18 



to tlie passing molecules, and which, therefore, do not occur any 



more in (17). But in any case the difference is of no impoilance, 



as these terms, which are independent of .'/>, remain finite with respect 



to the term tiiat depends on '/, and logarithmically approaches infinity. 



(In the case yi = 0, where — for infinitely large spheres of attraction — 



the entire quantity a would become infinite, and accordingly our 



1 

 derivation is no longer valid, the fact that log''- - becomes infinite, 



n 



is of no importance at all). 



We will still point out that for (p =: r/„ a does not only become 

 logarithmically infinite with the form of f{r) assumed by us, but 

 with any arbitrary assumption about this. Compare for this Appendix C. 



We suppose in the second place in {\Q) (f near qd (i.e. 7' near 0). 



Foi' the integral in (16) we may then write, as (f becomes very 

 large : 



a an 



/di' /rt , ci-\ fdr a a f dr 

 — log -+l+i=^X-= — ^-^z^ , 



I.e. 



1 /a — \/a'—r-Y 1 / a— [^a'—i 

 log I = — I log 1 — log 



Vk^if—iy r Js \/Pfp-l 



a 4- \/a'—s' 

 log 



\/Pfp—l 



When the factor before the sign of integration is taken into 

 account we get therefore: 



r ^ cc\ 1 11 + ]/l—n' 



^ X (b,)^ « X T7== % • (18) 



T^OJ n{l-n'-)-'"^ \/¥^^ 



This approaches therefore, when (p approaches oo (J' approaches 0). 

 We may write for k"^ ip — 1, after substitution of the value for fp, 



the expression ^ ~5~r7; — ^ ^^ s"^^^' ^'^''^^'^ ^ '^ "^^^' ^• 



Hence after the maximum for a at </ = fp^ the attraction steadily 

 decreases, and disappears at 0° abs. This result was to be foreseen. 

 In the original integral of the virial of attraction the radical quantity 

 in the denominator becomes namely = cc at 0° abs., when </ becomes 

 = 00. This radical quantity expresses the relative increase of velocity 

 in the sphere of attraction, and as this increase remains finite with 

 respect to u^ = 0, the relatin' increase will become infinitely great. 



