1892.] Mathematical Theory of Electro-magnetism. 



40J 



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 dissipation 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. What 

 was wanted was to bring this group of phenomena, which are un- 

 doubtedly 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. 



The way being thus paved, in the next principal division of the 

 paper are deduced the general results of the theory, the most im- 

 portant of which are the equations 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 examination 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 thermo-electric, thermo-magnetic, 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 con- 

 sequences. Where there is disagreement 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. 



Perhaps a clearer insight into the true bearings of the present 

 theory is obtained by the attempt below to explain thermo-electric, 

 thermo-magnetic, and the Hall effects, than by any other part of the 

 paper. Especially clearly do some of the restrictions imposed by the 

 condition 47rC = VvH come out. 



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 the aspects of a current of electricity it may be 



