and Conductance Operators. 489 



going on ; for the denial of the law that eF not only measures 

 the activity of an impressed force e on the current T, but 

 represents energy received by the electromagnetic system at 

 the very same place, lands us in great difficulties. 



Again, as regards the " electric force of induction."" We 

 cannot find the distribution through space of this vector from 

 the Faraday law that its line-integral in a closed circuit equals 

 the rate of decrease of induction through the circuit. We 

 may add to any distribution satisfying this law any polar dis- 

 tribution without altering matters, except that a different 

 potential function arises. In this case we do not even alter 

 the transfer of energy. The electric force of the field is 

 always definite ; but when we divide it into two distinct dis- 

 tributions, and call one of them the electric force of induction, 

 and the other the force derived from electric potential, it is 

 then quite an indeterminate problem how to effect the division, 

 unless we choose to make the quite arbitrary assumption that 

 the electric force of induction has nothing of the polar cha- 

 racter about it (or has no divergence anywhere), when of 

 course it is the other part that possesses the whole of the 

 divergence. This fact renders a large part of some mathe- 

 matical work on the electromagnetic field that I have seen 

 redundant, as we may write down the final results at the 

 beginning. In the course of some investigations concerning 

 normal electromagnetic distributions in space I have been 

 forcibly struck with the utter inutility of dividing the electric 

 field into two fields, and by the simplicity that arises by not 

 doing so, but confining oneself to the actual forces and fluxes, 

 which describe the real state of the medium and have the least 

 amount of artificiality about them. Similar remarks apply to 

 Maxwell's vector-potential A. Has it divergence or not ? It 

 does not matter in the least, on account of the auxiliary polar 

 force. When the electric force itself is made the subject of 

 investigation, the question of divergence of the vector-potential 

 does not present itself at all. 



The lines of vorticity, or vortex-lines of the vector impressed 

 force, are of the utmost importance, because they are the ori- 

 ginating places of all disturbances. This is totally at variance 

 with preconceived notions founded upon the fluid analogy, 

 which is, though so useful in the investigation of steady 

 states, utterly misleading when variable states are in question, 

 owing to the momentum and energy belonging to the mag- 

 netic field, not to the electric current. .Every solution 

 involving impressed forces consists of waves emanating from 

 the vortex lines of impressed force (electric or magnetic as 

 the case may be, but only the electric are here considered), 



