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

Rh 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 by which $$\psi$$ may be determined, the external coördinates, $$a_1$$, $$a_2$$, etc., contained implicitly in $$\epsilon$$, as well as $$\Theta$$, are to be regarded as constant in the integrations indicated. The equation indicates that $$\psi$$ 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 or, multiplying by $$\Theta e^{\frac{\psi}{\Theta}}$$, and setting