11 
of Achromatic Object-Glasses. 
5. From the log tangent of c subtract the log tangent of a ; con- 
sidering the remainder as a logarithm, find its natural 
number, and subtract that natural number from unity. 
6. Now, multiply this remainder by the index of refraction of 
prism A, and by the index minus 1 (or the decimal part of 
the index) of prism B. Multiply also the index of the re- 
fraction of B by the decimal part of the index of A ; lastly, 
divide the former product by the latter, and the quotient 
will be the ratio of dispersion between the two glasses. 
Or, Add the logs of the three former numbers together, and 
the logs of the two latter, and the difference found by 
subtracting the latter from the former will be the log of 
the ratio sought * *. 
Note .— It is assumed in the preceding rule, that the prism 
B owes its higher dispersion to its greater dispersive 
power, the angles being nearly equal ; but with a less 
dispersive power (by having a greater angle), its disper- 
sion may still be greater than prism A. In this case, 
the same rule will also obtain ; only in the part number- 
ed (5) in the above rule, we must add the natural num- 
ber to unity instead of subtracting it ; the reason of 
which will be seen in the algebraical formula. 
IS. Example . 
Shewing the results of observation and calculation on the two 
prisms Plate No. 1. and Flint No. 1., of which we have already 
determined the angles and indices, viz. 
Angle of Plate prism A = 24° 51' index = 1.528 *f* 
Do. Flint B 24 49 index = 1.601 
* The analytical expression for this rule is, 
Sin a — r - tan b cos M tan B =. tan b 
rl 
Dispersive ratio — {tan (b — a) cot a -{- 1} 
r being the index of refraction of A, and R that of R. 
*j- Three places of decimals are quite sufficient, and we have taken these to the 
nearest figure ; both a little in excess. 
