122 Prof. H. A. Wilson on the 



number of "cells " into which the cether is supposed divided 

 for radiation of the wave-length under consideration. 6 is 

 a function of the temperature, and is the same for all the 

 different sets of cells. 



To determine the relation between 6 and the temperature 

 (0 on the conventional absolute scale we have Boltzmann's 

 expression for the entropy S = &log W, where W denotes the 

 number of ways in which the system can be arranged in its 

 actual state. Hence 



— =k-±-f ^ = /;log(l+ - 



an an \ n J 



for the system consisting of the n elements distributed among 

 N cells. If wis increased by unity, the increase of entropy is 

 e/t, so that 



f -***(!+ ;[)-«*. 



Itencc a 1 



Larmor shows that Xccl/X 3 and eoc 1/X ; so that lifter 

 multiplying by 1/A. to allow for the variation of d\ we get, 

 putting € = /w/X, 



(he \-i 



where C\ denotes the energy density per unit range of wave- 

 length and c the velocity of light. To get (o we can make 

 use of the value of e K for long wave-lengths calculated by 

 H. A. Lorentz and Jeans, viz., e K = S7rkt/\ i . Hence 



G \kt _ SttH . 

 X 3 he A. 4 ' 



so that r Q , . SirhrV *£ X" 1 



b=zb7rnc and e x = <b~[ eXkt — lf 



which is Planck's formula. 



Ne 

 In the formula ne= - kt ^ if we suppose e indefinitely 



diminished while X is kept constant, we get ??e = N&f, so that 

 the energy per cell is kt and is the same for all the sets of cells. 

 This is merely equipartition of: energy and corresponds with 

 e\ = S7rkt/\ i i It seems therefore that e cannot be made 



