90 platinized copper). These were joined up in circuit by means of very thick copper wire, and the heat developed during the solution of 33 grm. of zinc observed as before. The result was 18674 units, i.e., almost exactly the same as before. A small electromagnetic engine was next in troduced into the circuit, and the heat observed, first, v.-hen it was at rest; secondly, when it was in motion, but consuming all its energy in heat owing to friction, <fec. ; and thirdly, when it was doing work in raising a weight. The quantities of heat in the three cases were 186G7, 18657, and 1 8374 units respectively. In the first four experiments, therefore, the heat developed in the circuit is sensibly the same, the mean being 18670; the heat developed in the last case is less than this by 296, which is the equivalent of the potential energy conferred on the raised weight. From this result the value of the mechanical equivalent of heat ought to be 443. This differs considerably from the best value (423 to 425), but not more so than might be expected from experimental errors. Dynamical Theory of the Electromotive Force of the fiattery. In two very important papers published in the Philosophical Magazine for 1851, Sir William Thomson laid the foundations of the Dynamical Theory of Electro lysis, one of the objects of which, to use very nearly his own words, is to investigate, for any circuit, the relation between the electromotive force, the electrochemical equi valents of the substances operated on, and the dynamical equivalent of the chemical effect produced in the consump tion of a given amount of the materials, and by means of this relation to determine in absolute measure from experi mental data the electromotive force of a single cell of Daniell s battery, and the electromotive force required for the electrolysis of water. The relation sought for is found as follows. Let E be the electromotive force 1 of the battery. Then, by the definition of electromotive force, E is the whole work done in the circuit by a unit current during a unit of time. This work may appear as heat developed in the conductors or at the junctions according to the laws of Joule and Peltier, as the intrinsic energy of liberated or deposited ions, as work done by electromagnetic forces, as " local heat " in the battery (see below, p. 91), or otherwise. Let e be the electrochemical equivalent of any one of the elements which take part in the chemical action from which the energy of the current is derived, i.e., the num ber of grammes of that element which enter into the chemical action during the passage of unit current for a second; and let 6 be the thermal equivalent of that amount of chemical action in tlio battery into which exactly a gramme of the element in question would enter, in other words, the amount of heat that would be developed were the whole energy of the amount of chemical action just indicated spent in heat. Then it is obvious that the energy of the chemical action that takes place in the battery during the passage of unit current for a unit of time is SeO, where J is Joule s equivalent. Hence, by the principle of conservation, we must have E = JeB ; or, in words, the electromotive force of any electrochemical apparatus is, in absolute measure, equal to the dynamical equivalent of the chemical action that takes place during the 2)assage of unit c^lrrent for a unit of time. The value of J is known, being 4156 x 10 4 in absolute units. The value of e has been found by various experi menters (see below, p. 104), the most accurate result being probably that deduced from the experiments of Kohl- rausch, viz. e= 003411 for zinc. 1 All our quantities are measured, of course, in C. G. S. absolute units. [ELECTROMOTIVE FORCE. We may find 6 by direct calorimetric experiments on Calcu the heat developed in the circuit. In this way Joule tionft found for the thermal equivalent of the chemical action of lieat a Daniell s cell during the solution of 65 grammes of zinc j 6 ?/ 1 47670 (grm. deg. C.), and Ilaoult 2 , by a somewhat similar drcui process, obtained the number 47800. These give for the heat equivalent of the chemical action during the solu tion of 1 grm. zinc 733 and 735 respectively. Substitut ing these values in our formula, we get for the electro motive force of Daniell s cell in absolute C. G. S. units l 039x!0 8 or l-042x 101 But we may proceed in a totally different way to find Calcu the value of 6. Direct observations have been made ontionf the heat evolved in a great variety of chemical actions, cnemi and from these experiments we can calculate, with a con- (lata- siderable degree of accuracy, the value of 0, and thus deduce the electromotive force of a battery from purely chemical data. This method of procedure must of course be adopted if we wish to test the dynamical theory. Now, neglecting refinements concerning the state in which the copper is deposited, the state of concentration of the solu tion, (fee., the chemical action in a Daniell s cell may be stated to be the removal of the Cu from CuS0 4 in solu tion, and the substitution of Zn in its place. Now, Favre and Silberman have found for the heat developed in this chemical action 714 (grm. deg. C.) per grm. of zine. This will give, by the above formula, for the electromotive force of Daniell s element l - 012xlO H . The chemical action might also be stated as the combination of zinc with oxygen, and the solution of the zinc oxide thus formed in sulphuric acid, the separation of copper oxide from sulphuric acid, and of the copper from the oxygen. The quantity of heat evolved in the first two actions per grm. of zinc is, according to Andrews, 1301 +369 = 1670 (grm. deg. C.), and that absorbed in the last two actions 588 + 293 = 881. Hence = 789; this gives MIS x 10 M . Professor G. C. Foster 3 has calculated from Julius Thorn- sen s experiments values 805, 1387, and 017 of for the cells of Daniell, Grove, and Smee respectively; the values of the electromotive forces corresponding to these are 1 -141 x 10 s , 1 -966 x 10 s , and -875 x 10 8 . These results are in fair agreement with the different values of the electromotive force obtained from direct experiment. It follows from Thomson s theory that a certain mini Limit mum electromotive force is necessary to decompose water; electi and he calculated from the data of Joule that this mini- motiv mum was 1*318 times the electromotive force of a Daniell s e ^ r cell. Favre and Silberman found for the heat developed lysis. in the formation of H 2 O 68920, from which we conclude that the minimum electromotive force required to electro lyse water is 68920 + 47800, i.e., 1 44 times that of a Daniell s cell. 4 Development of Heat at the Electrodes. In a remarkable j j0ca ] paper, 5 which we have already quoted, Joule investigated heat, directly the disturbing effect of the electrodes on the heat s Wiedemann, Bd. ii. 2, 1118. 3 Everett, Illustrations of C. G. S. System of Units, p. 77. No reference to the source is given. 4 Verdet (Thiorie Mec. de la Chaleur, torn. ii. p. 207) states that Favre was the first to point this out, but gives no citation. It seems unlikely that Favre considered the matter so early as 1851. (See Violle s bibliography at the end of Verdet s volume.) 8 Mem. Lit. and Phil. Soc. Manchester, ser. 2, vol. vii., 1843. This paper seems to have been in a great measure lost sight of. In his earlier papers (Poyg. Ann., ciii. 504, 1S58) Bftsscha says he had not seen it. Poggendorff, in a note, p. 504, appreciates it in a manner which appears to us unjust. This may have arisen from misunderstanding of Joule s terminology, however. Verdet (Chaleur, torn. ii. p. 204J does not seem to have been acquainted with it. It is mentioned in the bibliography by M. J. Violle, however, under 1846, which is the date of the volume of the Mcmmrs in which it
was published. The paper was actually read Jan. 1843.