388 M. R. Clausius on the Discovery of 



and usiug this in (22), we have 



''=y-Mi" (^«'- 



I Tt 



Jr 



This expresses the full amount of heat taken in through the 

 agency of the current y, of which the mechanical equivalent is 

 therefore the work clone by the current. Hence (according to 

 principles fully explained above, §§ 109, 110) the thermal cir- 

 cumstances must actually cause an electromotive force Y, of which 

 the amount is given by the equation 



^ jdt (27), 



to act along the bar from left to right of the diagram ; which 

 will produce a current unless balanced by an equal and contrary 

 reaction. This result both establishes Proposition II., enunciated 

 above in § 149, and shows the amount of the electromotive force 

 producing the stated effect in terms of T and T', the tempera- 

 tures of the two sides of the bar, the obliquity of the bar to the 

 crystalline axis of symmetry, and the thermo-electric properties 

 of the substance; since if 6 and ^ denote its thermo-electric 

 powers along the axis of symmetry, and along lines perpendicular 

 to this axis, at the temperature t, and a> the inclination of this 

 axis to the length of the bar when the substance is at the tem- 

 perature t, we have 



0= y (^ — ^) sin tocos 0) .... (28). 



155. By an investigation exactly similar to that of § 115, 

 which had reference to non-ciystalline linear conductors, we 

 deduce the following expression for the electromotive force, when 

 the ends of the bar are kept at temperatures T, T' from the ter- 

 minal thermal agency IT, of a current investigated in § 153 : — 



dt (29), 





where n= j (^ cos^w + sin^o)) .... (30). 



[To be continued.] 



XLIX. On the Discovery of the true form of Carnot's Function. 

 By R. Clausius. 



To the Editors of the Philosophical Magazine and Journal. 

 Gentlemen, 



IN a paper communicated to the Royal Society of Edinburgh 

 in 1851*, Prof. W. Thomson ascribed to Mr. J. P. Joule 

 the discovery of the theorem, that Carnot's function, which Cla- 

 * Edinb. Trans, vol. xx. ; and Phil. Mag. 4th series, vol. ix. 



