416 Mr. S. H. Burbury on Boltzmann' s Law of 



That is the difficulty. And if Boltzmann's theory of gases is 

 to be taken without modification, I see no mode of escape, 

 unless conceivably a gas in Boltzmann's state (e~ 2A x), and a 

 gas as in van der Waals' theory, though mathematically dis- 

 tinct, and each refusing to recognize the other, may exist 

 together in the same room. 



21. If instead of Boltzmamr's e"-* Sm ( tt2 +» 2+w2 ) we use my 

 form of Q in e _AQ , we have a possible limit at which the 

 mathematically abrupt change may take place, namely when 

 Q — 0, Q passing from positive to negative, as for suitable 

 values of temperature and volume it will do. As at constant 

 temperature we compress the gas, that change will, or may, 



occur before J~ becomes zero, that is before liquefaction 



jins. There will then remain a certain non-liquid con- 

 dition in which the law e~ 2hx no longer holds. And in this, 

 as well as in the liquid condition, the substance obeys van 

 der Waals. The " zweiphasen Raum "" of van der Waals 

 and Boltzmann remains with all its properties. 



22. The curve p —f(w) would, according to this theory, 

 have the same general form as it has in Boltzmann's diagram, 



Vorlesungen, Part ii. p. 45, but the " schief schraffirt " 

 portion would be bounded on the right, towards the greater 

 volume, by the curve Q = 0, instead of by the isotherm of 

 critical temperature. 



The difficulty exists independently of my. or any, modifi- 

 cation of Boltzmann's theory. All that my modification does 

 is to point out a possible escape from the difficulty. 



Concerning the Partition of Energy. 



23. As local variations of density may exist in a gas though 

 we cannot observe them, and may have physical consequences, 

 so also molecular streams may exist, though they may affect 

 only aggregates of neighbouring molecules too small to be 

 detected with the means of observation at our command. 

 Their existence is a necessary consequence of the inequalities 

 of density, and therefore of the law e~ 2h X. And if such 

 streams do exist, then it is not true that molecules of unequal 

 masses have equal mean energies of translation. The energy 

 which is equally partitioned is not the whole energy of trans- 

 lation, but only a certain definite portion of it, as shown in 

 my paper on the " Partition of Energy," Phil. Mag. December 

 1900. 



24. With regard to the energy belonging to other modes 

 of motion, of which I did not treat in my former paper, 

 Boltzmann, in his Vorlesungen, Part ii.., gives his proof of 



