Polarization of Sky Light, 



89 



and in winter from '37 to "50 is clearly due to the increase 

 in the earth light. But it is not so easy to explain the 

 difference between winter and summer with a horizontal sun. 

 It must depend on some material difference in the atmosphere. 

 It is possible that the brightness of the sky is augmented in 

 the ratio 56 to 37, owino- to an increase either in the number 

 of the fine particles or in their average size. The size is 

 particularly important, as the light scattered by a fine particle 

 is proportional to the square of its volume ; so a little mois- 

 ture deposited on dust particles would increase their light- 

 giving power enormously. On the other hand, the difference 

 might be due to the sky never being as pure in the summer 

 as in the winter. The presence of dust particles larger than a 

 wave-length would of course depolarize the scattered light. 



Rubenson gives a few observations at Rome of the polariza- 

 tion in the vertical plane at distances from the sun other than 

 90^. They were taken for the sake of fixing the maximum 

 point, but they are interesting to us for another reason. 



Rome, June 21st, 1861. 



Hour. 



Solar Distance. 



r. 



Zenith Distance. 



h m 



O 





1 



9 15 A.M. 



90 



•288 



61 9 



9 26 „ 



120 



•490 



83 35 



9 43 „ 



GO 



•5(10 



26 



9 57 „ 



90 



•297 



68 27 



3 26 P.M. 



90 



•277 



43 59 



3 43 „ 



110 



•382 



60 50 



3 58 „ 



70 



•380 



17 34 



4 19 „ 



90 



•279 



34 24 



These are all in the vertical plane through the sun. Let us 

 compare these values at 60° and 120° with those deduced from 

 Rayleigh's laws on the assumption that the particles are all 

 small. We must presuppose something about the polarization 

 of the subsidiary light. Now, from Brewster's observations 

 at St. Andrews, the neutral point below the sun (called after 

 his name) is at an angular distance of about 10°, when the 

 sun is at 54° above the horizon. This supplies what we 

 want, at least approximately. Let u, v be the components 

 of the light which reached the particles directly from the sun, 

 and X, ij the components of the subsidiary light, polarized in 

 the vertical plane and in a plane at right angles thereto re- 

 spectively. At the neutral point we have 



y — x = u — v — u—xi cos^10° = '03m. 



