G98 
MR. A. McAULAY OX THE MATHEMATICAL 
Perhaps a clearer insight into the true bearings of the present theory is obtained by 
the attempt below to explain thermoelectric, thermomagnetic, and the Hall effects 
than by any other part of the paper. Especially clearly do some of the restrictions 
imposed by the condition 47 tC = YVH come out. 
21. In the last sub-division it will be found that I disagree entirely with Professor 
Poynting’s interpretation of his own results, and show how quite a different and, I 
think, simpler flux of energy may be made to account for the changes of intrinsic 
energy in different parts of the field. In particular, this interpretation would restore 
credence in what Professor Poynting considers he has shown to be a false view, viz., 
that among other aspects of a current of electricity it may be looked upon as some¬ 
thing conveying energy along the conductor. This part of the subject, although 
deduced from the present theory, is shown to be true on Professor Poyntlng’s own 
premisses. 
22. It is w r ell here to call attention to what might prove confusing otherwise. In 
what follows E, e, E, $, and some allied symbols, stand for certain external forces. 
But there are three different meanings given in different parts of the paper to these 
symbols. They are originally defined as the whole external forces of the different 
types. But in treating of frictional forces, &c. (§§ 35 to 42) it is convenient to regard 
them as meaning only those parts of the forces which are due to friction and the like. 
Again from § 50 onwards it is convenient to regard them as meaning only those parts 
of the forces which are independent of friction and the like. This inconvenience is 
incurred to avoid the greater evil of a large additional array of symbols. 
With this exception,and one or two other trifling ones, which are noticed in their 
places, nowhere has the meaning of a symbol been changed throughout the paper. 
II. Groundwork of Theory. 
A. Fundamental Assumptions. 
23. We assume that the Lagrangian function, L, of all matter in space can be 
expressed in the form 
.(i). 
j|Ws + . . 
where l, l s are functions of certain independent variables which determine the state of 
the body at the point. The volume integral extends throughout space, and the sur¬ 
face integral over certain specified surfaces. The entropy F of all matter in space 
will be assumed to be of the form 
* Since completing the paper I have discovered a notable exception which is not otherwise noted than 
in this footnote. It does not seem likely to lead to confusion; therefore I retain it. Most frequently in 
the present paper q stands for the typical scalar coordinate of a dynamical system, but it is not 
infrequently used, as in the former paper, for the quaternion of the rotation-operator q ( ) q -1 . 
