and Electromagnetic Theory, 349 



typical form r~~}f(r — Vt). The quantity R is the required 

 denominator and for points xy z and dy l z\ 



R 8 =(l-2p 8 )2(a?-*') J + (SiJ(a?-^)) 3 . 



R is not altered by interchanging oc and x' and also not 

 altered by reversing the sign of [pqr) or (nvw). Hence 

 with this denominator the last section of (64), that con- 

 taining cross-products, disappears in integration. At the 

 same time it would seem impossible to ignore the part of the 

 scalar potential due to i x ..., in determining the potential of 

 any conductor which may be in question, unless %p¥ = or 

 2p» z =0. In that connexion this special case is important. 



When the whole solution is expressed in terms of t/t, F , 

 G , H , it stands 



(1R*. dG , dilr d\jr ^ /1 v 9 .dy)r d ^ ^ 



v M 2 .d^r dyfr d-dr f d d d\ 1? 



a -(-«5+ ^4 -« r a5) H »-(-* r sr« r ;| +r=7 l) G J 



in which form the seolotropic character of each solution 

 plainly appears. 



§ 19. There is an important difference in the energies 

 attached to the two solutions, the scalar solution with p, \]r 

 and the vector solution with i x ...'F Q ... In the solution for 

 charge p essentially determines X... (in a dielectric KX,...), 

 though the motional form is given by the intervention of 

 other variables. The solution is therefore momentul in 

 character, and for it we write 



P=-^, and E=S-2«^=S+T. . (66) 



In the solution for current i x ... essentially determine a/..., 

 that is quantities with the character of velocities, and for 

 this solution we write 



JW fits' 



P=^, and E'=S' + 2tt^-=S' + T'. . (67) 

 du du v ' 



The various quantities refer to integrated results. The dis- 

 tinction is valid apart from any translation, i. e. there is 

 always a distinction between KX and X or between Ma and 

 a, although it may be lost sight of when K and M are 

 each written = 1. 



If we consider the charge alone, we have a' = j3' = y' = ; 



