no. 3 



ATMOSPHERIC SCATTERING OF LIGHT — FOWLE 



For the range of wave-lengths utilized in table 4, 0.2 to 0.5 /x, the 

 mean value of N obtained from the liquid-water data is 2.90 X io lft 

 which though large is of the right order of magnitude and quite as 

 accurate as the accuracy of the data warrants. For these wave- 

 lengths therefore liquid water scatters transmitted radiation just as 

 would the same amount of water in gaseous state according to 

 Rayleigh's theory. 1 



Values of N of quite a different order of magnitude are obtained 

 when based on the transmission coefficients for atmospheric aqueous 

 vapor. A graphical rather than a least-squares method has been 

 resorted to in the present case. N tp , the number of molecules per 

 cm. 3 at the pressure p and the temperature t, may be derived from 

 the expression 2 



(n—i)p \ 2 (i+at)y6ox io 3 i_ 



(0.81 )p 



k=* 2 

 3 



(l+a07OO 



AV 



+ D 



„ o.8ip x io -8 . ■ * 1 a. • i_* £ 



Here -, — > ^ is approximately the weight of aqueous vapor in 



grams per cm. 3 , or in other words the reciprocal of the height of a 

 column 1 cm. 2 containing 1 cm. precipitable water at the temperature 

 t and the pressure p. Plotting the observations with (n— i) 2 /a* 

 and k as variables and calling M the tangent made by the best repre- 

 sentative right line with the X axis, then Ntp may be obtained through 

 the equation 



N _ 32"- 3 . pXIO 3 I 



tP 3 0.8l (I + at) 760' M 



Figure 1 shows the graphical steps and the following table the result- 

 ing values : 



Table 5. — Number of Molecules N t{) , derived from the Transparency of 

 Atmospheric Aqueous Vapor 



1 For shorter wave-lengths greatly decreased transmission is found as the 

 great metallic reflection band at 0.115 m is approached (Martens, Annalen 

 der Physik, 6, p. 603, 1001), and for wave-lengths greater than 0.50 m as a region 

 of selective absorption is approached. For metallic reflection and selective 

 absorption the molecular formula would not hold. 



3 Astrophysical Journal, 38, p. 400, 1913. 



