346 Mr. R. Hargreaves on Radiation 



But SwX=2t«X' f and 



M M 



and with these the above becomes 



^ +SOC'+pSuX'+ ^2u(w-i/3) = -T2^(Yy-Z/3). (58) 



The flux of energy to the unit-volume fixed in the di- 

 electric accounts for (1) increase of E, (2) Joule's effect, and 

 (3) the work done by electric and electromagnetic forces in 

 virtue of the translation (u v iv) . At first sight the use of 

 multipliers X, a instead of X 7 , a! threatens difficulties as 

 regards Joule's effect : these are resolved by the difference 

 showing the work done by electromagnetic force, that work 

 not appearing in (56), because the standpoint implied the 

 translation. 



If pu\... are written for % x ... , (u'v'tv') being a velocity 

 additional to the general translation, Joule's effect is replaced 

 by work done in virtue of the motion (u'v'w'), viz. pZu'X.' ; 

 and the conservation of charge is then expressed by 



The mechanical side of electrical action may be separately 

 shown by forming the time-rate of the momentum of radia- 

 tion, that rate taken from the standpoint of the dielectric ; 

 that is, we start from (55) and form 



;^(X/3-Y«). 



dK ^KM 



dt ° r dt 



In the course of the work the terms 



M 7 sg and Z{K2§-P| 



are introduced, and the result is 



(dZ x dZ v dZ z \ „,- M,. Q . s^dU 



That is, the rate of increase of (P Q R) together with forces 

 on charge and current (where they exist), is expressible as the 

 body-force of a stress. Here the coefficients K and M occur 

 in the stress, i. e., 



Z r =-(KZX + M 7 «), Z*= |(XHY 2 -Z 2 ) + ~(a 2 + /3 2 - 7 2 ). 



