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 formule, 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. 8. E., Dec. 15, 1851, or extract of Proceedings R. S., May 1854, quoted 
above, § 124. 
