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 magnitude, 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. The Laws of Cooling in Bodies having the same Temperature 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 another 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 contains many bodies subject to their mutual influence upon each other, the determination of their temperatures would depend on the integration of a system of simultaneous equations, which are only linear in the case of ordinary temperatures, but in which we cannot separate the variables when we investigate high temperatures, and when the radiation 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 very 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 difficulties which the Committee of the Institute, which awarded the prize of 1812[1] to Fourier, had raised against the exactitude of the principle upon which his method was sustained. The equation under consideration is applicable both to homogeneous and heterogeneous bodies, solid or fluid, at rest or in motion. It was unnecessary, as they appeared to have thought, to find for fluids an equation different from the one I ob-
