Statistical Relations of Radiant Energy. 649 



of that state. By means of a priori considerations of this 

 nature, Planck has been guided to an expression for E A of 

 the form 



E = Cl ^ C 



x 5 if. 



f AT -i 



which corresponds exceedingly well with the empirical law 

 deduced from the experimental data. His considerations, 

 however, involve, as Lorentz points out, the assumption of a 

 finite atomic structure for the energy in radiation. 



In the hope of elucidating the difficulties in this mode of 

 formulation of the problem, JRayleigh* and Jeans f have 

 applied the same fundamental argument, but in another and 

 more direct manner. Th^se authors have examined the 

 partition of energy among the various oscillatory degrees of 

 freedom of a mass of some elastic substance enclosed in 

 perfectly reflecting walls. After the number of possible 

 modes of oscillation has been counted, each of them is re- 

 garded as corresponding to a possible degree of freedom in 

 the ordinary dynamical sense, which can share equally well 

 with all the degrees of freedom of other types in the general 

 distribution, so that in the steady chaotic distribution of the 

 vibrations in the medium the amount of energy associated 

 with each period is the same. In this way a formula is 

 obtained for <f> which gives E x in the form 



E,=CT§, 



a result which is not only in total disagreement with experi- 

 mental facts, but also with ordinary common sense. 



Thus, on the one hand, we find that the result deduced 

 from ordinary considerations is too absurd to be correct, 

 whereas, on the other hand, a theory which is based on a 

 very doubtful hypothesis leads to a result which if not 

 actually correct is nevertheless so closely in agreement with 

 experiment that it may for the present be so regarded. The 

 following considerations, evolved in an attempt to obtain 

 greater consistency in the general treatment of the statis- 

 tical aspect of this problem, will show, however, that the 

 two points of view are in reality not so much opposed to one 



* Lord Rayleigh, " Remarks upon the law of complete radiation," 

 Phil. Mag. [5] xlix. p. 539 (1900). 



f J. H. Jeans, " On the partition of energy between matter and aether," 

 Phil. Mag. [6] x. p. 91 (1905). 



Phil. Mag, S. 6. Vol. 2$. No. 167. Nov. 1914. 2 U 



