A rainbow can never be greater than a semicircle, if the spectator be not on elevated ground ; for if it were, the centre of the bow would be above tho horizon, and the sun, which is in a line drawn through that centre and the eye, would then be below the horizon ;• but, in this case, the sun could not shine on the drops of rain, and consequently there would be no bow. When the rain-cloud is of small extent, there is seen only that portion of the bow which. the cloud can form ; yet the bow is sometimes seen against the blue sky, which happens when the rain in falling is seen on a part of the sky which is free from cloud; and a portion of a bow is frequently seen in an inverted position on the ground by the refraction of the light in drops of rain adhering to the grass or the leaves of trees. It may be added that a coloured bow similar to that which is produced by rain may be observed in the spray from a waterfall, or from a fountain, when the jet of water is agitated by the wind, and also in the mists which at times lie upon low grounds.
The lunar rainbows appear in general in white ; and when they are coloured, they differ from those produced by the sun only in the colours being much more faint. The faintness of the colour, or its entire absence, is accounted for by the fact that when light is exces sively faint, all perception of colour is lost.
The circle of light which is occasionally seen surrounding the sun or moon at a considerable distance from the diso of the luminary is called a halo, and is caused by the refractions of light in particles of ice which float in the air. It must not be confounded with a corona, which consists in one or two coloured rings immediately surrounding the luminary, and is distinguished from a halo by the variability and comparative smallness of its diameter, and by the order of the colours, —red outside, blue inside—which is the reverse of the order in a halo.
The corona is due to the globules of water constituting a thin veil of cloud, and is a phenomenon of interference, which may be imitated by viewing a candle seen against a dark background through a piece of glass dusted with lycopodium. The two halos most commonly seen have radii of about 22° and 46°. The phenomenon of halos having some resemblance to that which has been just described, a brief explanation of it may be with propriety introduced in this place.
The cause of the halo was first investigated by Des Cartes, who observes (' Meteors,' cap. ix.) that this phenomenon differs from the rainbow, inasmuch as the latter is seen only while rain is falling, whereas bales are never seen at such times; and he ascribes their formation to refractions of light in star-shaped crystals of ice, which be remarks are thicker in the middle than at the edges, and are there fore proper to produce refractions.
Sir l&a.ae Newton also ascribes the halo to refraction in floating hail or snow ; but it appears that Mariotte in SG) was the first who considered it to be produced by refraction in the small equilateral prisms of ice which abound In the air in a separate state before they unite together and form the flakes which descend during severe huts ; and Dr. Young, without being aware of Marietta's hypothesis, enter tained and developed the same idea.
According to this philosopher, there may be in the air an immense number of prismatic particles whose transverse sections are equilateral triangles, or equiangular hexagons, the planes of the sections deviating but little from one passing through the ann or moon and the spectator.
Now by the laws of refraction in water, when a pencil consisting of parallel rays of light, as s t (Ay. 4) is incident on a face of such prisms and makes the angle of incidence a I P equal to about 50,' the axis z of the emergent pencil will make an equal angle E F Q on the other face, and the angle of deviation s a r, or the angle between the incident and emergent ray, will be 23° 40'. Therefore if the line r s produced to the spectator's eye were to revolve conically about a line joining the gun and spectator as an axis (which line, since the sun is very remote, may bo considered as parallel to B A), all the prisms similarly situated on such conical surface would transmit to the eye pencils of parallel rays, if the light were of one colour, and thus there would be produced the perception of a bright circle in the heavens, having the sun for its centre ; its radius subtending at the eye an angle of about 23° 40'. The angle a a r varies very slowly, the variation amounting only to about 3°, when the angle e I P varies as much as 30°, con sequently there may be innumerable prisms in the air in such positions that the angle a I r, for pencils incident upon them, does not vary more than 15° on either side of that which has been above supposed ; and these will transmit to the eye light in such abundance as to pro duce the appearance of an annulus about 3° broad. This is the appearance of the common halo, the slight excess of the calculated radius over that observed being accounted for by the fact that water is a little more refractive than ice.
The larger halo is accounted for in a similar manner, by refraction through ice prisms of 90°, this angle being contained between the plane ends and side faces of hexagonal prisms of ice. The radius, calculated with P310 for the refractive index of ice, is about 45* 46', which agrees very well with the angle observed.
The horizontal parhelia which' are seen at the same altitude as the sun, a little outside the smaller halo, are accounted for by re fraction through prisms of ice of 60°, which, instead of being placed on the average alike in all directions, have their axes vertical, in con sequence of the resistance of the air as they fall under the influence of gmvity. As the incident and emergent rays make with the axis of the prism an angle equal to the zenith distance of the sun, the minimum deviation is greater than what corresponds to refraction in a plane perpendicular to the axis of the prism, which accounts for the parhelia being situated a little outside the halo. This is the commonest example of that curious class of halo phenomena, where the appearance is no longer the same (except as to interruptions in the icy clouds) all round the line joining the eye and the sun, but has reference to the vertical. The reader who desires further infor mation on this point is referred to an elaborate memoir by M. Bravais in tho 31st eahier of the 'Journal de l'Ecole Polytechnique,' where the subject is almost exhausted.