Statistical Relations of Radiant Energy. 663 



collocation, whereas Larmor's cells representing receptacles 

 of elements o£ disturbance are of equal opportunity among 

 themselves, but are differentiated from each other by the 

 relative size of the energy element which becomes attached 

 to the element of disturbance when it gets into the cell. 

 The two points of view may ultimately be the same, but the 

 one I have adopted appears to be more consistent with the 

 preliminary discussions given in the former part of this 

 paper. 



The one difficulty involved in Larmor's scheme is that the 

 fundamental constant k is to be taken different for the mole- 

 cular and oscillatory coordinates ; but this difficulty is pro- 

 bably unavoidable until a complete and unassailable specifi- 

 cation of the mode of counting the probability applicable to 

 every part of the system is obtained. In the above mode of 

 formulation I preferred to retain the one constant k, and 

 have therefore thrown the existing doubtfulness over on to 

 the calculus of the probability, an ultimately hypothetical 

 procedure, which is, however, to a certain extent justified by 

 my preliminary discussions. 



7. Conclusion. 



In conclusion it may be of interest to again notice how it 

 appears that the special characteristics of radiation in its 

 present aspects are governed entirely by the necessary analy- 

 tical restrictions involved in the possibility of resolving the 

 irregularities in steady thermal radiation into its harmonic 

 constituents by a Fourier series, and are in no way connected 

 with any special or peculiar physical structure of the mole- 

 cule, electron, or sether. It may be considered difficult to 

 understand how it is that the indefinite fact of convergence 

 could lead to any definite result such as is actually obtained. 

 It must, however, be insisted that nowhere is this asserted to 

 be possible. All I have attempted to do is to show that a free 

 interpretation of the simplest suitable test of convergence 

 can be shown to lead to a formula which is identical with 

 Planck's in probably all attainable regions of the spectrum. 

 After all, the simplest test is probably the correct one to 

 apply. It is, however, interesting to notice how the simplest 

 known test of convergence, when applied as above, corre- 

 sponds to the law of equi-partition for the finite parts of the 

 system. This test, therefore, fails in the case of radiation 

 probably because there are an infinite number of different 

 coordinates in any finite region of the spectrum : and we 



