t 414 ) 



axis of -, wliich passes (lirongli the point P, — — ^^ =z 0. 



.fc*"' 



111 this way, the electric force in the aetlier immediately l)efoi"e 

 the plate is found to be 



Its amplitude is 



(38) 



4 jr c^ r 



and that of the current (F^ within the plate 



rtj w* S/ 

 4 jr c' r 

 This must be equal to the expression (37). The solution of our 

 problem is therefore 



(39; 



4 JT (• I y/"2 k « (In 



"' = ^r\/^s^ 



In the preceding formulae Ö means the \olume of the portion of 

 the plate we have considered. Now, after having decomposed this 

 portion into a lai-ge number of elements of volume s, we may bring- 

 about just the same radiation by applying in each of these an 

 electromotive force in the directioii of OJi with the amplitude 



„^=t^\y^2s!i± (40) 



n V s 



provided only we suppose the electromotive forces in all these 

 elements s to be independent of each other, so that their jdiases are 

 distributed at random over the elements. 



Indeed, from the fact that the force whose amplitude is (39), 

 acting in the space S, gives rise to a radiation represented by (36), 

 we may conclude that an electromotive force with the amplitude 

 (40), when applied to the element s, will produce a flow of eiiergy 



^ s «J f- oi' dn 

 c r^ 

 across the element a>'. A similar expression holds for each elements 

 and, on account of the circumstance that the vibrations due to the 

 separate elements have all possible phases, we may add to each other 

 all these expressions. We are thus led back to the result contained 

 in (36). 



§ '14. Whatever be the nature of the processes in the interior of 

 an element of volume, by which the radiation is caused, they can 



