29-i Prof. Thomson on the Dynamical Theory of Heat. 



137. In the first place, it is to be remarked that if the two 

 vertical branches be kept at temperatures a little above and below 

 the point of maximum density, no current will be produced ; and 



therefore if Tq denote this temperature, the equation F = I — dt 



gives n(To) = 0. Again, if one of the vertical branches be kept 

 at Tq, and the other be kept at a temperature either higher or 

 lower, a current will set, and always in the same direction. 



dt has the same sign, whether T be greater or less 



Hence I - — 



hot 



than Tq, and consequently n(^) must have contrary signs for 

 values of t above and below TqJ which, by attending to the 

 signs in the general formul?e, we see must be such as to express 

 evolution of heat by the actual current in the second vertical 

 branch when its temperature is below, and absorption when 

 above T^. As the current in each case ascends in this vertical 

 branch, we conclude that a slight diminution of pressure causes 

 evolution or absorption of heat in water, according as its tempe- 

 rature is below or above that of maximum density ; or conversely, 

 that when water is suddenly compressed, it becomes colder if 

 initially below, or warmer if initially above, its temperature of 

 maximum density. This conclusion from general thermo-dynamic 

 principles Avas first, so far as I know, mentioned along with the 

 description of an experiment to prove the lowering of the freezing- 

 point of water by pressure, communicated to the Royal Society 

 in January 1850*. The quantitative expression for the eff"ect, 

 which was given in § 50 of Part III., may be derived with ease 

 from the considerations now brought forward. The other thermo- 



dynamic equation -^— - — ' = — -j— shows that the specific heat 



of the water must be greater in the upper horizontal branch 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 with- 

 out referring to any of the mathematical formulae, merely by an 

 application of the general principle of mechanical efi"ect, when 

 once the conclusion regarding the thermal eftects of condensation 

 or rarefaction is established ; exactly as the conclusion regarding 

 the specific heats of electricity in copper and in iron was first 

 arrived atf. For if we suppose one vertical branch to be kept 



* See ' Proceedings ' of that date, or Philosophical Magazine, 1850. 

 t Proceedings of the Royal Society of Edinburgh, Dec. 15, 1851; or 

 extract of Proceedings of the Royal Society, May 1854, 



