Page:Elementary Principles in Statistical Mechanics (1902).djvu/61

Rh words. Let us therefore suppose that in forming the system $$C$$ we add certain forces acting between $$A$$ and $$B$$, and having the force-function $$-\epsilon_{AB}$$. The energy of the system $$C$$ is now $$\epsilon_A + \epsilon_B + \epsilon_{AB}$$ and an ensemble of such systems distributed with a density proportional to would be in statistical equilibrium. Comparing this with the probability-coefficient of $$C$$ given above (95), we see that if we suppose $$\epsilon_{AB}$$ (or rather the variable part of this term when we consider all possible configurations of the systems $$A$$ and $$B$$) to be infinitely small, the actual distribution in phase of $$C$$ will differ infinitely little from one of statistical equilibrium, which is equivalent to saying that its distribution in phase will vary infinitely little even in a time indefinitely prolonged. The case would be entirely different if $$A$$ and $$B$$ belonged to ensembles having different moduli, say $$\Theta_A$$ and $$\Theta_B$$. The probability-coefficient of $$C$$ would then be which is not approximately proportional to any expression of the form (96).

Before proceeding farther in the investigation of the distribution in phase which we have called canonical, it will be interesting to see whether the properties with respect to