245 
determining the dispersive ratio oj glass^ &c. 
Observing that ^ ^ / being the focal length; 
or writing A, B, C, D, for the several coefficients, making 
also p' z=z Q p af, and calling jy = i, it is 
/ __ A 5'* “H ® ? 4 C 
’ ——Djf+ir~ 
( 8 ). 
9. This equation in the common form of object-glasses 
belongs only to the plate or crown lens, which receives the 
direct or parallel rays; therefore the value of a, which enters 
into it, may always be considered to fall within the limits 
a = 'SO, and a = *53. 
When a = *50, this in numbers reduces to 
4‘5 y* 4 g 4 
(? 4 0 * 
and the solution gives 
p'—'So ± V] (p' — *50 )®4 (p'-“i-i6) (4*5 —./) 
9 =—- - -- - - - ( 9 )- 
When ^ ==*51, 
p' — ' 53 ±V { (?'—* 53 )® 4 (p'— 1*146) ( 4*47 — p') i 
> - - (10). 
When a = *52, 
p'__.r6± v' ({P'—*56)^4 (»'— 1*127) (4-44—.p')i 
When a =' 53 , 
P'—'S^± (p—*58)® + (p'-—1*11) (4-42—;)')l 
10. Having thus (equat. 7.) found a general expression 
for the aberration of a lens when the rays emanate from a 
given point, and in (equat. 8.) the expression for the aberra¬ 
tion of a lens receiving parallel rays, the indirect method by 
which an equal and contrary aberration in the two lenses is 
produced may be thus described. 
