Page:Elementary Principles in Statistical Mechanics (1902).djvu/92



to the case of a canonical distribution, we have for the index of probability of configuration as appears on comparison of formulae (142) and (161). It follows immediately from (142) that the average value in the ensemble of any quantity $$u$$ which depends on the configuration alone is given by the formula where the integrations cover all possible configurations. The value of $$\psi_q$$ is evidently determined by the equation

By differentiating the last equation we may obtain results analogous to those obtained in Chapter IV from the equation As the process is identical, it is sufficient to give the results: