247 
determining the dispersive ratio of glass, &c. 
(c 4 c 4 (g' + 2 ) y 
(a'c — q') c (a' c' 4 a' -f i)® 
I (c' 4 i )^ ^ (c‘ + 2 —b) q' 
r (f>c‘ + ly ^ d 
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 f", r", and r"' in the preliminary equations, we 
obtain 
^ _ a' , dq' dq' 
. — (g' 4 I) ^ — hiq' 4 i-dq') ^ g' (I— d) (? 4 0 ’ 
and lastly. 
(c 4 q'y C 4 (a 4 2 ) -v 
(a'c— q'Y ^ c(g'c' 4 g 4 1 )* ad _ , 
4. (c'4 0* w (c' 42 — 5)9' ^ 4 J ^ * 
^ (5c'4 0® c' 
{ 14). 
And this value of p' substituted in equations (8), v/ill 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" (i — d) ~ equal focal length of plate. 
f = f"" ( ^ ) = equal focal length of flint. 
= /^('9 +1) 
= ist surface -j 
-f-VV) 
2 nd surface J 
plate. 
= 
= sd surface i 
► flint. 
= /'«'(9'4i) 
= 4 th surface J 
* The value of y being the same in both lenses is omitted, or considered as 
unity in both expressions. 
