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.

PROF. LAMB, AN ELECTROMAGNETIC ILLUSTRATION, ETC. 349
The conception of a spherical molecule with an enormous specific inductive capacity
is adopted here for purposes of illustration only; and is not put forward as a definite
physical hypothesis. In order to comply with current numerical estimates of molecular
magnitudes, it is necessary to assume that for the substance of the sphere K has
some such value as 107. This assumption may be somewhat startling; but it is not
necessarily inconsistent with a very moderate value of the specific inductive capacity
of a dense medium composed of such molecules arranged in fairly close order. And
it may conceivably represent, in a general way, the properties of a molecule, regarded
as containing a cluster of positive and negative 'electrons.' In any case the author
may perhaps be allowed to state his conviction, that difficulties (such as they are) of
the kind here indicated will prove to be by no means confined to the present theory.
The main result of the investigation may be briefly stated. For every free period
of vibration (with a wave-length sufficiently large in comparison with the diameter of
a molecule), there is a corresponding period (almost exactly, but not quite, coincident
with it) of maximum dissipation for the incident waves. When the incident waves
have precisely this latter period, the rate at which energy is carried outwards by the
scattered waves is, in terms of the energy-flux in the primary waves,
+................................................
where X is the wave-length, and n is the order of the spherical-harmonic component
of the incident waves which is effective. In the particular case of n= 1, this is equal
to 477X2. Hence in the case of exact synchronism, each molecule of a gas would, if
it acted independently, divert per unit time nearly half as much energy as in the
primary waves crosses a square whose side is equal to the wave-length. Since under
ordinary atmospheric conditions a cube whose side is equal to the wave-length of sodiumlight would contain something like 5 x 106 molecules, it is evident that a gaseous
medium of the constitution here postulated would be practically impenetrable to radiations of the particular wave-length.
It is found, moreover, on examination that the region of abnormal absorption in
the spectrum is very narrowly defined, and that an exceedingly minute change in the
wave-length enormously reduces the scattering.
It may be remarked that the law expressed by the formula (1) is of a very general
character, and is independent of the special nature of the conditions to be satisfied
at the surface of the sphere. It presents itself in the elastic-solid theory; and again
in the much simpler acoustical problein where there is synchronism between plane waves
of sound and a vibrating sphere on which they impinge.
It has unfortunately not seemed possible to render this paper fairly intelligible
without the preliminary recital of a number of formulae which have done duty before,
notably in Prof. Love's paper. The analysis has however been varied and extended in
points of detail, with a view to the requirements of the present topic. In particular,