TOLMAN. — ELECTROMOTIVE FORCE PRODUCED IN SOLUTIONS. 113 



In the present investigation, a new attempt was made to increase 

 the accuracy of this method of determining transference numbers, by- 

 substituting for the effect of gravity the force produced by a centrifugal 

 machine of considerable power. As will be seen in the sequel, the 

 average deviation between successive measurements has in this way 

 been reduced to a very small amount. An estimation of the actual 

 error in the results is, however, somewhat difficult to make. 



2. Derivation of an Expression for the Electromotive Force. 



In order to derive an expression for the electromotive force produced 

 in an electrolytic solution by the action of gravity, let us consider a 

 vertical tube of height h, filled with the solution and provided with 

 electrodes at the top and bottom. If E is the potential difference in 

 volts between the upper and lower electrodes produced by the action 

 of gravity, then by allowing one faraday of electricity to flow under 

 this electromotive force we could obtain the external work l(f EF 

 ergs. The passage of this electricity through the solution is accom- 

 panied, however, by the transfer of a certain net weight of material 

 from the upper electrode to the lower one. From the principles of 

 energetics, it is evident that this external energy 10" EF which we 

 could obtain will just be sufficient to restore the solution to its original 

 condition, that is, will do the work of raising the transferred material 

 back from the lower electrode to the upper one. For the sake of 

 definiteness, let us suppose that the electrolyte is a solution of an 

 iodide (C"^ I~) and that we are using iodine electrodes, consisting in 

 practice of platinum electrodes with a small amount of iodine dissolved 

 in the solution. If, now, we let one faraday of electricity flow through 

 the solution, we know from the experiments of Faraday and of Hittorf 

 that one atomic weight of iodine or Mj grams will be liberated at the 

 anode or upper electrode and will disappear from the lower electrode, 

 and at the same time that there will be a change in the ratio of salt to 

 water at the two electrodes such that TcM^ gms. of salt will have 

 apparently been transferred from the anode to the cathode, where 

 Tc is the ordinary or Hittorf transference number of the cation and 

 Mg is the molecular weight of the salt. In order, therefore, to restore 

 the solution to its original condition of uniform concentration, it is 

 necessary to raise T^ M^ gms. of salt from the lower electrode to the 

 upper one at the same time lowering one atomic weight of iodine. If 

 we raise and lower these substances through the solution it is evident 

 that they will be buoyed up by force equal to the weight of the volume 

 of solution which they displace. Hence if g is the acceleration due to 



VOL. XLVI — 8 



