Page:Scientific Papers of Josiah Willard Gibbs.djvu/464

428 We may regard $$\frac{v}{v' - v}$$ as constant in integrating (for small $$\gamma_{\text{D}}$$), which gives Now Rh Raoult found values about 5 per cent, larger than this, which agrees very well with the fact that $$\frac{At}{v' - v}$$ is somewhat larger than $$\frac{PM_{\text{S}}}{m_{\text{S}}}\cdot$$ It is also to be observed that $$M_{\text{D}}$$ relates to the molecules in the solution, but $$M_{\text{S}}$$ to the molecules in the vapor. Or, with a coexistent vapor phase of the solutum (alone or mixed with other vapors or gases), we have which makes $$\frac{\gamma_{\text{D}}}{\gamma_{\text{D}}'}$$ constant for the same solvent, solutum, and temperature, according to Henry's Law.

So for the galvanic cell which you first consider, I should write $$\gamma_{a}', \gamma_{a}''$$ being the densities, supposed small, of the cation (a) in the two electrodes, which are supposed identical except for the dissolved (a). Here $$a_{a}$$ has reference to the solution and $$M_{a}$$ to the electrodes. It may be more convenient to divide a a into the factors $$E_{a}, a_{\text{H}}$$, where $$a_{\text{H}}$$ is the weight of hydrogen which carries the unit of electricity, and $$E_{a}$$ the weight of (a) which carries the same quantity of electricity as the unit of weight of hydrogen. In other words $$E_{a}$$ is Faraday's "electrochemical equivalent" and $$a_{a}$$ is Maxwell's "electrochemical equivalent." This gives where $$a_{\text{H}}A$$ is your $$R$$ and $$\frac{M_{a}}{E_{a}}$$ your $$v, v'.$$