24 6 Mr. Barlow on the rules and principles for 
Since, when the aberration in the flint lens is so propor- 
tioned as to counteract that of the plate, all the rays converge 
to the mean focal point ; so, conversely, if we suppose rays 
emanating from that focal point, they will have precisely the 
reverse route, after their refraction at the flint lens, to that 
which they have when they are converging towards it in an 
opposite direction from the plate lens ; consequently, the aber- 
ration of the flint lens for rays emanating from the mean or 
compound focus, must be equal to the aberration from the 
plate lens for parallel rays in the opposite direction. And in 
the former case, when the amount of aberration has been 
ascertained, this will be also that due to the latter ; whence 
the ratio of the surfaces which will produce this aberration, 
or the value of q may be computed by means of the general 
quadratic equation (8.) or the particular equation belonging 
to the given plate index. Hence we may proceed as follows: 
l i . First, to compute the aberration of the flint lens for rays 
assumed to emanate from the compound focal point. 
Here the distance —f", index = i -f- a', dispersion = d ; 
and let the radii of the surfaces (for distinction sake) be 
r"', r" ; and the ratio of r" : r"‘ : : l : q. Then 
f = f" ( i — d ) = focal length plate. 
f — f" | 1 ~ ~ J == focal length flint. 
r w — f a' ( q'-J- l ) = outside surface flint. 
r" == f a! ( q t - ■) = inside surface flint. 
^ ft o _ \ jCII ..III 
(13.) 
J ' In' I \ f" 
f 
a'f' — r" 
d‘ 
'z— N 
+ 
r" 
af" — r "‘ > 
f" 
b a ' - 
r" 
’ 0 d + i » 
are all known quantities ; and consequently, 
