Fifth Fundamental Equation of Maxwell-Lore ntz Theory, 297 

 electromagnetic field 



curlH = 47rpu+ -^ (5) 



™ lE =~-cft ■•:-■"• TO 



div. E = 47r/> ........ (7) 



div. H = (8) 



If these equations are true descriptions of electromagnetic 

 phenomena, it is evident then by the first postulate of rela- 

 tivity that similar equations 



cnrlH' = 4wpV+* ~, ... (9) 



™ l * = -- e W> do) 



div. E' = 4*y>', (11) 



div. H' = 0, (12) 



must hold when the phenomena are described by an observer 

 moving with the system S'. 



It has been shown by Einstein that the following equations, 

 together with the kinematic relations (1-4) already given are 

 necessary and sufficient for transforming equations (5, 6, 7 

 and 8) into (9, 10, 11 and 12) *. 



E/=E* (13) 



E/=^=(^+>) (15) 



Hx' = H*. .......... (16) 



* For the purposes of this transformation, it is necessary to use not 

 only the simple kinematic relations (1-4), but also the following relations 

 which can be directly derived from them : — 



u.i — 



l _uxv> i( y UxV ' u% ~ UxV 



w (1-50 



, _ 9Ex' &Ey' ^' _ V 1 ""! 5 " / P 



p "" d*' ay d*' " (1-f) 

 Phil Mag. S. 6. Vol. 21. No. 123. March 1911. X 



