Physics. — “On the Equation of State for Arbitrary Temperatures 
and Volumes. Ill. On the Law of Force between the Molecules 
of Mon-atomic Substances”. By Dr. J. J. van Laar. (Com- 
municated by Prof. H. A. Lorentz). 
(Communicated at the meeting of November 26, 1921). 
§ 8. General Considerations. 
In the two preceding papers *) it has been demonstrated that a 
closer consideration of the problem of the movement of a molecule 
to and fro between the two adjacent molecules (for the sake of 
simplicity reduced to a problem of one-dimension) necessarily leads 
at /ow temperatures to an expression of the form 
2A 
e= + Aal 
e RT — 1 
in which A represents the zero-point energy, i.e. the energy of the 
active forces, which remains when the temperature (determined 
by the time-average of w*) has become = 0 [loc. cit. p. 1198 (A is 
there represented by ZE) and p. 905]. 
If it could be proved that in this A —*/, Nhv, the analogy with 
Pianck’s formula would become identity. But to reach this, we 
should have to know the accurate law of attraction, i.e. a law 
which takes into account the motion in closed orbits of the negative 
electrons round the positive nucleus of the atoms. The prevalent 
laws of attraction have not taken this into account as yet; either 
because the integrability of the equations of motion required a 
simple — although still plausible — law of attraction, so that the 
accurate law had to be purposely set aside for one of a simpler 
form; or because in the derivation of the required law the influence 
of the said motion was (consciously or unconsciously) eliminated 
1) These Proc. Vol. XXI, N°. 9, p. 1184, and These Proc. Vol. XXIII, N°. 6, 
p. 887. 
