142 PROCEEDINGS OF THE AMERICAN ACADEMY. 



sure, the equation actually used is obtained. As a matter of fact both 

 the density of the solution and the partial volume of the salt will vary 

 with the pressure, and hence as we move the salt through the solution 

 from one electrode to the other at each level it will displace a different 

 weight of solution, and will hence be buoyed up by a different amount. 

 We have no data for the variation of r^ and V/, with the pressure, but 

 an upper limit for the error which has been introduced by taking them 

 as constant, may be calculated. 



Assuming that isd and Vj^d vary linearly with the pressure, since the 

 pressure equals 2,iT^nVd^^ where d is approximately unity, we may 

 write the equations 



V^d = V^ (1 + 2 TT^/^V^ai), 

 Vj^d = Vj^^(l + 2 irhlS'^a^), 



where Vsd and Vj,d^ are the values for zero pressure, and aj and oa are. 

 the linear coefficients for the fractional change of t'sd and v^jJ with 

 the pressure. Substituting into equation (o) and integrating we obtain 



^'=^ (^-2^ - n^) [TJI, (1 - Vsd) - M, (1 - vJ)-\ 



— J^^T {^2^ — t'l") {Tc Ms ai Vsd_^ — Ml as V]/l^. 



The second term in the expression is seen to be the error introduced 

 into the calculation of the electromotive force, by neglecting the change 

 of the density and partial volumes with the pressure. Since the par- 

 tial volumes will jirobably decrease with pressure and partly neutralize 

 the increase in density, to obtain an upper limit for the error let us put 

 ai and Og = 4 X 10 ~ -^^ the value for the fractional change in the 



density of water per —^-. Making this substitution, the value of the 



above term becomes only 0.00018 millivolts, for the experiment on po- 

 tassium iodide, at 80 revolutions per second. We see that no appre- 

 ciable error has been introduced by neglecting the change in the 

 density and the partial volumes produced by pressure. 



Before leaving the consideration of the pressure gradient in the tube, 

 it must be pointed out that the transference number determined in 

 these experiments is the transference number which exists when the 

 solution is actually under the influence of that particular pressure gra- 



*' Tliis is strictly true only when the liquid reaches way to the center of 

 the rotating ai)paratus. 



