Page:Elementary Principles in Statistical Mechanics (1902).djvu/146

122 average value of $$u$$ in an ensemble in which the whole system is microcanonically distributed in phase, viz., where $$\phi_1$$ and $$V_2$$ are connected by the equation  and $$u$$, if given as function of $$\epsilon_1$$, or of $$\epsilon_1$$ and $$\epsilon_2$$, becomes in virtue of the same equation a function of $$\epsilon_2$$ alone. Thus  This requires a similar relation for canonical averages  Again  But if $$n_1 > 2$$, $$e^{\phi_1}$$ vanishes for $$V_1 = 0$$, and  Hence, if $$n_1 > 2$$, and $$n_2 > 2$$,