DYNAMICAL THEORY OF HEAT. 131 



Let an electro-motive force be made to act continuously and uniformly be- 

 tween these electrodes ; as may be done for instance by means of a metallic disc in- 

 cluded in the circuit touched by electrodes at its centre and a point of its circum- 

 ference, and made to rotate between the poles of a powerful magnet, an arrange- 

 ment equivalent to the " engine" spoken of above. Let the amount of this electro- 

 motive force be denoted by P, to be regarded as positive, when it tends to pro- 

 duce a current from E through the principal conductor, to E'. Let the absolute 

 strength of the current, which, in these circumstances, passes through the principal 

 conductor, be denoted by 7, to be considered as positive, if in the direction of P 

 when positive. 



109. Then, P7 will be the amount of work done by the electro-motive force in 

 the unit of time. As this work is spent wholly in keeping up a uniform electric 

 current in the principal conductor, it must be equal to the mechanical equivalent 

 of the heat generated, since no other effect is produced by the current. Hence, if 

 — A7 + B7 2 be, in accordance with the preceding explanations, the expression for 

 the heat developed in the conductor in the unit of time by the current 7, and if 

 J, as formerly : denote the mechanical equivalent of the thermal unit, we have 



P7 = J(-A7 + B7 2 ) .... (3), 



which is the expression for the particular circumstances of the first Fundamental 

 Law of the Dynamical Theory of Heat. 

 Hence, by dividing by 7, we have 



P = J(-A + B 7 ) (4), 



from which we deduce 



P + JA ... 



7=- T b~ • • • («)■ 



110. These equations show that, according as P is greater than, equal to, or 

 less than- J A, the value of 7 is positive, zero, or negative ; and that, in any of the 

 circumstances, the strength of the actual current is just the same as that of the 

 current which an electro-motive force equal to P + JA would excite in a ho- 

 mogeneous metallic conductor having J B 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 in- 

 trinsic electro-motive force in the principal conductor, 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, J A, applied either by means of 

 a perfect non-conductor, or some electromotor, placed between E and E', in order 

 that there may be electrical equilibrium in the principal conductor ; 



And (2.) That J B, 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 con- 

 ductors is reduced to a knowledge of all the circumstances on which the value of 



VOL. XXI. PART I. 2 N 



