Page:Elementary Principles in Statistical Mechanics (1902).djvu/110

as many times as we choose, and in any order, the average value of the result will be zero. Or, if we apply the same operators to $u$, and finally take the average value, it will be the same as the value obtained by writing the sign of average separately as $u$, and on $\epsilon$, $A_{1}$, $A_{2}$, etc., in all the operators.

If $u$ is independent of the momenta, formulae similar to the preceding, but having $\epsilon _{q}$ in place of $\epsilon$, may be derived from equation (179).