M. POISSON ON THE MATHEMATICAL THEORY OF HEAT. 125 



formed of the same material. After having considered the influence 

 of the air upon radiation which we had at first eliminated, we give at 

 the end of this chapter a formula which expresses the instantaneous 

 variations of temperature of two material particles of insensible magni- 

 tude, by means of which the exchange of heat takes place after one or 

 many reflexions upon the surfaces of other bodies through air or through 

 any gas whatever. 



Chapter III. TTie Laws of Cooling in Bodies having the same Tem- 

 perature throughout. — While a homogeneous body of small dimensions 

 is heating or cooling, its variable temperature is the same at every 

 point ; but if the body is composed of many parts formed of different 

 substances in juxtaposition, they may preserve unequal temperatures 

 during all the time that these temperatures vary, as we show in an- 

 other chapter. In the present we determine, in functions of the time, 

 the velocity and the temperature which we suppose to be common to 

 all the points in a body placed alone in a sphere either vacuous or 

 full of air, and the temperature of which is variable. If the sphere 

 contams many bodies subject to their mutual influence upon each other, 

 the determination of their temperatures would depend on the integra- 

 tion of a system of simultaneous equations, which are only luiear in the 

 case of ordinary temperatures, but in which we cannot separate the 

 variables when we investigate high temperatures, and when the radia- 

 tion is supposed not to be proportional to their differences. 



Experiment has shown that in a cooling body, covered by a thin 

 layer or stratum of a substance different from that of which it is itself 

 composed, the velocity of refrigeration only arrives at its maximum when 

 the thickness of this additive stratum, though always veiy small, has 

 notwithstanding attained a certain limit. We develop the consequences 

 of this important fact in what regards extension of molecular radiation, 

 and explain how those consequences agree with the expression of the 

 passage of heat found in the preceding chapter. 



Chapter IV. Motion of Heat in the Interior of Solid or Liquid 

 Bodies. — We arrive by two different processes at the general equation of 

 the motion of heat ; these two methods are exempt from the difiiculties 

 which the Committee of the Institute, which awarded the prize of 1812* 

 to Fourier, had raised against the exactitude of the principle upon which 

 his method was sustained. The equation under consideration is appli- 

 cable both to homogeneous and heterogeneous bodies, solid or fluid, at 

 rest or in motion. It was unnecessarj-, as they appeared to have 

 thought, to find for fluids an equation different from the one I ob- 



• This Committee consisted of MM. Lagrange, Laplace, Legendre, Haiiy and 

 Malusi. 



