( 815 ) 



a' for the instant, at wliicli the local time in P is t' , we must take 



Q and Q u', snt'h as they are in \\\v elcnionl <]S af tlic inslant at 



r' 

 which the local time of that element is t' . 



§ H. It will sut'lice foi' our purpose to considei' two special cases. 

 The first is that of an electrostatic system, i. e. a system having' 

 )io otiiei* motion hnl the translation \\itli the xcloeity //;. In this case 

 u' ^ 0. and therefore, by (12), a' = 0. Also, 7 ' is inth-pcndcnl of /', 

 so that the ecpiations (11), iloj and '14, rcdnce to 



L' .-p' =: — (^>\ 1 



(10) 



b' = — ;irnd' </', W = 0. \ 



After having- determined the \ector b' l>y means of these erpiations. 

 we know also the electric force actin*;- on electrons that belong to 

 the system. For these the formnlae (lO) become, since u' = 0, 



The resnlt may be pnt in a sim])le form if we compare the moxing 



system ^ with which we are concerned, to another electrostatic 



system 2' which lenuiins at rest and into which — is changed, if 



the dimensions parallel to the axis of .f are mnlti[)lied by /,•/, and 



the dimensions which lune the direction of // or that of :, by /, 



a deformatioji foi' which (//, /, /) is an aj)j)roi)riale symb(»l. In this 



new system, which we may suppose to be place<l in the abo\c 



mentioned space ;S'', we shall give to the density the \alne (/. 



determined by (7), so that the charges of coi-respondin^ clcmcjits of 



volnme and of correspotiding electrons are the same in Ji" and 2i". 



Then we shall obtain the forces acting on the electrons of the moving 



system 2S, if we first deternnne the con-esponding forces in 2l', and 



next multiply their components in the dii-ectioji of ihc axis of .u by 



I" 

 l\ and their components jtei'pejidicnlar to that axis by — . This is 



conveniently expressed by (he lorninla 



k 



m^)^[^> ^l^p^-) (21) 



It is further to be ivmarked that, after ha\ ing found t»' l»v (19), 

 we can casdy calcidatc the clcclromaünctic momentum in the mo\ ing 

 system, oi' I'athci- its compojienl iji the diicctioii of the motion. 

 Indeed, the formula 



