Page:Elementary Principles in Statistical Mechanics (1902).djvu/43

The values of the coefficient and index of probability of phase, like that of the density-in-phase, are independent of the system of coördinates which is employed to express the distribution in phase of a given ensemble.

In dimensions, the coefficient of probability is the reciprocal of an extension-in-phase, that is, the reciprocal of the $n$th power of the product of time and energy. The index of probability is therefore affected by an additive constant when we change our units of time and energy. If the unit of time is multiplied by $c_{t}$ and the unit of energy is multiplied by $c_{e}$, all indices of probability relating to systems of $n$ degrees of freedom will be increased by the addition of

$n\log c_{t}+n\log c_{e}.$

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