92 Applications of the Formulas 



899. If we apply the formula to air supposedly motionless, 

 as it would be if heated from above, we would certainly obtain 

 but a rather vague approximation, on account of the large expan- 

 sion that it would experience and the unknown variations of its 

 conductivity with increase of temperature. However, as the 

 results of the calculation may at least give an idea of the rapidity 

 with which heat disseminates itself in air we will indicate them. 

 After one minute and at distances : 



.04" 4." 4" 40" 



the temperatures given by the formula are: 



0.9997" 0.9967" 0.9607" O.62O7" 



If the formula employed was truly applicable to air it would 

 result that the dispersion of heat in air would be grater than in 

 any other substance ; but we may certainly conclude from these 

 figures that the diffusion of heat in air takes place with great 

 rapidity. Furthermore this fact explains many phenomena which 

 appear very strange. 



900. In churches heated by warm air escaping from a num- 

 ber of openings in the floor, the temperatures of the air at heights 

 of 6^ feet and 66 feet differ by less than two degrees as has been 

 proven at L,a Madeleine and Saint -Roch. 



In the cooling of bodies by contact of air, the quantity of 

 heat emitted diminishes very slowly with increase of height of 

 the body, which can only be explained by the rapid diffusion of 

 the heat in the surrounding air. Another result of this fact is 

 that in the heating of rooms by open fire places, not only a part 

 of the radiation is utilized but also that portion of the heat pro- 

 duced which is transmitted by diffusion to the surrounding air. 



901 . M. Darcy , chief engineer of the ponts et chausstes made 

 very interesting experiments on the cooling of warm water pass- 

 ing through pipes buried in tke ground. The total length of the 

 cast iron pipe was 7610 feet. Its diameter varied between 6.4" 

 and 9.84". The weight of water passing in one second was 8.12 

 pounds, the cooling was from 80.16 to 69.64 that is to say 

 10.52, the loss of heat per second in B. T. U. was then 8.12 X 

 10.52 = 85.5 and per hour 85.5 X 3600=307800; and as the pipes 

 had a total surface of 16450 square feet, the quantity of heat in 

 B. T. U. per square foot per hour was 1 8. 68 for a mean temper- 



