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.

AND THE INFLUENCE OF A MAGNETIC FIELD ON OPTICAL PHENOMENA. 387
where DF/dt must represent the rate of change of F at the electron as it moves,
namely
DF dF dF dF dF
- - + Xd+YdY+Zd
dt dt dx dy dz
The vanishing of the coefficient of &x for each element of volume gives
m /=e DF d dF dG dX d)
(x =e- dt +x-7+Y -d+ZJ(ii).
=e(.-/ d7F dc\.
=e(.... dt dx).
Similar expressions hold good for my and mz.
The form of W shows that 47r-C2 is the coefficient of aethereal elasticity corresponding
to the type of displacement (f, g, h): the right-hand sides of equations (i) are therefore the
expressions for the components of the forcive (P', Q', R') inducing aethereal displacement:
thus this force, which will be called the aethereal force, is given by equations of type
p. dF d'
dt dx
The form of equation (ii) shows that the right-hand side is the component of the
force e (P, Q, R) inducing movement of an electron e: this force reckoned per unit electric
charge is called the electric force (P, Q, R) and is given by
p _j - _ dt dx
or, in terms of physical quantities only, by
P= yY- /Z + 4qra2f.
We do not now go into the case of a magnetically polarized material system, for
which in certain connexions* (a, b, c) replaces (c, f9, y) in this formula.
These expressions for the aethereal force and the electric force, together with a
complete specification of the electric current and the experimentally determined constitutive
relations of the medium, form the foundation of the whole of electrical theory.
MOTION IN AN IMPRESSED MAGNETIC FIELD.
When the electrons or ions constituting a molecule describe their orbital motions
in a uniform magnetic field (~a, 3o,, y,), its influence is represented by an addition to the
vector potential (F, G, H) of the term
(oY - oZ, az - yx, ox - coy).
* Cf. Ioc. cit. ante.
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