﻿Cosine Law of Radiation. 241 



by the element rfS, we have the familiar form of the Cosine 

 Law 



I = Io -"IT ( 6 ) 



§ 3. In cases where the cosine law of emission fails we 

 conclude that it is not legitimate to replace the volume dis- 

 tribution of vibrating elements by a surface distribution over 

 the boundary. Wo must, therefore, examine departures 

 from the cosine law in the light of the more complete ex- 

 pression (4). We notice first of all that for incandescent 

 bodies for which k is considerable, practically all the radiation 

 which reaches P comes from a very thin surface-layer, 

 perhaps only a few wave-lengths in thickness. We are 

 therefore justified in neglecting effects of reflexion and re- 

 fraction at the boundary, since these can hardly obey the 

 optical laws in so thin a transition layer. 



Formula (4) shows us to some extent on what conditions 

 the efficiency of a radiating surface depends. Practically all 

 actual means of exciting radiations in an incandescent body 

 depend on maintaining an expenditure of energy throughout 

 the entire volume, while the only portion of the body which 

 contributes to the intensity of the radiation at an exterior 

 point is an excessively thin surface-film. If it were possible 

 to concentrate the same amount of energy throughout this 

 thin exterior film, we shou'd expect a considerably higher 

 efficiency. It seems probable that the high efricienc}^ of the 

 phosphorescent light emitted by glow-worms and fire-flies 

 may depend on just such a surface-concentration of energy, 

 due in this case to chemical transformations at the boundary. 



It seems, remarkable that the Cosine Law of Emission 

 should not have hitherto been presented in the light of ab- 

 sorption theory. Fourier *, in his memoir on c Heat,' cites 

 a reference to one of his earlier papers, in which he probably 

 deduced the law along lines just given. It will be noticed 

 from (5) that the total intensity inside a cavity in an infinite 

 solid, or at any rate in one bounded by an exterior surface so 

 large that contributions from portions near the exterior are 

 small compared with those from portions near the cavity, is 

 given by AT 



1 = 4^. 



K 



I is independent of the shape and size of the cavity, and 



* Fourier, ' Chaleur,' Paris, 1822, p. 31, Chap. 1. The paper referred 

 to is in Mem. Acad, des Sc. tome v., Paris, 1826, pp. 1 7d 213. 



