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Let a completely ionised solution of 1 equiv. of salt be electrolysed with a potential gradient of 1 volt per cm. The ions move with speeds of u and v cm. per sec., and since the total charges on each kind of ion are +F and -F, respectively, the charges transported per sec. are +uF and -vF. Negative charge moving in one direction is equivalent to positive charge moving in the opposite direction, hence the total charge transported per sec. is uF + vF, which is the same as the current, viz., Λ∞, or lc + la. Hence:
lc + la = F(u+v) or lc = Fu and la = Fv.
Hence, since F = 96,500, the mobilities u and v in cm. per sec. for a potential gradient of 1 volt per cm. can be calculated from the values of lc and la in the above table. In this way the values in the table in Migration of Ions were found: they are confirmed by direct measurements, as. there described.
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