26 
The quadratic equation above alluded to expresses the 
relation of these coefficients, or, in other words, the relation 
between the period of vibration and the length of the wave. 
When the action of the molecules of the ether and of the 
body, inter se, and on one another, is governed by the same 
law, this equation is resolvable into simple factors, one of 
which only seems to belong to the problem, the other giving 
an expression for the velocity of propagation independent of 
the length of the wave. The author accordingly proceeds 
to develop the former of these formulz, converting the triple 
sums which it contains into triple integrals, according to the 
method of M. Cauchy. 
Among the consequences deducible from this development 
is the following:—In the expanded expression for the velocity 
of propagation, each term consists of two parts, one of which 
is due to the action of the ether, and the other to that of the 
body. It is not improbable that there may be bodies for 
which the first or principal term is nearly nothing, the two 
parts of which it is composed being of opposite signs, and 
nearly equal. In this case the principal part of the expres- 
sion for the velecity will be that derived from the second 
term; and, if that term be taken as an approximate value, it 
will follow that the refractive index of the substance must be 
in the sub-duplicate ratio of the length of the wave, nearly. 
Now, it is remarkable that this law of dispersion, so unlike 
anything observed in transparent media, agrees pretty closely 
with the results obtained by Sir David Brewster in some of 
the metals. In all these bodies the refractive index (inferred 
from the angle of maximum polarization) ¢ncreases with the 
length of the wave. Its values for the red, mean, and blue 
ray, in silver, are 3.866, 3.271, 2.824; the ratios of the 
second and third to the first being .85 and .73. According 
to the law above given, these ratios should be .88 and .79, 
