1872.} | its Imperfections and their Remedy. 49 
correction of the observed indices of refraction; because it 
is regulated by peculiar laws, and the indices may be cor- 
rected by bringing them into conformity to those laws. If 
uw represent the refractive index in any medium corresponding 
to the undulation belonging to any fixed line, we have, of 
course, in every case, 
But it is only where pw, the index of refraction, is quite cor- 
rect that the quantities represented by x conform to their 
proper laws. 
These quantities represent additions to or abstractions 
from the internal wave-lengths, that would arise from the 
more simple formula, 
[OPA 
—«a. 
ee 
They constitute an evidence of a transfer of energy from 
one set of waves to another within the medium, and by its 
action. Now the general law of the conservation of energy 
requires that this transfer should involve an exacét compen- 
sation,—that what is lost in length by one set of waves 
should be exactly the same as what is gained in length by 
another set, or, symbolically, the quantities represented by 
+x must be exactly equal to those represented by —x. In 
every good set of observations on the indices there is a close 
approach to this equality, and this constitutes the first law 
regulating those quantities. It applies to all media, whether 
regular or irregular. 
In all regular media the sign of x is plus for the three 
waves corresponding to the lines D, E, and F, and minus 
for the four waves corresponding to the lines B, C, G, and H. 
In the former the formula is always 
for the latter it is 
If by, cx, dy, &c., represent the quantities x, corresponding 
to each internal wave, we have, in all regular media, 
30x + 2¢x—dx=3hxt2gx—fx. 
VOL, II. (N.S.) H 
