Page:Elementary Principles in Statistical Mechanics (1902).djvu/117

Rh substitute it in the general expressions (286), and obtain the following values, which are perfectly general:

It will be observed that the values of $$V_p$$ and $$\phi_p$$ for any given $$\epsilon_p$$ are independent of the configuration, and even of the nature of the system considered, except with respect to its number of degrees of freedom.

Returning to the canonical ensemble, we may express the probability that the kinetic energy of a system of a given configuration, but otherwise unspecified, falls within given limits, by either member of the following equation Since this value is independent of the coördinates it also represents the probability that the kinetic energy of an unspecified system of a canonical ensemble falls within the limits. The form of the last integral also shows that the probability that the ratio of the kinetic energy to the modulus