( 61G ) 

 i-i- ƒ(.! . I J^ + oq I ) JS - ^J(a . < riö + (>q | ) dS = 



Now, it appears from (9) (hat 



-ir(a.|rfb + rm|)r/5 (12) 



is tlie change the magnetic energy of the system would undergo, if 

 we gave to the current tlie cliange db + (>q. We shall write tf'lfor 

 t/ds variation of (he currem, and rff), ff' 7Mbr the corresponding 

 variations of f) and 7'. As to rf' I, it may be defined as the current 

 that would exist if tlie changes represented by q and rfb were accom- 

 plished in unit of time. 



On the oilier hand, j(b.rfb)<y6' is the variation of the electric 



energy L/ and the last integral in (11) is (), because the vector 

 (fb + Q] is solenoidally distributed. Tims, the first term in (10) becomes 



For the last term in that equation we lind, integrating by parts, 

 — f(rof ci . <olq .\i\])dSr=---lQ(l) . I q. ^,\ ) JS = y (^(^l • U^ • ')J)'^'^'' 

 so that finally 



dr = ^ + rf/:^ + pTq . |b4--i[o.()lj\/5. 



Now, the ecjuation (YII) shows that the last term is precisely the 

 work dojie, during the displacements q, by the electric forces exerted 

 bv the aether on the electrons. 



Wi-iting öI'J for this woi'k, we have 



öE=(f{r—r) — 13) 



cit 

 an equation closely corresponding to dWt-embert's principle in common 

 dynamics. 



§ 7. The motion of the electrons themselves may be determined 

 by ordinary methods; it will be governed by the electric forces 

 x^hose work has been denoted by (fJ^, together with forces of any 

 other kind that may come into [)lay. We shall confine ourselves 

 to those cases in which these latter forces dspend on a potential 

 energy L'\ ; then the total virtual work of all forces acting on the 



