occasioned by Differences of Concentration. 351 



since in the stationary current 



!^ + !^ + !^ = o. (ia) 



dx oy oz 



0n the contrary, at the surface of the electrodes the required 

 inflow of water through the surface-element day would be 



q(l— w)[wcos a + vcos b + w cosc~]dco, . . . (1 b) 



if a, b, c denote the angles between the normal, directed to the 

 liquid, of the element dco and the positive coordinate-axes. 



Integrating over the entire volume of the liquid the above 

 expression which is multiplied by dx, dy, dz, we obtain, by 

 known methods of partial integration, the same value that the 

 last expression (multiplied by dco) gives when integrated over 

 the surface. 



The water, then, which collects in the whole interior, and, 

 according to our supposition, is to be removed by evaporation, 

 will exactly suffice, when again precipitated at the surfaces of 

 the electrodes, to give the supply required there. Of course the 

 collection of the water within the liquid, as well as its preci- 

 pitation on the surface, may in places have also negative values. 



(3) The evaporation, or, where it is negative, the precipita- 

 tion of the vapour, can be managed thus : — By conveying heat 

 to each of the volume-elements the temperature is kept con- 

 stant during the evaporation. As long as water is to be ex- 

 tracted from a volume-element of the liquid, the vapour is left 

 in contact with it.; finally the two are separated, and the vapour, 

 under a further supply of heat, is permitted to expand at con- 

 stant temperature until it has reached a constant pressure p lm 

 Where the evaporation is to be negative, of course the vapour 

 is withdrawn from the pressure p 1} and giving up heat at con- 

 stant temperature is compressed at first out of, and afterwards 

 in, contact with the liquid, until it turns to water. Since the 

 vapour which is in contact with the more concentrated por- 

 tions of the liquid has less pressure than that which is in con- 

 tact with the more dilute portions, work will be gained in this 

 evaporation when water is carried over from the more dilute 

 to the more concentrated portions, lost when the reverse is the 

 case. 



(4) The electric current can be made to pass so slowly that 

 the heat-development (proportional to the square of its inten- 

 sity) on account of the resistance of the conductor becomes 

 vanishingly little in comparison with those actions which we 

 have hitherto discussed, and which are proportional to the first 

 power of the intensity. 



In like manner the diffusion which takes place between the 



