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. : 
Cuapter Il. 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, ceteris 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 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 (flu) 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 tem- 
perature will vary according to the place it occupies. The general ex- 
pression of the passage of heat through every 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 72 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 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 tempe- 
rature and that of the inclosure only, at least when these bodies are 
