of Thermo-electric Phenomena. 541 



Now (4) 



7 , 6a e \oga — a 6 + l 7/1 

 dr = h L d6; 



hence, integrating, 



®={ di de = A(h / -h")fa e i-a e *-( 9la ~ddl, (27) 



a force acting in the direction from hot to cold when h' — h" is 

 positive. 



This, then, is the coefficient of Thomson's effect ; or if a 

 current of strength u be sent through the metal in opposition 

 to the above force, the heat generated per second is (§ 28) 



j^h (28) 



which will show itself as a convexion of heat by the current in 

 one direction or the other, according as N is greater or less 

 than h n . Thus, if the current generates heat or " carries heat 

 with it" in passing through the metal from hot to cold, the 

 electromotive force ® must be acting from cold to hot ; and 

 therefore the bite of the buttons on the negative cord must be 

 greater than on the positive, or Ji" must be greater than h' . 

 This is the case in copper. But, on the other hand, if the cur- 

 rent absorbs heat in passing from hot to cold, so that the heat 

 appears to travel against the current (that is, if the " spe- 

 cific heat of vitreous electricity " be negative), then the electro- 

 motive force @ must be acting with the current, or from 

 hot to cold ; that is, h f is greater than hf', and the positive cord 

 is most acted on. This is the case in iron. 



The quantity of heat carried down small unit difference of 

 temperature in unit time by unit positive current (that is, by 

 unit quantity of vitreous electricity), Thomson calls (" with- 

 out theory, but by an obvious analogy ") the specific heat of 

 vitreous electricity in the substance A, and writes it <r a ; in other 

 words, the reversible heat generated by forcing a current 

 u against the force @ from a point at a temperature 6 to a point 

 at a temperature 6 + dd is 



jud& = -<rude (29) 



The value of a in any substance is therefore (26) 



a a =-jAe— de - 



= - i A(/4-/^)^.^(^- 1 ), . (30) 

 and similarly, of course, for erj. Hence (23) obviously follows 



