313 
of Achromatic Object-Glasses . 
ply by that difference the number standing in the third column. 
If the given index exceed the tabular index, put the sign ( ; plus 
or minus ), as found in the table, before the product ; but if the 
tabular index be the greater, then prefix to the product the con- 
trary sign to that given in the table. 
Next, take the difference between the given index of the flint 
and that in the table, and proceed exactly in the same manner, 
viz. multiply this difference by the number in the fourth column, 
observing, also, the same rule with regard to the sign of the pro- 
duct. 
Then, if the two products have the same sign, add them to- 
gether ; but if different signs, subtract them, and prefix the pro- 
per sign ; that is, the sign of the products themselves when alike ; 
or that of the greater when they are different. 
Lastly, if the resulting sign is plus (+), add the number to 
which it is prefixed to the tabular radius above found ; or if 
minus ( — ) subtract it ; and the sum or remainder will be the 
corrected radius for the 1st surface of the plate. 
Proceed exactly in the same way with the flint lens, using 
the 5th, 6th, and 7th columns, and we shall then have the cor- 
rected radius for the fourth surface. 
These rules are illustrated in the following continuation of 
the example proposed. 
The dispersive ratio of our flint and plate, being, by experi- 
ment, *683, the radii for the refractive indices of the table would 
be for the first surface = 6*7356 inches, and for the fourth sur- 
face = 12*7423 inches. 
These have now, therefore, to be corrected for the given in- 
dices, viz. plate = 1*528, and flint = 1*601. 
The difference between the tabular index of the plate, and 
that given, is *004 : Hence, 
No. in 3d column = -f *414 
Multiplied by *004 
Gives -{- *01656 
Next the difference between the tabular index of the flint, and 
that given, is *016 : Hence, 
