Mr. 0. J. Lodge on Thermo-electric Phenomena. 351 



*e 



The errors in the original theory are rather subtle, and are 

 worth pointing out, not for the purpose of casting any slur on 

 the valuable work of Professor Avenarius, but as illustrating 

 the slight though important difference between the present 

 theory which includes Thomson's effects, and the two hypo- 

 theses which ignored them and which were also independent 

 of the laws of thermodynamics. 



First hypothesis. That the electromotive force of a thermal 

 joint is expansible in terms of the (Centigrade) temperature, 

 thus 



e = a + bt + ct 2 (1) 



Second hypothesis. That in a complete circuit there is no 

 electromotive force anywhere except at the junctions of differ- 

 ent metals, or that the electromotive force of a thermo-electric 

 pair, with two joints at different temperatures, is obtained 

 simply by subtracting ttie electromotive force of the joint at 

 the temperature t 2 from that of the joint at the temperature 

 h, or 



E = ^-. 2 (2) 



Conclusion following from these, the law of Avenarius — 

 E=6(* 1 -« 2 ) +<*?-£> (3) 



Now the first hypothesis taken by itself is a tolerably safe 

 assumption, and, as it happens, is actually true as it stands. 

 But when the second hypothesis is also made, the general 

 theory of heat-engines requires the constant c to be zero, 

 which would render most of the subsequent investigation 

 meaningless, and would make (3) entirely discordant with ex- 

 periment. This, in fact, is the very discrepancy which led 

 Sir William Thomson about 1851 or 1852 to seethe falsehood 

 of hypothesis No. 2, and hence to the discovery of an electro- 

 motive force between different portions of one and the same 

 metal at different temperatures, which, under the form of the 

 " electric convection of heat," he subsequently caused to be 

 verified by a most laborious series of experiments*. 



The falsehood of the second hypothesis is fully admitted by 

 Professor Avenarius in 1873 f. 



The conclusion when considered alone is correct, as I have 

 said above ; but the constants b and c have not the same mean- 

 ing as they had in (1). If we consider them to have the same 

 value in (1) and (3), we shall be led into error as regards mat- 

 ters of fact, just as Professor Avenarius was. 



* Phil. Trans., Bakerian Lecture, 1856. Oddly enough this memoir is 

 quoted by Professor Avenarius in the original paper where the Thomson- 

 effects are ignored. 



t Pogg. Ann. vol. cxlix. footnote, page 374. 



