hinted above, by a laborious method of trial and 
