THE ATMOSPHERIC SCATTERING OF LIGHT 

 By Frederick E. Fowle 



Rayleigh has indicated how the amount of energy scattered from 

 a beam of light within a gaseous medium may be used to determine 

 the number of molecules in that medium. It will be shown in what 

 follows that, whereas the application of the process to the enumera- 

 tion of the number of molecules in dry air leads to normal results, 

 its application to atmospheric aqueous vapor leads to an anomaly. 

 Further, this anomaly, like the aurora and certain atmospheric optical 

 phenomena, seems to be related to certain phases of solar activity. 



In the process of determining the intensity of the sun's radiation 

 as it reaches the outside of the earth's atmosphere, certain so-called 

 atmospheric transmission coefficients are obtained. 1 These coefficients 

 express the fractional amounts of the sun's energy incident at the 

 outer limits of the atmosphere which would reach an observer at the 

 earth's surface with the sun in the zenith. They are determined at 

 some 40 different wave-lengths between 0.35 and 2.5 fi. In the follow- 

 ing discussion only those values will be considered which belong to 

 the region from 0.35 to 0.57 yu practically free from any complication 

 due to selective or banded absorptions. 



These, which for the moment may be called " crude " transmission 

 coefficients, a,\, will be subjected to several " refining " processes. It 

 will first be assumed that the composition of dry atmospheric air 

 remains in general practically unchanged from day to day above an 

 altitude like that of Mount Wilson (1,730 meters) where the air is 

 nearly free from dust contamination. The amount of aqueous vapor, 

 however, changes many-fold. Let the coefficient ci\ for wave-length A 

 be assumed composed of two parts, a ax , proper to dry air,- and a w f due 

 to an amount of aqueous vapor above the station, which, if pre- 

 cipitated, would form a layer of water w centimeters thick. Then 



or taking logarithms, 



log a x = log a aX + a- log a irX . 

 If the logarithms of the observed transmission coefficients, log a\, 

 are plotted as abscissae against the precipitable water, w, as ordinates, 



1 Annals of the Astrophysical Observatory of the Smithsonian Institution, 

 vol. 2, p. 13 c t seq., 1908. 



Smithsonian Miscellaneous Collections, Vol. 69, No. 3 



