Applications of the Formulas 79 



Thus assuming a single envelope and designating by / and /' the 

 temperatures of the surfaces of the vase and the envelope, and by 

 /" the temperature of the exterior air, we have: 



, M=(tt') K+-~ 

 from which : 



Assuming two envelopes and designating by the tempera- 

 ture of the second surface, we have: 



M=(t0') 



\ c / 



M=(6-t') '-' CN ^rom which 



(t-t") 





Increasing successively by one the number of envelopes we 

 find that the coefficient of ( K^ K' ) in the denominator of the 

 fraction increases successively by one, and we are led to the gen- 

 eral formula: 



c 



K+ 

 (t-t") 



in which K is the radiation from the interior surfaces, K v that of 

 the exterior surface, K' the quantity of heat abstracted from the 

 exterior surface by contact of the external air, C the conductivity 

 of the air, e the thickness of the air spaces, and J/the number of 

 envelopes. 



If we take ^=^ = .772, A"=.788 C=.$2 and ^=.04" for 

 the following values of m, 



01234 

 we find that the relative values of M are, 



i .87 .77 .69 .62 



