IF. Ferret — Law of Thermal Radiation. t 27 



ture of the sun as deduced from (36) with the value of e in 

 (23). And this expression, with the constants used, represents 

 observation fairly well throughout the whole range of experi- 

 ment with lampblack and bare glass radiating surfaces, while 

 the others do not, especially that of Dulong and Petit's law. 

 But this temperature, as well as that of Pouillet's from Dulong 

 and Petit's law, is doubtless much too low. And this is not 

 surprising, for it has not been claimed or supposed that this 

 new law, although it represents observation better throughout 

 the short range of experiment of only about 240°, can be ex- 

 tended with safety up to the high temperature of the sun. 

 The scattering results obtained indicate that no reliability can 

 be placed in such methods, to show which has been the princi- 

 pal object in touching upon this part of the subject here. 



25. According to Langley's deductions from his experiments 

 at the Edgar Thompson steel works near Pittsburg,* solar heat 

 radiation is about 100 times greater than that of melted iron at 

 a temperature of at least 1800°, angular area for area. Sup- 

 posing both to have the same relative radiativities we could 

 arrive at the sun's temperature if we knew the law of the 

 increase of radiation with increase of temperature from this up 

 to the sun's temperature. We have seen that none of the pre- 

 ceding laws can be relied upon for this purpose, though they 

 of -course would give better results by starting at the high 

 temperature of 1800° than, in commencing down at ordinary 

 temperatures and extending them through a range 1800° 

 greater. Using Dulong and Petit's law we would have 



l-0077 r =100xl-0077 T ' 



as the condition for determining the solar temperature r, r' 

 being equal to 1800°. The solution of this gives r= 24:00°. 

 As this law gives results demonstrably too small, this is, no 

 doubt, too small, but much more nearly correct than that of 

 Pouillet's obtained by extending the law through a much 

 greater range of temperature. By Stefan's law we should have 



T 4 =100T' 4 



The solution of this, putting ^=1800+273=2073, gives 

 T = 6555° or r=6282° for the sun's temperature. This does 

 not differ greatly from the preceding value of r as obtained by 

 Stefan's law from (36). With the exponent equal to 4*2, 

 which, we have found, satisfies observation better, we get 

 r=5933°. These last results are undoubtedly much better, as 

 obtained from these data, than that obtained with Dulong and 

 Petit's law, which, we have reason to think, is very erroneous 

 for high temperatures. If the : ' 100 times" in the comparison 



* Proc. of the Am. Academy of Arts and Sciences, 1878. 



