40 Professor Airy on the Spherical Aberration 



We may consider the image formed by the object-glass as being 

 perfectly plane and equally distinct in every part. Considering, then, first, 

 the ravs in a perpendicular plane, we have a — A = 0; 



.■.. = Z-U.^. 



2 

 Now 2 + a' = interval between 1st and 2d lenses = Z + A' ; 



.-. a'-A'=2-z = V.'^. 



Hence, .'=0'-J,(a'-^')-f/'.V = ^'-|^^-T-^'^- 

 But it is well known that 



Hence, a" - A" = Z' -z' = (, U+ U') ^ , 



and hence, in the same manner, 



s" = S"_(f/+(7'+(7")^. 



Suppose, now, the eye-piece to consist of four lenses (our reasoning will 

 apply equally to any number). That the center of the last image may 

 be distinctly visible, it must be in the focus of the fourth eye-glass, or 

 A'" must = F'".- In this case we have for the distance to which the rays 

 converge after refraction, 



F'"" 



a"'-A"' + U"'f^ 

 2 



Here a"' - A'" = Z" -z" = (U +U' + U") ^ : 



