72 THEOKY OF HEAT. [CHAP. I. 



He n 

 m *- n *=~K ^~ m ^ 



rij a = b m 1 . 

 Adding these equations, we find 



The expenditure of the source of heat necessary to maintain 

 the surface of the body A at the temperature b is US (b a), 

 when this surface sends its rays to a fixed surface maintained at 

 the temperature a. The expenditure is HS (b m^ when we place 

 between the surface of the body A, and the fixed surface maintained 

 at temperature a, a numberj of isolated laminae; thus the quantity 

 of heat which the source must furnish is very much less in the 

 second hypotheses than in the first, and the ratio of the two 



quantities is . If we suppose the thickness e of the 



laminae to be infinitely small, the ratio is -. The expenditure 



f+i 

 of the source is then inversely as the number of laminae which 



cover the surface of the solid. 



91. The examination of these results and of those which we 

 obtained when the intervals between successive enclosures were 

 occupied by atmospheric air explain clearly why the separation 

 of surfaces and the intervention of air assist very much in re 

 taining heat. 



Analysis furnishes in addition analogous consequences when 

 we suppose the source to be external, and that the heat which 

 emanates from it crosses successively different diathermanous 

 envelopes and the air which they enclose. This is what has 

 happened when experimenters have exposed to the rays of the 

 sun thermometers covered by several sheets of glass within which 

 different layers of air have been enclosed. 



For similar reasons the temperature of the higher regions 

 of the atmosphere is very much less than at the surface of the 

 earth. 



