Physics. “On the Equation of State for Arbitrary Temperatures 
and Volumes. Analogy with Planck's Formula.” 1. By Dr. 
J. J. van Laar. (Communicated by Prof. H. A. Lorentz). 
(Communicated at the meeting of November 27, 1920). 
§ 7. Some Notes to § 1—6. 
It will be soon two years ago that I wrote thé first part of this 
Article’); studies of various kinds prevented me from continuing 
the subject, and not until now could I take it up again. 
Before I proceed to the derivation of the equation of state, based 
on the found general expression (6) on p. 1194 loc. cit. for the 
time-average of the square of velocity w,’, expressed in w,* (in which 
u, represents the velocity with which the considered molecule passes 
the neutral point in its motion to and fro between two neighbour- 
ing molecules), I will add a few remarks to elucidate and complete 
what was treated before. 
1. In the first place a few words about the transition of some 
‘linear’ quantities to the corresponding “spatial” quantities. 
If we have linear quantities, we can consider all our velocities 
as the components of the relative velocities directed normally; as we 
always imagine a molecule moving rectilinearly to and fro between 
two molecules at rest. We know that u=2u*, and that the mean 
value of the component of u”, directed normally, in its turn is the 
third part of this, so that we have (cf. also p. 1195 loc. eit): 
CANS EN in 
Hence we may write: 
1 Nan”) - l te 
| m3 m (uy eae Sy ot ee 
or also, denoting the tüne-average by the index t: 
il Ten 
bd oe Nm (u?)t. 
1 ee 
En Nm (un ht == 5 
3 
In this 4, Nm (w°y;(="/,pv in ideal gases) ='*/, RT, so that we 
may henceforth write: 
1) These Proe., Vol. XXI, p. 1184. 
