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 and completed by James Prescott Joule, of Manchester, in 1841. Joule, who believed that heat is producible from mechanical work and convertible into it, measured the amount of heat evolved in unit time in a metallic wire, through which a current of known strength was passed; he found the amount to be proportional to the resistance of the wire multiplied by the square of the current-strength; or (as follows from Ohm's law) to the current-strength multiplied by the difference of electric tensions at the extremities of the wire.

The quantity of energy yielded ap as heat in the outer circuit being thus known, it became possible to consider the transference of energy in the circuit as a whole. "When," wrote Joule, "any voltaic arrangement, whether simple or compound, passes a current of electricity through any substance, whether an electrolyte or not, the total voltaic heat which is generated in any time is proportional to the number of atoms which are electrolyzed in each cell of the circuit, multiplied by the virtual intensity of the battery: if a decomposing cell be in the circuit, the virtual intensity of the battery is reduced in proportion to its resistance to electrolyzation." In the same year he enhanced the significance of this by showing that the quantities of heat which are evolved by the combustion of the equivalents of bodies are proportional to the intensities of their affinities for oxygen, as measured by the electromotive force of a battery required to decompose the oxide electrolytically.

The theory of Roget and Faraday, thus perfected by Joule, enables us to trace quantitatively the transformations of energy in the voltaic cell and circuit. The primary source of energy is the chemical reaction: in a Daniell cell, Zn|Zn SO4|Cu SO4|Cu, for instance, it is the substitution of zinc for copper as the partner of the sulphion. The strength of the chemical affinities concerned is in this case measured by the difference of the heats of formation of zinc sulphate and copper sulphate; and it is