SECT. VI.] HEATING OF CLOSED SPACES. 67 



different consequences, if we were not treating here of entirely 

 new problems, whose results may be of direct use. 



86. We know that animated bodies retain a temperature 

 sensibly fixed, which we may regard as independent of the tem 

 perature of the medium in which they live. These bodies are, 

 after some fashion, constant sources of heat, just as inflamed 

 substances are in which the combustion has become uniform. 

 We may then, by aid of the preceding remarks, foresee and 

 regulate exactly the rise of temperature in places where a great 

 number of men are collected together. If we there observe the 

 height of the thermometer under given circumstances, we shall 

 determine in advance what that height would be, if the number 

 of men assembled in the same space became very much greater. 



In reality, there are several accessory circumstances which 

 modify the results, such as the unequal thickness of the parts 

 of the enclosure, the difference of their aspect, the effects which 

 the outlets produce, the unequal distribution of heat in the air. 

 We cannot therefore rigorously apply the rules given by analysis ; 

 nevertheless these rules are valuable in themselves, because they 

 contain the tine principles of the matter : they prevent vague 

 reasonings and useless or confused attempts. 



87. If the same space were heated by two or more sources 

 of different kinds, or if the first inclosure were itself contained 

 in a second enclosure separated from the first by a mass of air, 

 we might easily determine in like manner the degree of heating 

 and the temperature of the surfaces. 



If we suppose that, besides the first source u, there is a second 

 heated surface TT, whose constant temperature is y&, and external 

 conducibility j, we shall find, all the other denominations being 

 retained, the following equation : 



\ 



m n= - 



n^jfe t I t l\ 

 K + H + h) 



_ 

 s \& H h 



If we suppose only one source a; and if the first enclosure is 

 itself contained in a second, s, h , K , H , e, representing the 



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