Kinetic Theory of Gases. 787 



where jo is the pressure, v the volume, k the gas-constant for 

 one molecule, N the number of molecules, and /(T) is a 

 function o£ the absolute temperature T which can be calcu- 

 lated exactly. Now it is precisely in this form that 

 Kamerlingh Onnes has prepared his extensive data on tbe 

 equations of state of the simpler gases. Actually * he 

 assumes tbe form 



^.A+5 + C + C + S F ... (2) 



J. V V Z V* IT IT ' 



and determines A, . .., F as functions of T to fit the obser- 

 vations. The coefficients A, ..., F he calls tbe first, second, 

 etc., virial coefficients. It is clear that when the observed 

 second virial coefficient B is obtained in this way it is 

 strictly comparable to the calculated /(T) of equation (1). 

 Moreover, it appears to me that nothing much less than the 

 -exhaustive numerical analysis of Kamerlingh Onnes allows 

 a legitimate comparison between theory and experiment to 

 be made. 



Such comparisons have already been made in certain cases 

 and on certain assumptions by Keesom (loc. cit.), hut without 

 consideration of the corresponding viscosity data. I hope 

 to take ui) the question in detail in a future paper. For the 

 present I must content myself with the following obser- 

 vations. Keesom finds that the observed and calculated 

 second virial coefficients for Argon, between the absolute 

 temperatures 123° and 293° on the centigrade scale, can be 

 reconciled on the assumption that the argon atom behaves 

 like a sphere of diameter, cr = 3*29xl0~ 8 cm., surrounded 

 by a field of force $(?') = a?* -5 , of such intensity that the 

 work IT(cr) done in separating two molecules from contact 

 (r=.(r) to infinity is 1*63 X 10 -14 erg |. The exponent 5 is 

 a little doubtful, but is probably better than the exponents 

 4 or 6 and presumably better than any other integral 

 •exponent. 



These values of a and <j>(r) correspond to definite values 

 of b (van der Waals') and S, Sutherland's constant. The 

 values of b and o~ are related by the well-known formula 



J = |7rNa 3 , .'..... (3) 



* Kamerlingh Onnes, Proc. Sect, of Sciences, Amsterdam, vol. iv. 

 p. 125 (1902), or Communications Phvs. Lab. of Leiden, No. 71. 



t Keesom (loc. cit. p. 646) gives 146xl0~ 14 , but this is based on the 

 incorrect value 6'85xl0 23 for Loschmidt's number. I have reworked 

 ihe calculation with the more recent figure 6 - C6xl0 23 . 



3 E 2 



