44 Professor Airy on the Spherical Aberration 



to be smaller rather than larger. The best construction, then, will 

 be found by making 



2(^) + i2({)=0, or2(F)+ii2(;f) = 0. 



5th. But there is one advantage in the eye-piece satisfying 

 the condition 2 (^) = O. Since the rays converge accurately to 

 a point, by bringing the retina hearer to the crystalline, or (which 

 produces the same effect) by pushing in the eye-piece, we shall have 

 the series of images in Fig. 9, and shall, therefore, have a point. 

 The space occupied by the diffusion is always circular. And the 

 equation 2(^^) =0 can be satisfied in many cases where the equation 



s(r)-t-is({)=o 



is impossible. Whenever, then, the last equation cannot be satisfied, 

 or nearly satisfied, it will be best to make 2 (^) =0. 



6th. If neither of these can be satisfied, 2 (^') is essentially 

 positive, and we must, for the most advantageous construction, make 

 2 (^) a minimum. 



Ex. 1. Let the eye-glass be a single lens. 

 Here C= F, e = - •{ ; A--= F. g= -^ . and 



^_ 1 /W-H2 , 3n-2 \ 



f\n " ^ An{n-\fJ ) ' 



1st. Neither of the above equations is possible, and we must, 

 therefore, make V a minimum. This gives w=0, or the lens is 

 equi-convex. ^ 



