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.

406 MR LARMOR, ON THE DYNAMICS OF A SYSTEM OF ELECTRONS OR IONS:
for natural vibrations of the system, which would be differently affected and therefore
separated by the impressed magnetic field.
This analysis is wide enough to apply to a system consisting of a continuous
electrical distribution, whose parts are held together in their relative positions either
by statical constraint or by kinetic stability: for then the potential energy still depends
on the relative configurations of the elements of mass of the system.
We have however not arrived at any definite representation of the dynamical
system constituting a molecule, except that it consists of moving electric points either
limited in number or so numerous as to form a practically continuous distribution:
but reasoning from the definiteness and sharpness of the periods in the spectrum, and
the facts of polarization of light, it has been inferred that the vibrations of the
molecule form a 'cycloidal' system and therefore arise from a quadratic potential energy
function: the total potential energy function must therefore consist of two independent
parts, that belonging to the steady motion, in which the coordinates of the vibrations
do not occur, and this part belonging to the disturbance which is quadratic in its
coordinates: as a whole it must depend on the configuration of the system and not
on the axes of coordinates, hence this quadratic part is invariant with regard to change
of axes: this confines it to the form given above,-which had been found to be
demanded by the existence of the Zeeman phenomena.
It has thus been seen that the fact that the vibrations belonging to the Zeeman
constituent lines are exactly circular, and not merely elliptic with a definite sense of
rotation, requires that the right-handed and left-handed groups of vibrations shall form
two independent systems: as the magnetic field may be in any direction as regards
the molecule, this requires that its vibrations, when the magnetic field is absent, can
be resolved into three independent systems of parallel linear vibrations directed along
any three mutually rectangular axes. This again involves that an electric force acting
on the molecule will induce a polarization exactly in the direction of the force, and
proportional to it*: that in fact notwithstanding its numerous degrees of freedom the
molecule is isotropic. Thus the source of double refraction in crystals or strained
isotropic substances would reside in the aeolotropic arrangement of the molecules and
not in their orientation: but there can also be an independent intrinsic electric polarity
in the molecule depending on its orientation and not on the electric field, such as is
indicated by piezoelectric effects in crystals.
If the molecules were not thus isotropic as regards induced electric polarity, the
electric vibration induced in the molecules, when a train of radiation passes across a
medium such as air, would not be wholly in the wave-front. In the theory of optical
dispersion the coefficients t would then be averages taken for a large number of mole* Cf. Kerr's striking result, Phil. Mag., 1895, that in velocity of propagation affected.
the double refraction produced in a liquid dielectric by an t e.g. K, cl, C.,... cl', c2',... in Phil. Trans. 1897 A,
electric field, it is only the vibration polarized so that its p. 238.
electric vector is parallel to the electric field that has its