DYNAMICAL THEORY OF HEAT. 151 



the whole range (being, as proved above, equal to I <pdt), in the case of each ele- 



ment, the theorem expressed by these equations is true of the thermo-electric 

 forces in the single elements for all ranges of temperature, provided the absolute 

 temperatures of the hot and cold junctions be the same in the different elements. 

 The second equation, by successive applications of which the first may be derived, 

 is the simplest expression of a theorem which was, I believe, first pointed out and 

 experimentally verified by Becqueeel in researches described in the second volume 

 of his Traite d'Electricite. 



140. For brevity, we shall call what has been denoted by (p (B, C) the thermo- 

 electric relation of the metal B to the metal C ; we shall call a certain metal (per- 

 haps copper or silver) the standard metal ; and if A be the standard metal, we 

 shall call (p (A, B) the thermo-electric power of the metal B. The theorem expressed 

 by the last equation may now be stated thus : The thermo-electric relation between 

 two metals is equal to the difference of their thermo-electric powers ; which is nearly 

 identical with Becquerel's own statement of his theorem. 



§§ 141-146. Elementary Explanations in Electro-cinematics and Electro-mechanics. 



141. When we confined our attention to electric currents flowing along linear 

 conductors, it was only necessary to consider in each case, the whole strength of 

 the current, and the longitudinal electro-motive force in any part of the circuit, 

 without taking into account any of the transverse dimensions of the conducting 

 channel. In what follows, it will be frequently necessary to consider distributions 

 of currents in various directions through solid conductors, and it is therefore con- 

 venient at present to notice some elementary properties, and to define various 

 terms, adapted for specifications of systems of electric currents and electro-motive 

 forces, distributed in any manner whatever throughout a solid. 



142. It is to be remarked, in the first place, that any portion of a solid traversed 

 by current electricity may be divided, by tubular surfaces coinciding with lines of 

 electric motion, into an infinite number of channels or conducting arcs, each con- 

 taining an independent linear current. The strength of a linear current being, as 

 before, defined to denote the quantity of electricity flowing across any section in 

 the unit of time, we may now define the intensity of the current, at any point of a 

 conductor, as the strength of a linear current of infinitely small transverse dimen- 

 sions through this point, divided by the area of a normal section of its channel. The 

 elementary proposition of the composition of motions, common to the cinematics 

 of ordinary fluids and of electricity, shows that the superposition of two systems 

 of currents in a body gives a resultant system, of which the intensity and direc- 

 tion at any point are represented by the diagonal of a parallelogram described 

 upon lines representing the intensity and direction of the component systems 

 vol. xxi. part i. 2 s 



