650 PROCEEDINGS OF THE AJVIERICAN ACADEMY. 



with the line for lead. The representative lines for copper and iron are 

 here made straight, though in a later figure they are shown as curves. In 

 accordance with the ordinary interpretation of a temperature-entropy 

 diagram, unit q.uantity of electricity, ten coulombs, flowing (in the or- 

 dinary sense) from C^ to C in copper or from I to Iq in iron absorbs 

 heat, and mce versa, the Thomson effect ; flowing from C in copper to 

 / in iron, it absorbs heat, and vice versa, the Peltier or Seebeck effect. 

 If now we denote by — ©^ ^^ the area T^TCCqTq and by — 0, the 

 area T^TIIJ^q, the total, or net, thermo-electric force, in a copper-iron 

 couple having one junction at T^ (absolute zero) and the other junc- 

 tion at T, is represented by the area 



C,CII,C, = - 0, + ©,. (U) 



If we let ttg = the line T^Co and a; = T^^I^, we can write 



_0, = a,^+i/3,r^ (la) 



and -0, = a,^+iAn (16) 



where (S, = {C'C -- T) and P^ = -(11' -^T). 



These equations (15) and (16) correspond to equation (55) of Voigt's 

 paper. 



It is evident from our diagram that, if we allow a very small increase 

 of temperature, from Tto T + dT, and if we let aS", represent the en- 

 tropy of ten coulombs at /, the conventional zero of entropy being so 

 taken that >S< = Tl, we have 



-pdT=S,dT, or -^ = ^i. (17) 



Now the 0' of the Voigt formula (13) is -pr,, and is therefore equal to 



our —Si. It is numerically equal to the "thermo-electric height" of 

 iron relative to lead.^*^ 



The relation of &\ to St, the mechanical equivalent of the Thomson- 

 effect coefftcient, is readily found. The mechanical equivalent of the 

 Thomson-effect heat absorbed by ten coulombs in rising in iron from 



^' We use the — sign here in order to conform to the use of Voigt. 



^^ At least is has been so taken by Moreau in his empirical test of the 

 Voigt formula, without protest, so far as we know, from Voigt, though the 

 latter docs not, perhaps, say explicitly that his @'m for any metal m has refer- 

 ence to lead. 



