248,249] :.; ELECTROMAGNETIC WAVES. 519 



whose components are 



the energy-current-density. 



The equation (3) accordingly states that the quantity of energy 

 R is transferred per unit of time across the unit of surface tangent 

 to the direction of both the electric and the magnetic force. This 

 is Poynting's* remarkable theorem. 



It has been remarked by J. J. Thomson, Heaviside and Hertz 

 that this determination of the energy current is not the only 

 possible one, since we may add to the above vector any solenoidal 

 vector without changing the surface-integral in (3). Hertz has 

 also pointed out that, as this makes energy flow at all points where 

 fields of both kinds exist, it involves the continuous flow of energy 

 (in closed tubes) when a magnetic pole and an electrified point 

 exist in each other's presence. In many cases, however, the notion 

 of the motion of the energy here given is a very fruitful one. It 

 has been further developed in several papers by Wienf. The 

 vector R is sometimes called the radiant vector. 



249. Plane Waves. Let us again consider a perfect insu- 

 lator. The equations 247 (2) are all satisfied by any function of 

 the argument s = Ix + my -\-nz- at, where a = l/A Veyu.. 



(i) <f> = (f> (loc 4- my + nz at). 



For we have 







and therefore 



* Poynting, Phil. Trans. 2, p. 343, 1884. 



t Wien. "Ueber den Begriff der Localisirung der Energie." Wied. Ann. 45, p. 

 685, 1892. "Ueber die Bewegung der Kraftlinien im electromagnetischen Felde." 

 Wied. Ann. 46, p. 352, 1892. 



