or HALO, in Optics, a luminous circle surrounding the sun, the moon, the planets, or fixed stars. Sometimes these circles are white, and sometimes coloured like the rainbow; sometimes one only is visible, and sometimes several concentric coronas make their appearance at the same time. Those which have been seen about Sirius and Jupiter were never more than three, four, or five degrees in diameter; those which surround the moon are also sometimes no more than three or five degrees; but these, as well as those which surround the sun, are of very different magnitudes, viz., of 12° 0', 22° 35', 30° 0', 38° 0', 41° 2', 45° 0', 46° 24', 47° 0', and 90°, or even larger than this. Their diameters also sometimes vary during the time of observation, and the breadths both of the coloured and white circles are very different, viz. of two, four or seven degrees.

The colours of these coronas are more diluted than those of the rainbow; and they are in a different order, according to their size. In those which Newton observed in 1692, they were in the following order, reckoned from the inside: In the innermost were blue, white, and red; in the middle were purple, blue, green, yellow, and pale red; in the outermost, pale blue and pale red. Huygens observed red next the sun, and a pale blue outwards. Sometimes they are red on the inside and white on the outside. Weidler observed one that was yellow on the inside and white on the outside. In France one was observed in 1683, the middle of which was white; after which followed a border of red; next to it was blue, then green, and the outermost circle was a bright red. In 1728 one was seen of a pale red outwardly, then followed yellow, and then green, terminated by a white.

These coronas are very frequent. In Holland, says Muschenbroek, fifty may be seen in the day-time, almost every year; but they are difficult to be observed, unless the eye be so situated that not the body of the sun, but only the neighbouring parts of the heavens, can be seen. Middleton remarks, that this phenomenon is very frequent in North America, there being generally one or two about the sun every week, and as many about the moon every month. Halos round the sun are very frequent in Russia. Epinus relates, that from the 23rd of April to the 20th of September 1758, he himself had observed no less than twenty-six, and that he has sometimes seen twice as many in the same space of time.

Coronas may be artificially produced by placing a lighted candle in the midst of steam in cold weather; also, if glass windows be breathed upon, and the flame of a candle be placed some feet from it, while the spectator is also at the distance of some feet from another part of a window, the flame will be surrounded with a coloured halo; and if a candle be placed behind a glass receiver, when air is admitted into the vacuum within it, at a certain degree of density, the vapour with which it is loaded will form a coloured halo round the flame. This was observed by Otto Guercke. In December 1756 Muschenbroeck observed, that when the glass windows of his room were covered with a thin plate of ice on the inside, the moon appearing through it was surrounded with a large and variously coloured halo; and on opening the window, he found that it arose entirely from that thin plate of ice, for none was seen except through it.

Similar in some respects to the halo was the remarkable appearance which Bouguer describes, as observed by himself and his companions on the top of Pichinchia, in the Cordilleras. When the sun was just rising behind them, so as to appear white, each saw his own shadow projected in the air, and no other. The distance was such, that all the parts of the shadow were easily distinguishable, as the arms, the legs, and the head; but what was most surprising was, that the head was adorned with a kind of glory, consisting of three or four small concentric crowns, of a very lively colour, each exhibiting all the varieties of the primary rainbow, and having the circle of red upon the outside. The intervals between these circles continued equal, though the diameters of them all were constantly changing. The last was very faint; and at a considerable distance was another great white circle which surrounded the whole. As nearly as Bouguer could compute, the diameter of the first of these circles was about 5° degrees, that of the second 11, that of the third 17, and so on; but the diameter of the white circle was about 76 degrees. This phenomenon never appeared but in a cloud consisting of frozen particles, and never in drops of rain like the rainbow. When the sun was not in the horizon, only part of the white circle was visible, as frequently observed afterwards by Bouguer.

Similar also to this curious appearance was one observed in Scotland. The observer saw a rainbow round his shadow in the mist, when he stood upon an eminence above it. In this situation the whole country seemed, as it were, buried under a vast ocean, nothing but the tops of distant hills appearing here and there rising above the flood. In those upper regions the air was at that time very pure and agreeable to breathe. At another time the same individual observed a double range of colours round his shadow in these circumstances. The colours of the outermost range were broad and very distinct, and everywhere about two feet distant from the shadow. Then there was a darkish interval, and after that another narrower range of colours, closely surrounding the shadow, which was very much contracted. He was of opinion that these ranges of colours are caused by the inflection of the rays of light, the same that occasioned the ring of light which surrounds the shadows of all bodies, observed by Maraldi and others. But the prodigious variety in which these appearances are exhibited seems to show that many of them do not result from the general laws of reflection, refraction, or inflection, belonging to transparent substances of a large mass; but depend upon the alternate reflection and transmission of the different kinds of rays, peculiar to substances reduced to the form of thin plates, or consisting of separate and very minute parts. But where the dimensions of the coronas are pretty constant, as in the usual and larger halo, which is about half the diameter of the rainbow, they may perhaps be explained on the general principles of refraction only.

Sir Isaac Newton does not appear to have given any particular attention to the subject of halos, but he has hinted at his sentiments concerning them occasionally; by which we perceive that he considered the larger and less variable appearances of this kind as produced according to the common laws of refraction, but that the less and more variable appearances depend upon the same cause with the colours of thin plates.

He concludes his explication of the rainbow with the following observations on halos and parhelia:—“The light which comes through drops of rain by two refractions, without any reflection, ought to appear the strongest at the distance of about twenty degrees from the sun, and to decay gradually both ways as the distance from him increases; and the same is to be understood of light transmitted through spherical hailstones; and if the hail be a little flatted, as it often is, the transmitted light may be so strong, at a little less distance than that of twenty-six degrees, as to form a halo about the sun or moon; which halo, as often as the hailstones are duly figured, may be coloured, and then it must be red within by the least refrangible rays, and blue without by the most refrangible ones; especially if the hailstones have opaque globules of snow in their centres to intercept the light within the halo (as Mr Huygens has observed), and make the inside of it more distinctly defined than it would otherwise be; for such hailstones, though spherical, by terminating the light by the snow, may make a halo red within and colourless without, and darker within the red than without, as halos are used to be. For of those rays which pass close by the snow, the red-making ones will be the least refracted, and so come to the eye in the straightest lines.”

Some further thoughts of Newton on the subject of halos are subjoined to the account of his experiments on the colours of thick plates of glass, which he conceived to be similar to those which are exhibited by thin ones. “As light reflected by a lens quicksilvered on the back side makes the rings of the colours above described, so,” he says, “it ought to make the like rings in passing through a drop of water. At the first reflection of the rays within the drop, some colours ought to be transmitted, as in the case of a lens, and others to be reflected back to the eye. For instance, if the diameter of a small drop or globule of water be about the 500th part of an inch, so that a red-making ray, in passing through the middle of this globule, has 250 fits of easy transmission within the globule, and all the red-making rays which are at a certain distance from this middle ray round about it have 249 fits within the globule, and all the like rays at a certain further distance round about it have 248 fits, and all those at a certain further distance 247 fits, and so on; these concentric circles of rays, after their transmission, falling on a white paper, will make concentric rings of red upon the paper, supposing the light which passes through one single globule strong enough to be sensible; and in like manner the rays of other colours will make rings of other colours. Suppose now that in a fair day the sun should shine through a thin cloud of such globules of water or hail, and that the globules are all of the same size, the sun seen through this cloud ought to appear surrounded with the like concentric rings of colours, and the diameter of the first ring of red should be $7\frac{1}{4}$°, that of the second $10\frac{1}{2}$°, that of the third $12\frac{3}{4}$°; and according as the globules of water are bigger or less, the ring should be less or bigger.”

This curious theory, Newton informs us, was confirmed by an observation which he made in the year 1692. He saw by reflection, in a vessel of stagnating water, three halos, crowns, or rings of colours about the sun, like three little rainbows concentric to its body. The colours of the first or innermost crown were blue next the sun, red without, and white in the middle, between the blue and red. Those of the second crown were purple and blue within, and pale red without, and green in the middle; and those of the third were pale blue within, and pale red without. These crowns inclosed one another immediately, so that their colours proceeded in this continual order from the sun outward; blue, white, red; purple, blue, green, pale yellow, and red; pale blue, pale red. The diameter of the second crown, measured from the middle of the yellow and red on one side of the sun to the middle of the same colour on the other side, was 9½ degrees or thereabouts. The diameters of the first and third he had not time to measure, but that of the first seemed to be about five or six degrees, and that of the second about twelve. The like crowns appear sometimes about the moon. In the beginning of the year 1664, on February 19th, at night, he saw two such crowns about her. The diameter of the first or innermost was about three degrees, and that of the second about five degrees and a half. Next about the moon was a circle of white; and next about that the inner crown, which was of a bluish-green within, next the white, and of a yellowish and red without; and next about these colours were blue and green on the inside of the outer crown, and red on the outside of it.

At the same time there appeared a halo at the distance of about 22° 35' from the centre of the moon. It was elliptical, and its long diameter was perpendicular to the horizon, verging below farthest from the moon. He was told that the moon had sometimes three or more concentric crowns of colours encompassing one another next about her body. The more equal the globules of water or ice are to one another, the more crowns of colours will appear, and the more lively the colours will be. The halo, at the distance of 22° 35' degrees from the moon, is of another sort. By its being oval and more remote from the moon below than above, he concludes that it was made by refraction in some kind of hail or snow floating in the air in a horizontal posture, the refracting angle being about 50 or 60 degrees. Dr Smith, however, makes it sufficiently evident that the reason why this halo appeared oval and more remote from the moon towards the horizon, is a deception of sight, and the same with that which makes the moon appear larger in the horizon. See Chromatics.

Botany, the circumference or margin of a radiated compound flower. It corresponds to the radius of Linnæus.

Corona Australis, or Meridianalis, the Southern Crown, a constellation of the southern hemisphere, the stars of which in Ptolemy's catalogue are thirteen, and in the British catalogue twelve.

Corona Borealis, the Northern Crown, or Garland, in Astronomy, a constellation of the northern hemisphere, the stars of which in Ptolemy's catalogue are eight, in Tycho's as many, and in Flamsteed's twenty-one.

Roman Antiquity. See Crown.