We will not comment further on these statements at this time, leaving such discussion of their relations to the section on physical interpretations.
PART II
ANALYTICAL EXPRESSIONS FOR A FEW PRIMARY RELATIONS
At the beginning of this presentation we disclaimed any purpose of giving a rigorous proof for any of the many formulas with which this subject bristles. We propose only to give in some cases an outline of the main steps of the demonstration and merely for the purpose of getting a clearer physical insight into certain states and relations. Pre-eminent in importance is the state of thermal equilibrium (see pp. [19], [52], [53]) and we will therefore consider first its main characteristic:
SECTION A
MAXWELL'S LAW OF DISTRIBUTION OF MOLECULAR VELOCITIES
Without giving a full proof of the law we will give the main steps which lead to its analytical statement, in so doing following the presentation given by HANS LORENZ on pp. 526-529 of his "Technische Wärmelehre," and will then point out its main features and consequences.
We suppose the gas to contain in a unit of volume
molecules each possessing a different velocity and direction. Let there be a system of three co-ordinate axes,
. A fraction