Applications of the Formulas 95 



little by little even to the inner surface, and if the new tempera- 

 ture of the exterior air lasts sufficiently long, a new regime is 

 established in the wall. During this interval the temperatures of 

 the different points of the walls would undergo changes which it 

 would be actually impossible to calculate, since the calculations 

 would be even more complicated than those regarding the trans- 

 mission of heat in an unlimited medium at constant temperature 

 (897) . But, since walls are rarely more than twenty inches thick, 

 and as the dissemination of heat through bodies, even of the rather 

 low conductivities of materials of construction, takes place with 

 great rapidity, and as the difference of temperature of the two sur- 

 faces are not generally more than a smallnumber of degrees, we may 

 assume that, during all the changes of temperature which precede 

 the establishment of the new regime, the temperatures of the dif- 

 ferent points of the wall increase uniformly from the exterior to 

 the interior. This supposition is never realized, but it allows us 

 to follow approximately the phenomena which accompany a fall 

 of the exterior air temperature. 



Consider a wall belonging to a room of which none of the 

 other walls are exposed to the exterior air; assume as in para- 

 graph 868, 7^=59, 0=42.8, C=i3.7i and e=ig.jo, we will 

 have /=54.62, /'48.i9 and M=$.o8, If the exterior temper- 

 ature became 32, the formula (a) (864) would give ^=51. 56, 

 /'=39-42, and .$/=8.45, the quantity of heat lost by the wall 

 per square foot in passing from the former regime to the latter 

 would be : 



and as this cooling takes place while the temperature of the outer 

 surface falls from 48.19 to 39.42, the cooling is decreasing; 

 admitting the hypothesis of a uniform variation of temperature, 

 this cooling would take place in the same time as if the excess of 



temperature of the outer surface was equal to or 11.81; 



and since for an excess of temperature of 16.19, the loss of heat 



*This figure is just twice that given in P6clet although the equations are other- 

 wise identical. This error appears in both the later editions. 



