{ 619 ) 



B being a constant infinitely small factor. From these assumptions 

 it follows at once that 



No\v the magnetic energy may l)e considcM-ed as a homogeneous 

 quadratic function of the comnouenis of ilic ciiriviil ; it will llierefore 

 change in ratio of 1 to 1 -{- "2 f, if the ciii-i-ent becomes (i + f) '. Thus: 

 Ö' '/= 2 e T. 



We may also infer from our assumptions thai the position ol' tiie 

 electrons and the values of ^ aix\ in the varied motion at the lime 

 /, what they are in the real motion at the time t ~\- b, so that the 

 only difference between the two motions is that the one is iu advance 

 of the other Iw an interval e. 



In this way it is seen that 



clT ,^ dU dh öd'() 

 61 = e—-. (fi —s-—, ffi) z= e ^- . ^- (fb ^0. 



(It (h èt dt 



Substituting these values in the e((uation (J 6), we get, after division 

 by e and multiplicatio]i by dt, dejioling by (IE the work done by 

 the electric forces in the real motion, during the time df, 



(IE = -,/{T^ r) — c,/f i [b. f)]„ </(j. 



(17) 



This is the equation of energy. The last term represents the How 

 of energy through the surface. 



h. Applying (17) to a single electron, whose motion is a Iranslalion 

 with variable velocity aloiig a straight line, one may calcidale the 

 force with which it is acted on by the aether, and which, imder 

 certain sinqjlifying assunqMions, is found to be [)ro})oi-tional to (he 

 acceleration and directed oppositely to it. The quotient of this force, 

 divided by the acceleration, may ap|)roj)rialely i)e called the e/('ctjv- 

 nhKjiu'tic in((ss of the electron. 



r. Thei-e will likewise be a force proportional and opposed to 

 the acceleration, if the latter is perjjejidicular to the direction of 

 motion. In this case however, of \\ liich the ujiifoi-m uiolion of an 

 electron in a circle fiirinshes the simplest example, we nnist recur 

 to the equalion (i()), in order to determine the force. The surface o may 

 i>e supposed to lie at iidinite distaJice and the \irtual dis|)lacement 

 must be taken iji the direction of the acceleration. The ratio of the 

 force and the acceleration may again be called the c/cc/ivii/df/nc'tlc 

 )u(hs.>!, though, e.\ce|)t foi- suiall \elocities, its value is not e(pial to 

 that of the corresponding j-atio in the case f>. 



In both cases the result agre(>s with what has l»eeii found hy 

 xVbr.miam. 



