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 PHIENOMENA. 385
the complete specification of the deformation of the medium must include these processes
of primary creation of the electrons, and the medium would have to be dissected in
order to reveal the discontinuities, after the manner of a Riemann surface in functiontheory*.
3. We have now to apply dynamical principles to the specification of the energies
of the medium thus obtained. The question arises as to what are dynamical principles.
It may reasonably be said that an answer for the dynamics of known systems constituted
of ordinary matter is superfiuous, as the Laws of Motion formulated by Newton practically
cover the case. Waiving for the present the question whether the foundations of that
subject are so simple as may appear, the present case is one not of ordinary matter
but of a medium unknown to direct observation: and its disturbance is expressed in
terms of vectors as to the kinematic nature of which we have here abstained from
making any hypothesis.
Now the dynamics of material systems was systematized by Lagrange in 1760 into
equations which amount to the single variational formula
f(T- W)dt=O,
in which the variation is to be taken subject to constant time of passage from the
initial to the final configuration, and subject to whatever relations, involved in the constitution of the system, there may be connecting the variables when these are not mutually
independent,-the only restriction being that these latter relations are really constitutive,
and so do not involve the actual velocities of the motion although they may involve
the time. This equation is known to include the whole of the dynamics of material
systems in the most general and condensed manner that is possible. It will now be
introduced as a hypothesis that the cognate equation is the complete expression of the
dynamics of the ultra-material systems here under consideration. Even in the case of
ordinary dynamics it can be held that there is no final resting-place in the effort towards
exact formulation of dynamical phenomena, short of this Action principle: in our present
more general sphere of operations the very meaning of a dynamical principle must be
that it is a deduction from the Action principle. This attitude will not be uncongenial
to the school of physicists which recognizes in dynamical science only the shortest and
most compact specification of the actual course of events.
We have then to apply the Principle of Action to the present case. In the first place
the coordinates in terms of which T and W are expressed are not all independent, for
when the distribution of (f, g, h) is given that of the electrons is involved. The connexion
between them is completely specified by the relation
I(df gd dh\,
J \dx dy dzj
* More concretely, the relation curl (a, (3, y) =4wr (fj, hg, ) kind whose velocity is (a, fi, y), that are required to introinvolves f(lf+mg+nh) dS=O: now (lf(f mg + n+h) dS is not duce the existing intrinsic strain must involve discontinuous
zero but is equal to Se: hence the displacements, of the processes. Cf.' Aether and Matter,' Appendix E.
VOL. XVIII. 49