ON THE THEORY OF EXCHANGES. 97 



On the Theory of Exchanges, audits recent extension. 

 By Balfour Stewart, A.M. 



It is now somewhere about seventy years since Professor Pierre Prevost 

 of Geneva conceived the rudimentary idea which ultimately became de- 

 veloped into the Theory of Exchanges. In the 'Journal de Physique' for 

 April 1791, we find a memoir by him "'On the Equilibrium of Heat;" and 

 from that period until 1832 he wrote many memoirs in confirmation and 

 extension of his views. 



The leading feature of this hypothesis is perhaps best expressed in the words 

 which Prevost himself employed to characterize it, when he called his theory 

 that of a moveable equilibrium of temperature. 



In order to comprehend more precisely the meaning of this phrase, let us 

 imagine to ourselves a large vacuum-chamber, the walls of which are black, 

 and do not reflect light or heal. Lampblack will therefore be the most 

 appropriate substance with which to cover them. Let us also suppose that 

 the whole chamber is kept at a uniform temperature, and that we place a 

 thermometer in the enclosure. It is well known that this thermometer will 

 ultimately denote the same temperature to whatever portion of the enclosure 

 it may be carried, and that this temperature will be that of the Avails of the 

 chamber. The bulb of the instrument is therefore in a state of equilibrium 

 with regard to heat, — a condition of things brought about and sustained, not 

 by currents of air, since the chamber is supposed to be a vacuum, but by that 

 faculty called radiation, in virtue of which a hot body communicates its heat 

 to a distant cold one, even through an absolutely vacant space. This equili- 

 brium may be of two kinds. 



1. It may be a statical or tensional equilibrium, that is to say, an equili- 

 brium of repose, in which, from the exact balancing of two opposite tendencies, 

 the bulb of the thermometer neither receives heat nor gives it away. 



2. It may also be an active, or, as Prevost calls it, a moveable equilibrium, 

 in which the bulb is constantly giving away heat to the enclosure and re- 

 ceiving back in return precisely as much as it gives away, so that its tem- 

 perature is neither increased nor diminished. 



It was this latter view of the subject which Prevost took, — a view which, 

 besides having a certain amount of inherent probability, has, I think, earned 

 a fair claim, from the great number of facts which it groups together under 

 one law, to be viewed as a correct expression of the truth. To return to our 

 thermometer: the bulb, under the circumstances above mentioned, is supposed 

 by this theory to be constantly giving forth radiant heat at a rate depending 

 only on the temperature of the bulb, and independent of that of the enclosure. 

 On the other hand, it is receiving back from tiie enclosure an amount of heat 

 depending only on the temperature of the enclosure, and wholly independent 

 of that of the bulb. Thus its expenditure depends upon its own temperature, 

 its receipts upon that of the enclosure, and when these two are of the same 

 temperature, the expenditure of the bulb is exactly balanced by its receipts. 



The circumstance which seems to have brought this idea vividly before 

 the mind of Prevost, was the well-known experiment by whicii Professor 

 Pictet* showed what may be termed the reflexion and concentration of cold. 

 That philosopher took two concave reflectors, making them face one another, 

 and while in the focus of the one he placed a thermometer, in that of the 

 other he placed a lump of ice, the effect of which was tliat flic temperature 

 of the thermometer immediately began to fall. If we admit that cold is a 

 positive principle, and not a mere negation, we shall of course be able to ex- 



* Essais de Phvs. p. 82. 

 1861. „ 



