78 RESEARCH COMMITTEES. 
7. Summary of Expressions for Electromotive Force. 
We have now the following expressions for the relation between 
the e. m. f. of a cell and various thermodynamic quantities :— 
3 SE 
E=— 5 (—Ts) =—37 re a) 
SE su 
oe es 
B+3@)=—> =H an 
The practical utility of the expressions (C), (D), and (E) has 
been already indicated ; that of (B) is due to the fact that = is 
sometimes calculable when nothing can be directly determined 
with regard to ¢ and its differential coefficients. 
8. Electromotive Lorce and Free Energy. 
Helmholtz has calculated the variation of free energy due to 
the passage of the current in two important cases, and compared 
the results with experiment. 
(2) Liquid cells. 
At the surface of contact of two solutions, of the same electro- 
lyte but of unequal strengths, an e. m. f. is set up ; if the circuit 
be closed by means of nonpolarisable electrodes a current will 
flow, and will go on flowing with gradually diminishing intensity 
until the concentrations become equalised ; in this way work may 
be obtained from the arrangement. The liquid cell thus con- 
stituted is reversible ; for the passage of a current through it in 
the opposite direction will set up a difference of concentration. 
In this particular case, however, the results are complicated by 
the Peltier effects ; Helmholtz eliminated these by employing two 
calomel cells,* similar in all respects save that the solutions of 
zine chloride contained in them were of different strengths ; 
coupling these so as to oppose each other, the resulting e. m. f. is 
the same as that of a liquid cell without Peltier eftects—since 
every kind of junction is traversed in both directionst—a ‘ simple 
liquid cell” as it may be termed; the only sources or sinks of 
‘energy being (a) the solution of zine chloride in the weaker cell, 
(4) its passage out of solution in the stronger. 
* The calomcl cell is arranged thus— 
Za | Zn Cl, | Hg, Cl, | H: 
+ The inequality in the concentration of the zine chloride solutions does not give rise to 
any difficulty, as experimenters agree in affirming that the Peltier effects at the boundary 
of electrolytic solutions are (@) small, (0) independent of the concentration. The insoluble 
character of the calomel also helps in the same direction. 
