TOLMAN. — ELECTROMOTIVE FORCE PRODUCED IN SOLUTIONS. 141 



The Accuracy of the Results. 



The last column in the table gives the extremely small " probable 

 error " introduced into the value of the transference number, by the 

 deviations between the different measurements of E/n^. It was ob- 

 tained by dividing the mean deviations by the square root of the num- 

 ber of observations. It is not a satisfactory measure of the reliability 

 of the transference numbers, since there is considerable probability 

 that the " residual " electromotive force existing between the electrodes 

 during rotation were more likely to be in one direction than the 

 other. The value ±0.010 maybe taken as a fairer measure of the 

 probable accuracy of the determinations. In the case of KI, this 

 would correspond to an average error of about 0.1 millivolt in the 

 electromotive force. 



The Effect of Pressure on the Results. 



In deriving the equation on page 114 for the potential difference of a 

 cell under the influence of centrifugal force, the tacit assumption was 

 made that the quantities Vg, Vj, and d are, throughout the solution, the 

 same as those calculated from density measurements made at atmos- 

 pheric pressure. This is not strictly true, since there is considerable 

 pressure produced in the solution by the centrifugal force. The follow- 

 ing equation in which the quantities are considered as variables is 

 exact. 



W EF= r\ ttV r [ Tc3Is (1 - v^d) -3Ij(l- Vj,d)] dr (5) 



The derivation of the equation is obvious. IQi^EFis the external 

 work obtained when one faraday of electricity flows through the solu- 

 tion under the potential difterence E produced by the centrifugal ac- 

 tion. This quantity of energy is equal to the work required to restore 

 the solution to its original condition. To accomplish this TcMg gm. 

 of salt must be brought back from r^ to 7\, and this quantity, multiplied 

 by Vsd, is the number of gm. of displaced solution which will automati- 

 cally move in the opposite direction as we move the salt through the 

 solution, 3Ij and Vj^d are the same quantities for the iodine, which 

 has to be transferred from ri to r^. The centrifugal force acting on the 

 material which is to be moved is the product of the mass into 

 47^^?^V and the total work done is obtained by multiplying by dr, and 

 integrating between r^ and ri. If the integration is made on the as- 

 sumption that Vg, Vj^ and d do not vary with r, that is, with the pres- 



