LIGHT 451 at particular angles, it follows that much of the light that is transmitted through the air is more or less polarized in consequence of being reflected from the surfaces of the numerous contained particles of atmospheric dust and vapor. If the sky is examined through a M- col's prism, it will be found that the greatest amount of polarization is in rays that come from directions at right angles to the sun ; that is to say, when the sun is in the horizon, from an arc passing through the zenith, each end meeting the horizon 90 from the po- sition of the sun. If the sun were in the zenith, the greatest amount of polarization would be in the circular horizon. It is evi- dent, therefore, that if a polarizing apparatus is held with its axis perpendicular to the path of the sun, an interposed selenite plate or other double-refracting crystal, by causing in- terference of polarized light, will afford an in- dication of the time of day. An instrument based upon this principle invented by Sir Charles Wheatstone, called a polar clock, is another of the practical applications of the more refined discoveries in molecular physics. (See POLAR CLOCK.) Prof. Tyndall, in making experiments upon minute quantities of gaseous vapors, found that when condensation com- menced, if a powerful ray of light was sent through the experimental tube, an " incipient cloud " was illuminated, which upon examina- tion was found to reflect polarized light. This at first would be a very pure blue, and nearly perfectly polarized in a direction perpendicular to the beam of light ; but as the vapory par- ticles became larger the cloud became whiter, and the amount of polarization diminished till at last it was not perceptible. The vapor which gave the greatest effect was that of nitrite of butyle. He concludes that at the first forma- tion of the cloud the vapory particles are less in diameter than the length of a wave of light, so that the most refrangible rays are the first to be scattered, the addition of the others pro- ducing white light. It is therefore concluded that the blue color of the heavens is owing to the scattering of the more refrangible rays of light by the minute particles of aqueous vapor held in the atmosphere before any visible con- densation has taken place, and that the white color of clouds is owing to the scattering of all the rays. It appears that the polarizing angle for matter in a state of vapor does not follow the ordinary law and change with the substance, but that it is always 45, so that the polarized is always at right angles to the reflected beam. Several facts in regard to atmospheric polarization were observed many years ago by Sir David Brewster, bir John Herschel, and others. The verification of Fresnel's prediction in regard to circular po- larization was one of the great tests of the un- dulatory theory of light, as well as an exam- ple of the transcendent power of genius. An equally remarkable example was the deduc- tion from Fresnel's theory of double refrac- FIG. 81. tion of a result which that mathematician had not himself foreseen. This deduction was made by Sir "William Hamilton, and experi- mentally verified by Dr. Lloyd of Dublin. According to Fresnel's theory of double re- fraction in biaxial crystals, the wave surface intersects the plane of the crystal in a circle and an el- lipse whose magnitude is such that they intersect at four points, as represented in fig. 31. Dr. Lloyd's explanation is as follows: "When two rays pass within the crystal in any common direction, as O A B, their velocities are represented by the radii vec- tores of the two parts of the wave O A and O B, and their directions at emergence are determined by the positions of the tangent planes at the points A and B. But in the case of the ray O P, whose direction is that of the line joining the centre with one of the four cusps which are formed by the in- tersections of the circle and ellipse, the two radii vectores unite, and the two rays have the same velocity. There are still, however, two tangents to the plane section at the point P ; so that it might be supposed that the rays pro- ceeding with this common velocity within the crystal would still be divided at emergence into two, and two only, whose directions are de- termined by the tangent planes; and this seems to have been Fresnel's view. But Sir William Hamilton has shown that there is a cusp at each of the four points just men- tioned, not only in this particular section, but in every section of the wave surface passing through the line O P, or that there is a conoi- dal cusp on that surface at the four points of the intersection of the circle and ellipse, and consequently an infinite number of tangent planes which form a tangent cone of the sec- ond degree. Hence a single ray, such as P, proceeding within the crystal in one of these directions, should be divided into an infinite number of rays at emergence, whose directions and planes of polarization are determined by the tangent planes. Again, it is evident that the circle and ellipse have four common tan- gents, such as M N; and the planes passing through these tangents, and perpendicular to the plane of the section, are perpendicular to the optic axis of the crystal. Fresnel seems to have thought that these planes touched the wave surface in the two points just mentioned, and in these only; and consequently that a single ray (incident upon a biaxial crystal in such a manner that one of the refracted rays should coincide with an optic axis O M) will be divided into two within the crystal, O M and O N", determined by the points of contact. But Sir William Hamilton has shown that the four planes touch the wave surface, not in two points only, but in an infinite number of points, constituting each a small circle of con-
