the Spherical Aberration in a Lens-System. 87 



Substituting for 



S % 2 " Si 2 



the value 



or o~?/i 2 © before obtained, the expression takes the final 

 shape 



x=i i^=i 



or A K = — ^ x above expression. 



(the last five terms being required by the higher order of 

 approximation). 



To test this let us apply it to the case of a single thin lens 

 of radii r and s in air, and let w, s, v be the distances of the 

 object and its successive images from the lens. We have 



~ 1 .1 /l 1\ ^ /l l\*f/t+l l\/*-l 



A' 2 = ^y(® 1+ © 2 ). 



Also 1 



1 _/»«+l M-l 



w /^ ///w ytrr 



1 t i.Ai.H 



T — 9 T 9~ • 



flSi V /jb^V fl £ S 



