Memoirs presented to the Cambridge philosophical society on the occasion of the jubilee of Sir George Gabriel Stokes, bart., Hon. LL. D., Hon. SC. D., Lucasian professor.

XVIII. An Electromagnetic Illustration of the Theory of Selective Absorption
of Light by a Gas. By Professor HORACE LAMB, M.A., F.R.S.
[Received 13 December 1899.]
THE calculations of this paper, so far as they are new, were undertaken with a
view of obtaining a definite mathematical illustration of the theory of selective absorption of light by a gas. The current theories of selective absorption apply mainly to
the case of molecules in close order, and it has not been found possible to represent
the dissipation of radiant energy except vaguely by means of a frictional coefficient.
It seems therefore worth while to study in detail some case where the dissipation can
be exactly accounted for; and to consider in the first instance the impact of a system
of plane waves on an isolated molecule.
If we assume that the molecule has a spherical boundary, then, whether we adopt
the electric or the elastic theory of light, the requisite mathematical machinery is all
ready to hand. It is necessary, however, for our present purpose to devise a molecule
which shall have a free period of vibration, whether mechanical or electrical, of the
proper order of magnitude. The inechanical analogy was in the first instance pursued,
the aether being represented by an incompressible elastic medium. This enables us to
illustrate many special points of interest, but for the purpose of a sustained comparison
with optical phenomena the elastic-solid theory proved in the end to be unsuited from
the present point of view, as well as on other well-known grounds.
As regards the electric theory, the scattering of waves by an insulating sphere has
been treated by various writers*, with however the tacit assumption that the dielectric
constant (K) of the sphere is not very great. In the present paper attention is specially
directed to the case where K is a very large number. On this supposition free
oscillations (of two types) are possible, whose wave-lengths (in the surrounding medium)
are large compared with the periphery of the sphere, and whose rates of decay (owing
to dissipation of energy in the form of divergent waves) are comparatively slow. And
when extraneous waves whose period is coincident, or nearly coincident, with that of
a free oscillation encounter the sphere, the scattered waves attain an abnormal intensity,
and the original wave-system is correspondingly weakened.
* Lord Rayleigh, Phil. ag., Feb., 1881, and April, 1899; Prof. Love, Proc. Lond, Math. Soc,, t. xxx., p. 308;
G. W. Walker, Quart. Journ. Mlath., June, 1899.