Page:Elementary Principles in Statistical Mechanics (1902).djvu/145

Rh which shows that $$d\phi\, d\log V$$ approaches the value unity when $$n$$ is very great.

If a system consists of two parts, having separate energies, we may obtain equations similar in form to the preceding, which relate to the system as thus divided. We shall distinguish quantities relating to the parts by letters with suffixes, the same letters without suffixes relating to the whole system. The extension-in-phase of the whole system within any given limits of the energies may be represented by the double integral taken within those limits, as appears at once from the definitions of Chapter VIII. In an ensemble distributed with uniform density within those limits, and zero density outside, the average value of any function of $$\epsilon_1$$ and $$\epsilon_2$$ is given by the quotient which may also be written  If we make the limits of integration $$\epsilon$$ and $$\epsilon+d\epsilon$$, we get the