482 W. LeConte Stevens — Experimental 



5 represent the quantity of heat radiated in unit of time, 6 the 

 temperature of the enclosure, t the excess of temperature of 

 the radiating body over that of the enclosure, a a constant 

 whose value they determined to be 1*0077, and m another con- 

 stant whose value depends on the nature of the substance and 

 the condition of its surface, the law of Dulong and" Petit is 

 expressed by the formula 



S = ™(a) e (a*-1) (1) 



In order to compare this formula with others presently to be 

 given, it will be best to express d and t in terms of absolute 

 temperature. Letting T stand for the absolute temperature 

 of the heated body, and T that of the enclosure, we have 



6 = T — 273, and t = T — T . The formula now becomes 



S = m(10077) To - 273 (r0077 T - To -l) (2) 



The range through which the value of T — T was varied in 

 these experiments was 240° C, while the temperature of the 

 enclosure was varied from 0° to 60° C. 



Subsequent investigators have tested the formula of Dulong 

 and Petit, and have found that although it may seem to cor- 

 respond nearly to the truth within the limits selected, it gives 

 very erroneous results at higher temperatures, the radiation 

 revealed by measurement being much less than that which is 

 calculated by means of the formula. De la Provostaye and 

 Desains tested it with thermometers whose bulbs were covered 

 with a plating of metal, and found that under this condition 

 the factor, m, varies with the temperature.* Draper, Tyndall, 

 and Ericsson have published researches which showed the 

 insufficiency of Dulong and Petit's formula. This formula 

 may therefore be considered now as of only historic interest. 



In an exhaustive comparison of the work done by these 

 physicists, Professor Stefan, of Vienna, proposed a formula 

 which, like those that preceded it, is empirical, but which cor- 

 responds much more nearly to the results of measurement 

 than does that of Dulong and Petit.f He found that the 

 amount of heat emitted in unit of time was proportional to 

 the fourth power of the absolute temperature ; or, in the nota- 

 tion already employed, 



S = mT 4 (3) 



Since there is an exchange of heat between the radiating body 

 and the surrounding medium, the effective radiation is 



S=mT 4 -mT 4 



This is obviously reducible to the form 



* Ann. de Chimie et de Physique, III, xvi. 



f Sitzungsberichte der K. Akademie der Wissenschaften, Wien, lxxix, 1879. 



