118 THEORY OF HEAT. [CHAP. II. 



place of that of the air, and the movement of heat would be the 

 same in either case : we can suppose then that this cause exists, 

 and determine on this hypothesis the variable state of the solid ; 

 which is what is done in the employment of the two equations 

 (A) and (B). 



By this it is seen how the interruption of the mass and the 

 action of the medium, disturb the diffusion of heat by submitting 

 it to an accidental condition. 



149. We may also consider the equation (B), which relates 

 to the state of the surface under another point of view : but we 

 must first derive a remarkable consequence from Theorem in. 

 (Art. 140). We retain the construction referred to in the corollary 

 of the same theorem (Art. 141). Let x, y, z be the co-ordinates 

 of the point p, and 



x+Sx, y + %, z + z 



those of a point q infinitely near to p, and taken on the straight 

 line in question : if we denote by v and w the temperatures of the 

 two points p and q taken at the same instant, we have 



, 5 , dv , dv 2 , dv 5, 



w = v 4- bv = v + -j- ox + -j- o y + -y- oz ; 

 dx dy dz 



hence the quotient 



Sv dv 8x dv dy dv z 



-5- = -j- -Z- + -J- * + j- -F&quot; i 



be dx be dx ce dz ce 



thus the quantity of heat which flows across the surface &amp;lt;y placed 

 at the point m, perpendicular to the straight line, is 



dv Sx dv Sv dv Sz 



7 r\ 



The first term is the product of K-j~ by dt and by CD -K-. 



dx 06 



The latter quantity is, according to the principles of geometry, the 

 area of the projection of co on the plane of y and z ; thus the 

 product represents the quantity of heat which would flow across 

 the area of the projection, if it were placed at the point p perpen 

 dicular to the axis of x. 



