certain of their assumptions were somewhat arbitrary, yet the general validity of the theory has been demonstrated by the researches of J. G. Galle and A. Bravais. The memoir of the last-named, published in the Journal de l’École royale polytechnique for 1847 (xviii., 1–270), ranks as a classic on the subject; it is replete with examples and illustrations, and discusses the various phenomena in minute detail.
The usual form of ice-crystals in clouds is a right hexagonal prism, which may be elongated as a needle or foreshortened like a thin plate. There are three refracting angles possible, one of 120° between two adjacent prism faces, one of 60° between two alternate prism faces, and one of 90° between a prism face and the base. If innumerable numbers of such crystals fall in any manner between the observer and the sun, light falling upon these crystals will be refracted, and the refracted rays will be crowded together in the position of minimum deviation (see Refraction of Light). Mariotte explained the inner halo as being due to refraction through a pair of alternate faces, since the minimum deviation of an ice-prism whose refracting angle is 60° is about 22°. Since the minimum deviation is least for the least refrangible rays, it follows that the red rays will be the least refracted, and the violet the more refracted, and therefore the halo will be coloured red on the inside. Similarly, as explained by Henry Cavendish, the halo of 46° is due to refraction by faces inclined at 90°. The impurity of the colours (due partly to the sun’s diameter, but still more to oblique refraction) is more marked in halos than in rainbows; in fact, only the red is at all pure, and as a rule, only a mere trace of green or blue is seen, the external portion of each halo being nearly white.
The two halos are the only phenomena which admit of explanation without assigning any particular distribution to the ice-crystals. But it is obvious that certain distributions will predominate, for the crystals will tend to fall so as to offer the least resistance to their motion; a needle-shaped crystal tending to keep its axis vertical, a plate-shaped crystal to keep its axis horizontal. Thomas Young explained the parhelic circle (P) as due to reflection from the vertical faces of the long prisms and the bases of the short ones. If these vertical faces become very numerous, the eye will perceive a colourless horizontal circle. Reflection from an excess of horizontal prisms gives rise to a vertical circle passing through the sun.
The parhelia (p) were explained by Mariotte as due to refraction through a pair of alternate faces of a vertical prism. When the sun is near the horizon the rays fall upon the principal section of the prisms; the minimum deviation for such rays is 22°, and consequently the parhelia are not only on the inner halo, but also on the parhelic circle. As the sun rises, the rays enter the prisms more and more obliquely, and the angle of minimum deviation increases; but since the emergent ray makes the same angle with the refracting edge as the incident ray, it follows that the parhelia will remain on the parhelic circle, while receding from the inner halo. The different values of the angle of minimum deviation for rays of different refrangibilities give rise to spectral colours, the red being nearest the sun, while farther away the overlapping of the spectra forms a flaming colourless tail sometimes extending over as much as 10° to 20°. The “arcs of Lowitz” (L) are probably due to small oscillations of the vertical prisms.
The “tangential arcs” (T) were explained by Young as being caused by the thin plates with their axes horizontal, refraction taking place through alternate faces. The axes will take up any position, and consequently give rise to a continuous series of parhelia which touch externally the inner halo, both above and below, and under certain conditions (such as the requisite altitude of the sun) form two closed elliptical curves; generally, however, only the upper and lower portions are seen. Similarly, the tangential arcs to the halo of 46° are due to refraction through faces inclined at 90°.
The paranthelia (q) may be due to two internal or two external reflections. A pair of triangular prisms having a common face, or a stellate crystal formed by the symmetrical interpenetration of two triangular prisms admits of two internal reflections by faces inclined at 120°, and so give rise to two colourless images each at an angular distance of 120° from the sun. Double internal reflection by a triangular prism would form a single coloured image on the parhelic circle at about 98° from the sun. These angular distances are attained only when the sun is on the horizon, and they increase as it rises.
The anthelion (a) may be explained as caused by two internal reflections of the solar rays by a hexagonal lamellar crystal, having its axis horizontal and one of the diagonals of its base vertical. The emerging rays are parallel to their original direction and form a colourless image on the parhelic circle opposite the sun.
References.—Auguste Bravais’s celebrated memoir, “Sur les halos et les phénomènes optiques qui les accompagnent” (Journ. École poly. vol. xviii., 1847), contains a full account of the geometrical theory. See also E. Mascart, Traité d’optique; J. Pernter, Meteorologische Optik (1902–1905); and R. S. Heath, Geometrical Optics.
HALOGENS. The word halogen is derived from the Greek
ἅλς (sea-salt) and γεννᾶν (to produce), and consequently
means the sea-salt producer. The term is applied to the four
elements fluorine, chlorine, bromine and iodine, on account of
the great similarity of their sodium salts to ordinary sea-salt.
These four elements show a great resemblance to one another
in their general chemical behaviour, and in that of their compounds,
whilst their physical properties show a gradual transition.
Thus, as the atomic weight increases, the state of aggregation
changes from that of a gas in the case of fluorine and chlorine,
to that of a liquid (bromine) and finally to that of the solid
(iodine); at the same time the melting and boiling points rise
with increasing atomic weights. The halogen of lower atomic
weight can displace one of higher atomic weight from its hydrogen
compound, or from the salt derived from such hydrogen compound,
while, on the other hand, the halogen of higher atomic
weight can displace that of lower atomic weight, from the
halogen oxy-acids and their salts; thus iodine will liberate
chlorine from potassium chlorate and also from perchloric acid.
All four of the halogens unite with hydrogen, but the affinity
for hydrogen decreases as the atomic weight increases, hydrogen
and fluorine uniting explosively at very low temperatures and
in the dark, whilst hydrogen and iodine unite only at high
temperatures, and even then the resulting compound is very
readily decomposed by heat. The hydrides of the halogens are
all colourless, strongly fuming gases, readily soluble in water and
possessing a strong acid reaction; they react readily with basic
oxides, forming in most cases well defined crystalline salts which
resemble one another very strongly. On the other hand the
stability of the known oxygen compounds increases with the
atomic weight, thus iodine pentoxide is, at ordinary temperatures,
a well-defined crystalline solid, which is only decomposed on
heating strongly, whilst chlorine monoxide, chlorine peroxide,
and chlorine heptoxide are very unstable, even at ordinary
temperatures, decomposing at the slightest shock. Compounds
of fluorine and oxygen, and of bromine and oxygen, have not
yet been isolated. In some respects there is a very marked
difference between fluorine and the other members of the group,
for, whilst sodium chloride, bromide and iodide are readily
soluble in water, sodium fluoride is much less soluble; again,
silver chloride, bromide and iodide are practically insoluble
in water, whilst, on the other hand, silver fluoride is appreciably
soluble in water. Again, fluorine shows a great tendency to form
double salts, which have no counterpart among the compounds
formed by the other members of the family.
HALS, FRANS (1580?–1666), Dutch painter, was born at
Antwerp according to the most recent authorities in 1580 or
1581, and died at Haarlem in 1666. As a portrait painter second
only to Rembrandt in Holland, he displayed extraordinary
talent and quickness in the exercise of his art coupled with
improvidence in the use of the means which that art secured to
him. At a time when the Dutch nation fought for independence
and won it, Hals appears in the ranks of its military gilds. He
was also a member of the Chamber of Rhetoric, and (1644) chairman
of the Painters’ Corporation at Haarlem. But as a man he
had failings. He so ill-treated his first wife, Anneke Hermansz,
