388 Conduction in Solutions and Gases, 



the system would be decreased if the piston were to move 

 outwards so as to admit more solvent into the solution; and 

 therefore this movement of the piston would be assisted by a 

 force the "osmotic pressure of the solution," as it is called.* 



Consider, then, the case of a single electrolyte supposed to 

 be perfectly dissociated ; its state will be supposed to be the 

 same at all points of any plane at right angles to the axis of x. 

 Let v denote the valency of the ions, and V the electric potential 

 at any point. Sincef the available energy of a given quantity of 

 a substance in very dilute solution depends on the concentration 

 in exactly the same way as the available energy of a given 

 quantity of a perfect gas depends on its density, it follows that 

 the osmotic pressure p for each ion is determined in terms of 

 the concentration and temperature by the equation of state 

 of perfect gases 



Mp = ETc, 



where M denotes the molecular weight of the salt, and c the 

 mass of salt per unit volume. 



Consider the cations contained in a parallelepiped at the 

 place x, whose cross-section is of unit area and whose length 

 is dx. The mechanical force acting on them due to the electric 

 field is - (vc/M) d Vfdx . dx, and the mechanical force on them 

 due to the osmotic pressure is - dp/dx . dx. If u denote the 

 velocity of drift of the cations in a field of unit electric force, 

 the total amount of charge which would be transferred by 

 cations across unit area in unit time under the influence of the 

 electric forces alone would be - (uvc/M) d V/dx ; so, under the 

 influence of both forces, it is 



_uvcidV_ ET dc\ 

 M\dx cv dx) 



Similarly, if v denote the velocity of drift of the anions in a 



* Cf . van't Hoff, Svenska Vet.-Ak. Handlingar xxi (1886), No. 17; Zeitschrift 

 fiir Phys. Chem. i (1887), p. 481. 



t As follows from the expression obtained, supra, p. 383. 



