46 THEORY OF HEAT. [CHAP. I. 



the lower plane A is maintained, by any cause whatever, at a 

 constant temperature a ; we may imagine for example that the 

 mass is prolonged, and that the plane A is a section common to 

 the solid and to the enclosed mass, and is heated at all its points 

 by a constant source of heat; the upper plane B is also main 

 tained by a similar cause at a fixed temperature b, whose value is 

 less than that of a ; the problem is to determine what would be 

 the result of this hypothesis if it were continued for an infinite 

 time, 



If we suppose the initial temperature of all parts of this body 

 to be b, it is evident that the heat which leaves the source A will 

 be propagated farther and farther and will raise the temperature 

 of the molecules included between the two planes : but the tem 

 perature of the upper plane being unable, according to hypothesis 

 to rise above b } the heat will be dispersed within the cooler mass, 

 contact with which keeps the plane B at the constant temperature 

 b. The system of temperatures will tend more and more to a 

 final state, which it will never attain, but which would have the 

 property, as we shall proceed to shew, of existing and keeping 

 itself up without any change if it were once formed. 



In the final and fixed state, which we are considering, the per 

 manent temperature of a point of the solid is evidently the same 

 at all points of the same section parallel to the base; and we 

 shall prove that this fixed temperature, common to all the points 

 of an intermediate section, decreases in arithmetic progression 

 from the base to the upper plane, that is to say, if we represent 

 the constant temperatures a and b by the ordinates AOL and Bj3 



\ 



Fig. 1. 



(see Fig. 1), raised perpendicularly to the distance AB between the 

 two planes, the fixed temperatures of the intermediate layers will 

 be represented by the ordinates of the straight line aft which 



