82 RESEARCH COMMITTEES. 
In an earlier memoir Helmholtz* had discussed the e. m. f. of 
liquid cells from a different point of view. Taking such a cell as 
Cu | Cu SO, dil | Cu SO, strong | Cu 
he showed that the e. m. f. could be deduced thermcdynamically 
from the vapour pressures, the electrcchemical equivalent of the 
salt, and Hittorf’s migration constant. If we suppose 1 equivalent 
of the salt to be dissolved in a quantity , of water in one 
solution, and in w, in the other, and if » denote the migration 
constant, Helmholtz finds 
Pa 
E = fiw. C2 ioldpe .o2 |) eee) 
DP 
For a moderate range of concentraticns the following relaticn 
holds good— 
b 
Pp = = 
w 
where 6 is constant. In such cases (8) reduces to 
w 
—— BO Nae (lee aE) LOC eer 
W, 
P 
The accuracy of the calculation of e. m. f.’s by this formula was 
confirmed experimentally by J. Mosert; but, as Helmholtz 
himself pointed out, the introduction into the theory of migration 
constants—which are not known with any great accuracy §—is a 
source of weakness in the method as far as the verification of the 
thermodynamic theory is concerned, for which purpose he gives 
the preference to the experiments with opposed cells. 
This mode of investigation has however been applied by Moser || 
to the more accurate determination of migration constants, from 
measurements of e. m. f., vapour pressure, and concentration ; but 
very little has so far been done in this way, though it would seem 
to open up a promising line of research. 
(>) The relation between the e. m. f. required for the decom- 
position of water and the pressure of the evolved gases. 
In his third memoir on the “Thermodynamics of Chemical 
Processes” Helmholtz treats this case at great length, obtaining 
expressions for the free energies of water and of detonating gas, 
and deducing the e. m. f. of agas-battery. All his results contain, 
however, an arbitrary constant, so that only differences are of 
any practical use; the calculations of e. m. f. possessing individually 
* Monatsb. d. Akad. der Wiss., Berlin, 1877; Wied. Ann. iii, p. 201; Phil. Mag. [5], V., p. 348. 
} The analysis is not reproduced, being quite straightforward ; the notation in the results 
is altered to agree with that employed in the previous discussion. 
¢ Wied. Ann. iii, p. 201. 
§ We are indeed almost in the dark as to the relation between the migration constant and 
the concentration. 
|| Sitzungsb. d. k, Akad. der Wiss. Wien, Bd. xcii. Abth. ii, p. 652. 
