114 PROCEEDINGS OF THE AMERICAN ACADEMY. 



gravity, and d the density of the solution, the downward forces acting 

 respectively on the salt and the iodine will be g T^ Mg (1 — Vg d) and 

 g Ml (1 — Vi„ d) where Vs and Vi^ are the " partial " specific volumes * 

 of the substances. Equating the external electrical work to the work 

 done against these forces in transferring the substance from one elec- 

 trode to the other, we have the desired relation ^ 



\0''EF=hg[TMs{l-Vsd)-M,{l-ViM (1) 



If instead of using a gravity cell we should rotate our solution 

 n times per second, with electrodes at ri and r^, since the centrif- 

 ugal force acting on one gram at any radius r is 4 ir"^ fi" r, the 

 work done in carrying one gTam from 7-2 to ri would evidently be 



''4 77^ ^2 r dr = 2 TT^ n^ {r^ - r^^) 6 



£ 



and our equation for electromotive force becomes 



WEF= 2 TT^ n^ (r,' - r,') [r,il/, (1 - v^d) - 31, ( 1 - r,/;]. (2) 



We see that the value of the electromotive force which is to be 

 measured is proportional to the factor hg or 27r- ??^ {r\ — ri^). In 

 the experiments of Des Coudres on gravitational cells, the factor /ig 

 was 360,000, while with his rotating apparatus the value of the 

 corresponding factor was 583,000. In the centrifugal experiments 

 which are to be described in this paper the value of the factor was 

 raised to 114,000,000. 



The Effect of Hydration. 



It has been shown by the careful researches of Buchbock^ and 

 especially of Washburn ^ that it is possible to distinguish between the 

 ordinary Hittorf transference number and the so-called " true " trans- 

 ference number in which the motion of the ions is referred to a non- 



* For a definition of "partial" volumes, see page 131. 



" In order to derive tins equation, any reversible method mijjjlit be used for 

 restorinfj the solution to its original condition of uniform concentration. For 

 example, tlie apparent difficulty of moving the substances through the solution 

 can be ol)viated by removinn; them from the solution with the help of semi- 

 permeable membranes. It is easy to show, however, that the relation derived 

 is the same. 



^. It may also be pointed out that the expression 2ir- v? (r^* — rf) is the in- 

 crease in kinetic energy when one gram of material is transferred from ri to ro. 



7 Ruchbiick, Z. phvsik. Chem. 55, 563 (1900). 



8 Washburn, Tech. Quart. 21, 164 (1908), Joum. Amer, Chem. Soc. 31, 322 

 (1909). 



