As regards the polarisation of skylight, the greatest stumbling-block has hitherto been, that, in accordance with the law of Brewster, which makes the index of refraction the tangent of the polarising angle, the reflection which produces perfect polarisation would require to be made in air upon air; and indeed this led many of our most eminent men, Brewster himself among the number, to entertain the idea of aerial molecular reflection. [Footnote: 'The cause of the polarisation is evidently a reflection of the sun's light upon something. The question is on what? Were the angle of maximum polarisation 76°, we should look to water or ice as the reflecting body, however inconceivable the existence in a cloudless atmosphere and a hot summer's day of unevaporated molecules (particles?) of water. But though we were once of this opinion, careful observation has satisfied us that 90°, or thereabouts, is the correct angle, and that therefore whatever be the body on which the light has been reflected, if polarised by a single reflection, the polarising angle must be 45°, and the index of refraction, which is the tangent of that angle, unity; in other words, the reflection would require to be made in air upon air!' (Sir John Herschel, 'Meteorology,' par. 233.) Any particles, if small enough, will produce both the colour and the polarisation of the sky. But is the existence of small water-particles on a hot summer's day in the higher regions of our atmosphere inconceivable? It is to be remembered that the oxygen and nitrogen of the air behave as a vacuum to radiant heat, the exceedingly attenuated vapour of the higher atmosphere being therefore in practical contact with the cold of space.] I have, however, operated upon substances of widely different refractive indices, and therefore of very different polarising angles as ordinarily defined, but the polarisation of the beam, by the incipient cloud, has thus far proved itself to be absolutely independent of the polarising angle. The law of Brewster does not apply to matter in this condition, and it rests with the undulatory theory to explain why. Whenever the precipitated particles are sufficiently fine, no matter what the substance forming the particles may be, the direction of maximum polarisation is at right angles to the illuminating beam, the polarising angle for matter in this condition being invariably 45°.