Applications of the Formulas 83 



MULTIPLE WINDOWS 



884. In the case of several parallel windows, separated by 

 intervals sufficiently large to allow the air to move freely, the two 

 surfaces of each window are sensibly at the same temperature, 

 and we may obtain the value of M, in the first case that we have 

 considered, by supposing the thickness e, e* , e" equal to zero in 

 the general formula (875). Then for 2, 3, 4 . . n windows, 

 the values of M would be 

 Q(Te) Q(T0) Q(TQ) Q (T0) 



2 + 1 2 + 2 2 + 3 2 + I 



and the relative values ot these quantities to that of a single 

 window are 



212 2 



3 ; 2 ; 5 i+ 



Curtains, more or less thick, would produce sensibly the 

 same effect. If the distance between the windows was less than 

 .79", the transmission would be increased, because the transmis- 

 sion through the air ;f-f is equal to the transmission by contact 

 of air and its renewal, and at smaller distances the transmission 

 through the motionless air would be greater. 



In the second case, that we considered in regard to walls, 

 the calculation relative to the transmission of heat through win- 

 dows, would be extremely complicated, because it is necessary 

 to take into account the surfaces of the windows, and we could 

 arrive at no exact conclusions, on account of the influence of 

 floors and ceilings, the effect of which could not be evaluated. 



The case first examined evidently gives the maximum trans- 

 mission ; it is the only one in which we can calculate with suffi- 

 cient exactitude the quantity of heat transmitted by the windows, 

 and the figures obtained suffice in any case to give a sufficient 

 appreciation of the quantity of, heat lost. 



TRANSMISSION OP HEAT THROUGH CYLINDRICAL ENVELOPES 



885. The case that we will now consider is, for example, 

 that of a metal pipe traversed by steam, and surrounded by some 

 material of low conductivity, in order to diminish the loss of 

 heat from the steam during its passage. 



Let M represent the quantity of heat in B T U transmitted 



