Physics. - "Deduction of the third virial coefficient for material 

 points {eventually for ricjid spheres) j lohich exert central forces 

 on each other". By Prof. W. H. Kkksom and Mrs. i). Nordström- 

 VAN Lekuwen. (r-ommuiiication N". 3^? from (he Lal)oraton 

 of Physics and Physical Chemistry of the Veterinary College 

 at Utrecht). (Communicated by Prof. H. Kamkrlingh Onnks). 



(Gommunicaled in the meeling of September 29, 1918). 



§ i . introduction. This paper contains a continuation of the research, 

 started in Supplement N". 24(ï of the communications from the 

 physical laboratory at Leiden (These Proceed., June 1912), in which 

 the existing data on the virial coefficients B and C in Kamehmngh 

 Onnes' ') empirical equation of state*) 



i B C D E F\ 



/>^' = ^ 1 + --+-!+ -, -f -^ + -^ . . . • (1) 



I V V V V V \ 



were compared with formulae, which can be derived for those 

 virial coefticients starting fiom different hypotheses on the structure 

 and mutual actions of the molecules. 



In the preceding*) papers on this subject especially the second 

 viria! coefficient B was considered. In the present communication 

 the third virial coetiicient 6' will be treated. To that purpose there 

 will be derived in § 2 a general expression for this third virial- 

 coefTicient for material points (eventually rigid spheres) which exert 

 central forces on each other. In § 3 (' is calculated for the case 

 that the molecules (rigid spheres) do not attract each other. The thus 

 obtainea value is at the same lime the first term of a series of 

 ascending powers of T -^, in which (' can be developed for the 

 case that the attraction between the molecules varies with the 

 distance according to a law r - 9-t-i> (potential energy proportional to 

 7 — ■?). In Comm. N°. 36 the development will be given for the next 

 two terms of this series foi' the laws of force i — ^ and r^ ^. 



These calculations had already been started, when the importaiu-e 



i)"H. Kamerlingh Onnes. Comm. Leiden N". 71; These Proceed. June 1901. 

 Comm. N'\ 74; Arch. Néerl. (2) 6 (19Üli, p. 874. 



») Gomp. H. Kamerlingh Onnes and W. H. Keesom. Die Znstandsgleichung. 

 Math. Enz. V 10. Leiden Suppl. N<>. 23 (1912), § 36. 



») VV. H. Keesom. Comm. Leiden Suppl. N". 246 (These Proc. June 1912i, 

 25 (Sept. 1912), 26 (Oct. 1912), 39a (Sept. 1915), 396 (Oct. 1915), W. H. Keesom 

 and Miss C. van Leeuwen, Leiden Suppl. N". 39r (March 1916i. 



