and its application to the observation of the Sky. 27 



zontal polarization be combined with an equal one making a 

 small angle 2a with the vertical, the resulting polarization 

 will be inclined to the vertical at the angle 45° + a, or nearly 

 at the angle 45°. 



We can thus account for the fact that the polarization at 

 the side of the neutral point is inclined about 45°, by sup- 

 posing that the polarization directed to the sun or antisolar 

 point is combined with a uniform horizontal polarization of 

 equal amount at the height of the centre of the neutral point ; 

 and the explanation admits of extension to the whole pheno- 

 menon. 



The polarization due to the sun must obviously be considered 

 as increasing regularly from sun or antisolar point to the great 

 circle at right angles to the line joining them. This polariza- 

 tion must therefore be in the first stage of Tyndall's experi- 

 ments — not in a more advanced one, as supposed in my former 

 paper ; the imperfect polarization at right angles to the sun 

 must arise from some other cause. 



The question then is, to what is the horizontal polarization 

 in the neighbourhood of the horizon due ? 



The most obvious answer is that which Brewster gave : it 

 seems as if it might be due to polarization by refraction through 

 the atmosphere, in the same way that light is polarized by 

 oblique refraction at a surface of glass. Brewster, however, 

 did not compute the value of this polarization, which the 

 astronomical-refraction tables permit us to do. 



It is commonly said that the maximum polarization by re- 

 fraction takes place at the polarizing angle. But this is not 

 true. If we consider the Brewster-Fresnel formula, 



ratio of components after refraction 1 



ratio of components before refraction """cos (i— r) ? 



we see that the polarization by refraction increases up to the 

 limiting incidence*. 



To calculate the maximum polarization producible by hori- 

 zontal refraction through the atmosphere regarded as homo- 

 geneous, we can suppose the incident light unpolarized, and 

 pat i— r= 33 x , which is the value of the astronomical horizontal 

 refraction. 



If we then calculate the resulting value of R (where 

 sin 211 = polaiization), we find that it amounts only to a few 

 seconds of arc. 



* See Jamin, iii. 2. p. 679, where it is assumed that because the 

 difference of the intensities of the components has a maximum, the po- 

 larization has one : but this does not follow. 



