64 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 65 



Together with the observations treated in the foregoing chapters, 

 the present result gives us support for the following conclusions : 



1. An increase in the water- vapor pressure will cause a decrease 

 in the effective radiation to every point of the sky. 



2. The fractional decrease is much larger for large zenith angles 

 than for small ones. 



If we regard the atmosphere as a plane parallel layer, having 

 uniform density, p, and a temperature uniformly equal to the tem- 

 perature at the earth's surface, the effective radiation of a certain 

 wave length, X, in different directions, may be expressed by 



J x =Ce~ 7 '^^ (1) 



where C and y are constants and 4> is the zenith angle. For another 

 density, p ', of the radiating atmosphere we have : 



J\ = Ce 7 cos0 (2) 



and from (i) and (2) 



£ = *-*[£&] ( 3 ) 



If /o is greater than p, J\ will always be less than 7'\. It is evi- 

 dent from the relation (3) that the ratio between 7 X and J\ dimin- 

 ishes as the zenith angle approaches 90 . The general behavior of 

 the radiating atmosphere is therefore consistent with the case that 

 only a single wave length is radiated and absorbed. But the detailed 

 conditions are naturally very complicated through the lack of 

 homogeneity of the radiation. Especially for the curves correspond- 

 ing to high humidity the radiation falls off much quicker with the 

 approach to the horizon than is to be expected from the dependence 

 of the total radiation on the humidity. Especially is this the case 

 after we have reached a value of the zenith angle of about 60 or 70 

 degrees. In part this is due to the increasing influence of the radia- 

 tion of wave lengths whose radiation coefficients are small and can 

 be neglected for smaller air masses, but which for the very large air 

 masses that correspond to zenith angles not far from 90 must come 

 into play and produce a rapid decrease of the effective radiation 

 to points near the horizon. But here other influences are also- to be 

 considered. The observations of the total radiation, compared in 

 regard to the diffusing power of the atmosphere for visible rays, 

 show that the influence of diffusion can be neglected in comparison 

 with the other more fundamental influences, as far as the total radia- 



