S68 'MiV on ^Achromatic Object-Glasses. 
. The dimensions in the above Table are‘ computed on the sup- 
position of the focal length of the object-glass being 10; and to 
adjust them to any other assigned focal length, all that is re- 
quired is to increase or diminish the radii here set down, in the 
proportion of the assigned focal length (in inches, feet, or parts 
of any given scale) to 10 parts of the same scale. 
When the refractive powers of the two media are exactly 
1.524 and 1.585 (which are nearly their average values) respec- 
tively, and the dispersive ratio is any one of the numbers in the 
first column, this table gives at once the exact values of the ra- 
dii required ; but when this is not the case, we must proceed as 
follows : 
Suppose (for example’s sake) we would find the proper radii 
for the surface of an object-glass of 80 inches focal length, the 
refractive index of the crown lens being 1.519, and that of the 
flint 1 .589, the dispersive power of the former being to that of 
the latter as 0.567 : 1, or 0.567 being the dispersive ratio. 
The computation must first be made as for an object-glass of 
10 inches focus ; and first we must determine the focal lengths 
of the separate lenses. To this end, 
1. Subtract the decimal (0.567) representing the dispersive 
ratio from 1.000 ; and the remainder, multiplied by 10, is the 
focal length of the crown lens (in this ease 10 x 0.438, or 
4.830). 
% Divide unity by the decimal above mentioned (0.567), 
subtract 1.000 from the quotient, and multiply the remainder 
by 10, and we get the focal length of the flint lens. In the case 
before us, = 1.7685, and 0.7685 x 10 =: 7.685 is the focal 
0.5 d7 
length required. 
We must next determine, by the tables, the radii of the 1st 
and 4th surfaces for the dispersive ratios there set down (0.55 
and 0.60), next less and next greater than the given one. For 
this purpose we have 
Refractive powers given, - 1.519 and 1.589 
Refractive powers in Table, - 1.524 1.585 
Differences, — 0.005 + 0.004 
the given refraction of the crown being less, and the flint great- 
er, than their average values on which the tabic is founded. 
