This idea was adopted by W. Hittorf, of Münster, who, in the years 1853 to 1859, published[1] a series of memoirs on the migration of the ions. Let the velocity of the anions in the solution be to the velocity of the cations in the ratio v:u. Then it is easily seen that if (u + v) molecules of the electrolyte are decomposed by the current, and yielded up as ions at the electrodes, v of these molecules will have been taken from the fluid on the side of the cathode, and u of them from the fluid on the side of the anode. By measuring the concentration of the liquid round the electrodes after the passage of a current, Hittorf determined the ratio v/u in a large number of cases of electrolysis.[2]
The theory of ionic movements was advanced a further stage by F. W. Kohlrausch[3] (b. 1840, d. 1910), of Würzburg. Kohlrausch showed that although the ohmic specific conductivity k of a solution diminishes indefinitely as the strength of the solution is reduced, yet the ratio k/m, where m denotes the number of gramme-equivalents[4] of salt per unit volume, tends to a definite limit when the solution is indefinitely dilute. This limiting value may be denoted by λ. He further showed that λ may be expressed as the sum of two parts, one of which depends on the cation, but is independent of the nature of the anion; while the other depends on the anion, but not on the cation—a fact which may be explained by supposing that, in very dilute solutions, the two ions move independently under the influence of the electric force. Let u and v denote the velocities of the cation and anion respectively, when the potential difference per em. in the solution is unity: then the total current carried through a cube of unit volume is mE (u + v), where E denotes the electric charge carried by one gramme-
- ↑ Ann. d. Phys. lxxxix (1853), p. 177; xcvii (1856), p. 1; cii (1858), p. 1: cvi (1859), pp. 337, 513.
- ↑ The ratio v/(u + v) was termed by Hittorf the transport number of the anion.
- ↑ Ann. d. Phys. vi (1879), pp. 1, 145. The chief results had been communicated to the Academy of Göttingen in 1876 and 1877.
- ↑ A gramme-equivalent means a mass of the salt whose weight in grammes is the molecular weight divided by the valency of the ions.
