124 M. POISSON ON THE MATHEMATICAL THEORY OF HEAT. 



also give the law of absorption of radiant heat in the interior of homo- 

 geneous bodies. 



Chapter II. Laws of Radiant Heat. — If a body be placed within a 

 vacuous sphere on every side (enceitite videfermee de toutes parts), the 

 temperature of which is supposed to be invariable and everjnvhere 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, cceteris paribus, to the cosines of the angle which the normal 

 to the second element fonns 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 consi- 

 dering the number of successive reflexions which take place at the 

 surface of the sphere we demonstrate also that in general the pas- 

 sage (Jlux) of heat through everj' 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 tem- 

 perature will vaiy according to the place it occupies. The general ex- 

 pression of the passage of heat through everj' element of the surface of 

 a body of which the temperature varies, is composed of one factor re- 

 lative 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 for- 

 mula, which will -serve to solve the problems of the catoptrics of heat, 

 the principal applications of which we indicate. When aU 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 tempe- 

 rature tuid that of the inclosure only, at least when these bodies are 



