64 THEORY OF HEAT. [CHAP. I. 



as that of which we have already treated, and we must apply 

 to it the linear equations which have been stated in former 

 articles. 



83. Thus in the permanent state which we are considering, 

 the flow of heat which leaves the surface cr during a unit of time, 

 is equal to that which, during the same time, passes from the 

 surrounding air into the inner surface of the enclosure ; it is 

 equal also to that which, in a unit of time, crosses an inter 

 mediate section made within the solid enclosure by a surface 

 equal and parallel to those which bound this enclosure ; lastly, 

 the same flow is again equal to that which passes from the solid 

 enclosure across its external surface, and is dispersed into the air. 

 If these four quantities of flow of heat were not equal, some 

 variation would necessarily occur in the state of the temperatures, 

 which is contrary to the hypothesis. 



The first quantity is expressed by a (a. m) g, denoting by 

 g the external conducibility of the surface cr, which belongs to 

 the source of heat. 



The second is s (m a) h, the coefficient h being the measure 

 of the external conducibility of the surface s, which is exposed 

 to the action of the source of heat. 



The third is s K, the coefficient K being the measure of 



6 



the conducibility proper to the homogeneous substance which 

 forms the boundary. 



The fourth is s(b n}H, denoting by H the external con 

 ducibility of the surface s, which the heat quits to be dispersed 

 into the air. The coefficients h and H may have very unequal 

 values on account of the difference of the state of the two surfaces 

 which bound the enclosure ; they are supposed to be known, as 

 also the coefficient K: we shall have then, to determine the three 

 unknown quantities m, a and 6, the three equations : 



f N a b r , 

 a (a m) g = s - A, 



G 



cr (a - m) g = s (b n) H. 



