200 On the Equation of State. 



In this connexion it may be pointed out that when v is 

 large in comparison with ¥, ¥ is the volume of the sphere 

 whose radius is the mean minimum distance between the 

 centres of two molecules during a collision. Bearing this in 

 mind and comparing equations (3) and (1), it will be seen 



that PI v — J is two-thirds of the mean kinetic energy of a 



molecule, and therefore 



Pfi' 



kt F¥ 2mY 2 



kt ^r~ + Y^ =1 d~2~ (4) 



The left-hand side of (4) with hv substituted for P// is 

 Planck's modified expression for the mean energy of a 

 resonator of period v. 



The distinction which is drawn above between thermo- 

 dynamic temperature and the kinetic energy of a degree 

 of freedom we regard as a provisional hypothesis which 

 needs to be more carefully examined. 



Note. — The above communication is a portion of a paper 

 written in January 1919. It has been kept with a view to 

 testing its practical applicability. However, in the corre- 

 spondence of the April number of this Journal, M. N. Shaha 

 and 8. N. Basu refer to a paper on the Equation of State 

 published by them in 1918 which had escaped our notice. 

 In this communication the authors deduce from the well- 

 known Boltzmann's entropy theory the equation 



m, v-2i> 



which (since 2b = ¥) is identical with the characteristic 

 equation deduced by us from apparently entirely different 

 considerations. This agreement in the final results of two 

 different modes of attacking the problem makes it desirable 

 that the publication of our method of obtaining the above 

 equation should not be further delayed. 



Jesus College and St. John's College, 

 Oxford. 



