Page:Elementary Principles in Statistical Mechanics (1902).djvu/224

200 that is, Since equation (503) gives  the preceding equation may be written  Again, equation (526) gives  Eliminating $$d\Omega$$ from these equations, we get  If we set   we have

The corresponding thermodynamic equations are   These are derived from the thermodynamic equations (114) and (117) by the addition of the terms necessary to take account of variation in the quantities ($$m_1$$, $$m_2$$, etc.) of the several substances of which a body is composed. The correspondence of the equations is most perfect when the component substances are measured in such units that $$m_1$$, $$m_2$$, etc., are proportional to the numbers of the different kinds of molecules or atoms. The quantities $$\mu_1$$, $$\mu_2$$, etc., in these thermodynamic equations may be defined as differential coefficients by either of the equations in which they occur.