244 REPORT— 1885. : 
In order to account for the extreme transparency of a substance sucl q 
as water, we must suppose & to be so exceedingly small that Sir — 
William prefers to consider it as zero, and says: ‘I believe that the first — 
effect when ‘light begins, of period exactly equal to x), is that each — 
sequence of waves throws in some energy into the molecule. That goes — 
on until somehow or other the molecule gets uneasy. It takes in 
(owing to its great density relative to the ether) an enormous quantity 
of energy before it gets particularly uneasy. It then moves about, and 
begins to collide with its neighbours, perhaps, and will therefore give you 
heat in the gas if it be a gaseous molecule. It goes on colliding with — 
other molecules, and in that way imparting its energy to them. This 
energy is carried away (as heat) by convection, perhaps. Each molecule 
set to vibrating in that way becomes a source of light, and we may thus 
explain the radiation of heat from the molecule after it has been got into 
it by sequences of waves of light.’ 
Helmholtz’s equations are, of course, the more general, and apply to 
an absorption band as well as to the part of the spectrum for which the 
medium is transparent. It would seem that the term —y?dU/dt may 
rightly represent just the effect of that loss of energy in the form of 
heat due to the irregular collisions of which Sir William speaks, am 
effect which is only appreciable in the result when, owing to the 
coincidence of the periods, U tends to become large compared with w, or, 
in Thomson’s notation, z, large compared with &,and in this case 2, will 
not become infinite, for the amplitude will be multiplied by the factor 
e-**, and k being large, the limit of the product comes into consideration. 
Such a system of ether with attached matter molecules is thus shown 
to account for the phenomena of dispersion. A serious difficulty, how- 
ever, is encountered when we reach the problem of double refraction. 
§2. For we may suppose, in order to account for it, that C, is a fane- 
tion of the direction, and that for two principal directions it has the 
values C, and C,’, while C, is a constant independent of the direction. 
Then, with only one enclosed mass, 
i -6) 
i 2 
Gut he es ae 
p age eal seca bile 
7? 
= 1+ 
and to give a dispersion formula resembling Cauchy’s we must have 
m,|7? considerable compared with C., and C, large compared with either. 
Hence, if p’ be a second principal index, 
and therefore Be ( G my \ 
Wh ee Sa : (9M 
p (0, + 6, 2) (+ 5) 
T T 4 
which, remembering the relative magnitudes of the quantities, and writ- 
ing D and D’ for the approximate values of the denominators, becomes 
C, — Cy 
Fhe ea el v(m 
e 2 pUDD’ (™) 
we — p= — 
