DYNAMICAL THEORY OF HEAT. 149 



than in the lower; or that the specific heat of water under constant pressure is 

 increased by a diminution of the pressure. The same conclusion, and the amount 

 of the effect, are also implied in equations (18) and (19) of Part III. We may 

 arrive at it without referring to any of the mathematical formulae, merely by an 

 application of the general principle of mechanical effect, when once the conclu- 

 sion regarding the thermal effects of condensation or rarefaction is established ; 

 exactly as the conclusion regarding the specific heats of electricity in copper and 

 in iron was first arrived at.* For if we suppose one vertical branch to be kept 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 consequence 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 tem- 

 perature 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 constantly 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 there- 

 fore, exactly to the extent of the heat otherwise evolved, this must be over-com- 

 pensated 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 corre- 

 sponds exactly to the conclusion arrived at formerly, that if one metal passes an- 

 other in the direction from bismuth towards antimony in the thermo-electric scale, 

 the specific heat of electricity 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 origin in the two metals, although 

 the existence of such contrary effects is enough to show how difficult it is to con- 

 ceive the physical circumstances of an electric current as physically analogous to 

 those of a current of fluid in one direction. 



* 



* Proceedings R. S. E., Dec. 15, 1851, or extract of Proceedings R. S., May 1854, quoted 

 above, § 124. 



