396 BFJ.L SVSTE.\f TECHSICAL JOL'RX.U. 



It will be noted that there are only two lieUl vectors, E and B. 

 instead of the usual four vectors E, D. B, H, where D = kE and 

 B = iiH, and that the constants of the medium k and /u do not explicitK' 

 appear. This formal sim()lification is effected !)>• taking as the current 

 densii\' 



u = u + -|7+ curl M 



where u is llic condiiclinii currc-iil (Kmisjix , P i^ the pnlarizatinn, 

 defined as 



P = ^-^E, 



and M is licfmi-d 



47r u 



The equation of continuity 



1 a 



d,vu=-^--p 



iheii dcLerniines the charge density p. 



The advantage of this formulation is thai E and B tan now he 

 expressed in terms of the retarded scalar and \ector potentials <l> 

 and A. as follows: 



E=- . ^.'^-v*. 



whcTt 



B = curl A. 



*=/^Ji:i^)dv, 



u{t-r/c) , 



r 



The notation p(7 — r V) and U{t — r,c) indicates that p and U are taken 

 not at time / but at time l — r/c in e\aluating the integrals. It will 

 be obser\ed that with p and U defined as above, all effects arc trans- 

 mitted with the velocity of light, indeix'ndently of the characteristics 

 of the medium, a point of view in accordance with the modern dexelop- 

 meiit of electromagnetic lheor\'. 



