78 Applications of the Formulas 



877. It would seem at first sight, that it would be advan- 

 tageous to diminish the thickness of the layers of air in order to 

 render it motionless; but then there would be a direct transmission 

 of heat through the air and if the thickness were too small, the 

 transmission would be greater than if the air could move freely. 

 In such an air space the quantity of heat transmitted is given by 



(C \* C 



A"-| -- ; 1 and if we suppose e=.jg" would equal 



which is practically the value of A" and for a smaller 



value of e, the factor \K-\- - - j would be greater than Q.\ 



In order that air spaces may diminish the transmission of 



I 



heat, it is necessary that ^- be always smaller than . . , .\ 



L K + .32 



e 

 Evidently then the air spaces will be especially advantageous 



when the surfaces of the walls forming them have a very feeble 



radiating power. 



It results from the preceding that hollow bricks should trans- 



mit much less heat than solid ones of the same thickness, and 



this is perfectly confirmed by experiment. 



878. Similar results will be obtained in the second case that 

 we have examined (870), by making the same modifications in 

 the general formula relative to superimposed walls of different 

 materials; there will still be, as in the case which we have just 



g 

 studied, a decrease in the transmission whenever -^ would be 



larger than the transmission through a sheet of air, augmented by 

 the radiation between the opposite surfaces of the air space. 



879. It is now easy to find the loss of heat from a vessel 

 surrounded by envelopes separated by extremely small air spaces. 



*Radiation = K (xx 1 ) 



Conduction = (x x') 



Then M=(x-x')( K+- ) 

 Note that in 875 we assumed M=Q (xx')=(K+K') (xx') 



flf we take the value of Cfor air given in the foot note to page , does not 

 equal .4 until e has been diminished to .38". 



t This may be seen by observing the general formulas of 875. 



