Physios. — " Deve/o/nnent of tke third viiidl coefficient f or material 

 points {erentiKilhj rigid spheres), ivhich exert central attracting 

 forces on each other proportional roith r^^ or y—^." By Prof. 

 W. H. Kkksom and Mrs 0. Nordstrom-van Lekuvven. ((/ommii- 

 iiicatioii N". 36 from the Lal)oratorj of PlijsifS and Physical 

 Cheiiiislry of the Veterinary College at Utreclit). (Connnuni- 

 cated by Prof. H. Kamkrlingh Onnks). 



(Communicated in the meeting of September 29, 1918). 



§ 1. Ill Conini. N°. 'Aa a general expression was found for the 

 third virial coefficient for material points (eventually rigid spheres), 

 which exei't central forces on each otliei', while as a special case 

 the value of 6' was derived from that foiinula for spheres without 

 attraction. As has been remarked already theie the value of C' found 

 for this case may at the same lime be considered as the first term 

 in the development of C according to ascending powers of T ' for 

 a law of force /• ''z+i) (potential energy i)roportional with /-'?). 

 In this communication some of the next terms of that develop- 

 ment into a series will be calculated for (/=4 (^2) and (/=5 (§3). 



§ 2. Development for rigid spheres ivith attraction proportioiial 

 loith 7'^. Instead of (17) of the preceding communication we now put : 



r/(r)=^ for T>r>,T (21)^) 



r* 



and develop the exponential factor in P, R, and *S according to (13) 



according to ascending powers of h, indicating the succeeding terms 



by indices. 



In the same way C splits up into: 



C=C,-^C,^ C\ . . . . . . (22) 



C, has been calculated already in Comm. NV 3r/ ^ 3, see e(pi. (20). 

 With a view to C, we must calculate: 



S, = 24 rr^ he ffiy-^-^ ''^ 4 '^ j dr, dr, dr,. 



The domain of integration is divided in the same way as in § 3 

 1) The equations have been" numbered in continuation of those of Comm. N". 3a. 



