Page:Elementary Principles in Statistical Mechanics (1902).djvu/222

198 or  This may be called the probability of the petit ensemble $$(\nu_1,\ldots \nu_h)$$. The sum of all such probabilities is evidently unity. That is, which agrees with (506).

The average value in the grand ensemble of any quantity $$u$$, is given by the formula If $$u$$ is a function of $$\nu_1,\ldots \nu_h$$ alone, i. e., if it has the same value in all systems of any same petit ensemble, the formula reduces to  Again, if we write $$\overline{u}|_{\rm grand}$$ and $$\overline{u}|_{\rm petit}$$ to distinguish averages in the grand and petit ensembles, we shall have

In this chapter, in which we are treating of grand ensembles, $$\overline u$$ will always denote the average for a grand ensemble. In the preceding chapters, $$\overline u$$ has always denoted the average for a petit ensemble.