Prof. Thomson on the Dynamical Theory of Heat. 387 



alternate layers of copper and iron, the value of fl decreases to 

 zero as the temperatui-e 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 rever- 

 sible thermal 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 uni- 

 formly distributed through the length, as different points of the 

 same cross section can only differ in virtue of their different cir- 

 cumstances as to temperature. If there were no variation of 

 temperature, there could be no such effect anywhere in the inte- 

 rior of the bar ; and therefore if dt denote the variation of tem- 

 peratiu-e in an infinitely small space dx across the bar in the 

 plane of the diagram, and ^ an unknown element, constant or a 

 function of the temperature, depending on the nature of the sub- 

 stance, we may assume 



. di^ 



as the amount of absorption, per unit of the volume of the bar, 

 due to a current of intensity i, by means of the new agency. 

 The whole amount in a lamina of thickness dee, length /, and 

 breadth a perpendicular to the plane of the diagram, is therefore 



ix£cilds, 



As there cannot possibly be any other reversible thermal agency 

 to be taken into account, we may now assume 



2H,=y-^{[n(T)-n(T')]+Jjr//} . (22), 



XT 



The second general law, showing that 2 ~j- must vanish, gives 

 by the second of these equations, 



«m_2m^j^^,,=o . . . (24). 



Substituting in place of T, t, and differentiating with reference 

 to this variable, we have as an equivalent equation, 



4 



