Temperature of the Carbons of the Electric Arc> fyc. 27 



we may assume that we are dealing with a "black" surface of 

 approximately unit emissive power. 

 Let then 



T! = absolute temperature of bare platinum-strip at balancing 



point, 

 e = ratio of emissive power of a black surface to that of the 



bare metallic surface at this temperature, 

 A = ratio of the area subtended by the platinum to that sub- 



tended by the glowing carbon, at the receiving surface 



of the radio-micrometer, 



and q = /(T) be the " law of radiation " for a black surface, where 

 q = quantity of radiation as a function of the absolute temperature 

 T! of the radiating surface. 



Then the radiation from the carbon is A/e times the intensity of 

 that from a black surface at a temperature TV 



If the radiation from the platinum at the temperature TI be put 

 = 9*> 

 then q p = /(TO. 



Then the radiation from the carbon 



And if T 2 = required temperature of the carbon 



whence T 2 may be obtained, when we know (1) the law of radiation, 

 (2) the ratio of the emissive powers of bare and blacked platinum. 



We go on to discuss these two points together, as the experiments 

 on the first give us information on the second. 



The Law of Radiation and the Ratio of the Emissive Powers. 



In our paper already quoted we have given a series of experiments 

 on the radiation from bare platinum at temperatures up to 1600 C. 

 approximately, and we have shown that a simple fourth-power law 

 expresses the results very closely, so that for these experiments the 

 " law of radiation " is q = a(T 4 T 4 ), where T = absolute tem- 

 perature of radiating surface, T = temperature of surrounding 

 medium, a = a constant, and q = radiation in arbitrary units. At 

 high temperatures T 4 becomes unimportant, and the expression 

 simplifies still further to q = aT 4 . 



Experiments on a blackened surface are difficult to carry out at 



