﻿•800 Dr. W. Wilson on the Quantum- Theory 



On substituting this value of Ep in (12) we find that 



(hv v phv 

 i- e -m) e -Ja (is) 



Therefore the law of distribution of the oscillators among 

 the different loci is precisely that given by Planck *. 



From (13) and (17) we deduce for the average energy of 

 an oscillator 



E=-^-, (19) 



e^-1 



a well known result in Planck's theory. It may therefore 

 be said that the proposed theory includes that of Planck (at 

 least in one of its forms). 



We may regard the aether as a collection of oscillators 

 which, through the medium of matter, exchange energy 

 with one another. The number of these, per unit volume, in 

 the frequency range between v and v + dv, has been shown 

 by Jeans and others f to be 



$7rv 2 dv 



where c is the velocity of radiation in the sether. The most 

 probable distribution of these oscillators among the loci men- 

 tioned above, i. e. the distribution corresponding to maximum 

 ■entropy, is one which makes their average energy 



hv 



liv ' 



and therefore we get for the energy within the frequency 

 range v to v-\-dv, 



Sirhv* dv 



U v dv= 



liv_ 



which^is Planck's radiation formula. 



Theory of Line Spectra. 



We shall now show that Bohr's % assumptions, in so far at 

 any rate as we restrict ourselves to the type of atom or 



* M. Planck, ' Theorie d. Warmestrahlung,' p. 139, equations (220) and 

 (227), second edition. 



t J. H. Jeans, Phil. Mag. x. p. 91 (1905) ; M. Planck, loc. cit. p. 175. 

 + N. Bohr, Phil. Mag. xxvi. p. 1 (1913). 



