( 620 ) 

 Poiiili'romof'n'i' action on a si/stcn/ of electrons:. 



§ 10. A vii'liuil cliange of a verv simple kind is an iiifiiiitelv 

 small Iraiislatioii of all the electrons, eombiiied with what we mav 

 eall an cqnal translation in the same direction of the whole electric 

 field. Applying to these variations — which \ve j^ive as \\ell to the 

 part of the system onlside the snrface <J as to the part enclosed by 

 it — the eqnation (i(i), one may calcnlate the resnlting- force exerted 

 bv the aether on the electrons within the snrface. This force may 

 be shown to consist of two [larts, the first of whi^'h is the force with 

 which we should have to do, if the surface G were snbjected to the 

 stresses in the aether, whose com[)onents have l)een already determine(l 

 bv Maxwell, whereas the second part is determincil by the rate 

 of change of a certain integral, i-elating to the space S within o. 

 The latter part will therefore vanish if the state is stationary, an<l may 

 be left out of acconnt if, for periodic states, we wish only to knoAv 

 the mean value of I lie i-csnlting force, taken for a full period. I 

 nvi'iX not heiv work out the formnlae, having formerly deduced the 

 result in a uiorc diiccl way. The components of .Ma\\vki,i/s stress are 



1 1 



A.. = 



^ (b/ - b/ - b,^) + Y (V - K; - f):^), etc. ^ 



\ 



(18) 



X,,= JO- = b, ^;, -^r 1\,- IV ' *'*^'- 



and the jnst mentioned \olume-integral is 



J IS/, d S, 



®/j being the fhux of energy in the direction //, for which we seek 

 the resulting force. 



Thns, the resnlting force in the direction of ./• is giveji by 



S= j Xnd(J-—~ j ^,-dS (19) 



1 r 



The vector — | 2: d ,S is called by Abraham the e/cctronnn/netic 



monientnin. 



§ Jl. Similar results wonld be obtahied if we chose for the virtnal 

 variation, instead of a translation, an infinitely small rotation al)ont 

 an axis passing through the origin of coordinates; the equation (1(3) 

 would then serve to determine the resnlting couple, arising from 

 all the forces exei'ted by the aether oji the electrons within the 

 surface o. The moment of this couple may however be calculated 



