Water crystallizes in the form . of regular hexagonal prisms, sometimes with plane ends perpendicular to the sides, sometimes with hexagonal pyramids as terminals. There is also an immense variety of much•more complex forms; but upon the simpler and more common ones already mentioned, depend the ordinary cases of the phenomena we are about to describe. Now, if we consider any two non-parallel faces of one of the above crystals, it is clear that their combination must act as a prism, decomposing white light, which passes through them, into its constituent colors. Every such crystal, then, placed somewhere near the line joining the eye and sun, must in general send to the former some definitely colored ray from each effective pair of surfaces. The refrac tive index, however, of ice is such that no ray can pass through a prism of it whose angle is greater than about 99°.5; and we are therefore limited to pairs of faces whose inclination is not superior to this. The most important pairs are two alternate faces of the prism (fig. 1), where the inclination is -60°, and a face with a terminal plane, the angle being 90°.
Halo of 22° Radius.—We may now suppose prisms of ice, with refracting angles of 60', to be distributed (with every possible position of their axes) nearly between the sun and the spectator, and it is evident that the appearances produced must be symmetrical with regard'to the line joining the eye and sun. and must therefore consist of colored circles with the sun as center. To attain a more exact idea of the nature of these, circles, suppose that we are dealing with light of one color only (say red). Now (see Plasm). if a beam of homogeneous light falls on a prism, it is refracted without separa tion. If the prism be turned gradually and uniformly about its axis, the refracted ray also turns, but not uniformly—at first rapidly, then slower, till it reaches a point at which it appears to be stationary for a little; then, on further turning the prism, the refracted ray retrogrades, at first slowly, then faster. There is therefore, a position of the prism, called that of minimum deviation, for which a slight alteration of the prism produces none in the direction of the refracted ray. Hence, as we have supposed prisms to be in the cloud in every possible position, those which arc near the position of minimum deviation will conspire to refract light in the same direction, and their effects will be added. All time others will cause a greater deviation of the light, but few will conspire to send the light in any given direction. The appearance will therefore be a bright circle of red light surrounding time sun as center, its angular radius being the angle of minimum deviation, which, for a prism of ice of 60° angle, is about 21° 50'. Inside this circle there will be no light; outside, a feeble illumination only, becoming fainter as we go further from the sun. With orange light alone, there would be a somewhat larger circle, and so on. Hence, when white light falls on such a system, the
effect is a circular halo, dark within, red on its inner edge, and with a mixture of move or less of the colors of the spectrum from inside outwards; so that, like the rainbow, which it much resembles, it differs from the ordinary spectrum (q.v.).
If we consider next the light reflected from the surfaces of the prisms, this will be white, and diffused with approximate uniformity all about the sun.
But the prisms with plane ends are not likely to be suspended in the air in all posi tions alike. If the prism be long and fine, it will have a tendency to fall end foremost, i.e., with its axis vertical, or (it may be) horizontal. If it be a flat hexagonal cake (a frequent form of snow), it will tend in the main to fall edgeways, so that, in addition to the halo which depends upon the ice-crystals having every possible position, there are distinct phenomena depending on an excessof the crystals having their axes vertical or horizontal. If we consider the sun as just rising or setting, it is plain that the right and left hand portions of the halo will be much more strongly marked than the others, as these parts are formed by crystals whose axes are vertical, and which form the majority. There are therefore to right and left of time sun, and on the halo, bright colored images of the sun, which are called parhelia, or mock-suns.
It is perhaps a little more difficult to explain to the non-mathematical reader them formation of parhelia when the sun is:not on the horizon, and to show why they them separate from dui halo, and are formed externally still; however, the same altitude as the sun. We may, however, make the attempt as follows: Suppose av inde finitely long vertical prism; rays of sunlight falling on this are separated, as before, but if the sun be not on the horizon, they no longer fall on the prism perpendicularly to its edge. Optics, however, shows us that for this oblique incidence also there is a position of minimum deviation, and therefore one angular distance from the sun at which the effects of a great number of prisms conspire, while far fewer conspire at any other angle. It is also shown that this minimum angle is greater as the incidence is more oblique. Also the inclination of the incident and refracted rays to the edge of a prism is always the same, however the ray may fall. Hence, as the edges of tne prisms in question are vertical, the refracted rays appear to come from a point at the same altitude as the sun, and, by what was remarked above, further front the sun as the sun is higher. Hence the formation of the parhelia consisting of two colored images of the sun, at the same altitude as that body, and further beyond the halo as the sun is higher. Accurate measurements of their distance from the sun for different altitudes have been found to accord exactly with the results of calculation from the optical data. See PP (III.).