46 Professor Airy on the Spherical Aberration 



1st. The equation 



is impossible. 



The values which approach nearest to satisfying this con- 



dition are 



which give 



5 , 5 



v= — ~m, V = ~m; 



7 7 



■=\m, s=Lm, r=l^M, s' 



2 



then 2 (n= -It'"' 2(^)=2ii^' ^(^^=^- 



2d. The Equation 1.{V) = 0, or 



u+ - TO' +w -- ml --— m-=0, 



7 I 7 49 



may be satisfied in an infinite number of ways. Thus, suppose 



5 r , 5 |- 4 



t) + - to' =v - -m = -— 



7 7 49 



then v= -m, or - - wi. 



.The first value of v gives, for the first lens, a plano-convex lens, its 

 plane side towards the object-glass : the second gives 



r := - m, s = —m. 



4 ' 10 



The second lens, also, must have one of these forms, but must be 



