Page:Elementary Principles in Statistical Mechanics (1902).djvu/102

78 or since by (218)

In precisely the same way we may obtain for the potential energy

By successive applications of (231) we obtain where $$D$$ represents the operator $$\Theta^2\,d/d\Theta$$. Similar expressions relating to the potential energy may be derived from (232).

For the kinetic energy we may write similar equations in which the averages may be taken either for a single configuration or for the whole ensemble. But since the general formula reduces to  or