FUNDAMENTAL FORMULATIONS OF ELECTRODYNAMICS. 243 



some authors, but which is not satisfied by the results of our present discussion. 

 The vector determining the flux of electromagnetic energy has been seen to be 



S = j- [E, H'] 



and that determining the momentum is 



M = J [E, HI. 



47TC 



111 the absence of magnetic media and convective dielectric polarisations these two 

 expressions satisfy the equation 



but under the most general circumstances this relation is not satisfied. 



We have so far conducted the discussions as though the quantity derived as a 

 momentum is unique and definite, whereas, as a matter of fact, this is far from being 

 the case. We saw that the idea of the momentum arose from certain outstanding 

 terms which remained when attempting to reduce the electromotive forces to a 

 representation by a stress system. Now we can give a number of different forms to 

 this reduction and each one carries with it a different expression for the electro- 

 magnetic momentum. We can ; for instance, write 



_L[EH] = - * F^A H 1 -JL [V 0J H] 

 4TTC lire* ]_ at 47rc 



47JT 



, H | + - 



and the second term in this expression when differentiated with respect to the time 

 might be included in the stress specification. This would leave a new expression for 

 the electromagnetic momentum which is 



47T 



a form which would probably be suitable for use in connexion with a theory in which 

 the radiation phenomena are represented by MACDONALD'S form of the theory. 



This is not the only alternative to the usual theory for we can construct similarly 

 any number of others. It appears, however, that the usual presentation is probably 

 the simplest possible one, and this is a great advantage in its favour ; but subsequent 

 developments of the theory may require a modification, and then it is as well to 

 remember that there are other forms of the theory perfectly consistent with the 

 general relations of the electromagnetic field, both as regards its general and 

 dynamical aspects. 



