from Faraday to J . J. Thomson. 383 



fact, by the law of Kaoult, (p -pi)/po is approximately equal to 

 nv/ V ; so that the previous equation becomes 



p. V(v' -f.) -*/(/ F). 



Neglecting v in comparison with v', and making use of the 

 equation of state of perfect gases (namely, 



pjt = ST. 



where T denotes the absolute temperature, and R denotes the 

 constant of the equation of state), we have 



and therefore 



Thus in the available energy of one gramme-molecule of a 

 dissolved salt, the term which depends on the concentration is 

 proportional to the logarithm of the concentration ; and hence, 

 if in a concentration-cell one gramme-molecule of the salt 

 passes from a high concentration c 2 at one electrode to a low 

 concentration GI at the other electrode, its available energy is 

 thereby diminished by an amount proportional to log (c 2 /c,). 

 The energy which thus disappears is given up by the system in 

 the form of electrical work; and therefore the electromotive 

 force of the concentration-cell must be proportional to log (Cz/cJ.. 

 The theory of solutions and their vapour-pressure was 

 not at the time sufficiently developed to enable Helmholtz 

 to determine precisely the coefficient of log (c 2 /Ci) in the 

 expression.* 



An important advance in the theory of solutions was effected 

 in 1887, by a young Swedish physicist, Svante Arrhenius.f 



* The formula given by Helmholtz was that the electromotive force of the cell 

 is equal to b(l - ri) v log (czjc\), where ci and c\ denote the concentrations of the solu- 

 tion at the electrodes, v denotes the volume of one gramme of vapour in equilibrium 

 with the water at the temperature in question, n denotes the transport number for 

 the cation (Hittorfs 1/w), and b denotes q x the lowering of vapour- pressure when 

 one gramme-equivalent of salt is dissolved in q grammes of water, where q denotes 

 a large number. 



t Zeitschrift fur phys. Chem. i (1887), p. 631. Previous investigations, in 

 which the theory was to some extent foreshadowed, were published in Bihang 

 till Svenska Vet. Ak. Forh. viii (1884), Nos. 13 and 14. 



