FLUXES OF ENERGY IN THE ELECTROMAGNETIC FIELD. 
475 
the sides of a magnet. From actual experiments with bar magnets, needles, &c., one 
would naturally prefer to regard the polar regions as the seat of translational force. 
But the equivalent forcive 2j 0 B has one striking recommendation (apart from the 
dynamical method of deducing it), viz., that the induction of an intrinsic magnet is 
determined by curl h 0 , not by h () itself; and this, I have shown, is true when h 0 is 
imagined to vary, the whole varying states of the fluxes B, D, C due to impressed 
force being determined by the curls of e (l and h 0 , which are the sources of the dis¬ 
turbances (though not of the energy). 
The rotational peculiarity in eolotropic substances does not seem to be a very 
formidable objection. Are they not solid ? 
As regards the assumed constancy of p, a more complete theory must, to be correct, 
reduce to one assuming constancy of p, because, as Lord Rayleigh* has shown, the 
assumed law has a limited range of validity, and is therefore justifiable as a preparation 
for more complete views. Theoretical requirements are not identical with those of 
the practical engineer. 
But, for quite other reasons, the dynamically determined stress might be entirely 
wrong. Electric and magnetic “ force ” and their energies are facts. But it is the 
total of the energies in concrete cases that should be regarded as the facts, rather 
then their distribution ; for example, that, as Sir W. Thomson proved, the '‘mechanical 
value ” of a simple closed current C is -§LC 3 , where L is the inductance of the circuit 
(coefficient of electromagnetic capacity), rather than that its distribution in space is 
given by ^HB per unit volume. Other distributions may give the same total amount 
of energy. For example, the energy of distortion of an elastic solid may be expressed 
in terms of the square of the rotation and the square of the expansion, if its boundary 
be held at rest; but this does not correctly localise the energy. If, then, we choose 
some other distribution of the energy for the same displacement and induction, we 
should find quite a different flux of energy. But I have not succeeded in making any 
other arrangement than Maxwell’s work practically, or without an immediate intro¬ 
duction of great obscurities. Perhaps the least certain part of Maxwell’s scheme, 
as modified by myself, is the estimation of magnetic energy as -gHB in intrinsic 
magnets, as well as outside them, that is, by -|Ep _1 B, however B may be caused. Yet, 
only in this way are thoroughly consistent results apparently obtainable when the 
electromagnetic field is considered comprehensively and dynamically. 
* ‘ Phil. Mag.,’ January, 1887. 
