( 413 ) 



^ J2. We shall first put (lie (niestioii what nuist be Ihc amplitude 

 <Ti of an electroniotive force aeting in the direetioii of OX with the 

 frequency ii, if this force is to produce, on account of the electric 

 vibrations parallel to OX, a flow of energy 



/e's a, P (I)' dn 



—, (36) 



across the element to' at the point P. Since this flow may be 

 represented by 



- c ¥ to', 

 2 



if h is the amplitude of (iJa at the point P, we must have 



ƒ 



i = — 1/2^-6 «1 dn. 



cr 



The amplitude of the current ^x = ^'x must therefore be 



^/ . 



— V2k ^a,dn. . . . . . . (37) 



At this stage of our reasoning we may avail ourselves of the 

 theorem of § 7, a. Indeed, if the electromotive force (iex in the part S 

 of the plate must have the amplitude a^ in order to call forth at 

 the point P a current ^x wiiose amplitude has the value (37), a^ 

 will also be the amplitude we must give to an electromotive force 

 ^•ea, acting in an element of volume S of the aether near P, if we 

 wish to bring about by its action a current with the amplitude (37) 

 in the plate. This is (he condition by which w^e shall determine the 

 value of «!• 



§ 13. The solution is readily obtained by means of the formulae 

 (18) and (16). If, in an element of volume S of the aether, <iex = a^ e"^^, 

 (iey = 0, €'e- =: 0, we sliall have 



4 .T r ^ 



and 



0-^ 1\x n"- 



X' c' 



as may be easily seen, if the equations 



1 



i> = ^-1 '7=1, '^x = in ?l.r 

 iji 



are taken into account. 



In the differential coefficients of ^^l^ we may omit all terms con- 

 taining the square and higher powers of -. Hence, in a point of the 



r 



