DYNAMICAL THEOEY OF HEAT. 137 



shown in the following explanation ; which was communicated in full to the 

 Royal Society, when the theory was first brought forward in 1851, although only 

 the part inclosed in double quotation marks was printed in the Proceedings. 



Example 1. Copper and Bismuth. — " ' Failing direct data, the absolute value 

 of the electro-motive force in an element of copper and bismuth, with its two 

 junctions kept at the temperatures 0° and 100° Cent., maybe estimated indirectly 

 from Pouillet's comparison of the strength of the current it sends through a 

 copper wire 20 metres long and 1 millimetre in diameter, with the strength of a 

 current decomposing water at an observed rate ; by means of the determinations 

 by Weber, and others, of the specific resistance of copper and the electro-chemical 

 equivalent of water, in absolute units. The specific resistances of different spe- 

 cimens of copper having been found to differ considerably from one another, it is 

 impossible, without experiments on the individual wire used by M. Pouillet, to 

 determine with much accuracy the absolute resistance of his circuit ; but the 

 author has estimated it on the hypothesis that the specific resistance of its sub- 

 stance is *2\ British units. Taking 02 as the electro- chemical equivalent of water 

 in British absolute units, the author has thus found 16,300 as the electro-motive 

 force of an element of copper and bismuth, with the two junctions at 0° and 100° 

 respectively. About 154 of such elements would be required to produce the 

 same electro-motive force as a single cell of Daniell's — if, in Daniell's battery, 

 the whole chemical action were electrically efficient.* A battery of 1000 copper 

 and bismuth elements, with the two sets of junctions at 0° and 100° Cent., em- 

 ployed to work a galvanic engine, if the resistance in the whole circuit be equi- 

 valent to that of a copper wire of about 100 feet long and about one-eighth of an 

 inch in diameter, and if the engine be allowed to move at such a rate as by in- 

 ductive reaction to diminish the strength of the current to the half of what it is 

 when the engine is at rest, would produce mechanical effect at the rate of about 

 one-fifth of a horse-power. The electro-motive force of a copper and bismuth ele- 

 ment, with its two junctions at 0° and 1°, being found by Pouillet to be about 

 jjjQth of the electro-motive force when the junctions are at 0° and 100, must be 

 about 163. The value of ©„' " [i. <?., in terms of the notation now used, n (2737), 

 or the value of n {t), for the freezing point] " ' for copper and bismuth, or the 

 quantity of heat absorbed in a second of time by a current of unit strength in 



* M. Jules Regnauld has since found experimentally, that 165 copper- bismuth elements balance 

 the electro-motive force of a single cell of Daniell's (See Comptes Rendus, Jan. 9, 1854, or Biblio- 

 theque Univ. de Geneve, March 1854), a result agreeing with the estimate quoted in the text, more 

 closely than the uncertainty and indirectness of the data on -which that estimate was founded would 

 have justified us in expecting. The comparison of course affords no test of the thermo-electric theory ; 

 and only shows that, as far as the observations of Weber, and others alluded to, render Pouillet's 

 available for determining the absolute electro-motive force of a copper-bismuth element, the absolute 

 electro-motive force of a single cell of Daniell's, obtained by multiplying it by the number found by 

 M. Regnauld, agrees with that which I first gave on the hypothesis of all the chemical action being 

 electrically efficient (Phil. Mag., Dec. 1851), and so confirms this hypothesis. 



