of the 'Eye-pieces 'of Telescopes. 35 



We shall put Y for -^ + 3 F: hence, we have 



Z' Z' 8^ 



Z" /3" 



l^=Z-^,ia-A)-Y.!^, 



f 

 where Y = - + 3 F. 

 n 



If the rays in the paper-plane diverge from the distance v instead of a, 

 the value of ri when a = being A, we have merely to put in the forms 

 above, n for a. 



This expression, like the former, fails when A = F. By the same 



kind of investigation as in the last Proposition, it is found that the rays after 



F- 

 refraction converge to a line at the distance -^ . 



It appears, then, (supposing a-A = 0, and ri — A = o), 



1st. That the rays will converge accurately to a point if 

 3-^ = 0, or if /^ = 0. 



2d. That the whole image will be in the same plane if at the 



f 

 same time Z-z = 0, or if -^ + K= 0. 



n 



3d. That these conditions are incompatible : and, therefoie, 

 when rays proceed from an object, or a distinct image in one plane, 

 they cannot, after refraction . by a lens, form a distinct image in 

 another plane. 



E 2 



