of the Eye-pieces of Telescopes. 9 



and, therefore, b'—B' can be calculated by the expression 



B'^ ' 2 i n ^ 4 («- 1)') 



Finally, by substitution in the expression above, the values of Q, Q', &c. 

 can be found. 



These expressions fail when B = F. As the lens in this case is always 

 followed by another, we may investigate the effect of the combination. In 

 Fig. 2, let ^ be near the principal focus of the first lens. The ray, after 

 refraction, meets the axis at a very distant point E. Now we have found 

 that 



c F b ^2' 



'3 



f n^p 



where P = '^ (n + 2.v- + 4n + 4.e«+3n + 2.e-) + - . , "^ ,. 

 n ' 4(n—\) 



or, in this instance, 



^ /•/« + 2 „e , 2M + 2 ^ 3W + 2 n^ \ ^ 



1 1 I h-B „ o- b-B 



'''c=F-B^-B^'-^-2=-TP- ^^ -2' 



c, therefore, is very large. Let / be the distance between the lenses. The 

 ray falls on the second lens tending to converge to the distance c — / beyond 

 it, and, therefore, after refraction, it meets the axis at the distance c', where 



1 1 1 „, a' 



c' c-I F'^ 2' 



P' being =/' C-±l V-- 11^ fv- + ^V" + TT^/'O • 

 "•'Vn 71 •' An •' 4(n— I)"' / 



Now -, = - + -5 + &c., and -, is of the order a*, and, therefore, to be 



c- 1 c c^ f 



neglected. Hence, 



1 1 b — B „b' o, a' 



— = — J + P \- P — : 



c' F'B'2^2 



Vol. III. Part I. , B 



