224 Prof. Thomson on the Dynamical Theory of Heat. 



negative ; and that, in any of the circumstances, the strength of 

 the actual cui'rent is just the same as that of the current which 

 an electromotive force equal to P + Jxl would excite in a homo- 

 geneous metallic conductor having JB for the absolute numerical 

 measure of its galvanic resistance. Hence we conclude : — 



(1.) That in all cases in which the value of A is finite, there 

 must be an intrinsic electromotive force in the principal con- 

 ductor, which would itself produce a current if the electrodes 

 E, E' were put in contact with one another, and which must be 

 balanced by an equal and opposite force, JA, applied either by 

 means of a perfect non-conductor, or some electromotor, placed 

 between E and E', in order that there may be electrical equili- 

 brium in the principal conductor. 



And (2.), That JB, which cannot vanish in any case, is the 

 absolute numerical measure of the galvanic resistance of the 

 principal conductor itself. 



It appears, therefore, that the whole theory of thermo-electric 

 force in linear conductors is reduced to a knowledge of the cir- 

 cumstances on which the value of the coefficient A, in the ex- 

 pression — Ay + B7^ for the heat developed throughout any 

 given conductor, depends. 



110. To express the second general law, we must take into 

 account the temperatures of the different localities of the circuit 

 in which heat is evolved or absorbed, when the current is kept 

 so feeble (by the action of the electromotive force P against the 

 thermo-electric force of the system) as to render the frictional 

 generation of heat insensible. Denoting then by a^y the heat 

 absorbed in all parts of the circuit which are at the temperature 

 t, by the action of a cui'rent of infinitely small strength 7 : so 

 that the term — A7, expressing the whole heat generated not 

 frictionally throughout the principal conductor in any case, will 

 be the sum of all such terms with their signs changed, or 



A7=2a<7, 

 which gives 



2«,=A ........ (6); 



and denoting by F the value of the electromotive force required 

 to balance the thermo-electric tendency; we have 



F=J2«, (7). 



The second general law, as expressed above in equation (1), ap- 

 plied to the present circumstances, gives immediately 



2^ = (8); 



or, since y is the same for all terms of the sum, 



2-^=0 (9). 



