Chemical Affinity in terms of Electromotive Force. 365 

 whence 



(l + S)E = K.sin«.R 2 Sm/3 l > 



sina- 



1 + 8 



Evidently, if 8 be assumed = 0, the value of this expression 

 is greater than the value when 8 is not = 0; that is, the 

 assumption that the E.M.F. of the cell is constant throughout 

 leads to the calculation of a value for its E.M.F. greater than 

 the true value for the smaller current, and a fortiori greater 

 than the true value for the larger current*. 



In just the same w^ay an incorrect value is obtained for the 

 internal resistance of a cell by Ohm's method, which depends 

 on the same principles. If 1^ be the resistance of the cell 

 and R that of the rest of the circuit, a current is generated 



C 1 = Ksina= - R + -p , 



and by throwing in an extra resistance R 2 the current is 

 reduced to 



n ^ . E(l + 8) 



If it be assumed that 8=0, then 



xia — Jtt 2 — : — - — Jtt ; 



sin ex. — sin p 



but if 8 is not equal to 0, then 



T? _T? sin/3 p 



±il -- K2 (l + S)sin a -sin/3~ ±l ' 



which is manifestly less than the former value ; so that the 

 assumption that the E.M.F. of the cell is constant throughout 

 leads to the overvaluation of its internal resistance. 



100. The results above described have an important 

 bearing on a considerable amount of work performed by 

 Favre (Comptes Rendus, 1866 and following years). By 

 passing a current through an electrolytic cell placed in a 

 calorimeter, an external resistance being in circuit so large 



* In H. F. Weber's experiments on the value of J (§ 55), a trifling 

 sonrce of error exists in those observations made with a voltaic battery, 

 the mean E.M.F. of which during the experiment was measured as a 

 necessary part of the data ; for the measurement gives the E.M.F. corre- 

 sponding to a current C v whilst the heat evolved was that caused by a 

 different current C 2 . As, however, Weber states that C x was always ap- 

 proximately = C 2 , this source of error is not great and is probably negli- 

 gible, since the B.A. resistance values got by this method are sensibly the 

 same as those obtained by the two other independent methods employed. 



