174 Dr. L. Silberstein on Radiation 



atom. In connexion with this I should like to remark here 

 briefly, that the introduction of the above divisors is by no 

 means a purely mathematical artifice but seems to have an 

 obvious physical meaning. To see this, notice that assuming 

 e = e$. smut with e constant, i. <?. independent of n, is 

 equivalent to writing down the differential equation 



d 2 e 



d¥ !nV=0 ' 



and that using a set of the divisors in question is as much as 

 postulating, instead of this, a chain of equations 



d 2 e/dt 2 + n 1 2 e = e', 



d 2 e'idt 2 + n 2 2 e / = e / ', 



&c, &c, 



•ending, say, with e (m) = e {m) sin nt, where <? (wi) is a constant. 

 For this leads at once to 



. sin nt 



£ = const. 



(w 2 — iv{ 2 ) {w 2 — ic 2 2 ) . . . ' 



the supplementary oscillations of frequency n u 7i 2 , ... being 

 themselves irrelevant, since they are strictly self-contained 

 and thus do not contribute to the radiation of the source. 

 Now, a chain of differential equations of the above form is 

 suggestive of a linkage of entities otherwise unconnected. 

 I shall attempt to develop further these rapid remarks in a 

 later publication. 



Meanwhile let us return once more to the expressions (13) 

 and (14) for the mean energy and the rate of emission of the 

 electric source. Each of these is a function of \/a(_ = 2ir/w), 

 and contains, besides, a alone and e in its constant (or slowly 

 variable) factor. It is obviously interesting to consider the 

 ratio of emission to store of energy. Remember that U 

 stands for the mean energy of the whole source, while J is 

 the emission per (unit time and) unit volume of the sphere. 

 The period of oscillation being 2ir/n, define what might be 

 called the relative emissivity or the prodigality of the source by 



_ emission per period (2w/n) X vol. x J ( „. 



~~ mean store of energy ~ U ^ ^ 



By the definition (23), and by (13) and (14), we have, for 

 K= 1, and for any iv. 



