288 Messrs Laby and Garse, On a relation, etc. 



On a relation between the velocity and the volume of the ions of 

 certain organic acids and bases. By T. H. Laby, Fitzwilliam Hall, 

 and G. A. Carse, Emmanuel College; 1851 Exhibition Scholars. 



(Communicated by Professor J. J. Thomson, F.R.S.) 

 [Read 12 March 1906.] 



Since Ohm's law holds in the case of an electrolyte, at a 



dV 

 given temperature the current i = — k -=— , where k denotes the 

 6 r dx 



dV . 

 conductivity of the electrolyte and -p- is the potential gradient 



between the electrodes, and as the current is carried by n uni- 

 valent ions per cub. cm. with a velocity of u for the positive and 

 v for the negative ion, each having a charge of electricity e, then 



i = ne(u + v), 



. dV k dV 



.: ne (u + v) = — k - 1 —, or u + v = j~. 



dx ne dx 



Thus for dilute solutions of the same equivalent concentration, 

 i.e. n constant, and with a constant potential gradient of say 1 volt 

 per cm., u + v = k x constant, an equation which may be derived 

 in an independent manner from experiment by using Hittorf's 

 migration ratios. Thus the conductivity of an electrolyte is pro- 

 portional to the sum of the velocities of the ions. When the 

 values that have been found for the velocities of univalent ions 

 are reduced to the one potential gradient, the velocities are those 

 of the different ions moving under the same force, viz. that arising 

 from this electric field acting on the constant ionic charge. 



Kohlrausch* has shown that the fluidity (reciprocal of the 

 viscosity), and the conductivity — and therefore the velocities of 

 the ions of dilute solutions — vary with the temperature in a 

 similar manner, that is for a number of electrolytes the conduc- 

 tivity-temperature and the fluidity- temperature curves are similar. 

 This has been borne out by the work of Bousfield and Lowryj", 

 Lyle and Hoskingj, and others^. The former of these workers 



* "The Resistance of the Ions and the Mechanical Friction of the Solvent," 

 Proc. Roy. Soc. lxxi. 338 (1903). 



t Proc. Roy. Soc. lxxi. 42 (1902). 



+ Phil. Mag. March 1900, p. 274 ; May 1902, p. 487 ; May 1904, p. 469. 



§ For further references see H. C. Jones and Bingham, Am. Chevi. Journ. 

 xxxiv. 481, Dec. 1905. 



