( 409 ) 



aciion" at llio j)oiiit P in tlie direclioii //. We ma}' represent it by 

 the S3' m hol 



a S <"■"' 

 and we may consider its intensity and its pliase to be determined 

 by the real part of \<\\ St?"". 



In a similar sense we can also conceive a "magnetomotive action" 

 existing in some point of the system. 



These definitions being agreed npon, equation (26) leads to the 

 following remarkable conclusions. 



a. Let there be, in the first of the two cases we have distinguished 

 in the preceding paragraph, an electromotive action a S e'"' at the 

 point P in the direction h, and in the second case an electromotive 

 action a' S't?'"' at the point P' in the direction 11' , there being in 

 neither case a magnetomotive force. Then the integrals in (26) are 

 to be extended to the infinitely small spaces S' and S and the result 

 may be written in the form 



(a' . ^P') S' = (a . e'p) 3 , 

 if we represent by (Jp' the current produced in P' in the first case 

 and by ^' p the current existing in P in the second. 



Hence, assuming the equality 



I a I ? = I a' I S' , 

 we conclude that 



(Sa'P' = €'/iP (27) 



The full meaning of this appears, if we write the two quantities 

 in the form 



^h'P' = ft e '■('"+•0 and (i'/iP = J^t' e K»^+-'') . 



Indeed, (27) requires that 



JLt = ft' , I' = 1?' , 



and we have the theorem : 



If an electromotive action applied at a point P in the direction h 

 produces in a point F a current whose component in an arbitrarily 

 chosen direction /i' has the amplitude ft and the phase r, an equal 

 electromotive action taking place at the point P' in the direction k 

 will produce a current in P, whose component in the direction h 

 has exactly the same amplitude ft and the same phase v. 



h. Without changing anything in the circumstances of the tirst 

 case, we shall now assume, that in the second the vibrations are 

 excited not by electromotive forces, but by a magnetomoti\'e action 

 a' S' «'"', at the point P' in the direction li . We then find 



- (a' . ép') S' = (1 . S'p) S, 

 ami, if we put 



