FUNDAMENTAL FORMULATIONS OF ELECTRODYNAMICS. 241 



theory is to reduce these forces to a representation by means of an applied stress 

 system of ordinary character. This discussion leads in the usual way to the intro- 

 duction of the concept of electromagnetic momentum. 



The actual calculations for the present form of the results are not materially 

 different from those given in extenso elsewhere, so that it will again be sufficient to 

 outline the principal stages in the discussion. The method employed is to attempt to 

 express, say, the x component of the. force per unit volume in the form 



TI | 3T CT t 3T 



dx 3?/ 



Now the total forcive of electrodynamic origin acting on the medium of the field at 

 any place is such that its x component per unit volume is 



3B 



-[p, curl E],-[i, cm-IB],-! [V^l-fl FE,^ 



c L dtlcl dt 



Again writing 



it is proved just as in the usual form of the theory that the forcive of which this is 

 the representative component is represented in the main by a stress system in which 



and 



47T 



with symmetrical expressions for the other constituents ; but with this representation 

 there is an outstanding part of the complete forcive, viz., 



i d r-ij!T>i 1 ct r-rpTi * /nr i -^ \ ^ ^ n?ui * In- ~\ *'" 



r ~r" L-""*J "* T~ L**^J I L-*-"iJ> v~ / ~ ; r L-^-nJ ~ ['''mJ) ~* 



4c dt c dt c \ ox I -iTTC dt c \ c~ 



which cannot be so reduced. The first term in this outstanding part, being a complete 

 differential with respect to the time, is usually taken to represent a part of the 

 complete forcive arising as the kinetic reaction to a rate of change of momentum, and 

 this is the origin of the concept of electromagnetic momentum. This idea is however 

 partly destroyed by the remaining term in the above expression which cannot be 

 developed either as a forcive of ordinary type or as a kinetic reaction to a rate of 



L 2 . 



