of the Eye-pieces of Telescopes. 19 



Ex. 6. The eye-piece consists of four lenses of focal lengths 

 .3 M, 4 M, 4 M, and 3 M, placed at the intervals 4M,QM, and 5, 13 M. 

 (These numbers satisfy the equation of achromatism, Cambndge 

 Transactions, Vol. II, p. 247, and give a convenient form of the 

 four-glass eye-piece.) 



Here C=3 M, B'^M, C'=-tM,B"=~ M, 



o 3 



44 



C" = y M, B"= -3,67 . M, C" = 1,65 M. 

 Hence, e=-g, ^ = "-^' ^ =88' ~ "* ^ '^^^' 



Also "'=35 a" = -^ a, a"' = ,7645 X a. 



From these data we find, in the same way, > 



R = a^ \ ,5227 {V +,0276»i)-+,0640»l'}, 



R =-a' { ,0384 (w' + ,948 ni)- + , 01 42m*}, 



R' = -a- {2,7606 (u" -,i 106 »w)'+, 1300 m'}, 



- ii'"= a" { ,3750 (i;"'-,4107m)' +,0627771^}. 



From which we derive the following conclusions. 



1st. Q + Q' + Q" + Q'", 01 R + R + R' + R", may always be 

 made = 0, with any assumed values of© and v'". And, in most 

 cases, we may assume any three of the quantities, v, v', t/', v'", and 

 it will be possible to find the fourth, so that R+R+R'-\-R" =0. 



2d. If the first lens be plano-convex, its convex side towards 

 the object-glass, v=f=-, and iJ=^.,1322. If equi-convex, 



v = o, and R = v^ . ,0644. If plano-convex, its plane side toward the 



m -* 



object-glass, v=- -, and iJ = -^j . ,1129. 



c 2 



