Polarization of the Light of the Sky: 509 



We will now return to the sky. If any point be observed, we 

 nave only to imagine a series of illuminating beams drawn from 

 the sun to the points of the atmospheric track along which the 

 eye is directed, and we have the atmospheric phenomena referred, 

 according to the analogy first indicated by Tyndall himself, to 

 the same origin as the experiments. 



The first remark that this leads to is, that as in the experi- 

 ments the appearances are symmetrical all round the beam, so 

 in the sky the appearances must be symmetrical about the line 

 to the sun, allowing for the variation in condition between those 

 beams that lie overhead and those that lie nearer the horizon. 

 We are thus led to the assumption of the line to the sun as an 

 axis instead of the two axes of Brewster drawn to the neutral 

 points. 



In the first instance we may regard as a small quantity the 

 variation between the maximum polarization in zenith and 

 horizon. Brewster allows only (30° — 27°) = 3° of his measure 

 R for the normal difference. 



Employing, then, Brewster's data, we may represent R to a 

 first approximation thus : — 



B = 33i° sin (6>-18i°) SH1 (0 + 181°), 

 where is the angular distance from the sun of the point 

 observed. This expression has the same value as Brewster's 

 first term throughout the plane of sun, zenith, observer, but re- 

 presents the rest of the sky as if traced by the revolution of that 

 plane about the line to the sun. 



In the light of Tyndall's experiments we now see that the 

 diminution of maximum polarization from zenith to horizon 

 may be regarded as due to a small advance in the stage or mean 

 size of the diffracting particles. It will be then best expressed 

 by a variation of the maximum polarization due to the zenith- 

 distance ; and the formula becomes 



B = (33i° -31° sin z) sin (0-181°) sin (0+181°). 



The constant (3J°) gives pretty closely the same horizontal 

 value (27°) as Brewster's formula. The observations do not 

 admit of any considerable accuracy in fractions of degrees. The 

 variation from zenith to horizon deduced from some of Rubenson's 

 sets, and reduced to Brewster's measure, is about 8° ; and this 

 really accords better with some of Brewster's observations than 

 the smaller value he employs. 



But, further, it is clear from the symmetry that the polariza- 

 tion observed along the line to sun, excluding the effect of 

 indirect light, must be nil; for there is no reason why it should 

 be in one direction more than another. We must therefore 

 introduce a factor which will vanish along the solar line without 



