﻿992 Dr. J. R. Partington on the 



But e — '\jf ! l'N = \Q, the latent heat of vaporization per 

 molecule atT = 0; hence, with the substitutions £>V = N &T 

 = RT ; N w = M ; and \ = N \ ', we find 



log.*-- ^ + ?log.T'+§log.M + log« K Jg^ /2 , (15) 



where H = A 5 in the generalized space of five dimensions *. 



6. For a diatomic gas of the type considered in § 5, 

 0^ = 7/2, and hence 



logp(atm.) = - jJ^ + G p log T + 2*5 log M 



+ 2 log K+ 12-730. . (15a) 



(k = 1-37 x 10- 16 ; h = 6-55 X 10" 27 ; N = 6"06 x 10 23 ; 

 1 atm. = 1013250 abs. units. See Millikan, Phil. Mag. July 

 1917). 



The equation representing the vapour-pressure of a 

 diatomic substance at such low temperatures that the energy 

 of the condensate is negligible in comparison with that of 

 the vapour (which will generally occur before the gas begins 

 to lose its diatomic character, except in the case of molecules 

 of very small mass and diameter, such as hydrogen) is 



log e p = - ^ -f C p log, T + i, 



logXatm.) = - j^Tf + C P log T + C. 

 By comparison of (15) with these we find 



^2.51og e M + 2log e K+logv^ r ,^ ( (16) 



or C = 2-5 log M + 2 log K + 12-730. 



7. In the case considered, K 2 = r 2 , where r is the radius of 

 the molecule. For oxygen, r — l*8xl0~ 8 cm.f, M = 32, 

 hence Co 2 = 1*001. The four values given by Langen (loc. 

 cit.) range from 0*539 to 1*021, the mean being 0*829. In 

 the case of nitrogen, r = l*9xl0~ 8 cm., JV1=28, hence 

 Cn 2 = 0*904. Langen gives only one value for nitrogen, 

 — 0*05, from which one can perhaps only conclude that it is 

 somewhat less than the value for oxygen. The case of 



* The various methods of quantizing rotations are kept in mind. 

 t Jeans, ' Dynamical Theory of Gases/ 2nd edit. p. 34] ; all values of 

 r from this. 



