THEORY OF ELECTROMAGNETISM. 
097 
of Maxwell’s theory. At any rate the results, though not in every respect identical 
with Maxwell’s, are yet so nearly identical that the true matter for surprise is that 
they differ so little, and in such unimportant ways, from his. 
It must be added, to prevent misconception of my own views, that I by no means 
consider proven what I regard as the key to Maxwell’s theory, and what I have 
strictly adhered to in this paper, the assumption that under all circumstances 
4ttC = WH. My position rather is, that while this assumption may or may not be 
true, it is desirable to investigate as generally as possible what must be true, and 
what cannot be true if the assumption is made. In other words, I do not think that 
Maxwell’s theory has yet had a fair trial, even at the hands of mathematicians, and 
the present paper is an attempt to provide more ways and means than hitherto have 
been available for such a trial. The methods adopted are equally applicable to other 
sets of fundamental assumptions. 
19. Turning to the second part of the groundwork, the preliminary dynamical 
and thermodynamical considerations, it is necessary to remark that these considerations 
though not limited to an electric field, seemed absolutely necessary in order thoroughly 
to investigate the consequences of the assumptions. With regard to the first two 
sections of this part of the paper on the modified kinetic energy and the free energy, 
and on the entropy there is nothing which is likely to be questioned. In the third 
section on frictional forces, conduction of heat and dissfation of energy, I enunciate 
a principle which opens the way for much criticism. I would beg any readers to whom 
the form of enunciation is repugnant, to suspend their judgment as to the validity of 
the principle, not only until the first justification of it, but until they have seen it in 
action as it were, later in the paper. W hat was wanted was to bring this group of 
phenomena, which are undoubtedly closely connected, under the same sort of treatment 
as is accorded to the reversible phenomena of a system by means of its Lagrangian 
function, and the (dependent) entropy. 
20. The way being thus paved, in the next principal division of the paper are 
deduced the general results of the theory, the most important of which are the equa¬ 
tions of motion. These are considerably more general than the ordinary equations of 
the field, and thus we are led to the last division of the paper, the detailed examina¬ 
tion of these results. The chief sub-divisions of this part are the comparison with 
Maxwell’s results, a discussion from the point of view of the present theory of 
thermoelectric, thermomagnetic, and the Hall effects, and the transference of 
intrinsic energy through the field. 
In comparing with Maxwell’s results, wherever there is agreement, it is considered 
unnecessary to investigate further the detailed consequences. Where there is dis¬ 
agreement the physical consequences are traced with more detail, and in no case can 
it, I think, be said that the results of this part of the paper are condemnatory of the 
present theory. In this place, too, the bearing of the present theory on the question 
of convection currents is discussed. 
mdcccxcii.—A. 
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