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.

390 MR LARMOR, ON THE DYNAMICS OF A SYSTEM OF ELECTRONS OR IONS:
its electric vibration is along the same axis while the frequency is unaltered. In fact
each Fourier vibration of an ion, which previously consisted of a component disturbance
of the type of an elliptic harmonic motion, is no longer of harmonic type when the
precessional rotation cK is imposed on it-this precession being imposed additively on
the different constituents of the total motion: but it can be resolved into a rectilinear
vibration parallel to the axis, and two circular ones around it, each of which maintains
its harmonic type after the rotation is impressed and thus corresponds to a spectral line,
and which are differently modified as stated. These three spectral lines would be expected
to be of about equal intensities *.
It is however essential to this simple state of affairs that the charges belonging
to all the ions that are in orbital motion under their mutual influences should be of
the sane sign, as otherwise e/m could not be the same for all. It is also essential
that the ions of opposite sign, or the other centres of attraction under which the orbits
are described, should be carried round as well as the orbits with this small angular
velocity -/c in so far as they are not symmetrical with regard to its axis.
If we admit the hypothesis that the effective masses of these positive ions, or other
bodies to which the negative ions are attracted, are large compared with those of the
negative ions themselves, this state of superposed uniform rotation of the whole system
may still be expected to practically ensue from the imposition of the magnetic field.
For under the action of the mutual constitutive forces in the molecule, the orbital
motions of the larger masses will take place with smaller velocities. As the additional
forces introduced by the magnetic field are proportional to the velocities, they will thus
also be smaller for the positive ions. Let us then suppose these larger masses to be
constrained to the above exact uniform rotation, with angular velocity o', along with
the negative ions, and find the order of magnitude of the forces that must be impressed
on them in order to maintain this constraint. The motion of the negative ions will,
as has been seen, be entirely free, the forces due to the magnetic field exactly sufficing
to induce the additional rotational motion. As regards a positive ion of effective mass
mn, the radial and transversal forces, in the plane perpendicular to the axis of the
magnetic field, that are required to maintain the motion will be altered from
n (-rw2) and m d(r2o)
r dt
m d
to n {r -r (co + o')2} and T dt jr2 ( + o)}.
Thus, o' being small compared with w, the new forces required will be
-2mrwco' and m d (r2ow);
r dt
whereas the force arising from the magnetic field acting on an ion moving with velocity
v is 2mvo' at right angles to its path. These two systems of forces are for each ion
of the same order of magnitude: thus the forces required to maintain the imposed
* For more detailed statement, cf. Plai;. g., Dec. 1897.