TOLMAN. — ELECTROMOTIVE FORCE PRODUCED IN SOLUTIONS. 115 



electrolytic indicator dissolved in the solution instead of to the water. 

 If water is carried by the current, owing to hydration of the ions, then 

 the two transference numbers will be different. 



The Hittorf transference number gives, however, the actual number 

 of equivalents of salt which apparently disappear in the neighborhood 

 of one electrode and appear at the other when one faraday of electricity 

 is sent through the solution, and hence the Hittorf transference number 

 gives us the amount of salt which must be moved in order to restore 

 the solution to its original condition of uniform concentration. From 

 a consideration of the method by which the equation for the electro- 

 motive force was derived, it is obvious that the /^T/^or/" transference 

 number is the one which has been determined in this research. 



3. Kinetic Derivation of the Electromotive Force Expression. 



In order to derive the equations used in this article, we have con- 

 sidered the production of the electromotive force in a rotating solution 

 from a thermodynamic standpoint. The fact that more work was 

 needed to send a current through a salt solution from the outer to the 

 inner electrodes than in the reverse direction, could be predicted from 

 thermodynamic principles, and the electromotive force, corresponding 

 to this work, could be calculated merely from a knowledge of certain 

 properties of the solution such as transference number and density, 

 which can be experimentally determined. It is also instructive, how- 

 ever, to look at the question from a " kinetic " or molecular point of 

 view. The fact that an electromotive force is spontaneously produced 

 by centrifugal force gives us a real knowledge of the internal structure 

 of an electrolytic conductor. It is, indeed, the most striking proof of 

 the existence of fi-ee ions in an electrolyte. 



Considered from a " kinetic " point of view, a solution of potassium 

 iodide contains free potassium ions and free iodide ions. The iodide 

 ions, however, corresponding to their greater atomic weight, are much 

 denser than the potassium ions, and hence when the solution is rotated 

 they move more readily towards the outer portion of the solution and 

 charge it negatively. In fact from a consideration of the forces acting 

 on the ions in the solution, it is possible to derive the same equation 

 for the electromotive force of a gravity cell as that already obtained 

 from thermodynamic reasoning. The method of proof is similar to that 

 used by Nernst in his consideration of the diffusion cell. 



Consider an iodide (C"'"I~) of molecular weight 3Is dissociating into 

 the ions C"^ and I~ of atomic weights 3Ic and 3Ij. Let v^ be the par- 

 tial specific volume of the salt in solution and Vc and Vj be the same 



