ON THE THEORY OP EXCHANGES. 99 



I now come to the researches of Dulong and Petit on Radiation* (trans- 

 lated in the ' Annals of Philosophy,' vol. xiii. p. 241), which afford a peculiar 

 evidence in favour of the theory of exchanges. In order to perceive the bear- 

 ing of this evidence, let us take the case of a black body, say a thermometer 

 with a blackened bulb, cooKng in a black enclosure, devoid of air, through 

 the influence of radiation alone. In this case Dulong and Petit proved, by ex- 

 periment, that the velocity with which the bulb cools will be in every instance 

 accurately represented, if we suppose it to radiate heat at a rate depending 

 only on its own temperature, and to receive back heat at a rate depending only 

 on the temperature of the enclosure. Whatever evidence may be derived 

 from this research is therefore wholly in favour of the theory of exchanges. 



The next step in the progress of this theory was one which led to a truer 

 conception of that law of which the law of sines may be considered an approxi- 

 mate expression, and was made by Provostaye and Desains. In a paper pub- 

 lished in the ' Annales de Chimie' for 1848, these authors prove experiment- 

 ally that which was theoretically recognized by Fourier, viz. that, when there 

 is reflexion, the law of the proportionality of the radiating power to the sine 

 of the angle which the ray makes with the surface becomes altered. In the 

 case of glass in a field of constant temperature, they show that the sum of 

 the reflected and radiated heat at all angles will be a constant quantity, and 

 equal to 93*9 per cent, of the lampblack radiation of that temperature, the 

 difference, viz. 6'1 per cent., being supposed to be due to diffusion. The idea 

 which pervades this paper is one which had previously been recognized by 

 Prevost and Fourier, but which proved particularly fertile when worked out 

 by Provostaye and Desains. It may be stated thus. Returning to our 

 hypothetical chamber of constant temperature, with a thermometer placed 

 inside of it, this instrument will give the same indication in whatever manner 

 we alter the substance of the walls, provided their temperature be left the 

 same ; whence we may infer that the sum of the radiated and reflected heat 

 from any given portion of the walls which strikes the thermometer, will be 

 independent of the substance of which this portion is composed. We thus 

 perceive that it is not precisely correct to assert that the reflective power of a 

 body varies inversely as its radiative power, the proper statement being that, 

 in the case of constant temperature, the sum of the heat radiated and re- 

 flected by a body is a constant quantity. 



But these authors were aware that something more than this was necessary 

 in order to ensure a complete equilibrium of temperature; they perceived that 

 the sum of the radiated and reflected heat from a body, while equal to the lamp- 

 black radiation, must also be unpolarized, even as the heat from lampblack is 

 unpolarized, in order that both streams under comparison may behave in the 

 same manner with respect to any surface on which they may happen to fall. 

 Since therefore the radiated and reflected heat taken together must be un- 

 polarized, and since the latter portion is at a certain angle polarized in the 

 plane of incidence | it follows that the former, or the radiated heat, must be 

 partly polarized in a plane perpendicular to that of emission. Experimen- 

 tally this is known to be the case. It had been previously shown by Arago 

 that the rays which leave solid and liquid incandescent bodies obliquely 

 are polarized in a plane perpendicular to that of emission, and Provostaye 

 and Desains found the same law to hold with regard to heat. Their ex- 

 periments are contained in the ' Annales de Chimie ' for 1849, their source of 

 heat being a plate of platinum maintained at a red heat by the flame of an 

 alcohol lamp. 



We thus perceive that at this stage of the inquiry a perfectly distinct con- 

 • Ann. de Chiip. et de Phys. vol. vii. p. 113. t Professor Forbes, Edin. PhiL Trans. 1835, 



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