at the zenith- an assertion which we have already seen to be perfectly correct. In the 16th century Tycho Brahe also investigated the subject of refraction; and his results, though by no means so accurate as those of Ptolemy, are interesting from the fact that they were the first which were reduced to the form of a Table. Since this period many astronomers have devoted their attention to the matter, and the Tables now in most general use are those of Bessel.

Twilight. This is another phenomenon depending on the agency of the atmosphere with which the Earth is surrounded. It is due partly to refraction and partly to reflection, but chiefly to the latter cause. After sunset the Sun still continues to illuminate the clouds and upper strata of the air, just as it may be seen shining on the tops of hills long after it has disappeared from the view of the inhabitants of adjacent plains. The air and clouds thus illuminated reflect back part of the light to the surface beneath them, and thus produce, after sunset and before sunrise, in a degree more or less feeble according as the Sun is more or less depressed, that which we call "twilight." Immediately after the Sun has disappeared below the horizon all the clouds in the vicinity are so highly illuminated as to be able to reflect an amount of light but little inferior to the direct light of the Sun. As the Sun, however, sinks lower and lower, less and less of the visible atmosphere receives its light, and consequently less and less of it is reflected to the Earth's surface surrounding the position where the observer is stationed, until at length, though by slow degrees, all reflection is at an end, and night The same thing occurs before sunrise; the darkness of night gradually giving place to the faint light of dawn, until the Sun appears above the horizon and produces the full light of day.

ensues.

The duration of twilight is usually reckoned to last until the Sun's depression below the horizon amounts to 18°: this, however, varies in the Tropics a depression of 16° or 17° is sufficient to put an end to the phenomenon, but in England a depression of 17° to 21 is required. The duration of twilight

L

differs in different latitudes; it varies also in the same latitude at different seasons of the year, and depends in some measure on the meteorological condition of the atmosphere. Strictly speaking, in the latitude of Greenwich there is no true night from May 22 to July 21, but constant twilight from sunset to sunrise. Twilight reaches its minimum 3 weeks before the vernal equinox and 3 weeks after the autumnal equinox, when its duration is 1h 50m. At midwinter it is longer by about 17m, but the augmentation is frequently not perceptible, owing to the greater prevalence of clouds and haze at that season of the year, which intercept the light and hinder it from reaching the Earth. The duration is least at the equator (1h 12m), and increases as we approach the Poles, for at the former there are 2 twilights every 24 hours, but at the latter only 2 in a year, each lasting about 50 days. At the North Pole the Sun is below the horizon for 6 months; but from January 29 to the vernal equinox, and from the autumnal equinox to Nov. 12, the Sun is less than 18° below the horizon: so that there is twilight during the whole of these intervals, and thus the length of the actual night is reduced to 2 months. The length of the day in these regions is about 6 months, during the whole of which time the Sun is constantly above the horizon. The general rule is, that to the inhabitants of an oblique sphere the twilight is longer in proportion as the place is nearer the elevated polei.

Under some circumstances a secondary twilight may be noticed, "consequent on a re-reflection of the rays dispersed through the atmosphere in the primary one. The phenomenon seen in the clear atmosphere of the Nubian Desert, described by travellers under the name of the After-glow,' would seem to arise from this causek."

The "Astronomical" Twilight is that Twilight which has reference to the visibility and extinction of the smaller stars.

This is not quite literally 6 months owing to the operation of refraction. i A valuable memoir on twilight, by J. F. J. Schmidt, will be found in Ast. Nach., vol. lxiii. No. 1495, Oct. 14, 1864.

An abstract of it is given in the Intell.
Obs., vol. vii. p. 135, March 1865.

k Sir J. Herschel, Outlines of Ast., P. 34.

The following is a table of its duration for different seasons and latitudes :

BOOK IV.

COMETS.

CHAPTER I.

GENERAL REMARKS.

Comets always objects of popular interest, and sometimes of alarm.-Usual phenomena attending the development of a Comet.-Telescopic Comets.-Comets diminish in brilliancy at each return.-Period of revolution.-Density.-Mass. -Lexell's Comet.-General influence of Planets on Comets.-Special influence of Jupiter.-Comets move in 1 of 3 kinds of orbits.-Element of a Comet's orbit. For a parabolic orbit, 5 in number.-Direction of motion.-Eccentricity of an elliptic orbit.—The various possible sections of a cone.-Early speculations as to the paths in which Comets move.-Comets visible in the daytime. Breaking up of a Comet into parts.—Instance of Biela's Comet.— Liais's observations of Comet iii. 1860.-Comets probably self-luminous.Existence of phases doubtful.-Comets with Planetary discs.—Phenomena connected with the tails of Comets.-Usually in the direction of the radius vector.-Secondary Tails.-Vibration sometimes noticed in tails.-Olbers's hypothesis.-Transits of Comets across the Sun's disc.- Variation in the appearance of Comets exemplified in the case of that of 1769.-Transits of Comets across the Sun.

THE

HE heavenly bodies which will now come under our notice are amongst the most interesting with which the astronomer has to deal. Frequently appearing suddenly in the nocturnal sky, and often having attached to them tails of immense size and brilliancy, comets were well calculated in the earlier ages of the world to attract the attention of all, and to excite the fear of many. It is the unanimous testimony of history, during a period of upwards of 2000 years, that comets were always considered to

be peculiarly" ominous of the wrath of Heaven, and as harbingers of wars and famines, of the dethronement of monarchs, and the dissolution of empires." I shall hereafter examine this question at greater length. Suffice it for me here to quote the words of the Poet, who speaks of

"A Blazing Star,

Threatens the World with Famin, Plague, and War;
To Princes, death; to Kingdoms, many crosses;

To all Estates, ineuitable Losses;

To Heard-men, Rot; To Ploughmen, haplesse Seasons;
To Saylors, Storms; to Cities, ciuil Treasons "."

However little attention might have been paid by the ancients to the more ordinary phenomena of nature (which, however, were very well looked after), yet certain it is that comets and total eclipses of the Sun were not easily forgotten or lightly passed over; hence the aspects of remarkable comets seen in

olden times have been handed down to us, often with circumstantial minuteness.

A comet usually consists of 3 parts, developed, it may be, somewhat in the following manner:-A faintly luminous speck is discovered by the aid of a good telescope; the size increases gradually; and after some little time a nucleus appears-that is, a part which is more condensed in its light than the rest, and is sometimes circular, sometimes oval, and sometimes (but very

a Du Bartas, trans. J. Sylvester, 1621, p. 33.