Page:Scientific Papers of Josiah Willard Gibbs.djvu/469

Rh  The condition of no electrical current gives  Apply to both ends and add,  If we set, to abridge,  When the summations are for cations or anions separately, the last equation may be written

$$K_{1}'$$ is the part of the conductivity of the first electrolyte which is due to the cations.

If the first electrolyte contains only one cation (1) and one anion (2), and the second only one cation (3) and one anion (4), we have

like the formula which you quote.