68 THEORY OF HEAT. [CHAP. I. 



elements of the second enclosure which correspond to those of 

 the first which were denoted by 5, h, K, H, e ; we shall find, 

 p denoting the temperature of the air which surrounds the ex 

 ternal surface of the second enclosure, the following equation : 



The quantity P represents 



* (9 9* + 



7 r + j^^ 



s \li K. 



We should obtain a similar result if we had three or a greater 

 number of successive enclosures ; and from this we conclude that 

 these solid envelopes, separated by air, assist very much in in 

 creasing the degree of heating, however small their thickness 

 may be. 



88. To make this remark more evident, we will compare the 

 quantity of heat which escapes from the heated ^surface, with 

 that which the same body would lose, if the surface which en 

 velopes it were separated from it by an interval filled with air. 



If the body A be heated by a constant cause, so that its 

 surface preserves a fixed temperature b, the air being maintained 

 at a less temperature a, the quantity of heat which escapes into 

 the air in the unit of time across a unit of surface will be 

 expressed by h (b a), h being the measure of the external con- 

 ducibility. Hence in order that the mass may preserve a fixed 

 temperature b, it is necessary that the source, whatever it may 

 be, should furnish a quantity of heat equal to hS (b a), S de 

 noting the area of the surface of the solid. 



Suppose an extremely thin shell to be detached from the 

 body A and separated from the solid by an interval filled with 

 air; and suppose the surface of the same solid A to be still 

 maintained at the temperature b. We see that the air contained 

 between the shell and the body will be heated and will take 

 a temperature a greater than a. The shell itself will attain 

 a permanent state and will transmit to the external air whose 

 fixed temperature is a all the heat which the body loses. It 

 follows that the quantity of heat escaping from the solid will 



