252 
Mr. Barlow on the rules and principles for 
Thus, for example: having first computed the focal lengths 
of the two lenses, we must, according to these directions, 
assume any ratio, at least within practicable limits, for the 
radii of the surfaces of the plate ; viz. ^ ; then, by the 
above formula, find the value of p. Call now p' the aber¬ 
ration of the flint lens, computed by the same formula; then, 
independent of the correction above alluded to, we should 
have 
p __ 
fa — f a' 
or p' =p 
/« 
p X 
But the value of p' thus found, as might be expected, does 
not produce a good object-glass; and from experiment it 
was ascertained, that the best effect was obtained when the 
multiplier, instead of 
, was made equal to 
p' therefore is found by this formula 
a' a' ^ 
d a a ^ * 
a'y/ a ^ 
da^ 
Then, substituting this value oip' in the equation ■ 
_ 27 + 6 q + 7 
P — 6(74-1)- 
the value of q is obtained; and hence, of course, the radii 
sought. 
Now, although this may furnish a very good approximation 
in some cases, it seems likely that it must, in others, deviate 
very considerably from the truth. I was desirous therefore 
of comparing the results obtained by this empirical formula, 
with those of the correct numbers as above determined, and 
also to ascertain experimentally, within what limits we might 
be in error without producing a sensible change in the cor¬ 
rection of the object-glass; and through the assistance of 
