CHAPTER IX. 



OF THE DIFFUSION OF HEAT. 



FIRST SECTION. 



Of the free movement of heat in an infinite line. 



342. HERE we consider the movement of heat in a solid 

 homogeneous mass, all of whose dimensions are infinite. The 

 solid is divided by planes infinitely near and perpendicular to a 

 common axis ; and it is first supposed that one part only of the 

 solid has been heated, that, namely, which is enclosed between 

 two parallel planes A and B, whose distance is g ; all other parts 

 have the initial temperature ; but any plane included between 

 A and B has a given initial temperature, regarded as arbitrary, 

 and common to every point of the plane ; the temperature is dif 

 ferent for different planes. The initial state of the mass being 

 thus defined, it is required to determine by analysis all the suc 

 ceeding states. The movement in question is simply linear, and 

 in direction of the axis of the plane ; for it is evident that there 

 can be no transfer of heat in any plane perpendicular to the axis, 

 since the initial temperature at every point in the plane is the 

 same. 



Instead of the infinite solid we may suppose a prism of very 

 small thickness, whose lateral surface is wholly impenetrable to 

 heat. The movement is then considered only in the infinite line 

 which is the common axis of all the sectional planes of the prism. 



The problem is more general, when we attribute temperatures 

 entirely arbitrary to all points of the part of the solid which has 



