Comparison of Formulae for Total Radiation. 435 



To determine the value of the constant a, experiments were 

 made upon a variety of solid conductors, including carbon, 

 platinum, iron, and copper, raised to incandescence. For each 

 of these the same value was found, 



a = 0-0043 

 If it be desired to find the total radiation, rather than that 

 of a single wave-length, the equation just given must be inte- 

 grated between the limits X = and A = oc . We have then 

 for the total radiation, S, 



r 



S = / sdX 







The result of the integration is 



_ aT 



S = \n*Jn cbFe T 



Or, letting C represent the total emission constant, \it^/iz cb, we 

 have 



aT 



S = CFe T 



If the radiating body be surrounded by another body whose 

 constant absolute temperature we may call T , there is mutual 

 radiation between the two, and the resultant radiation of the 

 first becomes 



aT aT 



S = CFe T-CFe T 

 This is obviously reducible to the form 



; (~ 



'"Vr. 



Here the quantity outside of the parenthesis is made up of 

 constants, and the variation of S is dependent only on T. 

 For purposes of comparison therefore we may employ only 

 what is found within the parenthesis. 



This formula has been tested by applying it to the results of 

 experiments already published by Schleiermacher, Graetz, and 

 Magnus in Germany, Bottomley and Tyndall in England, 

 Violle, Garbe, Becquerel and Mouton in France, and Langley 

 and Nichols in America. A part of these results were in- 

 cluded in the communication to which reference has already 

 been made. 



In testing Stefan's formula* Schleiermacher measured the 

 loss of energy sustained in unit of time by a platinum wire, 

 heated to a given temperature within a good vacuum by means 

 of the electric current and surrounded by an envelope kept at 



* Wiedemann's Annalen, xxvi, p. 287. 



aT /T a(T-To) 

 S = CFe T„fie - 



