Physics. — "Oji the Course of the Values of a and b for 

 Hydrogen at Dijf event Temperatures and Volumes'. II. By 

 Dr. J. J. VAN Laak. (Communicated by Prof. H. A. Lorentz). 



/ (Communicated in the meeting of Jan 2(ï, 1918). 



IX. Influence of the field of force according to Boltzmann. 



When we substitute the value 



dN = 4.T r' dr X e-^f^r X r X ^ 



in the general Virial formula 



r dP, 



pv = RT — ^ 2 r/{r) = RT — ^ N \ dN r -— 



for dJSf, the number of molecules in tlje spherical sliell between 

 r and r -\- dr round the molecule under consideration, then pv 

 becomes : 



rn 



r dPr ,^ , 



pv = RT -- I JT N?i rr' e-^Pr dr. 



J dr 



s 



In this P,. represents, therefore, the function of force in the points 

 at a distance r from the centre of the considered molecule (thought 

 spherical), so that f{r) = dP, : dr. The integration extends from 

 r := s (the distance of the centres of two molecules — thought in- 

 compressible at the collision, so that s represents the diameter of 

 the molecule) as far as the field of force extends outside the mole- 

 cule {r = rn). 



The factor e-^^r is the well-known Boltzmann temperature "distri- 

 bution factor" under the influence of the field of force. The para- 

 meter 6 is = N^: RT, in which ^represents the total number of 

 molecules in the volume v, so that N=^nv, when n represents the 

 number of molecules in the unit of volume. 



The other factor t is the volume distribution factor. For r=s 



(at collision) T5 = will be =: (see further below), which will 



hg V — b 



approach to 1 for v =: 00 , as this fictitious quantity b then becomes 



= bg. For r =cc t is =1 1 for all values of v. But already at a 



short distance from the considered molecule t can be put = 1. 



