Page:Elementary Principles in Statistical Mechanics (1902).djvu/119

Rh   If $$n=2$$, $$e^{\phi_p} = 2\pi$$, and $$d\phi_p/d\epsilon_p = 0$$, for any value of $$\epsilon_p$$.

The definitions of $$V$$, $$V_q$$, and $$V_p$$ give where the integrations cover all phases for which the energy is less than the limit $$\epsilon$$, for which the value of $$V$$ is sought. This gives and  where $$V_p$$ and $$e^{\phi_p}$$ are connected with $$V_q$$ by the equation

If $$n>2$$, $$e^{\phi_p}$$ vanishes at the upper limit, i. e., for $$\epsilon_p = 0$$, and we get by another differentiation We may also write