( 431 ) 



electrostatic phenomena. In these we have v>= and S' independent 

 of the time. Hence, by (lie) and (Illc) 



S?' = 0, 



and by (IVc) and (Ic) 



9 J/' 9 s' 9 s' 9 a;' 9 .v' 9 y 



AV g'z=— l^^t>. 



These equations show that %' depends on a potential m, so that 

 d CO 9 « . d fo 



(T.' (X-' ft-' 



u* — '-, (toy — — ^ 7 1 u - — ;:^ r 

 ox' dy as 



and 



9^ ^. 9^, 4. (2) 



x~ ij~ a s~ />; 



Let 6' be the system of ions with the translation p^ , to which 

 the above formulae arc applied. AVe can conceive a second system 

 ''^'n with no translation and consequently no motion at all; we shall 

 suppose that •'^ is changed into >■',, by a dilatation in which the 

 dimensions parallel to OX are chang-cd in ratio of 1 to Z^-, the 

 dimensions perpendicular to OX remaining what they were. Moreover 

 we shall attribute eqnal charges to corresponding volume-elements 

 in /S and Sg- if then ('„ be the density in a point P of 5, the 

 density in the corresponding point 7^^, of ■% will be 



1 



Co = -J (>■ 



If a',ij,z are the coordinates of P, the quantities •'•', y', s', deter- 

 mined by (1), may be considered as the coordinates of Fq. 



In the system Sq, the electric force, which we shall call Cüg 

 may evidently be derived from a potential Wq; by means of the 

 equations 



(c. _ 9 '■''o «: _ 3 «0 , - 9 «0 



^w — ^ — r 1 ^ij'/ — — -1^7 1 'icic — — ^^ — r • 



■>■ ay OS 



