599 



case for the development of 6' according to (15) and (13) we put 

 (p{r) = — 00 for r <^ r/ . . . . . . (16) 



Y(r) = for T>r>fT (17) 



with which case we have to do when we consider rigid spheres 

 with diameter o- which do not attract each other. We must then 

 obtain the same resnlt found for the tirst time in another way by 

 Jager ^) as a second volnme correction in van der Waals' eqnation 

 of state. Notwithstanding this the calculation based upon the general 

 expression (15) we have derived above, will be discussed here rather 

 in details, because the term obtained here may be considered as 

 the first of the development of C in ascending powers of h for 

 (f{r) = ci — y. The calculation of the following in the next commu- 

 nication may then be discussed more shortly. 



As also for /• ^ t (f{r) = 0, the quantity t must evidently vanish 

 from the resnlt. 



We easily find that for (([r) according to (16) and (17): 



where the quantities P and R have been marked with an index J 

 in order to indicate that these values are the fii-st terms in the 

 development in ascending powers of k for (/{>■) =z cr—'i. 



(18) 



For the calculation of *S'j = I I I 24jr^ >\i\i'„ di\di\di\ it may 



l)e 



m 



useful that 2.t I I -^* (lt\d}\ represents the space at the disposal of 



molecule 3, when of the set of three the molecules 1 and 2 have 

 already taken their places. 



The mutual distances may be thus numbered that 





Now two parts of the domain of integration must be distinguished : 



1. 2r>r,>r. 



The sets of three belonging to this part must still be subdivided 

 into: 



a. r, — T ^ (7, 



h. 1\ — x<^a. 



We suppose namely t ^ %i, so that the case r, <^ In need not 

 be considered heie. 



Let as consider in details case a : 



') G. Jager. Wien Sitz.-Ber. ['2u\ 105 (1896), p. 15, 97. Vov further literature 

 see H. KXmerlinüh Onnes and W. H. Keesom. Die Zustandsgleichuug § 40(i. 



