74 Applications of the Formulas 



M=Q (t'O), equations which give, 

 M= - 



For any number of walls, of thicknesses e, e' y e*', and con- 

 ductivities C, C, C": 



868. To illustrate the method of using these formulas we 

 will apply the first (a) (864), to a particular case. Imagine a 

 wall built of limestone 32.8 feet high with a conductivity (7=13.71 , 

 the coefficients K and K' being .737 (794) and .40 (figure 7) we 

 have Q =1.1 37; we will suppose 7~=59 and #=.42.8, the value 

 of T is the ordinary temperature of dwellings and that of about 

 the average value of the exterior temperature at Paris during the 

 seven months of heating. 



The curves of figure 12 show the effect on m, t and /', of the 

 increase in thickness of the wall. 



869. The preceding formulas apply to the transmission of 

 heat through a wall exposed to the open air, only when all the 

 other walls of the room may be considered as having approxi- 

 mately the same temperature as the air within the room, a con- 

 dition which can hardly exist unless the first wall is the only one 

 exposed to the outer air. When all the walls of the room are 

 exposed to the outer air, all the inner surfaces are at temperatures 

 differing very little one from another, and lower than that of the 

 air in the room, and consequently for the same temperature of the 

 inside air, the quantity of heat transmitted under the same cir- 

 cumstances, per square foot per hour is smaller than in the case 

 previously considered. This is the case with isolated buildings 

 with only one room on a story, and also with churches. 



870. In the case where all the walls of a room are exposed 

 to the open air, the heating of the inside wall surfaces is effected 

 entirely through the movement of the air, for since these inside 

 surfaces have the same temperature their mutual radiation is with- 

 out effect. Then, keeping to the preceding notation, we have: 



