SECT. VI.] HEATING OF CLOSED SPACES. 65 



84. The value of m is the special object of the problem. It 

 may be found by writing the equations in the form 



adding, we have m n = (a. - m) P, 



denoting by P the known quantity ^ (| -f ^ -f J^ J ; 



whence we conclude 



m 11 = a n 



85. The result shews how m n, the extent of the heating, 

 depends on given quantities which constitute the hypothesis. 

 We will indicate the chief results to be derived from it \ 



1st. The extent of the heating m n is directly proportional 

 to the excess of the temperature of the source over that of the 

 external air. 



2nd: The value of m n does not depend on the form of 

 the enclosure nor on its volume, but only on the ratio - of the 



surface from which the heat proceeds to the surface which receives 

 it, and also on e the thickness of the boundary. 



If we double cr the surface of the source of heat, the extent 

 of the heating does not become double, but increases according 

 to a certain law which the equation expresses. 



1 These results \vere stated by the author in a rather different manner in the 

 extract from his original memoir published in the Bulletin par la Society Philo- 

 matique de Paris, 1818, pp. 111. [A. F.] 



F. H. 5 



