90 Applications of the Formulas 



and the same coverings covered with Russia iron : 



.318 .243 .196 .165 .141 (6) 



The influence of the Russia iron is very great, but it dimin- 

 ishes with the thickness, for the relations of the corresponding 

 numbers of series 5 and 6 are : 



.63 .71 .76 '.79 .80 (-]) 



As the steam pressure increases the percentage of saving due 

 to a covering somewhat increases.* 



i 



TRANSMISSION OF HEAT THROUGH SPHERICAL ENVELOPES 



895. Preserving the same notation as before, we find 



4 TT r * C d t x* j .. *jl r 



M=- -- -j - ; or 4* C' dt= M-~ 

 dr r 2 



and integrating between the limits / and /' for t and R and R' for 

 r we find 



whence M= 



K K 



But since M=<\ n R' 2 Q ( t ), we may eliminate / and obtain; 



**CQRR'(t-e) 



CR+QR' (R'R) 



an equation in which M represents the quantity of heat in B. T. 

 U. per hour emitted by the total surface of the sphere. To 

 obtain the emission per square foot, we must evidently divide M 

 by 4 *,'.*. 



DIFFUSION OF HEAT 



896. In all that precedes we have only considered the trans- 

 mission of heat through a body after the establishment of a per- 

 mament r6gime of temperature. In this case the laws of the trans- 

 mission are very simple, and the formulas that we have given 



*For a more modern example we may take a Scotch boiler twelve feet in diameter, 

 under liio pounds steam pressure, with the surrounding air at 100, and covered with two 

 inches of magnesia. The values of C', K, and K', will be .04, .74 and .42 



By the formula ./>/=- 53. 7 but by successive approximations thus becomes 55.7. 



If we jacket the covering with Russia iron the formula gives 44.7 and successive 

 approximations brings this to 48.2. 



The heat loss from the bare boiler would be (by 807) 685 B. T. TJ. per hour per square 

 foot. The plain covering has a loss of only eight per cent of this amount and when 

 jacketed with Russia iron only seven per cent. 



