CHAPTER VII.

THE MOON. (

Period, &c.-Its Phases.-Its motions and their complexity.-Libration.-Evection.— Variation - Parallactic Inequality.—Annual Equation.—Secular acceleration. -Diversified character of the Moon's surface.-Lunar mountains.-Seas.Craters.-Volcanic character of the Moon.-Bergeron's experiment.—The lunar mountain, Aristarchus.-Teneriffe.-Lunar atmosphere.-Researches of Schröter, &c.-Hansen's curious speculation.--The Earth-shine.—The Harvest Moon.— Astronomy to an observer on the Moon.-Luminosity and calorific rays.— Historical notices as to the progress of Lunar Chartography.-Lunar Tabies.— Meteorological Influences.

T

HE Moon, as the Earth's satellite, is to us the most important of the "secondary planets," and will therefore receive a somewhat detailed notice.

The Moon revolves round the Earth in 27d 7h 43m 11.4618, at a mean distance of 237,300 miles. The eccentricity of its orbit amounting to o-0662, the Moon may recede from the Earth to a distance of 253,000 miles, or approach it to within 221,600 miles. Its apparent diameter varies between 29′ 21′′ and 33′ 31′′. The diameter at mean distance is 31′ 5′′. It will fix this in the memory to note that the apparent diameter is the same as the Sun's, and equals 1°. The real diameter, according to Mädler, is 2159.6 miles; according to Wichmann 2162 miles. Recent researches shew that these values are too great; and that a correction of about 2′′ (Airy) or 2·15′′ (De La Rue) must be applied to the measured visual diameter of the Moon, to allow

These figures must be regarded as geometrically rather than practically true, for under varying circumstances of altitude above the horizon the diameter

of the Moon will be found to vary considerably. And the diameter at mean distance is not the arithmetical mean of the extremes of apparent diameter.

for the exaggeration of its dimensions by irradiation. This reduction amounts to about 2 miles. The most delicate measurements indicate no compression.

The Moon has phases like the inferior planets; and of the various influences ascribed to it, that which results in the tides of the ocean is the most important, and will hereafter be treated at some length.

The motions of the Moon are of a very complex character: they have largely occupied the attention of astronomers during all ages, and it is only within a recent period that they can be said to have been mastered.

Speaking roughly, we may say that the same hemisphere of the Moon is always turned towards us; but although this is, in the main, correct, yet there are certain small variations at the edge which it is necessary to notice. The Moon's axis, although nearly, is not exactly perpendicular to the plane of its orbit, deviating therefrom by an angle of 1° 32′ 9′′ (Wichmann); owing to this fact, and to the inclination of the plane of the lunar orbit to that of the ecliptic, the poles of the Moon lean alternately to and from the Earth. When the North pole leans towards the Earth we see somewhat more of the region surrounding it, and somewhat less when it leans the contrary way; this is known as libration in latitude. The extent of the displacement in this direction is 6° 47'. In order that the same hemisphere should be continually turned towards us, it would be necessary not only that the time of the Moon's rotation on its axis should be precisely equal to the time of the revolution in its orbit, but that the angular velocity in its orbit should, in every part of its course, exactly equal its angular velocity on its axis. This, however, is not the case, for the angular velocity in its orbit is subject to a slight variation, and in consequence of this a little more of its Eastern or Western edge is seen at one time than another; this phenomenon is known as the libration in longitude, and was discovered by Hevelius, who described it in 1647. The extent of the displacement in longitude is 7° 53′. In his Selenographia.

Librans, balancing.

The maximum total libration (as viewed from the Earth's centre) amounts to 10° 24'. On account of the diurnal rotation of the Earth, we view the Moon under somewhat different circumstances at its rising and at its setting, according to the latitude of the Earth in which we are placed. By thus viewing it in different positions, we see it under different aspects; this gives rise to another phenomenon, the diurnal libration, but the maximum value of this is only 1° 1′ 24′′.

This periodical variation in the visible portion of the Moon's disc seems to have been first remarked by Galileo-a discovery very creditable to him when we consider the materials with which he worked. According to Arago, the various librations enable us to see altogether of the Moon's surface, the portion always invisible amounting only to of the same.

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The following account of the chief perturbations in the motion of the Moon is, in the main, abridged from that invaluable repertory of astronomical facts, Hind's Solar System.

1. The Erection depends on the angular distance of the Moon from the Sun, and on the mean anomaly of the former. It diminishes the equation of the centre in the syzygies and increases it in the quadratures, increasing or diminishing the Moon's mean longitude by 1° 20′ 29.9′′. Period, about 31d 19h 30m. Discovered by Ptolemy, but previously suspected by Hipparchus.

2. The Variation depends solely on the angular distance of the Moon from the Sun. Its effect is greatest at the octants, and disappears in the syzygies and quadratures, the longitude of the Moon being altered thereby 35′ 41.6" when at a maximum. Period, half a synodical revolution, or about 14a 18h. Its discovery is usually ascribed to Tycho Brahe, but Sedillot and others claim it for Abùl Wefa, who lived in the 9th century. It was the first lunar inequality explained by Sir I. Newton on the Theory of Gravitation.

3. The Parallactic Inequality arises from the sensible difference in the disturbing influence exerted by the Sun on the Moon, according as the latter is in that part of its orbit nearest to,

or most removed from, the Sun. At its maximum it alters the Moon's longitude by about 2'. Period, one synodical revolution, or 29d 12h 44m.

4. The Annual Equation is that inequality in the Moon's motion, which results from the variation in the velocity of the Earth, caused by the eccentricity of its orbit. At its maximum the Moon's longitude is altered by 11' 11.97". Period, one anomalistic solar year, or 365d 6h 13m 49.3".

5. The Secular Acceleration of the Moon's mean motion had been supposed to be caused wholly by the diminution in the eccentricity of the Earth's orbit which has been going on for many centuries, as has already been pointed out; but in 1853 it was shewn by Professor Adams that the amount of this acceleration is just double that which such diminution per se would account for. At present the mean motion of the Moon is being increased at the rate of about 12" every 100 years. This inequality was detected by Halley in 1693 from a comparison of the periodic time of the Moon, deduced from Chaldæan observations of eclipses, made at Babylon in the years 720 and 719 B.C., and Arabian observations made in the 8th and 9th centuries A.D. Laplace first reasoned out and explained the theory of the inequality, and up to the date of Adams's researches his calculations were supposed to be complete. It was, however, shewn by our great geometer that Laplace had neglected certain quantities in his calculations, and so estimated the accelerating effect of the increase of the minor axis of the Earth's orbit at double its true amount. It has been suggested by Delaunay and others that half of this seeming acceleration has its origin in the real increase in length of our terrestrial day, which has actually lengthened and continues to lengthen by a small fraction of a second annually; and this slower rotation of the Earth (for that is what it amounts to) is conceived to have its origin in the friction of the tides, which act as a break on the Earth rotating beneath them.

Hansen elucidated, a few years ago, two other inequalities in the Moon's motion, due, the one directly and the other indirectly

to the influence of Venus; and it was hoped that when these were taken into account it would have been found possible to say that the position of the Moon deduced from theory is almost precisely the same as that obtained by direct observation, and therefore that our knowledge of the Moon's motion is almost perfect; but further research by Sir G. B. Airy has cast a doubt on the matter.

Some matters connected with the Moon's orbit which are of importance in relation to eclipses will be referred to when we come to deal with eclipses (Book II., post); but it is desirable to note here the fact that the line of nodes of the lunar orbit revolves round the ecliptic in a retrograde direction in 18 218 21h 22m 46. "This retrogression of the nodes is caused by the action of the Sun which modifies the central gravity of the Moon towards the Earth. It is not, however, an equable motion throughout the whole of the Moon's revolution; the node, generally speaking, is stationary when she is in quadrature, or in the ecliptic; in all other parts of the orbit it has a retrograde motion, which is greater the nearer the Moon is to the syzygies, or the greater the distance from the ecliptic. The preponderating effect at the end of each synodic period is, however, retrocessive, and gives rise to the revolution of the line of nodes in between 18 and 19 years.'

This motion must not be confused with the motion of the line of apsides of the lunar orbit. "The line of apsides or major axis of the lunar orbit has, from a similar cause, a direct motion on the ecliptic, and accomplishes a whole revolution in 8o 310d 13h 48m 53, so that in 4o 155a the perigee arrives where the apogee was before. This motion of the line of apsides, like the movement of the nodes, is not regular and equable throughout the whole of a lunar month; for when the Moon is in syzygies the line of apsides advances in the order of signs, but is

d The statement in the text is not quite correct, so far that in the case of one of these inequalities (the 239-year one) what Hansen did was to trace the operation on the Moon of that influence of Venus which Airy connected only

with the Earth. The second of these Hansen inequalities runs its course in 273 years. See on the whole subject a paper by Airy in Month. Not., vol. xxxiv. p. I. Nov. 1873.

Hind, Sol. Syst., p. 42.