70 THEORY OF HEAT. [CHAP. I. 



The quantity of heat lost by the solid was hS(b a), when 

 its surface communicated freely with the air, it is now hS (6 a) 



or hS(n a), which is equivalent to hS 



The first quantity is greater than the second in the ratio of 



In order therefore to maintain at temperature b a solid whose 

 surface communicates directly to the air, more than three times 

 as much heat is necessary than would be required to maintain 

 it at temperature Z&amp;gt;, when its extreme surface is not adherent 

 but separated from the solid by any small interval whatever filled 

 with air. 



If we suppose the thickness e to be infinitely small, the 

 ratio of the quantities of heat lost will be 3, which would also 

 be the value if K were infinitely great. 



We can easily account for this result, for the heat being 

 unable to escape into the external air, without penetrating several 

 surfaces, the quantity which flows out must diminish as the 

 number of interposed surfaces increases ; but we should have 

 been unable to arrive at any exact judgment in this case, if the 

 problem had not been submitted to analysis. 



90. We have not considered, in the preceding article, the 

 effect of radiation across the layer of air which separates the 

 two surfaces ; nevertheless this circumstance modifies the prob 

 lem, since there is a portion of heat which passes directly across 

 the intervening air. We shall suppose then, to make the object 

 of the analysis more distinct, that the interval between the sur 

 faces is free from air, and that the heated body is covered by 

 any number whatever of parallel laminse separated from each 

 other. 



If the heat which escapes from the solid through its plane 

 superficies maintained at a temperature b expanded itself freely 

 in vacuo and was received by a parallel surface maintained at 

 a less temperature a, the quantity which would be dispersed in 

 unit of time across unit of surface would be proportional to (b a), 

 the difference of the two constant temperatures : this quantity 



