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.

398 MR LARMOR, ON THE DYNAMICS OF A SYSTEM OF ELECTRONS OR IONS:
is controlled by that band alone*: thus the Faraday effect is there very large and of
anoinalous character, in correspondence with the experimental discovery of Macaluso and
Corbino. From another aspect of the same effect, we can conclude that light of any given
period, very near a natural free period of the medium, will travel in it with sensibly
different velocities according as its mode of vibration corresponds to one or other of
two principal types, elliptically (or in a special case circularly) polarized in opposite
directions, and thus will exhibit phenomena of double refraction.
THE INFLUENCE OF ROTATIONAL TERMS ON OPTICAL PROPAGATION.
8. The purely formal, i.e. non-molecular, theory of the magnetic influence on optical
propagation may be developed in a simple and direct manner, by use of the device of
a revolving coordinate-system as above employed. In a non-magnetizable medium the
exact relations connecting the magnetic force (a, /3, y), the electric force (P, Q, R), and the
electric current (u, v, w), are of types
dy d8 dR dQ da
_ - _ = 47f-7u, -
dy dz dy dz dt
-Thus V2p c d /dP dQ dR) du
Thus v2- - — h+ + --- =4,7r
dx \dx dy dz dt'
which will lead to the differential equations of the propagation when in it (u, v, w) is
expressed in terms of (P, Q, R) by means of the constitutive relation connecting them.
Now for the aethereal elastic displacement we have (f, g, h) =(47rc2)- (P, Q, R).
To determine the nature of the most general formal connexion between the material
polarization (f', g', h') and the electric force, that we are at liberty to assume without
implying perpetual motions, we must make use of the method of energy. The energy
of this electric polarization in any region is
W = f(Pf + Qg + Rh') dr,
where &r is an element of volume: thus its intensity per unit volume is a quadratic function
of (P, Q, R), and possibly also of d/dt (P, Q, R) and of the spacial gradient of (P, Q, R),
and it may be of gradients of higher orders as well: if the first time-gradients alone are
included we thus have the expression
F2 (P, Q, R) + a,,PdP/dt +... + alPdQ/dt + a2, QdP/dt +...,
F2 denoting a quadratic function. The variation of this energy must from the definition
of (P, Q, R) as the force moving the electrons, be
W= (Pf ' Q' + t RQ' îh) dr
= S f(Pf' + Qg' + Rh') dr- f'P + g'Q + h'SR) dr,
* Cf. Proc. Camlb. Phil. Soc., Mar. 1899: for similar who, by introducing dispersional terms of a certain simple
explanations but restricted to anomalous dispersion, cf. type including a frictional part into the equations of optical
Macaluso and Corbino, Rend. Lincei, Feb. 1899. propagation in a rotational medium, finds that each abReference should also be made to the converse pro- sorption line is tripled, but with an asymmetry introduced
cedure of Voigt (cf. Anlalen der Physik I. 1900, p. 390), by the frictional term.