of the Eye-pieces of Telescopes. 53 



ad. If we make 2 {V) a minimum, we find that all the lenses 

 must be equi-convex. This gives 'S.{V) = bm, whence 



3d. If either of the lenses be plano-convex, in either position, 

 ^{F) is increased by i m, 2(C/) by ^, and 2 (Y) by-^. 



4th. A single lens, to give the same power, must have the 

 focal length M, and, therefore, its smallest values of U and Y are 



7 .17 



— =-y and —TTi- 

 3 Af SM 



Ex. 6. The eye-piece is the four-glass eye-piece before de- 

 cribed. 



Here, (as before) 



m , 7m „ m ,„ _„ 



^=-6' ^=-8-' ^=i8' ' =-"'X'439. 



And, by tracing backwards the positions of the images, 



^"'=3M, S" = Mx2,13, ^"=-7l/x 4,556, 

 :^' =Mx 10,556, J' = Mx 6,4404, Z= -Mx 2,4404; 

 whence, g'=mx,5764, ^' = mx,0303, 



^"= -7WX ,3445, g"' = mx,l66l. 



Then F = (v + mx ,2^29)"- mx ,1466 ; 



y = '—L- (v' + mx ,6467)' + ?K X ,0065 ; 

 F" = • (t)" - mx, 2379)' -mx, 0133; 



^"'= ?^^^ (»"'-wx,1945r+mX,1002: 



