78 THEORY OF HEAT. [CHAP. I. 



interior of the mass to be limited to an extremely small distance, 

 but they would still be true, if the rays of heat sent out by each 

 molecule could penetrate directly to a quite appreciable distance, 

 but it would be necessary in this case, as we have remarked in 

 Article 70, to suppose that the cause which maintains the tem 

 peratures of the faces of the solid affects a part extending within 

 the mass to a finite depth. 



. SECTION VIII. 

 Measure of the movement of heat at a given point of a solid mass. 



96. It still remains for us to determine one of the principal 

 elements of the theory of heat, which consists in defining and in 

 measuring exactly the quantity of heat which passes through 

 every point of a solid mass across a plane whose direction is given. 



If heat is unequally distributed amongst the molecules of the 

 same body, the temperatures at ^ any point will vary every instant. 

 Denoting by t the time which has elapsed, and by v the tem 

 perature attained after a time t by an infinitely small molecule 

 whose co-ordinates are oc, y, z ; the variable state of the solid will be 

 expressed by an equation similar to the following v = F(x, y, z, t). 

 Suppose the function F to be given, and that consequently we 

 can determine at every instant the temperature of any point 

 whatever; imagine that through the point m we draw a hori 

 zontal plane parallel to that of x and y, and that on this plane 

 we trace an infinitely small circle , whose centre is at m ; it is 

 required to determine what is the quantity of heat which during 

 the instant dt will pass across the circle a&amp;gt; from the part of the 

 solid which is below the plane into the part above it. 



All points extremely near to the point m and under the plane 

 exert their action during the infinitely small instant dt, on all 

 those which are above the plane and extremely near to the point 

 m, that is to say, each of the points situated on one side of this 

 plane will send heat to each of those which are situated on the 

 other side. 



We shall consider as positive an action whose effect is to 

 transport a certain quantity of heat above the plane, and as 

 negative that which causes heat to pass below the plane. The 



