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

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UNPUBLISHED FRAGMENTS.
433
Let
Let

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

which gives
Now

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

or, since

like the formula which you quote.