48 Professor Amv on the Spherical Aberration 



A= - ^~^', Z = M, A' = M; g=--^ ,g = -. 



Hence V=^±^{v--^m) - ^ »' = 



Vn/ 9 

 1st. The equation 



S(F) + i2({)-0 



is impossible. The nearest approach to it is found by making 



5 5 



7 7 



whence r=|iM, s=-f M, /•'=^^, «'=5^' 



2(1. The equation S(F)=o may be satisfied in an infinite 

 number of ways : and all the forms thus found will give 



2(f/) = :s(Y) = ^. 



3d. If the first lens be plano-convex, the plane side towards 



IQ 5 



the object-glass, V=-^m. If equi-convex, y=~ m. If piano- 



convex in the other position^ V= - — . 



1 ^ 



