Page:Elementary Principles in Statistical Mechanics (1902).djvu/223

Rh Equation (505), which we repeat in a slightly different form, viz., shows that $$\Omega$$ is a function of $$\Theta$$ and $$\mu_1,\ldots\mu_h$$; also of the external coördinates $$a_1$$, $$a_2$$, etc., which are involved implicitly in $$\epsilon$$. If we differentiate the equation regarding all these quantities as variable, we have  If we multiply this equation by $$e^\frac\Omega\Theta$$, and set as usual $$A_1$$, $$A_2$$, etc., for $$-d\epsilon/da_1$$, $$-d\epsilon/da_2$$, etc., we get in virtue of the law expressed by equation (519),