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 this which determines the electromotive force of the cell. The amount of energy which is changed from the chemical to the electrical form in a given interval of time is measured by the product of the strength of the chemical affinity into the quantity of chemicals decomposed in that time, or (what is the same thing) by the product of the electromotive force of the cell into the quantity of electricity which is circulated. This energy may be either dissipated as heat in conformity to Joule's law, or otherwise utilized in the outer circuit.

The importance of these principles was emphasized by Hermann von Helmholtz (b. 1821, d. 1894), in a memoir which was published in 1847, and which will be more fully noticed presently, and by W. Thomson (Lord Kelvin) in 1851 ; the equations have subsequently received only one important modification, which is due to Helmholtz. Helmholtz pointed out that the electrical energy furnished by a voltaic cell need not be derived exclusively from the energy of the chemical reactions: for the cell may also operate by abstracting heat-energy from neighbouring bodies, and converting this into electrical energy. The extent to which this takes place is determined by a law which was discovered in 1855 by Thomson. Thomson showed that if E denotes the "available energy," i.e., possible output of mechanical work, of a system maintained at the absolute temperature T, then a fraction

of this work is obtained, not at the expense of the thermal or