occasioned by Differences of Concentration. 353 



By partial integration of the triple integral, and taking into 

 account equation (1a), we find 



f=J^.^ & . } .(l- S ){ a | + „| + ^}.(2 i ) 



Here n and W are functions of q. Consequently, if we put 



q(l-n)dW = d<P, (2 b) 



where <I> denotes a function of q, or 



4>=J q(l-n)^dp, (2c) 



in which p, the pressure of the vapour above the salt- solution, 

 is likewise a function of q, we get 



3= — J dco . <E>{wcos a + v cos^ + iycos c). . (2d) 



The parenthesis in this expression denotes the component of 

 the current perpendicular to the limiting surface of the elec- 

 trolyte. This differs from nil only at the parts of the limiting 

 surface turned to the electrodes. If the concentration of the 

 liquid, and therefore q, u, p, <3>, along each single electrode is 

 constant, then becomes 



s®=J(*,-* a ), (3) 



and the equation of the work becomes 



P*-P«=*«-4> 4 =[ a ?(l-n)^. . . (3a) 



But Pjfc — P a is the value of the electromotive force produced 

 by the electrolytic cell in the direction from the anode to the 

 cathode, consequently in the direction of our assumed current. 



This equation therefore indicates the existence of an electro- 

 motive force, the amount of which depends only on the con- 

 centration of the liquid at the two electrodes, not upon the 

 distribution of more concentrated and more diluted layers in 

 the interior of the liquid — a conclusion which is confirmed by 

 the experiments of Dr. J. Moser, recently communicated to 

 the Academy. 



At the temperature of the apartment, the diminution of 

 pressure shown by the vapour over the solutions of most of 

 the metallic salts is very inconsiderable ; and on this account 



the quantity ^ — may be supposed approximately constant 



within these narrow limits of the pressure. It can therefore be 

 placed before the symbol of integration. On the other hand, 

 Phil Mag. S. 5. Vol. 5. No. 32. May 1878. 2 A 



