ELECTROMOTIVE FOECE.j ELECTRICITY 91 i Its developed in an electrolyte. His method was as follows. j^ co ii O f w jre whose resistance was known in terms of a certain standard was inserted in the circuit of six Daniell s elements, and the heat evolved in it carefully measured by immersing it in a calorimeter. The resistance of the rest of the circuit, including that of the battery, was found by interpolating a known resistance in the circuit and observ ing, by means of a tangent galvanometer, the ratio in which the current was reduced. (The assumption is here made that the electromotive force of a Daniell s cell is constant for different currents.) Knowing the heat evolved in a part of the circuit of known resistance, and knowing the resistance of the whole circuit, the heat evolved accord ing to Joule s law in the whole circuit during the oxida tion of 65 grammes of zinc can be calculated from the indications of the tangent galvanometer previously com pared with a voltameter. Henc the thermal equivalent of the work done by the electromotive force of a Daniell s cell during the solution of 65 grm. zinc can be found. The value of arrived at by Joule in this way is 47670 (grm. deg. C. ). Electrolytic cells of various construction were then in serted into the circuit. The electromotive force resisting the passage of the current through the cells was found by taking the number of battery cells just sufficient to pro duce electrolysis, observing the current, then increasing the number of cells by one and observing the current again. If i be the current in the first case, corrected to bring it to the value it would have had if the resistance of the whole circuit had been the same as in the second case, and j the current in the second case, then, E being the number of battery cells used in the first case, the electro motive force Z opposing the current is given by the unit being the electromotive force of a Daniell s cell. Z being known and assumed constant for different currents within certain limits, the resistance of the whole circuit, electrolyte included, can be found by Ohm s method as above. The amount of heat H which ought to be de veloped in the electrolyte by Joule s law can then be calculated. The amount of heat H actually developed was observed. It was found that H is in general greater than II, the difference per electrolysis of 65 grm. zinc with various electrodes is shown in the following table : Electrode. Z ir-n L Z- L + i Ft ! Amg. Zn 2-81 66300 1-39 1-42 Pt j Pt 2-47 53000 I ll 1-36 AX 1 ! Ag> 1-75 16400 34 1-40 Pt 1 I Pt 1 1-90 28800 60 1-29 Pt 1 j Pt 1 1-90 26700 56 1-34 1 Platinized. The electrolyte in all these cases was dil. HJS0 4 , excepting the last case, where it was a solution of potash of sp. g. 1 063. In all the cases the chemical process is finally the same or very nearly so, viz., the freeing of the elements of water, hydrogen and oxygen, in the ordinary gaseous 1 state, and the transference of a certain quantity of H. 2 SO 4 from the negative to the positive electrode, or of alkali in the opposite direction. Yet the values of H - H (which we may call the local heat) are very different. It will be seen, however, that the values of H - H and Z rise and fall together; and, if we calculate the electromotive forces (L) corresponding to the values of H - H, by dividing by 47670, which was found for the thermal equivalent of the electro- 1 The amount of oxygen that final!} escapes in the active state ns ozone is very small. motive force of a Daniell s cell, and subtract the values of L thus found from Z, we get results which are not far from constant. The mean of the values of Z - L is 1 36, the thermal equivalent of which is 64800, which is not very different from 68900, the heat evolved in the com bination of 2 grm. of H with 16 grm. of O to form water. It appears, therefore, that the local heat corresponds to the excess of the electromotive force of polarization over the electromotive force requisite to separate w r ater into its component gases. In other words, the work done by the current against this residual electromotive force is accounted for by the local heat H - H developed in the cell (see Joule s statement above, p. 89). A glance at the column L in the above table shows that this residual electromotive force depends greatly on the nature of the electrodes. Thus when the positive and negative electrodes are plates of platinum and zinc respectively the residual electromotive force is 1 39, whereas with platinized silver plates it is only 34. Local heat and the corresponding electromotive force play a very important part in the working of batteries. Owing to this cause there is an evolution of heat in the cell itself which varies with the strength of the current, and uses up a certain definite fraction of the energy furnished by the solution of the zinc. By sufficiently increasing the external resistance, the amount of heat developed in the cell according to the law JH = HI 2 can be made as small a fraction as we please of the whole heat thus developed; but the amount of local heat generated in the cell during the solution of 65 grm. zinc is not greatly altered in this way, at least not in a cell of Daniell, or in any other of the so-called constant batteries. Did our space permit we might quote a great variety of experimental results to illustrate the principles we have been discussing. Most of these investigations are due to the French physicists Favre and Silbermann, whose researches have greatly ad vanced this department of the science of energy. Very copious extracts from the memoirs of these and other physicists who have worked in this department will be found in Wiedemann, Ed. ii. 2, 1121 sqq. The reader who desires to follow this interesting subject to the sources will find his labour much lightened by referring to M. J. Yiolle s excellent bibliography of the mechanical theory of heat, appended to the second volume of Verdet s Theorie Mecanique de la Chalenr. Much has been done for the theory of the subject by a series of papers on the mechanical theory of electrolysis by Bosscha, 2 in which the somewhat complicated phenomena involved are analysed in a remarkably clear and able way. Any reader who desires to know what has been done in this department will do well to consult these papers. We quote the fol lowing as nn example of Favre and Silbermann s results and of the calculations of Bosscha. The heat evolved in a cell of Smee 3 and in platinum wires of different lengths through which it was circuited was measured with the following result : Local heat and residual electro motive force. Favre aii ! Silver- maim. Bosscha. Heat in r e ll. Hrat in wire. Length of wire. Heat in cell calc. 13127 4965 25 mm. 13523 11690 6557 50 ,, 11788 10439 7746 100 1018S 8992 9030 200 9048 The heat in each case is that evolved during the libera tion of 1 grm. of hydrogen in the cell. If we assume that the whole heat in the cell and in the wire is generated according to Joule s law, and calculate on this hypothesis the resistance of the cell in mm. of the wire, we should get 8 Pogg. Ann., ci., ciii., cv., cviii., 1857. &
8 Amalgamated xinc arid platinized copper.