122 THEORY OF HEAT. [CHAP. II. 



hence the molecule loses across its surface a b c d a quantity of 

 heat equal to hv dx dy - . 



Now, the terms of the first order which enter into the expression 

 of the total quantity of heat acquired by the molecule, must cancel 

 each other, in order that the variation of temperature may not be 

 at each instant a finite quantity ; we must then have the equation 



dz dv dz , , dv 



j j ^ j- 



dx dx y dy dy 



, , dv , , \ , e , , 

 ax dy r dx dy} hv-dxdy = 0, 

 *\ d* * *J z 



he dv dz dv dz dv 

 or -==,v - -j- -j + -j -j --- j- . 

 K z dx dx dy dy dz 



153. Substituting for -r- and -7- their values derived from 

 & dx dy 



the equation 



mdx 4- ndy -\-pdz = 0, 



and denoting by q the quantity 



(w +w +p 8 ) , 

 we have 



dv dv dv 



thus we know distinctly what is represented by each of the 

 terms of this equation. 



Taking them all with contrary signs and multiplying them 

 by dx dy, the first expresses how much heat the molecule receives 

 through the two faces perpendicular to x, the second how much 

 it receives through its two faces perpendicular to y, the third 

 how much it receives through the face perpendicular to z, and 

 the fourth how much it receives from the medium. The equation 

 therefore expresses that the sum of all the terms of the first 

 order is zero, and that the heat acquired cannot be represented 

 except by terms of the second order. 



154. To arrive at equation (B), we in fact consider one 

 of the molecules whose base is in the surface of the solid, as 

 a vessel which receives or loses heat through its different faces. 

 The equation signifies that all the terms of the first order which 



