1196 



Let us at first only consider the exceedingly rarefied gas stale — 

 i. e. the planetary condition of matter — then t = 1 everywhere, 

 so that we may write : ^) 



s ^'a 



/dPr CdP, 

 — -e-^Py dr- | nr iVn r/ e-^Pr dr, (a) 

 dr J dr 



in which we assume that at the collision the distance of the mole- 

 cules remains = .* (no appreciable compression), and that also the 

 attraction extends only to a small distance from s, so that a mean 

 value r/ can be brought as a constant factor before the inte- 

 gration sign. 



In this Va is in any case to be supposed greater than s. For if 

 this were not so, and if the attraction only worked at an exceedingly 

 short distance .s' -f- (^ just before the collision, as is still sometimes 

 supposed, the virial of attraction would, for smaller volumes, be 

 subjected to the same volume distribution factor t^ as the virial of 

 collision ■ — with the consequence that the equation of state would 

 not contain tino distinct constants a and h, but only one, and would 

 assume the form p{v — i?) = RT. 



Critical phenomena — which can be explained theoretically 

 justly by the different behaviour of the two separate virial parts, 

 in this way that the factor t will have no or hardly any influence 

 on the virial of attraction for smaller volumes (as the middle value 

 T, can then always be assumed to be near 1), whereas it will exert 

 a great influence on the virial of collision (for v = vjc, where v = 3 

 or 2 times h, Xg will already have a value between 1,5 and 2) — 

 these phenomena would entirely fail to appear. For then there is 

 no distinction possible at all between the two constants a and b, 

 on account of which the equation of state can be brought in the 

 well-known form {p -\- ''/^^){v—b) =z RT (see also further below). 



It is, therefore, almost completely excluded that the attraction 

 should not take place until at immediate (or almost immediate) 

 contact of the molecules. For very small volumes (smaller than the 

 critical volume), where the centres of the molecules possess e.g. a 

 mean smaller distance (/) than r^, it may be expected that also the 

 virial of attraction will be somewhat influenced by the factor r, 

 so that a becomes dependent on v. But then we are already past 

 the critical point — where / = 6- 1^ 4 = 1,6 *-. (/•« will appear to 

 be not much greater than about 1,6 s). Hence the quantity a would 



1) Cf. also my Article in the Arch. Teyler (2) T VII, Troisième partie, 1901; 

 chiefly chapter X, p. 28—34. 



