64 Professor Airy on the Spfierical Aberration 



2 (F) = i^^i^ iv+mx,2929Y+ '-^^^ (r'+mx ,6467)= 

 + 1:^211 (t,"-mx ,2379)'+ ^-^ (t>"'-mx ,1945)^ -mx ,0532. 



m 



Also 2 (^) = I 7« =771 X ,7778 : f 2 (^) = ttix ,3889- 



1st. The equation 



2 (^) + i 2 ({) = 



cannot be satisfied. The nearest approach to it is found by making 

 each of the brackets equal to nothing. Then 



7- =il/x 24,75, s =Mx 1,597; r' = - Mx 2,521, s' = il/x 1,115 ; 



t" = Mx 2,050, s" = Mx 82,6 ; r" = M x 1,895, s"' = Mx 7,204 ; 



2(r)=-7»ix,0532, whence 2 ( (7)=^, 2(Y)=^. 



And this would be the most advantageous combination. 



2d. If the first lens be plano-convex, the plane side towards 

 the object-glass, F= - m x ,1444. If equi-convex, f^= — mx ,0256. 

 If plano-convex in the other position, ^=7/1 x, 4056. 



3d. If the second lens be plano-convex, the plane side toward 

 the first, F' = 7nx ,1351. If equi-convex, ^' = 7/1 x ,3485. If plano- 

 convex, its convexity toward the first, ^' = 7wx,6638. 



4th. If the third lens be plano-convex, the plane side toward 

 the second, V"=mx 1,0824. If equi-convex, ^"=7nx,2518. 

 If plano-jconvex in the opposite position, V"= —mx ,0128. 



5th. If the fourth lens be plano-convex, the plane side toward 

 the third, F"'= tti x ,6910. If equi-convex, F"'= 771 x ,1806. If 

 plano-convex in the other position, F"' = 77tx ,1411. 



