Polarization of Sky Ligltt. 83 



between 88° 23' and 92° %', the mean being 90° 2'. Of course 

 the polarization even at the maximum point is far from being 

 complete. For light reaches the scattering particles from the 

 sky and the earth as well as the sun. Every ray that im- 

 pinges on a particle sends a scattered ray to the observer. 

 And these scattered rays are polarized, some partially, some 

 completely, in all sorts of different planes. The net result is 

 a quantity of subsidiary light that dilutes the completely 

 polarized rays scattered from the direct sunshine. 



At points in the sky near the sun or antisolar point the 

 polarization of the light scattered from the direct sunshine 

 is very weak, according to Lord Rayleigh's laws, explained 

 above, and here we find that in the vertical plane through 

 the sun it is overpowered by a residual horizontal polarization 

 in the subsidiary light just mentioned. Thus are formed the 

 neutral [i. e. unpolarized) points discovered by Arago, Babinet, 

 and Brewster. Bosanquet (Phil. Mag. July 1876) has investi- 

 gated the direction of the polarization in the neighbourhood of 

 the neutral point, and his results point to this conclusion. He 

 found for instance that a little to the right or left of a 

 neutral point the polarization was inclined at forty-five degrees 

 to the vertical. Let us see if our explanation leads to this 

 result. Neglecting the unpolarized part of the subsidiary 

 light, we have at the neutral point two equally bright beams 

 polarized at right angles to each other. Just to the right or 

 left the beams are still equal, but the planes of polarization 

 are not quite at right angles, and it is obvious from symmetry 

 that the resultant polarization must bisect the angle between 

 them. 



An explanation of the residual polarization of the subsidiary 

 light is not far to seek. Take the light scattered by a particle 

 A in the horizontal direction AB. Light reaches the particle 

 from the sky and the earth. The ground below may be 

 roughly regarded as appearing equally bright in all directions, 

 and therefore, as I proceed to show, it will produce no 

 polarization. If A were in the centre of a uniformly bright 

 spherical envelope, the light scattered along AB would be 

 obviously unpolarized. The light from the upper and lower 

 hemispheres must from symmetry be polarized in the same 

 way, and, since the sum is unpolarized, each must be un- 

 polarized. The lower hemisphere is equivalent to the 

 uniformly bright surface of the ground ; so my point is 

 established. There remains therefore the light from the sky 

 to A to be considered. For obvious reasons the sky is much 

 brighter near the horizon than in the zenith, and it is clear 

 that the light scattered along AB from any point in the 



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