SECT. VIII.] MOVEMENT IX A SOLID MASS. 79 



sum of all the partial actions which are exerted across the circle 

 co, that is to say the sum of all the quantities of heat which, 

 crossing any point whatever of this circle, pass from the part 

 of the solid below the plane to the part above, compose the flow 

 whose expression is to be found. 



It is easy to imagine that this flow may not be the same 

 throughout the whole extent of the solid, and that if at another 

 point m we traced a horizontal circle co equal to the former, the 

 two quantities of heat which rise above these planes o&amp;gt; and o&amp;gt; 

 during the same instant might not be equal : these quantities are 

 comparable with each other and their ratios are numbers which 

 may be easily determined. 



97. We know already the value of the constant flow for the 

 case of linear and uniform movement; thus in the solid enclosed be 

 tween two infinite horizontal planes, one of which is maintained at 

 the temperature a and the other at the temperature b, the flow of 

 heat is the same for every part of the mass ; we may regard it as 

 taking place in the vertical direction only. The value correspond 



ing to unit of surface and to unit of time is K ( ),6 denoting 



the perpendicular distance of the two planes, and K the specific 

 conducibility : the temperatures at the different points of the 



solid are expressed by the equation v a ( - ) 



When the problem is that of a solid comprised between six 

 rectangular planes, pairs of which are parallel, and the tem 

 peratures at the different points are expressed by the equation 



the propagation takes place at the same time along the directions 

 of x, of y, of z\ the quantity of heat which flows across a definite 

 portion of a plane parallel to that of x and y is the same through 

 out the whole extent of the prism ; its value corresponding to unit 

 of surface, and to unit of time is cK, in the direction of z, it is 

 IK, in the direction of y, and aK in that of x. 



In general the value of the vertical flow in the two cases which 

 we have just cited, depends only on the coefficient of z and on 



the specific conducibility K\ this value is always equal to K-r- 



