NO. 3 RADIATION OF THE ATMOSPHERE — ANGSTROM IO, 



where e\ is the emission coefficient and a\ the absorption coefficient 

 for the wave length A. 

 Evidently : 



lim J x = ~d£l = E x dCl ( 2 ) 



r=* a \ v 



where E\ is the radiation from a black body for the wave length 

 A at the temperature 7\ It follows from this that, in all cases where 

 one can assume a x to be independent of the temperature, e\ must* 

 be the same function of the temperature as E\ multiplied by a con- 

 stant. That means that the radiation law of Planck must always 

 hold, as long as the absorption is constant : 



€ X = CA" 



_£l_ 



e*r -i 



If now the gas has many selective absorption bands we may write 

 instead of (i) : 



J = ZE x (i-e- a \R)dn (3) 



With the aid of (3) it is always possible to calculate the radiation 

 for any temperature, if the absorption coefficient, which is assumed 

 to be constant, is known. 



If R is taken so great that the product a\ • R has a very large 

 value for all wave lengths, the expression (3) will become 



lim J = 2E X = *T± (4) 



a x i?=oo 



which is Stefan's radiation law for a black body. 



If a x R cannot be regarded as infinitely great for all wave lengths, 

 the radiation, J, will be a more complicated function of T expressed 

 by the general relation (3). The less the difference is between the 

 radiation from the gas and the radiation from a black body at the 

 same temperature, so much more accurately will the formula (4) 

 express the relation between radiation and temperature. 



Dr. Trabert x draws from observations on the nocturnal cooling 

 of the atmosphere the conclusion that the radiation from unit mass 

 of air is simply proportional to the absolute temperature. If this 

 should be true, it can be explained only through a great variation 

 of a x for a variation in the temperature. Later Paschen 2 and Very 3 

 measured in the laboratory the radiation from air-layers at different 



1 Denkschriften der Wien. Akad., 59. 



2 Wied. Ann., 50, 1893. 



3 Very, Atmospheric Radiation, Washington, 1900. 



