[KING] NOTE ON THE COSINE LAW OF RADIATION 95 
3. In cases where the Cosine Law of Emission fails we conclude 
that it is not legitimate to replace the volume distribution of vibrating 
elements by a surface distribution over the boundary. We must, there- 
fore, examine departures from the Cosine Law in the light of the more 
complete expression (4). We notice first of all that for incandescent 
bodies for which x 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 reflection and refraction 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 should expect a considerably higher efficiency. 
It seems probable that the high efficiency 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 absorption theory. Fourier ! 
in his memoir on “ 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 
[fe IES 
K 
I is independent of the shape and size of the cavity, and also of the 
position of P in its interior. This result is employed by Fourier as a 
verification of the Cosine Law.? 
* Fourier “Chaleur,” Paris, 1822, p. 31, Chap. 1. The paper referred to is in 
Mein Acad. de Sc. V, Paris, 1826, pp. 179-213. 
? Fourier, loc. cit., p. 31, § 47. 
