Prof. Thomson on the Dynamical Theory of Heat. 295 



at the temperature of maximum density (corresponding to the 

 neutral point of the metals in the corresponding thermo-electric 

 case), and the other at some lower temperature, a current will 

 set downwards through the former branch, and upwards through 

 the latter. This current will cause evolution of heat, in conse- 

 quence of the expansion of the fluid, in the branch through 

 which it rises, but will cause neither absorption nor evolution in 

 the other vertical branch, since in it the temperature is that of 

 the maximum density. There will also be heat generated in 

 various parts by fluid friction. There must then be, on the 

 whole, absorption of heat in the horizontal branches, because 

 otherwise there would be no source of energy for the heat con- 

 stantly evolved to be drawn from. But heat will be evolved by 

 the fluid in passing in the lower horizontal branch from hot to 

 cold ; and therefore, exactly to the extent of the heat otherwise 

 evolved, this must be over-compensated by the heat absorbed in 

 the upper horizontal branch by the fluid passing from cold to hot. 

 On the other hand, if one of the vertical branches be kept above 

 the temperature of maximum density and the other at this point, 

 the fluid will sink in the latter, causing neither absorption nor 

 evolution of heat, and rise in the former, causing absorption ; 

 and therefore more heat must be evolved by the fluid passing 

 from hot to cold in the upper horizontal branch than is absorbed 

 by it in passing from cold to hot in the lower. From either case 

 we infer that the specific heat of the water is greater in the upper 

 than in the lower branch. The analogy with the thermo-electric 

 circumstances of two metals which have a neutral point is perfect 

 algebraically in all particulars. The proposition just enunciated 

 corresponds exactly to the conclusion arrived at formerly, that if 

 one metal passes another in the direction from bismuth towards 

 antimony in the thermo-electric scale, the specific heat of elec- 

 tricity is greater in the former metal than in the latter ; this 

 statement holding algebraically, even in such a case as that of 

 copper and iron, where the specific heats are of contrary sign in 

 the two metals, although the existence of such contrary eff'ects 

 is enough to show how difiicult it is to conceive the physical cir- 

 cumstances of an electric current as physically analogous to those 

 of a current of fluid in one direction. 



§§ 138-140. General Lemma, regarding relative thermo-electric 

 properties of Metals, and multiple combinations in a Linear 

 Circuit. 



138. The general equation (11), investigated above, shows 

 that the aggregate amount of all the thermal effects produced by a 

 current, or by any system of currents, in any solid conductor or 



