24 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 65 



B. DISTRIBUTION OF WATER VAPOR IN THE ATMOSPHERE 1 

 In applying observations of the effective radiation toward the sky- 

 to determine a relation between the radiation of the atmosphere and 

 its temperature and humidity, we are met by two great difficulties : 

 First, the measurement of the total quantity of water contained in 

 the atmosphere (I shall call this quantity hereafter the "integral 

 water vapor " of the atmosphere) ; second, the determination of the 

 effective atmospheric temperature. 



There have been several elaborate investigations made of the water 

 component of the atmosphere, by humidity measurements from 

 balloons and on mountains, and indirectly by observations of the 

 absorption, resulting from the water vapor, in the sun's radiation. 

 Hann 2 has given the following formula, applicable to mountains, by 

 which the water-vapor pressure at any altitude can be expressed as 

 a function of the water-vapor pressure e observed at the ground. 

 If ^ is the observed water- vapor pressure in millimeters of mercury 

 at a certain place, and h the altitude in meters above this place, the 

 vapor pressure en at the height h meters is 



--*- (1) 



e h = e e 2730 ^ > 



In the free air the decrease of the pressure with altitude is more 

 rapid, especially at high altitudes. From observations in balloons, 

 Suring has given the formula : 3 



e h = e e 2606 V T 20/ ^ ' 



If the atmosphere has the same temperature all through, the water 

 element contained in a unit volume will be proportional to the vapor 

 pressure. It is easy to see from the expression of Hann or of Suring 

 that in such a case the integral water vapor will be proportional to the 

 vapor pressure at the earth's surface. Through integration we shall 

 get from Hann's formula : 



F = 2-73fo- 10 3 (3) 



and from Siiring's formula : 



F = 2.i3/ -io 3 (4) 



where / is the water content in grams per cm. 3 at the earth's surface. 



1 See the concluding part of the preface. The discussion here given is for 

 the purpose of indicating how far observations of humidity and temperature 

 at the earth's surface may take the place of detailed information obtainable 

 only by balloon flights in the study of atmospheric radiation. 



2 Hann, Meteorologie, pp. 224-226. 



3 Arrhenius, Lehrbuch der Kosmischen Physik, p. 624. 



