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

86 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).