NO. 3 RADIATION OF THE ATMOSPHERE ANGSTROM 23 



vapor atmosphere, or, what is the same, the amount of water vapor 

 contained in a vertical cylinder of I cm. 2 cross-section. Here a x 

 has been considered as a constant. As has been shown by Miss von 

 Bahr, the law of Beer does not, however, hold for vapors, absorption 

 being variable with the total pressure to which the vapor is subjected. 

 As will be seen in the experimental part of the paper, this circum- 

 stance has probably introduced a slight deviation from the conditions 

 to be expected from the assumption of a constant value for a. 



From (10) we draw a similar conclusion to the preceding: with 

 decreasing water-vapor content] the radiation of the atmosphere will 

 also decrease and this decrease will be more rapid at a low water- 

 vapor content than at a high one. 



The simplest form in which (10) can be written is obtained from 

 the assumption that we can put: 



H + i%E x =K 

 and 



22 ( E x - E\ ) e~ a W R = Ce~ a m y m R = Ce~^ p 



where P is the height of the reduced water-vapor atmosphere. In 

 such a case we shall obtain for the radiation of the atmosphere : 



E a =K-Ce-P p (11) 



and for the effective radiation : 



J=E' + Ce~P p (12) 



We have heretofore supposed that the temperature of the radiating 

 layer is constant. If that is not the case, it will introduce a new 

 cause of variations. For every special wave length the radiation 

 law of Planck will hold, but the integration will generally give a 

 result different from the law of Stefan, dependent upon the different 

 intensities of the various wave lengths relative to those of a black 

 body. From the measurements of Rubens and Aschkinass on the 

 transmission it can be seen, as will be shown later, that the radiation 

 of the water vapor is very nearly proportional to the fourth power 

 of the temperature, and as an approximation one may write : 



E a =<rT*F(P) 



or for the simple case (n) : 



E a =cT i (K"-e-P p ) 



Use will be made of these considerations in the treatment of the 

 observations made. 



