Page:Scientific Memoirs, Vol. 1 (1837).djvu/136

124 also give the law of absorption of radiant heat in the interior of homogeneous bodies.

Laws of Radiant Heat.—If a body be placed within a vacuous sphere on every side (enceinte vide fermée de toutes parts), the temperature of which is supposed to be invariable and everywhere the same, we demonstrate that the result of the interchange of heat between an element of its surface and an element of the surface of the inclosing sphere, is independent of the matter of which the sphere is formed, and proportional, cæteris paribus, to the cosines of the angle which the normal to the second element forms with the right line from one to the other element. Experiments, not as yet made, only can decide whether this law of the cosine is equally applicable to the elements of the surface of the body, of which the temperature is not invariable like that of the sphere; and until such experiments are made we may be allowed to doubt its existence while the body is heating or cooling. By considering the number of successive reflexions which take place at the surface of the sphere we demonstrate also that in general the passage (flux) of heat through every element in the surface of the body which it contains is independent of the form, of the dimensions, and of the material of the sphere; there is no exception, but when the heat, in the series of reflexions which it experiences, falls one or many times upon the surface of the body. It follows from this theorem that a thermometer placed in any point whatever of the space which the sphere terminates, will finally indicate the same temperature, which will be equal to that of the sphere; but in the case of the exception just mentioned, the time which it will employ in attaining that temperature will vary according to the place it occupies. The general expression of the passage of heat through every element of the surface of a body of which the temperature varies, is composed of one factor relative both to the state of that surface and to the material of the body, multiplied by the difference of two similar functions, one of which depends on the variable temperature of the body, the other on the fixed temperature of the sphere, which are the same for all bodies; a result which agrees with the law of cooling in vacuo discovered by MM. Dulong and Petit. We next suppose in this second chapter, that many bodies differing in temperature are contained in the sphere of which the temperature is constant, and arrive then at a general formula, which will serve to solve the problems of the catoptrics of heat, the principal applications of which we indicate. When all these bodies form round one of them a closed sphere the temperature of which, variable with the time, is not the same throughout, the passage of heat to the surface of the interior body does not depend on its temperature and that of the inclosure only, at least when these bodies are