Theories of resi dual electro- motiva force. 92 values varying from 66 to 200 mm. If, however, we assume, in accordance with the principles explained above, that a constant fraction of the whole energy per grin, of liberated hydrogen appears as local heat in the cell, then, Q denoting the whole heat which appears in the cell, L the local heat, H the heat in the wire, R the resistance of the cell, S that of the wire, we have Q-L R H S ; audit is found that on making R = 32 3 and L = 7589, this formula will represent the results of experiment very fairly. The last column in the above table gives the value of Q thus calculated. In general so good an agreement ij not to be expected, because L may and does vary with the strength of the current. Thus far we have been dealing with the direct results of experiment, but when we inquire into the reason for the existence of this residual electromotive force and of the local development of heat corresponding to it, and, in particular, when w r e ask why the effect is so much greater with some metals than with others, the answers become less satisfactory. We meet, in fact, with considerable divergence of opinion. Joule s view was that the effect is due to the affinity of the metal of the electrode for oxygen. This is endorsed to a certain extent by Sir "William Thomson, who puts the matter thus: 1 "In a pair consisting of zinc and tin the electromotive force has been found by Poggeudorff to be only about half that of a pair consisting of zinc and copper, and consequently less than half that of a single cell of Smee s. There is therefore an immense loss of mechanical effect in the external working of a battery composed of such elements, which must be compensated by heat produced within the cells. I believe, with Joule, that this compensa ting heat is produced at the surface of the tin in con sequence of hydrogen being forced to bubble up from it, instead of the metal itself being allowed to combine with the oxygen of the water in contact with it. A most curious result of the theory of chemical resistance is that, in ex periments (such as those of Faraday, Exp. Res., 1027, 1028) in which an electric current passing through a trough con taining sulphuric acid is made to traverse a diaphragm of an oxidizable metal (zinc or tin) dissolving it on one side and evolving bubbles of hydrogen on the other, part (if not all) of the heat of combination will be evolved, not on the side on which the metal is being eaten away, but on the side at which the bubbles of hydrogen appear. It will be interesting to verify this conclusion by comparing the quantities of heat evolved in two equal and similar electro lytic cells in the same circuit, each with zinc for negative electrode, and one with zinc the other with platinum or platinized silver for the positive electrode." 2 Bosscha dissents from the theory of "chemical resistance" thus expounded, and advances a different explanation. According to him, the local heat arises from the energy lost by the liberated ions in passing from the active to the ordinary state. We know that the hydrogen which is being liberated at the surface of an electrode can effect reductions which hydrogen in the ordinary state cannot accomplish; it is liberated in fact in a state of greater in trinsic energy than usual. It is this excess of intrinsic energy which appears as local heat, and gives rise to the residual electromotive force in electrolysis. Different metals possess in very different degrees the power of re ducing active hydrogen to the ordinary state: and therefore 1 Phil. Mag., 1851 (2 p. 556. 2 The effect here predicted was afterwards observed by Thomson himself, Re.p. Brit. Assoc., 1852, and later still by Bosscha, Pogg. Ann., ciii. p. 517 ELECTRICITY [ELECTROMOTIVE FORCE. the proportion of hydrogen which gets away from the electrode in the active state differs according to circum stances. Bosscha s theory is that it is the intrinsic energy thus earned aioay from the electrode that appears as local heat. Similar remarks apply of course to oxygen, the active form of the gas being probably ozone. As a verifica tion of the theory, the fact is cited that at the surface of a plate of carbon, which possesses in an eminent degree the power of reducing ozone to the ordinary state, the residual electromotive force and local heat are very small. At all events the theory of " chemical resistance " is held to be inadequate to explain the facts ; for calculating from some results of his own, combined with those of Lenz and Saweljew, he finds for the residual electromotive force at electrodes of Pt 45 Fe 49 Cu 64 Sn Hg 1-20 Zn 1-20 from which it appears that the order of magnitude of the electromotive forces is not that of the affinities of the metals for oxygen. Electrical Measure of Chemical Affinity. In a paper 3 sent to the French Academy to compete for a prize offered for the best essay on the beat of chemical combination, Joule elaborates an ingenious method for measuring chemical affinity. By direct observation it is ascertained how much heat is developed in a given time in a certain standard coil of wire, when it is traversed by a current whose strength is measured by means of a tangent galvanometer. Then three readings of the tangent galvanometer are taken first, when the galvanometer alone is in circuit with the battery, secondly, when the standard coil is also inserted, thirdly, when an electro lytic cell is inserted instead of the coil. The amount of the ions liberated and the heat evolved in the cell during a given time is also observed in the last case. If A, B, C be the readings of the galvanometer in the three cases, and if x be the resistance of a metallic wire capable of retarding the current equally with the electrolytic cell,* then we easily get, taking the resistance of the standard coil as unitv, (A-C)B = (A-B)C Now if the resistance x were put in the place of the electrolytic cell, the current would be the same ; hence by Faraday s law the amount of chemical energy absoi bed in the battery would be the same. Also the heat evolved in the rest of the circuit, excluding x, would be the same. It follows, therefore, that the heat H which would be evolved in x is the equivalent of the whole energy given out in the electrolytic cell. If therefore we subtract from H the heat K which actually appears in the cell, the remainder H - K is the heat equivalent of the intrinsic energy of the liberated ions ; and, provided they appear finally in the "ordinary" 5 condition, II - K is the heat which would be developed when they are allowed to combine. In this way Joule found for the heat evolved in the combustion of 1 grm. of copper, zinc, and hydrogen respectively 594, 1185, 33553. Galvanic Batteries. It would be inconsistent with our general plan to attempt an exhaustive discussion of all the different electromotors which depend for their energy on chemical action. Wiedernann s Galvanismns, or books on telegraphy and other arts in which electricity is applied to technical purposes, may be consulted by the reader who wishes for fuller information. A brief discussion of some typical batteries will, however, be useful, were it only to illustrate the principles we have just been laying down. All the earlier batteries were one-fluid batteries. The
- Noticed in the Comptcs Rendus, Feb. 1846, and published at length
in Phil. Mag., 1852. 4 Notice that it is not Raid that x is equal to the resistance of the electrolyte. Bosscha in the papers we have quoted, either from not having seen the paper we are now analysing, or through a misunder standing, accuses Joule of error here. The reasoning (J ogg. Ann,, ci. p. 540) which he seems to quote from Joule is not to be found in this or in any other of Joule s papers that we know of. Polarization is taken into account by Joule (see Phil. Mag., 1852 (1), p. 485). The criticis ms of Verdet, who seems to follow Bosscha, are equally ground less (Theorie Mecaniijue de la Chalcur, t. ii. p. 204). 8 This word is left purposely a little vague, and is used to avoid a long discussion of points which need not be raised here. Mea- sure- nient chemi a tfinit
Joule