456 Prof. 0. Lodge on the Controversy 



cations are liberated at the electrodes, combined with the defi- 

 niteness of ionic charge, shows that in electrolysis the resultant 

 effective velocities of anion and cation substance relatively to 

 the electrodes are equal * . 



Consider now the charged atoms or ions in a cylindrical 

 space of volume Ada, with n of them in each unit of volume. 



Let them be subject to an applied potential gradient dV/dx, 

 and also to a self-excited osmotic pressure gradient dp/dx ; 

 then if e is the charge on each atom, the electrical force it 

 experiences is 



e — 



dx ' 



while the mechanical or osmotic force it experiences is the 

 whole pressure difference on the element shared among the 

 total number of atoms, which is 



Kdp % 1 dp 



nAdx n dx' 



This latter mechanical force acts equally on anions and 

 cations, but the electrical force acts oppositely on each set ; 

 so the total force on the one set is the sum, on the other set 

 is the difference of these two forces. If u^ and v l are the 

 usual migration constants representing the velocities of anion 

 and cation respectively under unit potential gradient, their 

 velocities under unit force will be u-Je and i^/e, and the actual 



* This statement seems to require a word of explanation or expansion. 

 So much stress has been laid upon the fact of different intrinsic -velocities 

 of opposite ions when under the same conditions, that it is apt to "be 

 forgotten that in ordinary electrolysis the conditions are such as to force 

 equal, or at least electrically equivalent velocities, on anion and cation 

 substance taken as a whole, in the steady state. The ions are propelled 

 not by outside forces acting from the electrodes, but by internal actions : 

 the readjustment of the whole material must be attended to. The intrinsic 

 speed of a projectile is greater than that of the gun-recoil, yet, after a 

 battery has fired, the centre of gravity of the whole is no nearer the 

 target than before. The mass-speeds are equal and opposite. In the 

 electrical case the charge-speeds are equal and opposite. Direct experi- 

 ments on specific migration velocity (such as those I described in the 

 Brit. Assoc. Report for'1886, pp. 393, 408) are allmade in purposely hetero- 

 geneous solutions ; so that the motion of specific portions of matter can 

 be discriminated and followed. Even in such heterogeneous liquids the 

 current- strength is the same across every section; but the local potential- 

 gradient depends on the local conductivity, and the concentration is 

 arbitrary : it is still true, however, that the potential-gradient is the same 

 for anion as for cation at any given place : and hence if they do ulti- 

 mately travel at the same pace in spite of intrinsically different ease of 

 travel, the fact must be expressible as due to an accumulated osmotic 

 pressure-gradient which opposes the quicker and helps the slower. 



