14 Professor Airy on the Spherical Aberration 



then Q = «^ ^fv - \r+ (^ -o'-Ip^I /=)] = 

 and (by using the value of h' - B' just found). 



Adding together Q and Q', and putting R and R' for those parts which 

 depend respectively on the first and second lens, 



1st. R is least when v-O, or the first lens is equi-convex : 

 then, its value = - . ^. If it be plano-convex, in either position, 



_ 5 a' 



2d. R' is least when v' = — f, which gives 



r'-Lp s'=-If fi'=iiH ± 



If the second lens be plano-convex, its plane side toward the first 

 lens, ^ = ^§7 ■ f'- " equi-convex, ^ == ■gT'E^- ^^ piano- 



convex in the other position, ■'^ =~ST"'f^* Of the common forms, 



then, the plano-convex, its convexity towards the first lens, is best ; 

 it ought to be slightly meniscus. 



3. A single lens to produce the same effect, must have had 



F 



a focal length — , and, therefore, by the last Example, the smallest 



