( 793 ) 



11 h 



qiiaiitilv "^ we lla^■c niiide .i siij>iK)si(ioii \\ liicli oiilv holds wlicn 



8 r 



nei>IectinQ: (lie terms with — , 



r 



We must further add to the luimerator the xohnue of' the distauee 

 spheres, lying within other distance spheres, which ([uajitity has heeu 

 twice instead of once subtracted in the term 'Ih. We get then 

 the form 



11 6 b-' lP> 



1 --- + i^ -+.... + A^- 

 8 v v V» 



' h lib' b' b» ^^ ^ 



V lb v' v^ v'i 



where 7i is a linite number; for a point cannot lie in more than a 

 finite number of distance spheres at the same time ; as van Laar ') 

 has made probable, in not more than twehe. We must however 

 keep in view, that the quantity r which occurs in (?, does not 

 represent the ro/ume r but the available volume and that this quan- 

 tity would therefore have to be determined from the equation of 

 the ))''' degree: 



17 b' b' />« 

 v„ = r — 2^ H + C, — . . . . iV, 



There is not much to be said about the coel'ticients, occurring in 

 the quantity ji. As Boltzmaxx ^) has shown they need not change 

 their signs, on account of the circumstance mentioned by him, as 

 we should expect if we did not take this circumstance into account. 

 So is e.g. as Boltzmann lias shown, (_\ not negative, but positive. 

 For the present there is not much chance that further coelllicients 

 Avill be determined on account of the exceedingly lal)orious calcula- 

 tions, which would have to l)e carried out. Yet formula (4i may 

 already in this form be of use for the (|uestion of the derixation 

 of the equation of state. 



ij The developmenis of Boltzmann's theory of Gas, p. 148 et seq. ftirllier con- 

 tinued, lead to the same form. 

 ■^) Arch. Tfa'ler (2) VII last page. 

 »; These Proc. I p. 3'JU. 



