Page:Elementary Principles in Statistical Mechanics (1902).djvu/229

Rh

This shows that the distribution of the grand ensemble with respect to the values of $$\nu_1,\ldots\nu_h$$ follows the "law of errors" when $$\nu_1',\ldots\nu_h'$$ are very great. The value of this integral for the limits $$\pm\infty$$ should be unity. This gives or  where  that is,

Now, by (553), we have for the first approximation and if we divide by the constant $$K$$, to reduce these quantities to the usual unit of entropy,