52 Professor Airy on the Spherical Aberration 



6th. A single lens to produce the same effect must have its 

 focal length = - — , and, therefore, its smallest values of U and Y 



4 



II u 28 .68 



would be .. , and 



2T M' 27 M' 



Ex. 5. The eye-piece is the old erecting eye-piece. 



Here A = F, and we must, for the first lens, resort to the investigation 

 which supplies the failure of the general expression. After refraction at 

 the first lens, the rays in a perpendicular plane converge to a line at the 



distance — -j^ = z : they are incident, therefore, on the next, converging 



2 

 to the distance z, nearly, or a' = —z, nearly : therefore, 



1 R"^ 1 /3"' F'- &""' 



F'~ a' F'^ ~z 



= F'-~ U^-V'^=F'-iU+U')!^, 



F- 2 2 *■ -' 2 



and, therefore, a" - A" = Z'-z' = {U+ U') ^ , 



the same form as in the other cases. We have, therefore, as in the other 

 examples, to find the values of 2(f/) and 2(Y). Now, 



_ m ,_^ „_ fn _m , m «_^ 



^~~ 2' ^ ~ 2 ' ^ ~ ~~2' ^~2' ^ ~ 2' S ~ 2" 



whence 2(F)= J— (v^+v" + v"^) + 5 nj. 

 ' 3 m 



1st. Neither of the equations 



2(^)+is({) =0, S(A')=o. 

 is possible here. 



