28.2 Prof. Thomson on the Dynamical Theory of Heat. 



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 2«<, besides 

 the terms depending on the passage of electricity from one metal 

 to another, which certainly exist, and terras 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-{-\ parts, of which the first and last are of the same 

 metal, and have their terminal portions (which we have called 

 the electrodes E and E') at the same temperature Tq. Let 

 Tj, Tg, T3, &c. denote the temperatures of the different junc- 

 tions in order, and let IT,, Hg, Hg, &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 

 yc^dt, ya^dt, ycr^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, 7, passing from a locality at tempera- 

 ture t + dt to a locality at temperature t. Without hypothesis, 

 but by an obvious analogy, we may call the elements cTj, o-g, &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 in 

 each metal respectively. It is easily shown (as will be seen by 

 the treatment of the subject to follow immediately) that if the 

 values of o-„ a^, &c. depend either on the section of the con- 

 ductor, or on the rate of variation of temperature along it, or on 

 any other variable differing in different parts of the conductor, 

 except the temperature, a current might be maintained by the 

 application of heat to a homogeneous metallic conductor. We 

 may therefore at once assume them to be, if not invariable, ab- 

 solute functions of the temperature. From this it follows, that 

 if ^t denote any function of /, the value of the sum J^tadt for 

 any conducting arc of homogeneous metal depends only on the 

 temperatures of its extremities, and therefore the parts of the 



sums Sa^ and — -, corresponding to the successive metals in the 



principal conductor, are respectively 



— I (J^dt, —I cx^dt, .... — I ajt, — \ o-ydt, 



and 



