286 Prof. Thomson on the Dynamical Theory of Heat. 



however rough, of the absolute values of the thermo-electric ele- 

 ments in any case in which observations that have been made 

 afford, directljf or indirectly, the requisite data. This I have 

 done for copper and bismuth, and copper and iron, in the manner 

 shown in the follo\\^ng explanation, which was communicated in 

 full to the Royal Society of Edinburgh when the theory was first 

 brought forward in 1851, although only the part enclosed in 

 double quotation marks was printed in the ' Proceedings/ 



118. Example 1. Copper and Bismuth. — " 'Failing direct data, 

 the absolute value of the electromotive force in an element of cop- 

 per and bismuth, with its two junctions kept at the temperatures 

 0^ and 100° Cent., may be estimated indirectly from Pouillet's 

 comparison of the strength of the current it sends through a 

 copper wire 20"* long and 1 millim. 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 resist- 

 ance of copper and the electro-chemical equivalent of water, in 

 absolute units. The specific resistances of different specimens of 

 copper having been found to differ considerably from one an- 

 other, 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 substance 

 is 2^ British units. Taking •02 as the electro-chemical equiva- 

 lent of water in British absolute units, the author has thus found 

 16,300 as the electromotive 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 electromotive force as a single cell of DanielPs — if, in 

 DanielFs 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° C, employed to 

 work a galvanic engine, if the resistance in the whole circuit be 



* M. Jules Regnaukl has since found experimentally, that 16.5 copper- 

 bismuth elements balance the electromotive force of a single cell of Daniell's 

 (see Comptes Rendus, Jan. 9, 1854, or Bibliotheque Universelle de Geneve, 

 March 1834), 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 ex])ecting. The compa- 

 rison 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 ren- 

 der Pouillet's available for determining the absolute electromotive force of 

 a copper-bismuth element, the absolute electromotive force of a single cell 

 of Daniell's, obtained by multiplying it by the number found by M. Reg- 

 nauld, agrees with that which I first gave on the hypothesis of all the che- 

 mical action being electrieally efficient (Phil. Mag. Dec. 18.t1), and so 

 fonfirms this hypothesis. 



