26 IT. Ferret — Law of Thermal Radiation. 



the sun at its mean distance, and A is the solar constant. For 

 the several laws of radiation H must be expressed in a function 

 of the temperature as in (1), (6), etc., and we then have the 

 relation between the temperature and the solar constant. Put- 

 ting according to Violle* S : o)— 183960, the preceding equa- 

 tion becomes by (1), in the case of Dulong and Petit's law, in 

 which «= 1*0077. 



(35) m(l-0077)r = 45990 A 



But here as we have seen, §21, there is great uncertainty 

 with regard to the true value of m, and there is also consider- 

 able with regard to that of A, to say nothing of the applica- 

 tion of a law based upon experiments through a range of only 

 160° being extended up to the temperature of the sun. This, 

 with Pouillet's large value of m= 1*146 and small value of 

 A = 1-75 gives a value of r=1454°. But putting a= 1-0082, 

 which has been shown to satisfy the results of Dulong and 

 Petit's experiments as corrected by Stefan, and using the 

 value of on .=0-7188, as obtained in §7, and also a greater value 

 of A, say 2*2, we get r=1456, very nearly the same, though 

 with the same solar constant it would have been considerably 

 less. The true solar constant is probably still considerably 

 greater than this. 



By means of (6) we get from (34) 



(36) ml — X = 45990 A 



This, with 6=4, as required by Stefan's law, and m=0*4, as 

 determined by him for lampblack and A = 2*2, we get 

 T = 6122° or r=5849° as the sun's temperature if it had the 

 radiativity of lampblack. The temperature of the sun ob- 

 tained upon this hypothesis is often called the " effective tem- 

 perature of the sun," but this must be very much less than the 

 real temperature, since the radiativity of the sun is undoubtedly 

 much less than that of lampblack. Pouillet supposed it might 

 not be more than one-tenth as much. 



With the value of e=4*2 which is required to satisfy the 

 results of Dulong and Petit's experiments as corrected by 

 Stefan, and using the values of on— 0*3296 corresponding, §7, 

 which, according to Lehnebach should be the same for a lamp- 

 black surface, we get from (36) with A=2*2, T=5528 or 

 r=5255°. 



If in (36) we regard e as a function of r of the form of (23), 

 and use the value of m= 0*438 as determined in §20, the value 

 of T = 2337° or r=2064° is required to satisfy this equation 

 with A=2-2. This latter is therefore the effective tempera- 



* Armales de Chimie et de Physique, vol. x, 1877. ■ 



