( 418 ) 



If (lie system of bodies is entirely shut olf from its surroundings, 

 the equality of the mutual radiation between any two elements 

 implies that the state is stationary. 



In order to show this, we fix our attention on one particular 

 element s, denoting all other elements by s'. By what has been 

 said, the sum ?t\ of all quantities of heat which s receives from 

 the elements s' will be equal to the sum n\ of the quantities of 

 heat it gives up to them. But, if the system is isolated from other 

 bodies, each quantity of energy lost by s will be found back in 

 one of the elements s'; )f\ is therefore the total amount of energy 

 radiating from s and the equality n\ = w, means that s gains as 

 much heat as it loses. 



^ 17. We shall finally assume that the system contains a certain 

 space which is occuj)ied by an isotropic and homogeneous body L, 

 perfectly transparent to the rays ; we shall examine the electro- 

 magnetic state existing in this medium, if all bodies are kept at the 

 same temperature. To this effect, we must begin by a discussion of 

 the radiation that would take place, if the body L extended to 

 infinity, and if it were subjected to an electromotive or magneto- 

 motive action (§ 7) at a certain point 0. 



A perfectly transparent body is characterized by the absence of 

 all thermal effects. This means that the coefficient « is zero, as 

 appears by (30). We have therefore 



P = -i^. (46) 



the coefficient q being real and positive, and the equation (17) becomes 



v=^c\/fqn, (47) 



I shall take here the positive value. 



Let us first apply to an element of xolume S at the point 0, 

 which I shall take as origin of coordinates, an electromotive force 

 ^\_^=zae"'', but no magnetomotive force. Then 



aS Ut--\ 



% = ^ e^ ''\ "il, = 0, ^^1, = 0, £1 = 0. 



4 .T r 



What we want to know, is the amount of energy radiating from 

 0, i. e. the How of energy through a closed surface surrounding 

 this point. In calculating this flow, the form and dimensions of the 

 surface are indifferent; we shall therefore consider a sphere with 

 as centre and with an infinite radius r. 



Then we may omit all terms in ^" and -C» containing the square 



and higher powers of -, and we find from (15) and (16), attending 



