Page:Elementary Principles in Statistical Mechanics (1902).djvu/116

92 The value of $$V_p$$ may also be put in the form Now we may determine $$V_p$$ for $$\epsilon_p=1$$ from (279) where the limits are expressed by (281), and $$V_p$$ for $$\epsilon_p=a^2$$ from (284) taking the limits from (283). The two integrals thus determined are evidently identical, and we have i. e., $$V_p$$ varies as $$\epsilon_p^{\frac{n}{2}}$$. We may therefore set where $$C$$ is a constant, at least for fixed values of the internal coördinates.

To determine this constant, let us consider the case of a canonical distribution, for which we have where

Substituting this value, and that of $$e^{\phi_p}$$ from (286), we get    Having thus determined the value of the constant $$C$$, we may