Applications of the Formulas 



If the coverings were enveloped with a sheet of tin we 

 would have A"=.O9, and consequently the values of Q would 

 become : 



.62 .60 .59 .58 .58 .55 



and we would find for the values of M : 



70.7 52.2 43.0 37.0 32.9 22.4 



The influence of the feeble radiation from the tin surface 

 diminishes as the thickness of the covering increases, because the 

 value of C' relatively to the term Q R' N is diminishing and 

 because if C' could be neglected, the value of M would be. 

 entirely independent of Q. 



889. In the preceding calculations we have taken C= .36 

 which gave .03 for C' ; if we suppose a conductivity two, four ; 

 eight. . . . N times as large, it would suffice, to obtain 

 the corresponding values of M, to multiply the numerators o/ 

 the fractions in the preceding table of values of M, by 2, 4, 8 



. N, and to add to the denominators : 

 03, .09, .21, 03 f i) 



It is in this way that we have obtained the numbers in the 

 following table. These correspond to the same values of R' anrt 

 to the same temperatures. The quantity of heat emitted frou 

 the bare pipe would of course remain 352 B T U. 



Quantities of Heat in B T / transmitted per foot run per hour by a 

 horizontal pipe 4. 5" outside diameter, heated to 212 and with 

 external air at 59 and covered with materials of different conduc- 

 tivities and different thicknesses : 



Value of 



.36 



5.76 



Value of 

 C' 



.03 



.48 



Thickness of covering in inches. 



11.52 .96 



890. We see from this table that the values of ^/decrease 

 very rapidly with increase of thickness when the conductivity is 

 very low ; that the variations are very small for values of C in the 

 neighborhood of 5.76, and that for greater values of Cthe values 

 of M increases with the thickness of the covering. For pipes of 



