240 Mr. Atry on Achromatic Eye-pieces of Telescopes, 
This must be positive; ... e<c’-—e<c(c—1). It appears that no 
combination of glasses, whose refractive powers are known, will 
satisfy this equation. We might make F negative, or suppose the 
crown-glass concave; but as we should in that manner lose one 
important advantage, viz., the diminution of the flint-glass, it is 
not worthy of consideration. 
(9) By using three sorts of glass, and also separating the 
lenses, besides making the object-glass truly achromatic we may 
diminish the aperture necessary for the flint lenses. Suppose two 
lenses of different kinds of flint-glass to be placed in contact, at 
the distance a from a crown lens: let F be the focal length of the 
latter, fand f’ those of the former: », 7’, 2", the refractive indices 
for mean ee mat the power for mean rays after the last refrac- 
tion, is 7 +a +3 which for other rays is changed to 
PL F én 
+ ayn n—1 + (4) 
ore pally wipe soe 
a ke prt Jn =A 
ie sei: ie én fe ( 2) x 
‘iota n—1 n—17 ~ 
Let — = 
then the power 
e{4 Ihiel ( F mites) on 
Si wee aay f° fF) n= 1 
+ (qr ay * a Go ‘ 
Making the latter parts pee = 0, 
F c Fa e 
co Gok 
Cir Fem gets. 
And the aperture necessary for the flint lenses would be that of 
the crown lens multiplied by a 
