Page:Elementary Principles in Statistical Mechanics (1902).djvu/99

Rh that there were means of measuring these quantities separately) had each separately uniform values. Exceptions might occur when for particular values of the modulus the differential coefficient $$d\overline\epsilon_q/d\overline\epsilon_p$$ takes a very large value. To human observation the effect would be, that in ensembles in which $$\Theta$$ and $$\overline\epsilon_p$$ had certain critical values, $$\overline\epsilon_q$$ would be indeterminate within certain limits, viz., the values which would correspond to values of $$\Theta$$ and $$\epsilon_p$$ slightly less and slightly greater than the critical values. Such indeterminateness corresponds precisely to what we observe in experiments on the bodies which nature presents to us.

To obtain general formulae for the average values of powers of the energies, we may proceed as follows. If $$h$$ is any positive whole number, we have identically i. e., by (108),  Hence  and