432 M. Wladimir Michelson on the Distribution 



intensity of the solar spectrum observed beyond our atmo- 

 sphere would be situated about X = 0' A *5. Hence if, according 

 to the preceding table, we take for 0A4 ax the round number 

 10,000, we obtain about 40,000° for the absolute temperature 

 of the sun. It should be remarked that this method only 

 supposes an analogy in the distribution of energy in the pri- 

 mitive spectrum of the sun and in that of lampblack ; but the 

 total emissive power may be very different for these two 

 bodies. 



5. Total Energy of Radiation. — By calculating the area of 

 each curve represented by the equation (10), I obtain the total 

 energy of radiation of the spectrum 



V=^I,d\=l;Bc-^VT( F + %)f(0)e p , . . (12) 



where T denotes the Eulerian integral of the second order. 



Comparing this formula with that obtained by eliminating 

 X between the two equations (10) and (11), that is to say, 

 with the maximum intensity of the spectrum, 



(n 4- 2V+ 2 

 P ~) A»)^ +> (13) 



Making abstraction of constant coefficients, expressions (12) 

 and (13) only differ because the second contains another 

 factor \/0. Hence the maximum intensity increases with the 

 temperature more rapidly than the total energy of radiation, 

 and their ratio 



l__ 2£^_ (p+2 y+ 2 



E ~T(p + ? 2 ){ e J ^ 6 > ' ' ' ( 14 ) 



increases in the direct ratio of the square root of the absolute 

 temperature of the source. 



Multiplying together equations (11) and (14), we obtain 



I max X max 2e-(P+ 2) , ,-p+f , M _. 



-^ = ro^fT)^ +2) =const - • • < 15 ) 



This interesting relationship shows that the total radiant energy 

 emitted by a solid bears a constant ratio to the product of the 

 maximum energy of the normal spectrum by the corresponding 

 wave-length, or, differently expressed, that the area of each 

 curve of energy bears a direct ratio to the area of the rectangle 

 having for sides the coordinates of the summits of this curve 

 (see further on, fig. 3). This constant ratio depends only upon 

 the value of p, which probably is the same for all bodies ; 

 for in our equations it is this value which characterizes the 



