as affording a distinct arch of each colour, and the whole disk as producing an arch about half a degree in breadth for each kind of light; so that the arrangement nearly resembles that of the com. mon mixed spectrum. There is, however, another cause of a further mixture of colours: the arch of any single colour, which belongs to any point of the sun, is accurately defined on one side only, while on the other it becomes gradually fainter, the breadth of the first minute containing about five times as much light as a minute at the distance of a quarter of a degree: the abrupt termination is on the side of the red, that is, without the inner bow, and within the outer; so that, for this reason, the order of colours partakes, in some degree, of the nature of the red termination of a broad beam of light seen through a prism; but it is more or less affected by this cause, on account of some circumstances, which will be explained when we examine the supernumerary rainbows, which sometimes accompany the bows more commonly observed. A lunar rainbow is much more rarely seen than a solar one, but its colours differ little, except in intensity, from those of the common rainbow.

In the highest northern latitudes, where the air is commonly loaded with frozen particles, the sun and moon usually appear surrounded by halos, or coloured circles, at the distances of about twenty-two and forty-six degrees from their centres; this ap. pearance is also frequently observed in other climates, especially in the colder months, and in the light clouds which float in the highest regions of the air. The halos are usually attended by a horizontal white circle, with brighter spots, or parhelia, near their intersections with this circle, and with portions of inverted arches of va rious curvatures; the horizontal circle has also sometimes anthelia, or bright spots, nearly opposite to the sun. These phænomena have usually been attributed to the effect of spherical particles of hail, each having a central opaque portion of a certain magnitude, mixed with oblong particles, of a determinate form, and floating with a certain constant obliquity to the horizon. But all these arbitrary suppositions, which were imagined by Huygens, are in themselves extremely complicated and improbable, and are wholly unauthorised by observation. A much simpler, and more natural, as well as more accurate explanation, which was suggested at an earlier period by Mariotte, had long been wholly forgotten, until

the same idea occurred to me, without any previous knowledge of what Mariotte had done. The natural tendency of water to crys. tallize, in freezing, at an angle of sixty degrees, is sufficiently established, to allow us to assume this as the constant angle of the elementary crystals of snow, which are probably either triangular or bexagonal prisms: the deviation produced by such a prism differs very little from the observed angle at which the first circle is usu. ally seen; and all the principal phænomena, which attend this circle, may be explained, by supposing the axis of the crystals to assume a vertical or a horizontal position, in consequence of the operation of gravity: thus the parhelia, which are sometimes a little more distant from the sun than the halo, are attributed by Mariotte to the refraction of the prisms which are situated vertically, and produce a greater deviation, on account of the obliquity of the rays of light with respect to their axis. The horizontal circle may be deduced from the reflection, or even the repeated refractions, of the vertical facets; the anthelia from two refractions with an intermediate reflection, and the inverted arch from the increase of the deviation, in the light passing obliquely, through prisms lying in a horizontal position. The external circle may be attributed either to two successive refractions through different prisms; or with greater probability, as Mr. Cavendish has suggested to me, to the effect of the rectangular terminations of the single crystals. The appearance of colours, in halos, is nearly the same as in rainbows, but less distinct; the red being nearest to the luminary, and the whole halo being externally very ill defined.

From the observed magnitude of these halos, I had concluded that the refractive power of ice must be materially less than that of water, although some authors had asserted that it was greater: and Dr. Wollaston afterwards fully confirmed this conclusion, by means of the very accurate instrument which has already been described; his measurement agreeing precisely with the mean of the best observations on these halos, so that ice must be considered as the least refractive of any known substances not aeriform.

Sometimes the figures of halos and parhelia are so extremely complicated, as to defy all attempts to account for the formation of their different parts; but if we examine the representations which have been given, by various authors, of the multiplicity of capri.

cious forms frequently assumed by the flakes of snow, we shall see no reason to think them inadequate to the production of all these appearances.

[Young Nat. Phil. Vol. I,

It is in his second volume that Dr. Young has favoured us with his abstract of Dr. Wollaston's observations on the quantity of ho rizontal refraction, which is as follows.

Dr. Wollaston notices Mr. Monge's Memoir on the Mirage, observed in Egypt, as containing facts which fully agree with his own theory formerly published. From his observations on the degree of refraction produced by the air near the surface of the Thames, it appears that the variations derived from changes of temperature and moisture in the atmosphere, are by no means calculable; but that a practical correction may be obtained, which, for nautical uses, may supersede the necessity of such a calculation. Dr. Wollaston first observed an image of an oar at a distance of about a mile, which was evidently caused by refraction, and when he placed bis eye near the water, the lower part of distant objects was hidden, as if by a curvature of the surface. This was at a time when a continuation of hot weather had been succeeded by a colder day, and the water was sensibly warmer than the atmosphere above it. He afterwards procured a telescope, with a plane speculum placed obliquely before its object glass, and provided with a micrometer, for measuring the angular depression of the image of a distant oar, or other oblique object; this was some. times greater when the object glass was within an inch or two of the water, and sometimes when at the height of a foot or two. The greatest angle observed was somewhat more than nine minutes, when the air was at 50°, and the water at 63°; in general the dryness of the air lessened the effect, probably. by producing evapo. ration, but sometimes the refraction was considerable, notwith. standing the air was dry. Dr. Wollaston has observed but one instance which appeared to encourage the idea, that the solution of water in the atmosphere may diminish its refractive power.

In order to correct the error, to which nautical observations may be liable, from the depression of the apparent horizon, in conse. quence of such a refraction, or from its elevation in contrary cir cumstances; and at the same time to make a proper correction for