374 Conduction in Solutions and Gases, 



This idea was adopted by W. Hittorf, of Minister, who, in the 

 years 1853 to 1859, published* 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.! 



The theory of ionic movements was advanced a further 

 stage by F. W. KohlrauschJ (I. 1840, d. 1910), of Wurzburg. 

 Kohlrausch showed that although the ohmic specific conduc- 

 tivity 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 of salt per unit volume, tends 

 to a definite limit, when the solution is indefinitely dilute. This 

 limiting value may be denoted by A. He further showed that 

 A 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 twos 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 cm. 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. Ixxxix (1853), p. 177 ; xcviii (1856), p. 1 ; ciii (1858), p. 1 ; 

 cvi (1859), pp. 337, 513. 



t The ratio v/(u + v) was termed by Hittorf the transport, number of the anion. 

 J Ann d. Phys. vi (1879), pp. 1, 145. The chief results had been communicated 

 to the Academy of Gottingen in 1876 and 1877. 



A gramme-equivalent means a muss of the salt whose weight in grammes 

 is the molecular weight divided by the valency of the ions. 



