386 Prof. Thomson on the Dynamical Theory of Heat. 



15-t. Let us uow suppose the two sides CD, CD' to be kept 

 at uniform temperatures, T, T', and the two ends to be kept with 

 equal and similar distributions of temperatures, whether a cur- 

 rent is crossing them or not. Then if a current of strength y 

 be sent through the bar from left to right of the diagram, in a 

 circuit 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 fi(T) -j-y, in a locality at the 



temperature T. 

 (2.) Evolution amounting to fl(T')y7, in a locality at the 



temperature T'. 

 (3.) Absorption amounting to Yi'y at one end (that 



beyond CC), 

 and (4.) Evolution amounting to 117 ^^ the other end; 



where, for brevity, n(T) and il(T') arc assumed to denote the 



values of -=- (<^ — ^"1 sin w cos w at the temperatures T and T' ; 



t 

 and n the mean value of -j- [6 cos^ m + ^ sin'^tw) 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 : — 



and 



rn(T)-n(T')]-^ y towards SH„ 



the thermal agencies at the ends disappearing from each sum in 

 consequence of their being mutually equal and opposite, and 

 similarly distributed through localities equally heated. Now 

 when every reversible thermal eflfect is included, the value 



of 2— ^ must be zero, according to the second general law. 



Hence cither —^ )=^ must vanish, or there must be a 



reversible thermal agency not yet taken into account. But pro- 

 bably " i, }rq-^ may not vanish, that is —may vary with the 



temperature, for natural crystals; and it certainly docs vary with 

 the temperature for metallic combinations structurally crystalline 

 (for instance, for a bar cut obliquely from a solid consisting of 



