( <^i3 ) 



llie jK)iiit8 of (ho ('loclroiis, accompanied l»v iiifniilosimal ('liaiif>os in 

 tlie dielectric displacement. 



We shall wi-ite rfb for llie difference, in a fixed point of the 

 aether, between the dielectric disj)hicenient before and after the 

 virtual change, the sign of variation ff having a similar meaning- 

 when it [>recedes other symbols re]M-esenting the value of some 

 ([uantiiy in a definite point. If it is alïixed to a letter representing 

 a quantity l)elonging to the system as a whole, such as the total 

 electric energy (\ it will simply serve to indicate the difference 

 between these values in the original or real and the varied states. 



The variations to be considered arc nol wholly arbitrary. We 

 shall limit our choice by supposing in the first |)lace that each 

 element of volume of an electron preserves its charge during the 

 displacements q; tiiis is expressed by the i-elation 



<fQ -i- </!>:{().]) = {) (7) 



which may be compared to (II). 



In the second place we shall su|)[)ose the variations of b not to 

 violate the condition (1). 



In virtue of these i-estrictions the vector 



db + ^q 



Avill present a solenoidal distribution. Indeed, we see from (I) that 



div rf b = rf ^, 

 and here we may, accoi-dijig to (7), i'e[)lace the right-hand member 

 l)y — div {q ^). 



Let us now conceive v^ and é ^ to be ciiosen for every instant /, 

 so that they vary cojitinuously with the lime. Then, in order com- 

 pletely to define the succession of varied states, or what we may 

 call the ,/ varied motion" of liie system, we shall su[)pose the varied 

 positions of the poiiits of each electi'on to be reached at the same 

 instants at wiiicli these |)oiii(s occupy the corresponding original 

 positions in the real molioji ; we assume likewise that, in every 

 point of space, the varied dielectric dis[)lacement exists at the same 

 moments as the original one in the succession of real states. 



l»y this llie varied motion ()f electricity is entirely determined ; 

 indeed, since we know the xclocily of uialtei- and the rate al which 

 ^ changes, ^ve are able to state what has become of the convection- 

 current, the displacement-curreni, and also of the total curi-eut 1. 

 The first thing we ha\ e to do will be to ex|)ress tf [ in q and tfb. 

 Of course we may ite sure beforehand that the disti-ibution of both 

 the Jiew i and the \ariation J 1 will be solenoidal. This nuist neces- 

 saiily be the case, because we know I^f . that, in the states that 

 succeed one another in the varied motion, each volume-element of 



