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

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CERTAIN IMPORTANT FUNCTIONS

The value of may also be put in the form

(284)
Now we may determine for from (279) where the limits are expressed by (281), and for from (284) taking the limits from (283). The two integrals thus determined are evidently identical, and we have
(285)
i. e., varies as . We may therefore set
(286)
where 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 from (286), we get

(287)
Having thus determined the value of the constant , we may