ON OPTICAL THEORIES. 219 
of the matter particle, will always be small unless r =¢. Omitting, then, 
these from consideration, it follows that 
Fad 
Emly se ee. CB) 
and the vibrations thus set up in the matter are shown to be the cause of 
refraction ; while if r = 6 we have 
€ = —a cos eae 
6 
ae bs a : . (46). 
— = ~ 49 
dt 6 
and these vibrations are the cause of absorption. 
So far, then, the results of this investigation agree with those 
Bonssinesq has given. They are, however, more general, in that they 
contemplate the possibility of the motions of the matter particles becoming 
appreciable, and so producing absorption. The next paper considers the- 
question of the manner in which the action between the matter and ether 
affects the velocity of light. At first the direct effect of the matter on the 
ether is neglected, and the refractive power of the substance is found by 
considering the energy lost by the ether and gained by the matter in each 
vibration. The refractive power is measured by n?—1, where n is the 
refractive index. 
Now consider a volume so small that all the ether particles in it 
may be treated as in the same phase, so large that it contains many 
matter particles, and suppose the reactions considered confined to the 
ether and matter of this element. 
Then it can be shown that if m’ be the density of the ether, a the ampli- 
tude of its vibration, the energy lost by the ether is (n?—1)2x2m/a/2/7?, 
while that gained by the matter is 2x?{Smz7?a,?/(7?—<?)} /72, whence the 
important formula 
Sf AE 
13 — here Sead fo a2 ot olanily a Gy, 
n'a! 
is obtained. 
We may write this— 
K 
hele eet ait Sane? ben ee 
32. 8 
where by = we mean that all the possible values of 8, the free period of the 
matter particles, are to be taken into consideration. Now let us suppose 
that r is greater than 6, and that the matter particles have only one free 
period, then the denominator of the fraction is positive, and decreases as 
t approaches ¢. The refractive power, therefore, increases as the period 
decreases (7.e., as we go up the spectrum), and as 7 approaches the critical 
value ¢ (v.e.,as we near the absorption band) the refractive power is 
abnormally increased. Above the absorption band, supposing there be 
but one, the fraction is negative, and decreases numerically in value as r 
is still further decreased ; and until + reaches a value for which Lis 
1/c?+K, n is imaginary. 
