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XXXII. A Mathematical Theory of Hsat. 

 By Professor Challis*. 



IT is a fact of experience, that when rays of light pass through 

 the earth's atmosphere, or other substance, its temperature 

 is increased. It would seem, therefore, that if we knew exactly 

 what rays of light are, we should have some clue for determining 

 the agency by which heat is produced. In the following outline 

 of a mathematical theory of heat, I adopt the hypothesis that 

 light-bearing undulations are such as were defined in my com- 

 munication to the Philosophical Magazine for February, and 

 that, while light is due to the transverse vibrations, heat is the 

 result of the mechanical action of the direct vibrations. The 

 heat -producing undulations are supposed to be compounded, as 

 stated in the same communication, of simple wave-rays, in such 

 a manner that the transverse vibi'ations destroy each other. 



The ultimate atoms of material substances are inert, because 

 the inertia of a mass is the result of the inertia of its constituent 

 parts ; they have magnitude and form, otherwise they are not 

 within the compass of mathematical reasoning; their form is 

 that of a sphere, because they are found by experience to have 

 individually the same relations to all parts of space ; and they 

 are hard and impenetrable, otherwise the spherical form is not 

 necessarily preserved. These hypotheses, which, with the ex- 

 ception of that of the spherical form, agree with the views ex- 

 pressed by Newton respecting the ultimate properties of matter 

 (Optics, Book III. Qu. 31), will be adopted in the following rea- 

 soning. If the constituent atoms of bodies have other proper- 

 ties, it will be time to inquii'e what they are when these are 

 found to be insufficient. Further, it will be assumed that, in a 

 substance of uniform density, the constituent atoms are distri- 

 buted uniformly in space, and, in conformity with an inference 

 drawn at the end of the communication above referred to, that 

 the space occupied by the atoms, even in the case of solid bodies, 

 is extremely small compared to the intervening space, so that 

 the radius of an atom is extremely small compared to the mean 

 distance between neighbouring atoms. 



If, now, a scries of plane-waves of alternate condensation and 

 rarefaction traverse any medium, just as light-bearing waves are 

 known to traverse transparent substances, each atom of the me- 

 dium becomes a centre of secondary waves, in a manner analo- 

 gous to the production of such waves when a small obstacle is 

 encountered by waves propagated on the surface of water. Ac- 

 cording to the hypothesis with which we set out, the caloric 

 repulsion of an atom is due to the agency of these subordinate 



* Commuuicated by the Author. 



