14 



might be thought concenlrated at a distance .s'V^ ' 1,55 = 1,16 .9 from 

 the centre of the considered molecule (the sphere of attraction 

 extends between s and l,67.s' for n ^ 0,6). 



We saw ah-eady that rp represents the quantity l/:7aft*^u*- I" 

 this Uo represents tiie mean relative velocity with which the mole- 

 cules penetrate the sphere of attraction. But this velocity is augmented 

 by a certain amount within the sphere of attraction, so that ii„ will 

 not be in direct relation with the tempevsihu'e. For very lai^ge volumes 

 we may, however, entirely neglect tiiis slight modification in the 

 velocity in comparison with the much larger part of the path passed 

 over with the velocity z/^. Only for small volumes this is no longer 

 allowed, and in consequence of this new complications will make 

 their appearance. 



We may now write : 



_ ^1/ - _ MN _ « _ V, « 



because the mean square of the relative velocity is twice thai of 

 the square of velocity U^* itself, and Va '^^^^ '"«ly be written for 

 \'^ jLt A' f V- According to all that was developed above, 



i + v.^ + r.(^)'+...). . . . (.5-) 



may therefore be written for a, according to (14") — at least for 

 not too low temperatures, and when also higher powers of <f are 

 taken into consideration ; whereas for loio temperatures (7^ near 

 <f^ =i : k^) an expression of the form 



a = a,(^l-;i%V,|x 1 -^,^ .... (156) 

 will better answer the purpose, according to (14^). In this x = k'- X 7s ^' = 



= X Vs f(> i" which it should be borne in mind that the log 



1 — 7r 



is now negative, so that the minus sign before A becomes positive 

 again. 



We have already pointed out before that the supposition of an 

 exceedingly thin sphere of attraction, as is sometimes assumed, must 

 be entirely excluded for several reasons^). To this comes the circum- 

 stance that torn — - 1 the limiting temperature 7\, in which a will become 

 logarithmically infinite (or at least maximum), is given by q^ = 1 -. k^ = 

 = {1 — ?i'):?^^ which for ?i = 1 would give the value for (fo>^-^- 

 T= 00. And as it has been experimentall}' found that the said 



^) Gf. our first paper. 



