﻿Partition of Energy and Neivtonian Mechanics. 391 



components of the radiation with wave-lengths differing only 

 inflnitesimally from X arise from the large number N of 

 vibrators. Their total energy E must, according to Planck's 

 law, be given by 



eke — 1 



he 

 where e= — , h being Planck's constant. Eliminating the 

 A, 



temperature between this and the equation 



we get 



= - ior 



5E-e lJ "( 1+ l)' 

 which gives on integration 



w[(N + 5),„ g ( S+ 5)-5io g !]. 



Thus on the usual bases of probabilities 



logW= [(N+5)log(s + f)-f logf], 



whence using P= — and with Stirling's approximation, 



'N + P^ T 



VV — V, ^ j 



Thus on the basis of our previous measure of probability, 

 we see that the space occupied by points representing the 

 system with coordinates corresponding to these vibrations 

 with their total energy between (E — \e, E + ^e) has a 

 volume 



V, 



[cS £Lf. 



If we made e infinitely small, as we should generally be 

 entitled to do, this formula reduces to 



V N = C'E% 



unless of course, Ne is comparable with E, in which case no 

 such simplification is possible. 



In any case, however, it appears to be quite impossible. 

 owing to our lack of knowledge regarding both ct s and X. to 



