Page:Elementary Principles in Statistical Mechanics (1902).djvu/67

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OF AN ENSEMBLE OF SYSTEMS.
43

We always suppose these external coördinates to have the same values for all systems of any ensemble. In the case of a canonical distribution, i. e., when the index of probability of phase is a linear function of the energy, it is evident that the values of the external coördinates will affect the distribution, since they affect the energy. In the equation

(105)
by which may be determined, the external coördinates, , , etc., contained implicitly in , as well as , are to be regarded as constant in the integrations indicated. The equation indicates that is a function of these constants. If we imagine their values varied, and the ensemble distributed canonically according to their new values, we have by differentiation of the equation
(106)
or, multiplying by , and setting
(107)