( «^1-^ ) 



.,. = - 



1 r\ 1 ri 



After luivinii" foiiiul <f uiitl ^i, u c^ m.-iv (lelennino Iho (lielectric 

 (lispliieeinent ^ and (lie maj^netic torcc» i) I>y means of llic relations ^) 



b = — — a — (p'ud (f , (4) 



c 



{) =z rot a (5) 



]\ is to l)e remai-ked tliat tlio two potentials are not mnlnally 

 independent; (liey are ('«)nnected by the eqnation 



1 . 

 (///' a = — <f (G) 



(' 



Theorems corre.'^pinKliiKi to the jie/'iicip/t' of d'Alk.mbert 

 tni</ flint of least action. 



§ 4. The i)hysi('ists who iiave endeavonred, l)y means of certain 

 hypotlieses on the uieeaiusni of eleetroinagnetic ])hen(miena, to deduce 

 the fnndamental ecpiations from the j)rinciples of dynamics, have 

 encountered considerahle difficnlties, and il is best, perhaps, to leave 

 this course, and to adopi the e(piations (1) — (VII) — or others, 

 eijuiAalent to them as the simplest cxpi-ession ^ve may find foi- 



the laws of ('le('troma<»-netism. Nevertheless, even if we prefer this 

 point of view, it deserves notice that the fundamental e(piations may 

 be transformed in snch a way that we arrive at theorems of the 

 same mathematical form as tlu^ ,ti;eneral princii)les of dynamics. This 

 has been done especially by Aiuiaiiam in his important paper 

 "Principien der Dynamik des Elektrons'""). The considerations in 

 this and the two next para<i;ra])hs agree wilh tlios(.M»f Ahramvm. th()ui>h 

 })resented in a form differing from his. 



We shall consider a system of electrons moving in the intiiiitely 

 extended aether, and \ve shall fix our attention on the dilfercjit 

 states of this system, the aether included, that succeed each othei- iji 

 the course of lime in any electromagnetic phenomenon. From every 

 one of these states we shall pass to another, dilfering infinitely little 

 from it, and which we shall call the reiried state. The variation 

 or -virtual change" will consist in infinitely small displacemeJits q of 



1) 1 shall write (jead y (, gradient of S') for the vector wliose components 

 d<p d(p d<f 



~) Dhude's AnnaU'n. 10, p. |or). 190:3. 



