636 



Physics. — The second virial coe/jicient for rigid upherical molecules, 

 'whose mutual attraction is equivalent to that of a quadruplet 

 placed at their centre". B3' Dr. W. H. Keesom. Supplement 

 No. 39a to the Cominnnioatious from t lie Piiysical Laboratory 

 at Leiden. (Comiimnicated by Prof. H. Ka.merlingh Onnes). 



(Communicated in the meeting of September 25, 1915). 



^ J. Tliis Communication forms a continuation of the investi- 

 gation started in Suppl. N". 24 f April 'J 2, these Proceedings June 

 'J2), tlie aim of which is to derive, on different suppositions concern- 

 ing structure and mutual interaction of the molecules, the first 

 terms in the development of the equation of state into ascending 

 powers of v~^ as functions of the temperature, in order to compare 

 them with the available expei'imental material. It is obvious that 

 in this problem it is indicated to proceed step by step from the 

 simplest to more complicated suppositions. 



In Suppl. N°. 246 § 6 the second viriai coefiicieni, i. e. B in the 

 equation of state : 



f B C \ 



was derived for rigid spheres of concentric structure, which carry 

 a doublet at their centre, or whose mutual attraction is equivalent 

 to that of such doublets. In a following paper it will be shown 

 i. a., that the limitation to molecules of concentric structure, observed 

 there, can be omitted as far as concerns the derivation of B. 



'In Suppl. N". 25 (Sept. '12) I then showed that the way in which 

 the second viriai coefficient of hydrogen between — 100° and -|- 100° C. 

 depends on the temperature agrees with that which was derived 

 for doublet-molecules of that structure. 



Meanwhile it has, however, become evident especially by Debije's ') 

 investigation concerning dielectric constant and refractive index, that 

 the molecules of the diatomic elementary gases do not possess a 

 moment such as that of a doublet. The next step in the theoretical 

 development of the equation of state now seems to be, that the 

 next term of the development of the attractive potential outside the 

 spherical molecule into spherical harmonics, i. e. that of the degree 

 — 3, is considered to be present alone. The corresponding surface 

 harmonic of the second order reduces to the zonal harmonic of the 

 second order for diatomic molecules, which in this paper as in Suppl. 



1) Cf. P. Debije, Physik. ZS. 13 (1912), p. 97. W.' G. Mandersloot, Ttiesis for 

 the Doctorate, Utrecht 1914, p. 56. iN. Bohr, Phil. Mag. (6) 26 '1913), p. 866. 



