SECT. VI.] HEATING OF CLOSED SPACES. 71 



would be represented by H (b a), H being the value of the rela 

 tive conducibility which is not the same as h. 



The source which maintains the solid in its original state must 

 therefore furnish, in every unit of time, a quantity of heat equal 

 toHS(b-a). 



We must now determine the new value of this expenditure 

 in the case where the surface of the body is covered by several 

 successive laminae separated by intervals free from air, supposing 

 always that the solid is subject to the action of any external 

 cause whatever which .maintains its surface at the temperature b. 



Imagine the whole system of temperatures to have become 

 fixed ; let m be the temperature of the under surface of the first 

 lamina which is consequently opposite to that of the solid, let n 

 be the temperature of the upper surface of the same lamina, 

 e its thickness, and K its specific conducibility ; denote also by 

 77&J, n lt m 2 , n 2 , m 3 , ?? 3 , ??i 4 , w 4 , &c. the temperatures of the under 

 and upper surfaces of the different laminae, and by K } e, the con 

 ducibility and thickness of the same laminae; lastly, suppose all 

 these surfaces to be in a state similar to the surface of the solid, 

 so that the value of the coefficient H is common to them. 



The quantity of heat which penetrates the under surface of 

 a lamina corresponding to any suffix i is HSfyi^mJ), that which 



J7-Q 



crosses this lamina is ( m i~ n i)f an( ^ the quantity which escapes 

 c 



from its upper surface is HS(n t m i+l }. These three quantities, 

 and all those which refer to the other laminae are equal ; we may 

 therefore form the equation by comparing all these quantities 

 in question with the first of them, which is HS (b mj ; we shall 

 thus have, denoting the number of laminae \&amp;gt;y j : 



He n 



i - n i = ^ ( b ~ 



He ,, . 

 - n, = (b - IflJ, 



