370 SCHAEFFER. 



/' / It' t \^ 



In the ratio R'/R = , . = I ;;— - ) , 7i is the intensity of X3404 



i 1 io \t 2 11/ 



for the exposures in the laboratory where the radiation suffers no 

 appreciable absorption, 7'i the intensity of X3404 after passing through 

 2300 meters of air, and I2 and I'z are in turn the corresponding in- 

 tensities for the lines X3250, 2981, 2881, 2748, and 2573. 



Molecular scattering. — It will be shown below that ozone absorption 

 has little if any effect on I'l and I'l but it is known that molecular 

 scattering plays an important part. The problem of the scattering 

 of light by small particles was studied by Lord Rayleigh more than 

 forty years ago. If ^'o is the initial intensity of the light, then the 

 intensity, i, after passing through a scattering medium of thickness x is 

 given by the equation i = io e~^^, where K is the coefficient of scatter- 

 ing. Rayleigh first calculated the value of K on the basis of the elastic 

 solid theory and found, 



327r3(M - 1)2 



K = 



3NX' 



where /x is the index of refraction for the light of wave-length X, and N 

 is the number of particles per cubic centimeter of air at N.T.P. The 

 same result was obtained by Rayleigh ^ later from the electromagnetic 

 theory, and Schuster ^^ and recently King,-^^ by quite different 

 methods, have also arrived at this result. The formula has been 

 tested experimentally by several investigators and found satisfactory. 

 The observations of Dr. C. G. Abbot ^^ on the intensities of sunlight 

 at Mt. Wilson and at Washington, D.C. agree very well with the 

 values calculated for molecular scattering according to the above 

 formula. 



It is necessary then to correct the intensity of the standard after the 

 light has passed through a considerable layer of air. Using the 

 Rayleigh formula, the calculated amount of scattering for light of 

 wave-length X3404 is 16% in the air path under consideration. Conse- 

 quently, the value 0.84 is taken as the intensity of X3404 after passing 

 throu,gh 2300 meters of air. For instance, consider a line of shorter 

 wave-length whose intensity appears to be equal to the standard when 

 the air path is small, then if the measured opacities show this line to be 



9 Rayleigh, Phil. Mag., 47, p. 375, 1899. 



10 Schuster, Theory of Optics, p. 325. 



11 King, Phil. Trans. Roy. Soc, London, 212A, p. 375, 1913. 



12 Abbot, v. (10). Ann. Astr. Abs. Smithsonian Inst. 2, p. 113, 1908. 



