The light reflected from the surfaces of the vertical prisms, of course appears to come from an image of the sun in a vertical mirror, which, by optical laws, must have the same altitude as the sun itself. Such images then form a white horizontal small circle, passing through the sun and the parhelia. This is often observed, and helps to cor roborate the above theory of the colored appearances. See the dotted line PSP (Ill.).
The light reflected from the horizontal terminals of these prisms must evidently pro duce a single white image of the sun, as much below the horizon as he is above it, and vice versa. This appearance is also common enough.
Tangent Arcs to the Halo of 22°.—We have seen that in many cases the prisms of ice are so short as to be hexagonal plates. Their natural position in falling will be edge foremost, or there will be a multitude of snow-crystals whose axes are nearly horizontal, but of course arranged in all directions in the horizontal plane. Let us consider first all those whose axes are perpendicular to the line joining the spectator with the sun; these evidently (by an explanation similar to that of the parhelia given above) form parhelia on the halo at its upper and lower points. Another set, whose axes are also nearly hori zontal and parallel, but slightly inclined to the former, will form parhelia to one or other side of the vertical plane passing through the sun, and on account of the obliquity of the incidence, the angle of deviation is increased, and these are outside the halo. They are further to the right or left of the sun's vertical plane, and further outside the halo as the crystals are more and more turned in their horizontal plane. The complete result.is brightly colored pair of arcs, which touch, the halo at its upper and lower points, and lie completely outside. For certain elevations of the sun, these combine, forming a curve like an ellipse, whose center is the sun, whose larger axis is horizontal, and which touches the halo externally at its upper and lower points.
Halo of 46°.—This depends upon the right-angled prisms, formed by combining a terminal plane with one of the faces of the hexagonal prism; and with the single excep tion of a different refracting angle, and its consequent greater dimensions, its explanation and its appearance are the same as those of the halo of 22°.
Perhaps the most magnificent, both for brightness and separation of colors, of all the halos, is the colored are which touches the halo of 46° at its upper point. This depends entirely upon the refraction of light through the upper edges of prisms having plane ends and whose axes are vertical. It is therefore due to the same cause as the parhelia of the halo of 22'; and it is a remarkable proof of the truth of this, that there is but one instance recorded in which the former appeared without the latter; and its absence was then easily accounted for by there being no cloud of ice-crystals near enough the suu to produce the parhelia. , See Ill. .
There are also sometimes.seen brightly colored arcs touching .one on each side the lower half of the halo of 46°. They are explained by the right angles of prisms whose axes are horizontal. Again, a parhe lion being itself a source of .light, sometimes very intense, may have its surrounding halos of 22°, etc. All phenomena of the latter class are termed secondary. They are in gen eral. as might be expected, much fainter than the primary ones, but in favorable circumstances have been distinctly observed.
In addition to our very imperfect sketch of the results of the prisms of 60' and 90°, we might consider shortly those due to various combinations of planes of the hexagonal pyramid with each other, or with planes of the prism ; hut the phenomena depending, on these, though easily enough predicted mathematically, are not well suited for ver bal explanation.
We conclude with a rough geometrical sketch of a tolerably complete set of halos, observed by Bravais in Sweden in 1839. The marks on the sketch will be sufficient m.o inform the reader to Nyllich of the classes above mentioned the various portions belong.