239 
determining the dispersive ratio of glass, &c. 
Then d = 
the dispersive ratio sought. 
First — _ — — 
f ~~ 38-89 8 - 4 + ’ 
Whence/' = 11*13 inches. 
_ 8 - 44 ^ _ . 
" 9*85 X11-13 
649 , 
On the computation of the radii for correcting spherical aberration 
and colour. 
5. We have seen, that to render an object-glass achromatic, 
it is only necessary to have the focal lengths in the direct 
ratio of the dispersive power of the two glasses. 
Let this ratio be 1 d\ then representing the compound 
focal length by f", we shall have 
/ = /" (1 — d) =. focal length of plate. 
f = f" ~ = focal length of flint. 
And these focal lengths, without any other condition, will 
give a compound focal length/", and produce achromatic 
correction. 
Let -14-^ = index of plate 
1 a! = index of flint, 
r, r' the radii of curvature in the plate, 
d', r'" those of the flint. 
The order of the radii reckoned from the object side being 
r, r', r", r'" , the two former being convex, and the latter 
concave, unless the contrary be stated. 
Then by a known formula we shall have 
> > . i 
