Prof. Thomson on the Dynamical Theory of Heat. 283 

 Hence the general equations (7) and (9) become 



F=j|n,+n2+ ■••• i-n^-Pv^-rV^- .... 



-( "~V„c?^- I '\,dt\ (10), 



-J,. 7-"=° (11). 



which are the fundamental equations of thermo-electricity in 

 non-crystalline conductors. In these, along with the equation 



P + P 



which shows the strength of the current actually sustained in 

 the conductor when an independent electromotive force, P, is 

 applied between the principal electrodes E, E', we have a full 

 expression of the most general circumstances of thermo-electric 

 currents in linear conductors of non-crystalline metals. 



114. The special qualities of the metals of a thermo-electric 

 circuit must be investigated experimentally before we can fix the 

 values of ITj, li^, &c., and a-^, cr^, &c. for any particular case. 

 The relation between these quantities expressed in the general 

 equation (11) having, as we have seen, a very high degree of 

 probability, not merely as an approximate law, but as an essen- 

 tial truth, may be used as a guide, but must be held pi'ovision- 

 ally until we have sufficient experimental evidence in its favour. 

 The first fundamental equation (10) admits of no doubt whatever 

 as to its universal application, and we shall see (§ 123*) that it 

 leads to most remarkable conclusions from known experimental 

 facts. 



The general principles are most conveniently applied by 

 restricting the number of metals referred to in the general 

 equations to two ; a case which we accordingly proceed to con- 

 sider. 



115. Let the principal conductor consist of two metals, one 

 constituting the middle, and the other the two terminal portions. 

 Let the junctions of these portions next the terminals E, E' be 

 denoted by A, A' respectively, and let their temperatures be 

 T, T'. Let also n(T), — n(T') be the quantities of heat absorbed 

 at them per second by a current of unit strength. We should 



* See Proceedings of the Royal Society, Phil. Mag. July 1854, p. 63. 

 U 2 



