Emission and Transmission of Heat 37 



constant temperature chamber was closed, the opening at the top 

 for the escape of air was so adjusted that its area was approxi- 

 mately equal to that of a horizontal section of the vessel, the agi- 

 tator within the vessel was turned continuously, and those of the 

 chamber were put in motion from time to time. 



The time required at a number of stages, for the thermome- 

 ter to fall through a few divisions was observed. The temper- 

 atures indicated by the thermometer were reduced to what they 

 would have been if the whole stem had been plunged in the 

 water, on the assumption, proved both by experiment and calcu- 

 lation, that the stem was exactly at the temperature of the sur- 

 rounding air. 



788. From these experiments the rate of cooling can be 

 readily deduced. 



After obtaining the values of the rates of cooling v, and 

 therefore (776) the values of M> the quantities of heat emitted, 

 for excesses of temperatures ranging from 45 to 117 degrees 

 Fahrenheit, I sought to connect them by some simple law, and 

 found that they satisfied the following, 



M=at(* + bt) 



This agrees perfectly with the formulas of Dulong and Petit 

 within the limits of temperature mentioned above, and it results 

 that these formulas are very probably exact up to an excess of 

 temperature of 470 F. as these two celebrated men have indi- 

 cated. 



Since cooling results from simultaneous radiation and con- 

 tact of air, it is necessary to separate the effects of these separate 

 causes, in order to determine the coefficients used in the formula. 

 To do this I have employed the following method. Let us sup- 

 pose that M represents the quantity of heat lost by a vessel coated 

 with lamp black, M' that which is lost by the same vessel with 

 a brilliant surface, A the quantity of heat lost by air contact, and 

 which is the same for both surfaces, and R and R f the quantity 

 of heat lost by radiation from the lamp black, and the metal 

 respectively. Then 



M= A + R; M' = A + R', and it follows that 



M M' = R R'. 

 Let R=cR' then the last equation becomes 



