82 Mr. J. C. McConnel on the 



divide the incident ray into two parts, tbat polarized in the 

 plane of deflexion and that polarized in the perpendicular 

 plane. Of the former the proportion deflected is the same in 

 every direction, but of the latter the proportion deflected 

 varies as the square of the cosine of the angle between the 

 original and the new directions of propagation, being zero 

 when this angle is a right angle. It may be added that the 

 proportion of light thrown straight backwards is independent 

 of the direction of the original polarization, as is indeed 

 obvious from symmetry. For the truth of these laws it is 

 essential that the particles should be small compared with the 

 wave-length of the kind of light involved. I gather that 

 they would be practically accurate for particles which were not 

 larger than a tenth part of the wave-length, while with 

 roundish particles whose diameter reached half a wave-length 

 quite different phenomena would set in. 



The experimental verification of these laws in the case of 

 the sky cannot be expected to be very accurate, owing to the 

 complexity of the problem. Still sufficient has been accom- 

 plished to render it almost certain that the greater part of 

 the light from a good blue sky has been scattered by small 

 particles, small, that is, compared with a wave-length. Lord 

 Rayleigh has compared the colour of sky light with that of 

 sunlight diff'used through white paper, obtaining very fair 

 agreement with the law of the inverse fourth power of the 

 wave-length (Phil. Mag. Feb. 1871). Further, Abney has 

 found, on measuring the relative intensities of the various 

 components of sunlight on different days and with different 

 altitudes of the sun, that the very considerable variations 

 could be explained on the assumption that practically the 

 whole of the light lost in traversing the atmosphere had been 

 scattered according to the above law *. This of course was 

 only the case when the atmosphere was quite clear. These 

 observations show not merely that the sky light is due to small 

 particles, but also that the true absorption (other than 

 scattering) of the visible radiation by the atmosphere is very 

 ,small. 



So much for the colour of the sky. With regard to the 

 polarization we find, as we should expect from the theory, 

 the maximum polarization at points in the sky about ninety 

 degrees from the sun. Rubenson, at Upsala, took eighteen 

 measures of the position of the point of maximum polariza- 

 tion in the vertical plane through the sun on different days 

 and at different hours. The distance from the sun varied 



* Phil. Trans. March 1887. He mentions, however, that Langley's 

 bolometer observations do not support this law. 



