98 Applications of the Formulas 



,820, M=.2i (r-Oj,A = 45 (.33 



.67*) 



for <? = 39-37 inches. 



t=.6oT+.4oO, /' = .i 4 r+.86^, M=.i6(T 0), A = 90 (.37 



for ^=59.07 inches. 



/= 68r+. 33 0, /' = .i 2 r+.8 9 0, M=.iT,(T OJ,A = i35 (.40 



7H-.600) 



INTERMITTENT HEATING 



907 . We have hitherto supposed the heating to be continu- 

 ous ; but it is often suspended during the night and at other times 

 it-only takes place during a very limited time : we have then two 

 cases to consider, the loss of heat due to the suspension of the 

 heating at night, and the quantity of heat which must be furnish- 

 ed in order to maintain a room at a certain temperature during a 

 certain length of time. 



HEAT LOST BY WALLS DURING THE SUSPENSION OF HEATING 



908. During this suspension which generally takes place at 

 night, the heat emitted from the outer surface of the walls is the 

 cause of a certain amount of cooling throughout their mass and 

 consequently a certain cooling of the interior which is added to that 

 arising from the windows. This cooling of rooms during the inter- 

 vals between heating is a very important question, unfortunately 

 very complicated, but in regard to which theoretical considera- 

 tions may nevertheless lead to some useful practical conclusions. 



909 . Considering the simplest case , that in which al 1 the walls 

 of a room are exposed to the outer air ; all the interior surfaces 

 will be sensibly at the same temperature, and the heat emitted 

 by the walls will be solely that contained within them. I have 

 attempted to calculate the temperatures of different points of the 

 wall at different periods of its cooling by employing the principles 

 and formulas of Fourier (TraitS analytique de la Chaleur);& very 

 simple equation giving the temperature of any point as a function 

 of all the given quantities of the question is in this way easily 

 arrived at. This equation contains arbitrary constants of which 

 the values are easily determined on the assumption that at the 

 beginning of cooling, the temperatures at the different points of 



