350 Prof. Helmholtz on Galvanic Currents 



(2). Under the influence of this through-current, in the elec- 

 trolytic cell, which we suppose provided with two electrodes 

 of the same kind of metal and filled with a solution of that 

 metal, there is brought about a transfer of the salt in the elec- 

 trolyte. The alteration hereby produced in the state of the 

 liquid we can get rid of by evaporating, from all the layers of 

 the liquid where the current attenuates the liquid, as much 

 water as is conveyed thither, and, conversely, where the cur- 

 rent produces concentration, introducing the corresponding 

 amount of water by precipitation of vapour. If in this way 

 the state within the liquid be maintained perfectly constant, 

 the anion must remain wholly in its own place, because at 

 neither end is any thing withdrawn from it, and nothing is 

 added to it. From the cation, on the contrary, an amount 

 perfectly equivalent to the current-intensity must pass through 

 each cross section of the path of the current, since a full equi- 

 valent is dissolved at the anode, and precipitated at the cathode. 

 Now, since the displacement of the anion against the water is 

 to that of the cation against the water as (1 — n) : n, the water 

 must move forwards with a velocity amounting to (1— n) of 

 that of the cation. Consequently, if 1 electrolytic equivalent 

 of the salt is combined with- q parts by weight of water, and 

 through a portion dco of the surface the current of density i is 

 to be led, and, expressed in equivalents, the quantity iolco of 

 the cation, then must q(l—n)i .dco parts by weight of water 

 pass through the same in order to keep the parts of the anode 

 in their place. 



This quantity of water, amounting to q(l—n)i .dco, carries 

 with it as dissolved constituents (1 — n)i . dco equivalents of the 

 cation as well as of the anion. Electrolysis impels through 

 the same cross section ni . dco of the cation forwards, and 

 (l—n)i . dco of the anion backwards ; hence, on the whole, one 

 equivalent of the cation goes forwards, and the anion remains 

 in its place. 



Therefore, if u, v, iv denote the components of the electric 

 flow parallel to x, y, z, reckoned according to the quantity of 

 electricity which passes the unit of surface in the unit of time, 

 the increase in the amount of water in the volume-element dx, 

 dy, dz is, according to known hydrostatic laws, for the unit of 

 time, 



-{^[ ? (i-»)»]+|b(i-»w + ^b(i-»wWj.& 



