of the Eye-pieces of Telescopes. 31 



where U= -L + f^ 

 n 



It will be observed that Z-^^{a-A) enters into these expressions as 



equivalent to . 



F~ I 



The expression fails when A = F, which makes Z infinite. We mio-ht 

 for this case give a different form to the latter part of the investigation, 

 but the following method will be more convenient. Suppose the direction 

 of the rays reversed: then (as the quantity U is the same in whatever 

 direction the rays be supposed incident, and as ji is then the breadth of 

 the second image) 



i_ ^ 2 



F I ■ 



hence 3 = 1 _ i + / ^ + iV ^ ^' _ i _ 1 1 ,,/3^ 

 a F z^ \F^ zJ -^^ 2 ~ F z'^ W 2' 



(since ~ would be if there was no aberration) : therefore 



z F a^ F"--"" 2- F- F+-^^rA 



^ F'' 2 ~ F^ +Y- ~2' 



'I'he rays converge, therefore, after refraction to a line whose distance is 



F°- 



2i 



