There is only one side of the subject respecting the direct correlation between thermochemical data and electro-motive force, which I think right to mention here, as it justifies the general conception, enunciated by Faraday, that the galvanic current is an aspect of the transference of chemical motion or reaction along the conductors. From experiments conducted by Favre, Thomsen, Garni, Berthelot, Cheltzoff, and others, upon the amount of heat evolved in a closed circuit, it follows that the electro-motive force of the current or its capacity to do a certain work, E, is proportional to the whole amount of heat, Q, disengaged by the reaction forming the source of the current. If E be expressed in volts, and Q in thousands of units of heat referred to equivalent weights, then E = 0·0436Q. For example in a Daniells battery E = 1·09 both by experiment and theory, because in it there takes place the decomposition of CuSO4 into Cu + O together with the formation of Zn + O and ZnO + SO3Aq, and these reactions correspond to Q = 25·06 thousand units of heat. So also in all other primary batteries (e.g. Bunsen's, Poggendorff's, &c.) and secondary ones (for instance, those acting according to the reaction Pb + H2SO4 + PbO2, as Cheltzoff showed) E = 0·0436Q.
The chief means by which we determine the valency of the elements, or what multiple of the equivalent should be ascribed to the atom, are: (1) The law of Avogadro-Gerhardt. This method is the most general and trustworthy, and has already been applied to a great number of elements. (2) The different grades of oxidation and their isomorphism or analogy in general; for example, Fe = 56 because the suboxide (ferrous oxide) is isomorphous with magnesium oxide, &c., and the oxide (ferric oxide) contains half as much oxygen again as the suboxide. Berzelius, Marignac, and others took advantage of this method for determining the composition of the compounds of many elements. (3) The specific heat, according to Dulong and Petit's law. Regnault, and more especially Cannizzaro, used this method to distinguish univalent from bivalent metals. (4) The periodic law (see Chapter XV.) has served as a means for the determination of the atomic weights of cerium, uranium, yttrium, &c., and more especially of gallium, scandium, and germanium. The correction of the results of one method by those of others is generally had recourse to, and is quite necessary, because, phenomena of dissociation, polymerisation, &c., may complicate the individual determinations by each method.