22 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 65 



This expression can easily be transformed into : 



Jx = irEx(i-2f> 2 \-?~dx) (9) 



where o = a\- h and x = a,. . When h = o, this expression ap- 



A cos $ 



proaches zero; when h=co, J\ approaches the value ttE\, which is 

 equal to the radiation of a black body under the same conditions. We 

 have, in fact : 



— — ax — lim — - — = hm — o 



X p = oo J _ I p = oo " 



2 ~jfi 



11m p- 



P = m J p 



and in a similar way 



limp s 



p=0 



— d'= — 



We shall now consider in what respects these relations are likely 

 to be true for the very complicated conditions prevailing in the 

 atmosphere. The atmosphere, considered in regard to its radiating 

 properties, consists of a low radiating layer up to about 10 km. made 

 up of water vapor and carbon dioxide, and a higher radiating layer 

 composed of carbon dioxide and ozone. These two layers naturally 

 merge into one another, but it is convenient here to suppose a clear 

 distinction, our surface of separation being at the altitude where the 

 water vapor ceases to have any appreciable influence upon the 

 radiation of the atmosphere. 



The radiation of the lower layer is chiefly dependent upon the 

 amount of water vapor contained in it, the strong radiation of the 

 carbon dioxide being at wave lengths where the water vapor itself 

 must radiate almost in the same way as a black body. At any rate, 

 the variations of the radiation in that part of the atmosphere must 

 depend almost entirely on the variations in the water-vapor element, 

 the carbon-dioxide element being almost constant, as well in regard to 

 time, as to place and to altitude. The probable slight influence of vari- 

 ations in the amount of ozone contained in the upper strata of the 

 atmosphere, we may at present ignore. Including the constant 

 radiation of the carbon dioxide in the radiation of the upper layer, 

 we can apply the expression (5) and arrive at 



J = H + lk[E x -(E x -E\)e- a \-y R ] (10) 



where R can be put equal to the height of the reduced water- 



