DYNAMICAL THEORY OF HEAT. 133 



to consider all the conditions which determine the generation or absorption of heat 

 in different parts of the circuit, whatever be the properties of the metals of which 

 it is formed. This we may now proceed to do ; first for non-crystalline, and after 

 that for crystalline metals. 



§§ 112-124. General Equations of Thermo-electric Currents, in non-crystalline 



Linear Conductors. 



112. The only reversible thermal effect of electric currents, which experiment 

 has yet demonstrated, is that which Peltier has discovered in the passage of elec- 

 tricity from one metal to another. Besides this, we may conceive that in one 

 homogeneous metal formed into a conductor of varying section, different thermal 

 effects may be produced by a current in any part, according as it passes in the 

 direction in which the section increases, or in the contrary direction ; and, with 

 greater probability, we may suppose that a current in a conductor of one metal 

 unequally heated, may produce different thermal effects according as it passes 

 from hot to cold, or from cold to hot. But Magnus has shown, by careful experi- 

 ments, that no application of heat can sustain a current in a circuit of one homo- 

 geneous metal, however varying in section ; and from this it is easy to conclude, 

 by equations (7) and (9), that there can be no reversible thermal effect due to the 

 passage of a current between parts of a homogeneous metallic conductor having dif- 

 ferent sections. Now, it is clear that no circumstances, except those which ha ye 

 just been mentioned, can possibly give rise to different thermal effects in any part 

 of a linear conductor of the same or of different metals, uniformly or non- 

 uniformly heated, provided none of them be crystalline ; and we have, therefore, 

 at present nothing in the sum 2a t , besides the terms depending on the passage 

 of electricity from one metal to another, which certainly exist, and terms which 

 may possibly be discovered, depending on its passage from hot to cold, or from 

 cold to hot in the same metal. 



113. Let the principal conductor consist of n different metals ; in all n + 1 parts, 

 of which the first and last are of the same metal, and have their terminal por- 

 tions (which we have called the electrodes E and E') at the same temperature T , 

 Let T x , T 2 , T 3 , &c, denote the temperatures of the different junctions in order, and 

 let n 1 , n 2 , n 3 , &c, denote the amounts (positive or negative) of heat absorbed at 

 them respectively by a positive current of unit strength during the unit of time. Let 

 y<r x dt, y<r 2 dt, ya- 3 dt, &c, denote the quantities of heat evolved in each of the 

 different metals in the unit of time by a current of infinitely small strength, y, 

 passing from a locality at temperature t + d t to a locality at temperature t. With- 

 out hypothesis, but by an obvious analogy, we may call the elements tr v o- 2 , &c, the 

 specific heats of electricity in the different metals, since they express the quantities 

 of heat absorbed or evolved by the unit of current electricity in passing from cold 

 to hot, or from hot to cold, between localities differing by a degree of temperature 



