19 



And this relative increase of velocity entirely determines the density 



in the sphere of alti-action, which is in inverse ratio to it. 



We observe once more here, that the earlier Boltzmann theory 



would give an exponentially Infinite value for a at 0° abs., whereas 



in reality it is = 0. 



1 X I j/j ^s 



For ?;=:! {a=zs) the limiting value of ^ will be =: log = 



= ,/:; -,- With /, , in V^k''(p—1 (see above) this becomes 



1 : n, so that then a will approach (^V)(»"X|/'^ • 



For 72 = {a great with respect to .s') the absolute zero coincides 



with the limiting temperature, given by (f^z=zl'.]c=i[\ — n''):?i^. 



1 1 2 



For then (fo^co (7'j=0). In (J 8) Lijyi _ log becomes further = —log—, 



n n ' 11 



12 1 



so that then a will approach {o,l) n X — l^^i —X , which 



V RT 



again becomes = for ^=0, so long as n is not absolutely =0, 

 which of course would be practically impossible. 



Summarising we can therefore state, in agreement with the above 

 developed exact theory concerning the quantity a for very large 

 volume, that a, from a limiting value at T = oo, steadily increases 

 to a maximum value at T =z T^, after which it decreases again, 

 till a has become = at the absolute zero. The mentioned limiting 

 temperature T^ is then determined by Rl\ = '^/^ a : ff^, in which 

 (f^ = (1 — n'') : n^. (/i = s : a, in which s represents the diameter of 

 a molecule, and a the radius of the Sjthere of attraction). For H.^ 

 1\ is about =:^7^i, the ratio of the values of a^, ajt, and a^ being 



In the next paper we shall briefly discuss the influence of Maxwell's 

 distribution of velocity, and then treat the course of the quantity 

 b from T = cc to 7'=0, likewise at large volume. Then the values 

 of a and b for small volumes will be considered, so as to make a 

 complete theoretical insight possible concerning the mliole course of 

 a and b along the boundary line, both along the vapour branch 

 and along the liquid branch. 



Fontanivent, January 1918. {To be continued). 



2* 



