On the Equation of State. 197 



to the action of monochromatic light, do not belong to the 

 absorption spectrum of monatomic iodine. 



Prof. Joseph Wierusz Kowalski has lent us some apparatus 

 and assisted us in a most generous manner; the same did our 

 colleagues from the different physical laboratories of Warsaw. 

 It may be permitted to express here to those gentlemen our 

 best thanks. 



A great part of the expense was covered by a subvention of 

 the Mianowski foundation. 



Warsaw, State Technical School, 



foimded by H. Wnwelberg and S. Rotwand. 

 January 1920. 



XX. On the Equation of State. By M. P. Applebey, M.A., 

 Fellow of St. Joints College, Oxford, and D. L. Chapman, 

 M.A., F.F.S., Fellow of Jesus College, Oxford*. 



IT has long been known that Clerk Maxwell's law of the 

 equipartition of energy between the degrees of freedom 

 cannot hold for the molecules of gases. The specific heats 

 of solids at low temperatures prove that the translational 

 kinetic energy of the atoms is not subject to the law, and 

 even the energy of free translation of the atoms of helium 

 has been shown to fall below the theoretical value 3/2 H at 

 high pressures and low temperatures f: We are therefore 

 no longer justified in assuming that the mean kinetic energy 

 of translation of a molecule is proportional to the temperature. 

 Apparently the dynamical definition of temperature must be 

 abandoned. 



The best known equation of state is that of Van der Waals. 

 It does not accurately represent the behaviour of gases ; but 

 this was scarcely to be expected, since in its deduction it was 

 assumed that the volume occupied by the molecules is small 

 in comparison with the volume of the gas, and the quantities 

 ci a ,f and " b " were taken as constant, whereas it is probable 

 that these magnitudes vary with the temperature and density 

 of the gas. On theoretical grounds, however, it seems to us 

 that fewer objections can be urged against Van der Waals' 

 equation than might be raised against other equations of state 

 which are in much closer accord with the facts. 



Van der Waals in deriving his equation assumed that the 



* Communicated by the Authors. 



t Eucken, Bar. Deutsch phys. Ges. xviii. p. 4 (1916). 



