NOTES ON THE USE OF THE FORMULAS 



911. None of these calculations which we have just been 

 making in regard to the transmission of heat, can be considered 

 rigorously exact. Those relating to elementary transmission 

 rest on two hypotheses which are only true within certain limits ; 

 Newton's Law of cooling, which is only approximate even for 

 small differences of temperature, and the supposition that all 

 points of a body exposed to the air are at the same tempera- 

 ture; which is not exact, for the lower portions are always at a 

 lower temperature than those above. In regard to the formulas 

 representing the transmission of heat through walls the two 

 assumptions that we have made (864 and 870) are actually only 

 extreme cases, between which any actual case will be found to 

 lie. But we must not deceive ourselves in regard to the practical 

 importance of rigorous exactness in the formulas or precision in 

 the calculations ; the lightest movement of the air has a great 

 influence on the quantity of heat which it carries away and for 

 bodies exposed to the open air the accidental and periodical 

 variations which it experiences never permit the existence of a 

 permanent regime in the interior temperatures. In the prelimi- 

 nary calculations we are obliged to use figures which are not per- 

 fectly exact for any of the materials except textile materials, for 

 they vary with the density, for stones with the state of their crys- 

 tallization, for wood with the direction of the fibres. Thus we 

 can only regard the results of the calculations as sufficient 

 approximations for the guidance of engineers. But heating and 

 ventilating apparatus has always under ordinary circumstances 

 an excess of power, because it should be calculated for the most 

 unfavorable conditions, and this excess of power is destroyed, 

 according to the indications of thermometers and anemometers, 

 by the adjustment of registers or the supply of fuel ; thus the 

 uncertainty of the calculation, which is always within sufficiently 

 narrow limits, is taken care of by the excess of power of the 

 apparatus, an excess of power which is only necessary in cases 

 of rare occurrence and of short duration. This is not at all 



