30 Emission and Transmission of Heat 



Thus, by observing the intervals of time 0, 0' , 0", and so on, 

 which correspond to successive coolings of one degree, one may 

 therefrom compute the quantities of heat which would be emit- 

 ted per hour per square meter for the corresponding excesses of 

 temperature. It then remains to find by trial the law which these 

 results follow expressed as a function of the excess of temper- 

 ature. 



776. When a vessel filled with warm water cools, we call 

 the ratio between the infinitely small variation of temperature dt, 

 and the time do in which this variation takes place, the rate of 



cooling thus, we have z>=~ Pdt represents the quantity 



of heat emitted in the time do. 



If the temperature of the vessel is kept constant, the quan- 

 tities of heat emitted during equal intervals of time will also be 

 constant, and that quantity emitted in unity of time will evi- 



dently equal P or Pv. 



Since the second represents unity of time we have 



Making v = which is to assume that the rate is constant 



during the cooling through one degree, we get the same value of 

 Mas found in 775. 



777. Newton's Law. Newton's hypothesis was that the 

 rate of cooling in air was) proportional to the excess of the tem- 

 perature of the body above that of the air, and his formula was 



v = qt 



t being the excess |of temperature and q a coefficient varying with 

 the nature of the body. 



This law is, however, inexact, the rate of cooling varying 

 much more rapidly. 



Dulong and Petit 's Laws. Dulong and Petit have made 

 numerous experiments on the cooling of the thermometer placed 

 in a closed vessel, maintained at a constant temperature by a 

 water bath and filled with different gases under different pressures. 

 These skilful physicists have established the following facts : 



