CONDUCTION AND RADIATION. 153 



je shown to be a necessary consequence of the assumed principle, by 

 very simple reasoning 1 , which I shall give in a general form in a Xote." 4 

 This reasoning is capable of being presented in a manner quite 

 satisfactory, by the use of mathematical symbols, and proves that Les- 

 lie's law of the sines is rigorously and mathematically true on Fourier's 

 hypothesis. And thus Fourier's theory of molecular extra-radiation 

 acquires great consistency. 



Sect. S. Discovery of the Polarization of Heat. t 



CHE laws of which the discovery is stated in the preceding Sections 

 jf this Chapter, and the explanations given of them by the theories 

 of conduction and radiation, all tended to make the conception of a 

 material heat, or caloric, communicated by an actual flow and emis- 

 sion, familiar to men's minds ; and, till lately, had led the greater part 

 of thermotical philosophers to entertain such a view, as the most pro- 

 bable opinion concerning the nature of heat. But some steps have 

 recently been made in thermotics, which appear to be likely to over- 

 turn this belief, and to make the doctrine of emission as untenable 

 with regard to heat, as it had been found to be with regard to light. 

 I speak of the discovery of the polarization of heat. It being ascer- 

 tained that rays of heat arc polarized in the same manner as rays of 



" 4 The following reasoning may show the connexion of the law of the sines 

 in radiant heat with the general principle of ultimate identity of neighboring 

 temperatures. The equilibrium and identity of temperature between an includ- 

 ing shell and an included body, cannot obtain upon the whole, except it obtain 

 between each pair of parts of the two surfaces of the body and of the shell ; 

 that is, any part of the one surface, in its exchanges with any part of the other 

 surface, must give and receive the same quantity of heat. Now the quantity 

 exchanged, so far as it depends on the receiving surface, will, by geometry, be 

 proportional to the sine of the obliquity of that surface : and as, in the ex- 

 changes, each mav be considered as receiving, the quantity transferred must 

 be proportional to the sines of the two obliquities ; that is, to that of the giv- 

 ing as well as of the receiving surface. 



Nor is this conclusion disturbed by the consideration, that all the rays of heat 

 which fall upon a surface are not absorbed, some being reflected according to 

 the nature of the surface. For, by the other above-mentioned laws of pheno- 

 mena, we know that, in the same measure in which the surface loses the power 

 of admitting, it loses the power of emitting, heat ; and the superficial parts gain, 

 by absorbing their own radiation, as much as they lose by not absorbing the 

 incident, heat ; so that the result of the preceding reasoning remains unaltered. 



