AI. Marione supposes halos to be produced by small filaments of snow moderately transparent, and having the form of an equilateral triangular prism. He conjectures, that the hard flakes of snow which fall during a hard frost, and which have the figure of stars, are composed of little filaments like equilateral prisms, particularly those which are like fern leaves, as may be easily seen by the micro scope. Upon examining the filaments which compose the hoar frost, he found them cut into three equal facets, and they exhibited rainbows when placed in the sun. Mariotte then supposes, that, before the hoar frost is form ed, some of these separate prisms float among the thin vapours in the air, before they unite into the compound figures. " These little stars," says he, " are very thin and very light, and the little filaments which compose them are still more so, and may often be supported a long time in the air by the winds. Hence, when the air is mode rately filled with them, so as not to be much darkened, many of them, whether separated or united, will turn in every direction as the air impels them, and will be dis posed to transmit to the eye for some time a coloured light, nearly like to that which would be produced by equilateral prisms of glass." M. Mariotte then calculates the angles ; and by deducting 16' for the sun's semidiame ter, and 30' for the deviation of the red rays, he finds 22° 50' to be the semidiameter of the halo produced by equian gular prisms.
In attempting to account for parhclia, Mariotte observes, " that they are usually at the same altitude as the sun. Among the prisms of snow, there are often many heavier at one end than at the other, and consequently situated in a vertical direction. These cause a bright parhelion with a tail, which cannot be above 70° long. I have read an account of a halo seen in May, soon after sun-rise, with parhelia in its circumference, which, after two or three Hours, were more than a degree distant from it. This ap pearance arises from the coincidence of the sun's rays with the transverse section of the prism, when they are nearly horizontal, and from their obliquity, when the sun is elevated, causing a greater deviation, and throwing the parhelia outwards, as may be shewn by an experiment on two prisms." See Mariotte Traiti des Couleurs, Paris 1686, or Oeuvres de Mariotte, vol. i. p. 272.
A theory of halos has recently been given by Mr Wood in the Manchester Transactions. He assumes, with Dr Halley, that vapour consists of hollow sphericles of water, filled with an elastic fluid, and having a thickness equal to of their diameter ; and he supposes the halos to be produced by refraction, and reflection from these, in the same manner as the rainbow is produced by solid drops. See Manchester Memoirs, vol. iii. p. 336. A similar opinion seems to be entertained by M. Brande. See Gilbert's Jour
nal, vol. xi. p. 414.
The subject of halos has recently been examined with much attention by our learned countryman Dr Thomas Young, who, before he was acquainted with the explana tion of Mariotte, had adopted the very same theory. Our readers will no doubt be gratified with an account of Dr Young's theory and calculations in his own words.
" It is well known, that the crystals of ice and snow tend always to form angles of 60°; now a prism of water or ice of 60° produces a deviation of about 23°, for rays forming equal angles with its surfaces, and the angle of deviation varies at first very slowly as the inclination changes, the variation amounting to less than 3°, while the inclination changes 30°.
Now if such prisms were placed at all possible angles of inclination, differing equally from each other, one half of them would be so situated, as to be incapable of transmit ting any light regularly by two successive refractions di rected the same way; and of the remaining two-fourths, the one would refract all the light within these 3°, and the other would disperse the light in a space of between 20° and 30° beyond them.
In the same manner, we may imagine an immense num ber of prismatic particles of snow to be disposed in all pos sible directions, and a considerable proportion of them to be so situated, that the plane of their transverse section may pass within certain limits of the sun and the spectator. Then half of these only will appear illuminated, and the greater part of the light will be transmitted by such as are situated at an angular distance of 23°, or within 3° of it, the limit being strongly marked internally, but the light being externally more gradually lost. And this is pre cisely the appearance of the most common halo. When there is a sufficient quantity of the prismatic particles, a considerable part of the light must fall, after one refraction, on a second particle ; so that the effect will be doubled and in this case the angle of refraction will become sup ficienf to present a faint appearance of colour, the red be ing internal, as the least refrangible light, and the external part having a tinge of blue.
These concentric halos of and 47°, are therefore sufficiently explicable, by particles of snow, situated pro miscuously in all possible directions. If the prisms be so short as to form triangular plates, these plates, in falling through the air, will tend to assume a vertical direction, and a much greater number of them will be in this situation than in any other. The reflection from their flat surfaces will consequently produce a horizontal circle of equal height with the sun ; and their refraction will exhibit a bright parhelion immediately over the sun, with an appear ance of wings or horns, diverging upwards from the par helion.