72 Applications of the Formulas 



air within the room be T and that of the outside air be 0. The 

 r6gime once established the quantity of heat which would traverse 

 the wall exposed to the air would evidently be equal to that which, 

 in the same time, would penetrate its inner surface, and to that 

 which would escape during the same time from its outer surface. 

 The interior surface would be at a temperature / lower than T and 

 the exterior surface would be at a temperature /' higher than 0, 

 We may admit that the heating of the inner surface and the cool- 

 ing of the outer take place according to the same laws. Thus in 

 designating by M the quantity of heat transmitted per square foot 

 per hour we would have three expressions for M, one in terms of 

 of the conductivity C of the material of the wall, the two others 

 in terms of the coefficients K and K' of cooling by radiation and 

 contact of air, from which equations we may deduce the values of 

 / and /' in terms of known quantities. . But if we employ Dulong's 

 formulas for cooling (794-797)^6 calculation would be impossible, 

 and even admitting the simpler formulas of 789 and 790 we would 

 be led to an equation of the second degree, rather complicated 

 and extremely difficult to handle. It is better to admit for the 

 cooling and the heating Newton's law (791) which is sufficiently 

 exact for small differences of temperature, and besides in all cal- 

 culations relative to the transmission of heat one can never expect 

 more than a rather rough approximation because there are cir- 

 cumstances which are impossible to take into account, such as 

 the increase of temperature of the outer surface according to its 

 height above the ground, the action of the wind, of the sun, and 

 so forth. According to this we have: 



equations which give, 



.T(C+Qe)+C9 0(C+Qe)+TC 



865. From this formula follow several important conse- 

 quences. If Qe was very small relatively to 2C and could be 



neglected, the formula reduces to M-- (T-0) and the value of 



CQ(T-e) 



