Prof. Thomson on the Dynamical Theory of Heat. 223 



probably to all currents due solely to the thermal electromotive 

 force^ even if A and B were in reality variable, provided the 

 limiting values of these quantities for infinitely small values of 7 

 be used. 



108. Let us consider a conductor of any length and form, 

 but of comparatively small transverse dimensions, composed of 

 various metals at different temperatures, but having portions at 

 its two extremities homogeneous and at the same temperature. 

 These terminal portions will be denoted by E and E', and will 

 be called the principal electrodes, or the electrodes of the principal 

 conductor ; the conductor itself being called the principal con- 

 ductor to distinguish it from others, either joining its extremities 

 or otherwise circumstanced, which we may have to consider again. 



Let an electromotive force be made to act continuously and 

 uniformly between these electrodes ; as may be done, for instance, 

 by means of a metallic disc included in the circuit touched by 

 electrodes at its centre and a point of its circumference, 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 electromotive force be denoted by P, to be re- 

 garded as positive, when it tends to produce a current from E 

 through the principal conductor, to E'. Let the absolute strength 

 of the cui-rent, which in these circumstances passes through the 

 principal conductor, be denoted by 7, to be considered as posi- 

 tive if in the direction of P when positive. 



109. Then p<y will be the amount of work done by the elec- 

 tromotive 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 + By^ be, in accordance with the preceding ex- 

 planations, 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(-Ay + B72) (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-fB7) (4), 



from which we deduce 



P + JA 

 -^^^^ (5)- 



1 10. 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 



