Applications of the Formulas 89 



poor conductor of heat. In this case we see that the denomina- 

 tor, like the numerator is nearly proportional to Q, and therefore 

 the value of Q has only a small influence. Thus the numerical 

 results that we have given may be considered sufficiently accurate 

 for many practical purposes, but this would no longer be true if, 

 for the same difference between the inside and outside radii, the 

 value of the inside radius was very large. In this case we find a 

 notable difference between the direct calculation and the method 

 of approximation which I have just indicated. 



894. I will take a steam boiler for an example. The sur- 

 face is generally covered with a poor conductor of heat, and it is 

 important to recognize the influence on the loss of heat of the dif- 

 ferent materials which may be employed, I will assume that the 

 cylinder forming the boiler has a diameter of 3.28 feet; the quan- 

 tity of heat emitted per hour per square foot is given by the fol- 

 lowing formula : 



M= Q ( l - e ) ' <*> 



C+,Q R' m (log R' log R) 



Assume as before ? -43+-75 = i-i8 and that the covering 

 material is sawdust mixed with a little clay and cows hair to ren- 

 der it plastic ; we may take C= .80 and therefore C' = .067. 



We will suppose the boiler to be filled with steam at 212 and 

 the surrounding air to be at 59 Fahrenheit. 



With the following thicknesses of the covering 

 .4" .8" 1.2" 1.6" 2.0" 



the formula (a) gives directly for M 



113.0 81.8 63.7 52.6 44.7 

 and by the method of approximation indicated 



132.0 89.5 67.4 54.5 45.8 



If the surface of the covering is finished by a sheet of Russia 

 iron, we have by the formula 



63.8 52.7 45.0 38.8 34.2 

 and by the method of approximation, 



82.7 63.0 51.0 42.8 36.5 (4} 



It follows from these numbers and from the fact that the 

 emission from the bare surface is 260, that the coverings reduce 

 the transmission to, 



.509 .344 .259 .210 .176 



