t 



DYNAMICAL THEORY OF HEAT. 157 



of which the remainder is the standard metal, there will be reversible thermal 

 action, consisting of the following parts, each stated per unit of time. 



(1.) Absorption amounting to n (t) - 7 , in a locality at the temperature T. 



(2.) Evolution amounting to a (t') - 7 , in a locality at the temperature T, 



(3.) Absorption amounting to 117 at one end, (that beyond C C',) 



and (4.) Evolution amounting to n 7 at the other end ; 



where, for brevity, a (t) and n (t') are assumed to denote the values of 

 j (<p-6) sin w cos w, at the temperatures T and T"; and n the mean value of 



Y (6 cos 2 oi + <p sin 2 w) for either end of the bar. The contributions towards the sums 



appearing in the general thermo-dynamic equations which are due to these items 

 of thermal agency, are as follows : — 



n (t) - a (t') r 7 towards 2 H t , 



and |— — M 1 r 7 towards 2 



|_ t t' J b 



the thermal agencies at the ends disappearing from each sum, in consequence of 

 their being mutually equal and opposite, and being similarly distributed through 

 localities equally heated. Now when every reversible thermal effect is included, 



XT 



the value of 2 — * must be zero, according to the second general law. Hence 



either — ^ M must vanish, or there must be a reversible thermal agency 



not yet taken into account. But probably — ^ 7— may not vanish, that is, 



— may vary with the temperature, for natural crystals, and it certainly does vary 



with the temperature for metallic combinations structurally crystalline : (for a 

 bar cut obliquely from a solid consisting of alternate layers of copper and iron, 

 for instance, the value of a decreases to zero, as the temperature is raised from 

 an ordinary atmospheric temperature up to about 280°, and has a contrary sign for 

 higher temperatures.) Hence, in general, there must be another reversible ther- 

 mal agency, besides the agencies at the ends and at the sides of the bar which we 

 have investigated. This agency must be in the interior; and since the substance 

 is homogeneous, and uniformly affected by the current, the new agency must be 

 uniformly distributed through the length, as different points of the same cross 

 section can only differ in virtue of their different circumstances as to temperature. 

 If there were no variation of temperature, there could be no such effect anywhere 

 in the interior of the bar ; and therefore, if d t denote the variation of tempera- 



