13 



That for (f = ^f, the value of a becomes logarithmically infinite, 

 and does not get near exponentially intinite, as is (he case on 

 assumption of Bgi.tzmann's temperature-distribution factor (for 



f{a)=z{e —^):''/rt becomes of (he order e"^ for 7'=0), is 

 alread}' to be esteemed an advantage. But the above found logarKhinic- 

 allj infinite will lead to an ordinarj' finite rnaxinmni, when we 

 consider that only the very definite velocity u„, which causes (f (o 

 be =: M : { (lu^* = 1 : k\ leads to this log oo. When we (ake 

 Maxwell's law of (he distribution of velocities into account, the 

 adjacent velocities will not lead (o log go, and this will accwdiiigly 

 pass in(o a finite maximum. We shall come back to (his later on. 



We will, however, point out already here that (he logaridiniic 

 infinity for y ^ <ƒ„ is not bound to our special assumption (8) concerning 

 F{r). We shall see that (his /t>y-infinite value of a for 7 =7^, is 

 found on any supposition concerning F{r). 



But (he numerical values of (he quantities a^ and y in (14") e.g. 

 will of course be dependejit on the said supposidon. We possess a 

 kind of control for the case r/= 0, 7i = 1. According to (14") a.^ (hen 

 becomes = Vie '^'^ X il>g)^i(, because (1 — sn.) (hen becomes =: J ~7i, 

 hence (1 — en) : nil — ?//) = 1 : ?z (J -)- n) = 7.^. But according to (he 

 ordinary (statical) theory, (he attractive virial (see § IX) must be 



a 



A, r ^^^'■ 



= ^/^ :fi\n\r^ — dr. When a z= s, r' ^= s' can be brought before 

 J dr 



s 



the integral sign, and we have '/> iVjis' {I\.f^ = '/,.t N'ns' (0— (—.1/))= 



= 7»^ -^^-^^ X ^^J^ '■ V (as n = N : v). Hence we find wi(h MN = a for 

 a the value {l>(j)^ X "> so that (he factor by which we have to muhiply, 

 would have to be = l, and not ^ 716^" = ^'^l''^> ^s we have (bund. 

 In my opinion this conclusion can oidy be drawn from i(, that 

 even in the limiting case 7'=oo(r/=0) the fac(or of dis(ribution 

 at the molecule surface (the sphere of at(rac(ion is infinitely (hin 

 on the assumption a =z s) is not=:l, as we assumed above in the 

 application of the statical method, but slightly less in consequence 

 of the influence of the passing molecules, which does not disappear 

 even for n ■=. 1, which is the cause (hat the full maximum value 

 M of the function of force is not reached. And the difi'erence will 

 depend on the nature of the function of force used. 



For n = 0,6 the faclor of {bci)^(« will ge( the value 



2,467 X 0,483 1,192 , , 



t= = 1.55, which comes (0 this, (ha( (he attraction 



1,2 X 0,64 0,768 



