II.─Ionic velocities

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Abstract
The general theory of electrolytic conduction, involving the laws of Faraday, Hittorf, Kohlrausch, and Arrhenius, may be briefly summed up by the formula C = A n /η (U + V) = A n /η π x ( u + v ), where C is the current, A is the area of cross-section of the conducting medium, η is the electro-chemical equivalent of hydrogen or 1/η is the charge per monad ion, n is the number of monad equivalents of the electrolyte per unit volume of solution, U is the average working velocity of the cations, V is that of the anions, π is the fall of potential per unit of length ( d P/ d l), called in the sequel potential slope, x is the coefficient of ionization, u is the velocity with which the same cations would travel if, all other things being equal, ionization were complete, and the potential slope had unit value, and v is the corresponding value for the anions. u and v are referred to in the sequel as specific velocities . In further explanation it may be pointed out that x may be taken as representing either that fraction of the total dissolved molecules which is at any given moment in he ionized state, or (which is the same thing) that fraction of the total time during which, on the average, any given dissolved molecule is ionized and that the relation of the working velocity U (or V) to the running velocity π u (or π v ) is therefore similar to that which holds between the average speed of a train for its whole journey, including stoppages, and its actual average speed between stations. Briefly, U = πx u and V = πx v .

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