247 
determining the dispersive ratio of glass, &c. 
(c + q‘Y c + (a' + 2) q 
(a'c — q') X c (a c' -f a' -f i) 9 
(c' + i) 9 (c' -f 2 — — b) q 
r (6 c' + i) 9 X c' 
is also known. This is the amount of aberration for the flint 
lens for rays supposed to diverge from the compound focal 
point ; and this, as we have seen, is also the amount of the 
aberration of the plate lens for parallel rays in an opposite 
direction ; but this latter is equal to (art. 8. ). Multiply- 
ing therefore the last found value of p by 2/ a, and substi- 
tuting for r", and r"' in the preliminary equations, we 
obtain 
k a' , d q' d q 1 
° — (7+ I) C — b(q' + l^d7J C — d (I— d) (q + I) *’ 
and lastly, 
(c + q'y C + (a -f z) q' 
(a'c — q'Y X c(a'c'+a- f i)* 
4- + O* w ( £/ + 2 — b) q' 
~ (bc'+iy c' 
And this value of p' substituted in equations (8), will furnish 
the proper value of q for the ratio of the radii of the surfaces 
of the plate lens ; and we shall then have 
f — f" ( 1 — d) — equal focal length of plate. 
f = | d j = equal focal length of flint, 
r = /<*(? + 1) = 1st surface 
r' = f a — 2nd surface 
r" = fell - ) = 3d surface 1 
J \ 9 1 I l flint. 
r'"= f'd(q' -J- 1 ) = 4th surface J 
* The value of y being the same in both lenses is omitted, or considered as 
unity in both expressions. 
a d 
7T -=P'- ( 14 )- 
