THEORY OH ELECTROMAGNETISM. 
693 
[compare for proof § 603 eq. (II) with the corresponding’ eq. (the last on p. 239) of 
§ 619], and similar remarks, apply to the treatment in § 630 et seq. of the energy of 
the field. How to bring these various parts of the subject under the dynamical 
treatment I did not see. strictly on Maxwell’s own lines. Again, in considering the 
general equations of the electromagnetic field (§§ 608, 609) he speaks of a generalised 
force E. This generalised force, quite contrary apparently to dynamical analogies, 
has, not a single definite effect, partly kinetic and partly static, but two independent 
effects, one static and the other kinetic. On trying to trace out the reason of this, I 
could not arrive at any certain result strictly on Maxwell’s own lines. It seemed to 
me as if the double effect of E was simply assumed. [If it merely were analogous to 
an ordinary dynamical reaction, then it could not be associated with such external 
forces as result from electrolysis.] 
13. Whether these and many other similar questions which occurred, some of which 
will appear below, can, strictly speaking, be denominated difficulties, is of no conse¬ 
quence. Suffice it that they Jed to the following considerations. Maxwell has 
built up a theory whose axioms can* be put down in a definite form. Cannot, then, 
all his results (electrostatic, electrodynamic, magnetic, and electromagnetic) be 
developed as consequences of these axioms in one application of dynamical reasoning \ 
Cannot we by such a single application obtain all Maxwell’s equations from (A) to 
(L) in §§591 to 614, as well as his stress results contained in other parts of the 
treatise, and by particular simplifying assumptions, shew that the ordinary electro¬ 
static and magnetic theories are particular consequences of our general results ? 
This led me to attempt to apply in a perfectly rigorous and general manner the 
well-known equation 
8 dt -f- % jQSgc^ = 0 . . . . .U) 
(where L is the Lagrangian function, i: modified” if necessary, of any mechanical s 5 T stem 
of which q is a coordinate, and Q the external force of type q, and where the initial 
and final positions and times are not subject to variation) to the present case. The 
way I proposed to apply it was to assume all matter to be in any possible state as to 
strain and as to electric phenomena, then to vary all the geometrical coordinates by 
simply giving to each element of matter an arbitrary displacement, and also to vary 
all the electric coordinates, and trace the mathematical consequences. [Note that on 
Maxwell’s theory (at least as I understand it) these two variations are all that can 
be made, a variation in the magnetism being determined by the above variations.] 
14. And it was here at the outset that the greatest difficulty of any met with in 
the investigation occurred. Consider a particular consequence of assuming that the 
electric coordinates are the three components of D for every point of space. If by 
* It would be more correct to say “ some of whose axioms.” I wish to imply that I thought it advis¬ 
able to till iu the remainder tentatively and seek the result. 
