﻿170 Mr. Gr. H. livens on Lorentzs 



It would, however, appear more probable that it is the 

 formula for a that is at fault* and not KirchhofF's more 

 general law, the truth of which can hardly be doubted. It is, 

 however, in any case interesting to notice that although the 

 formula for a adopted above may not be exact, the formula 

 necessitated by KirchhofE's law in combination with the 

 above analysis provides an interesting verification of its 

 general form. 



In any case, however, we may conclude that for all prac- 

 tical purposes the complete radiation formula applicable all 

 along the spectrum is given by the usual Rayleigh- Jeans 

 formula 



-cv-v t\* S7rmu m 2 

 * {\ - 1 ) = ^4- > 



as Lorentz predicts, a formula which is, however, only phy- 

 sically applicable in the extreme ultra-red part of the 

 spectrum. 



But this general conclusion is utterly absurd both from 

 a mathematical and a physical point of view, and it therefore 

 appears that some fundamental error has been committed 

 either in the physical assumptions made or in the mathe- 

 matical analysis based on these assumptions. 



It is very difficult, if not quite impossible, to indicate any 

 steps in the above analysis about whose mathematical rigour 

 any doubts can be raised, but it is worth noticing that the 

 final result obtained is not consistent with the preliminary 

 assumptions, inasmuch as the Fourier series initially assumed, 

 which can have no meaning unless it is convergent, ulti- 

 mately turns out to be divergent, so that the theory would 

 appear to lead to a result which is ultimately a contradiction 

 in terms, or, at least, apparently so. Some light is, how- 

 ever, thrown on this question by an examination of the 

 physical basis of the theory. 



The one advantage possessed by the present form of theory 

 over Lorentz's original form is that the number of physical 

 assumptions on which it is based is reduced from two to one, 

 so that it is now possible to determine the actual extent to 

 which the physical basis of the theory is responsible for the 

 result obtained. We have merely assumed that the duration 

 of every collision of an electron with an atom is vanishinglv 

 small compared with the other periods involved in our 

 analysis, and as long as this assumption is justified our 

 result must be correct. But, as a matter of fact, in actual 



* This probability is fully borne out by a more detailed investigation 

 of the question as to the proper expression for o\ 



