102 THEORY OF HEAT. [CHAP. II. 



the differential being taken with respect to x only. The quantity 

 of heat which during the instant dt enters the molecule, across 

 the first rectangle dz dx perpendicular to the axis of y, is 



Kdzdx--.~dt, and that which escapes from the molecule during 

 the same instant, by the opposite face, is 



Kdz dx 4- dt Kdz dx d ( -y- ) dt, 

 ay \dyJ 



the differential being taken with respect to y only. The quantity 

 of heat which the molecule receives during the instant dt, through 



its lower face, perpendicular to the axis of z, is Kdxdy-j-dt, 



dz 



and that which it loses through the opposite face is 

 ~Kdxdy^dt-Kdxdyd(~^dt, 



the differential being taken with respect to z only. 



The sum of all the quantities of heat which escape from the 

 molecule must now be deducted from the sum of the quantities 

 which it receives, and the difference is that which determines its 

 increase of temperature during the instant: this difference is 



Kdij dz d -. dt + Kdz dx d dt + K dx dy d dt, 



128. If the quantity which has just been found be divided by 

 that which is necessary to raise the molecule from the temperature 

 to the temperature 1, the increase of temperature which is 

 effected during the instant dt will become known. Now, the 

 latter quantity is CD dx dy dz : for C denotes the capacity of 

 the substance for heat; D its density, and dxdydz the volume 

 of the molecule. The movement of heat in the interior of the 

 solid is therefore expressed by the equation 



dv K fd^v d^v d*v\ 



. / j_ . i __ ( fj \ 



7 t ~&quot; f1 7~\ I 7 *2 * I 2 I 7 I I W Ji 



dt CD \dx dy* dz J ^ 



