536 REPORT— 1902. 



Tlie problem Is usually attempted by first forming tbe virial equation for the 

 molecules, which may bo •written 



and endeavouring to evaluate the terms. 



The first may be taken equal to RT. The second expresses the collision of the 

 molecules, and is in general a function of v and T. The third expresses the attraction 

 of the molecules, and is also a function of v and T. In many cases equations have 

 been deduced in accordance with the law by making certain simplifications in the 

 assumptions mentioned, but more specialisation introduces more constants. 



The equations of Boltzmann and Reinganum are the most satisfactory at 

 present known. The cyclical equation of v. d. Waals endeavours to advance by 

 considering the virial oi' the atoms in tlie molecule, but it is implicit and leads to 

 some false deductions, e.r/., that b=f{v) only. 



The empirical method has been most completely followed by Kamerlingh 

 Onnes ^ from Amagafs 1803 values for IL, 0^, N,, CO.,. 

 It is given in the form 



Xpo = 2£.«+ ^ + ... + S, 

 Xo X^o^ X8oS 



where 



2C = ^(l + aH0,S = ^,r + 6„ + 63^ + /;, \,&c. 



X = ( -' ) P, Wj 1" are reduced p, v, t. 



Since V is here expressed in terms of the theoretical normal volume, the 

 equation agrees strictly with the law. It expresses with considerable exactness 

 the reduced isotherm from r = 12'29 to 0-897, and^ = 3,000 A^ to 1. 



2. A strict adherence to the law of corresponding .states for the deduction of 

 equations of state is quite arbitrary, and is only justified by its general appli- 

 cability and our lack of accurate knowledge. 



PT 

 The burden of the proof of the law "^ " = K falls upon the critical data which, 



as shown recently by Blatthias, are in general very uncertain, and no advance can 

 be made until better results are to hand. 



To form an opinion as to the theoretical causes of divergence the various 

 axioms used for the deduction of equations of state are considered, and some 

 possible directions of advance indicated. 



■ An extension of the law is needed if the value of K for argon can be taken as 

 anywhere near correct, for then the values of K would vary from 2-67, equal to that 

 of V. d. Waals' original equation, to more than 3-4, the value given by his cyclical 

 equation, and found experimentally for oxygen and nitrogen, 



3. The values of the critical constants depend largely upon the exact experi- 

 mental conditions, and even their theoretical meaning is questioned. 



De Heen, Galitzine, and Traube consider that under their conditions of 

 experiment the fluid is not to be treated as homogeneous, but as a mixture of 

 two species of molecules, and the composition of which depends upon the tem- 

 perature. The critical point is then merely a point where the two species can 

 mix in all proportions, and where a sudden transformation from one to the other 

 occurs. 



This assumes that liquid, or at any rate a meniscus, can be formed above the 

 critical point. 



A discussion of Traube's work shows that his theory is not in accordance with 

 his and de Heen's observations, even if these are considered as free from experi- 

 mental errors due to the neglect of certain precautions such as stirring. 



' Communications, Leiden, No. 71, June 1901. 



