Simon Newcomb

“ The moon always presents nearly the same face to the earth, from which it follows that, when referred to a fixed direction in space, it revolves on its axis in the same time in which it performs its revolution. Relatively to the direction of the earth there is really no rotation. The rate of actual rotation is substantially uniform, while the arc through which the moon moves from day to day varies. Consequently, the face which the moon presents to the earth is subject to a corresponding variation, the globe as we see it slightly oscillating in a period nearly that of revolution. ”

“ Assuming the mean motion of the moon to be known and the perigee to be fixed, three eclipses, observed in different points of the orbit, would give as many true longitudes of the moon, which longitudes could be employed to determine three unknown quantities—the mean longitude at a given epoch, the eccentricity, and the position of the perigee. ”

“ Motion of the Moon.—The orbit of the moon around the earth, though not a fixed curve of any class, is elliptical in form, and may be represented by an ellipse which is constantly changing its form and position, and has the earth in one of its foci. The eccentricity of the ellipse is in the general average about 0·055, whence the moon is commonly more than 1/10 further from the earth at apogee than at perigee. The line of apsides is in continual motion, generally direct, and performs a revolution in about 12 years. ”

“ The distance of the moon can also be computed from the law of gravity, the problem being to determine the distance at which a body having the moon’s mass would revolve around the earth in the observed period. The measures of parallax agree perfectly with the computed distance in showing a mean parallax of 57′ 2·8′′, and a mean distance of 238,800 miles. The period of revolution, or the lunar month, depends upon the point to which the revolution is referred. Any one of five such directions may be chosen, that of the sun, the fixed stars, the equinox, the perigee, or the node. ”

“ Devoid of air and atmosphere, the causes of meteorological phenomena on the earth are non-existent on the moon. The only active cause of such changes is the varying temperature produced by the presence or absence of the sun’s rays. The range of temperature must be vastly wider than on the earth, owing to the absence of an atmosphere to make it equable. Elaborate observations of the heat coming from the moon at its various phases were made and discussed in 1871–1872 by Lord Rosse. ”

“ In 1856 William Ferrel showed that the action of the moon on the ocean tidal waves would result in a retardation of the earth’s rotation, a result, at first unnoticed, which was independently reached a few years later by Delaunay. The amount of retardation does not admit of accurate computation, owing to the uncertainty both as to the amount of the oceanic friction from which it arises and of the exact height and form of the tidal wave, the action of the moon on which produces the effect. ”

“ The height of the lunar mountains is a subject of interest. It cannot be stated with the same definiteness that we can assign heights to our terrestrial mountains, because there is no fixed sea-level on the moon to which elevations can be referred. The only determination that can be made on the moon is that of the height above some neighbouring hollow, crater or plain. ”

“ As an, atmosphere equal to ours in density would produce a deviation of an important fraction of a degree, it may be said that the moon can have no atmosphere exceeding in density the 1/5000 that of the earth. ”

“ Thus, in consequence of the evection, the equation of the centre comes out 2° 30′ larger from observations at the moon’s quarters than during eclipses.
The next forward step was due to Tycho Brahe. He found that, although the two inequalities found by Hipparchus and Ptolemy correctly represented the moon’s longitude near conjunction and opposition, and also at the quadratures, it left a large outstanding error at the octants, that is when the moon was 45° or 135° on either side of the sun. This inequality, which reaches the magnitude of nearly 1°, is known as the variation. ”

“ This excess is, however, subject to wide variation, owing to the obliquity of the ecliptic and of the lunar orbit to the equator, and therefore to the horizon. The smaller the angle which the orbit of the moon, when near the point of rising, makes with the horizon the less will be the retardation. ”

“ The former, if it existed at all, could be found only in the more depressed portions; and even here it would evaporate under the influence of the sun’s rays, forming a vapour which, if it existed in considerable quantity, would in some way make itself known to our scrutiny. ”

“ The subject was then taken up by Brown, who in a series of researches published in the Memoirs of the Royal Astronomical Society and in the Transactions of the American Mathematical Society extended Hill’s method so as to form a practically complete solution of the entire problem. The principal feature of his work was that the quantity m, which is regarded as constant, appears only in a numerical form, so that the uncertainties arising from development in a series accruing to its powers is done away with. ”