NO. 3 RADIATION OF THE ATMOSPHERE ANGSTROM 25 



When one wishes to compute the integral water vapor from the 

 pressure, the fall of temperature will cause a complication. From 

 (1) we get, instead of (3) : 



- h 

 T h 'fh = T f e 2730 



where T% denotes the absolute temperature at the altitude h meters. 

 Th is a function of the altitude. This function differs from time to 

 time and can be known only by balloon observations, but for present 

 purposes we may use an approximate formula for Tj,. We may write, 

 T h is equal to T when h — o and T h is equal to o° at h=co. Also, 



we must have — =0 at h=<x>. Accordingly (as the temperature 

 dh 



influence in the formula is not great) it may suffice to assume that 

 T on an average can be expressed by an exponential function of the 

 form: 



T h= T e- ah (6) 



where a is to be determined by assuming that for h = o — - is 



, ah 



equal to the observed fall of temperature at the surface of the 

 earth. For a fall of temperature of 0.7 degree per 100 m. one finds 

 a = 0.03. Introducing (3) into (1) we obtain the slightly different 

 result for the integral water vapor: 



F=2.94-/ - io 3 

 and in a similar way from Siiring's formula : 



F = 2.30-/V io 3 



Hann's formula, which holds for mountain regions, indicates that 

 here the element of water vapor contained in the atmosphere above 

 a certain place is the absolute humidity at that place multiplied by 

 a constant, the constant being independent of the altitude. This 

 is not the case for the. free air, if Siiring's formula may be taken as 

 a true expression of the conditions here prevailing. It is true that at 

 a certain place we shall have F=cf , c being a constant, but this 

 constant will differ at different altitudes. At an altitude of 4,400 m., 

 we shall have 



F= 1 .8 • /4,400 ( free air) 



Fowle has made an interesting study of the absorption pro- 

 duced by water vapor in the sun's energy spectrum at Mount Wil- 

 son. 1 He also finds that the amount of water vapor contained in 



1 Astrop. J., 37, N. 5, P- 359- 



