CHAP IV - THE LAW OF DISTRIBUTION OF VELOCITIES: COMPARISON BETWEEN THE METHODS OF THE TWO PRECEDING CHAPTERS

Summary

61. The problem of the present chapter will be to consider the relation between the methods of procedure adopted in Chapters II and III.

The discussion of Chapter II was based upon certain questions of probability, and an answer to these questions was made possible and was obtained by the help of the assumption of molecular chaos enunciated in § 15.

The discussion of Chapter III also rested, although in a different sense, upon the theory of probability. The generalised space filled with fluid supplied a basis for the calculation of probabilities, and as the motion of the fluid was proved to be steady-motion, it followed that this basis was independent of the time. For the present, we continue to take this generalised space as the basis of probability calculations. The question “What is the probability that a system satisfies condition p?” will be taken to mean: “For what proportion of the generalised space is condition p satisfied?” The further question: “Given that a system satisfies condition p, what is the probability that it also satisfies condition q?” will be interpreted to mean: “A point is selected at random from all those parts of the generalised space in which condition p is satisfied: what is the probability that at this point condition q also is satisfied?”