CHAPTER XIII.

ON THE MOTIONS OF THE MOON-SATELLITES-COMETS.

228. THE satellites also revolve in elliptic orbits round their respective primary planets, having the same law of periodic. times, but considerable deviations from the equable description of areas take place, in consequence of the disturbing force of the sun on the satellites, and of the satellites on each other.

The moon being a solitary satellite, we cannot apply the law of the periodic time to it. But its orbit is nearly an ellipse, and it nearly describes areas proportional to the times, the deviation from which arises from the disturbing force of the sun. This ellipse, however, does not retain the same position; that is, its points of greatest and least distance, called its apogee and perigee, do not retain the same position, but move according to the order of the signs, completing a revolution in about nine years.

The laws of the principal irregularities of the moon were discovered long before the cause of them.

229. The greatest difference between the true and mean place of the moon, arising from its elliptic motion, or the greatest equation of the centre, is 6° 18', and this is the most considerable deviation from its mean place. But besides the quick motion of the apogee, completing a revolution in nine years, the eccentricity of the ellipse is also variable: hence the motions of the moon appear so irregular, that it would have been almost

a The corrections for these irregularities (improperly so called) are styled equations.

impossible to have developed the elliptic motion from the phanomena; and therefore without a knowledge of the form of the planetary orbits, it is hardly to be supposed that an ellipse could have been applied for explaining the motions of the moon, although at first sight the superior advantage of being in the centre of the orbit might lead us to suppose that the laws of its motions would be more easily known.

230. The periodic time of the moon may be ascertained with great exactness from the comparison of ancient eclipses with modern observations. At an eclipse of the moon, the moon being in opposition to the sun, its place is known from the sun's place, which can, back to the remotest antiquity, be computed with precision. Three eclipses of the moon, observed at Babylon in the year 720 and 719 B. c. are the oldest observations recorded with sufficient exactness. By a comparison of these with modern observations, the periodic time of the moon is found to be 27d 7h 43m 111, not differing a second from the result obtained by recent observations. Yet we cannot use those ancient observations for determining the mean motion at the present time; for by a comparison of the above-mentioned eclipses with eclipses observed by the Arabians in the 8th and 9th centuries, and of the latter with the modern observations, it is well ascertained that the motion of the moon is now accelerated. This was first discovered by Dr. Halley, and, since his time, has been perfectly established by more minute computations. For a considerable time the cause remained unexplained; till M. Laplace shewed it to be a variation of a very long period, arising from the disturbance of the planets in changing the eccentricity of the earth's orbit. He has computed its quantity, which closely agrees with that deduced from observation. The moon's secular motion, the motion in a century, is now 7' greater than it was at the time the above-mentioned eclipses were observed at Babylon.

231. The two principal corrections of the mean place of the moon, beside that of the equation of the centre, are called the evection and variation. The evection depends upon the change of the eccentricity of the moon's orbit, and sometimes amounts to 1° 20′. This was discovered by Ptolemy. The variation which was discovered by Tycho Brahe depends upon the angular distance of the moon from the sun, and amounts, when greatest, to 35'. The other corrections arise only to a few minutes. But the number of corrections or equations used at present in computing the longitude alone of the moon, are thirtytwo, and in computing the latitude, twelve.

232. It was before mentioned, that the nodes of the lunar orbit move retrograde, completing a revolution in eighteen years and a half. This motion is not uniform. The inclination of the orbit remains nearly the same, but not exact. The motion of the apogee is subject to considerable irregularities its true place sometimes differs 121° from its mean place. This was known to the Arabian astronomers, but seems to have been first accurately stated by Horrox, whose extraordinary astronomical attainments will be afterwards noticed. He shewed the law of its change, and gave a construction for determining its quantity, which was adopted by Newton.

233. On all these accounts the computation of the exact place of the moon from theory is very difficult, and the formation of proper tables is one of the greatest intricacies in this science.

No small degree of credit is due to the industry of those who, by observation alone, discovered the laws of the principal irregularities. Ptolemy, by his observations and researches, determined the principal elements of the lunar motions with much exactness. Horrox, who adopted the discoveries of Kepler, formed, about the year 1640, a theory of the moon, founded partly on his own observations. From this theory, Flamstead, about the year 1670, computed tables, which he found gave the

place of the moon far more accurate than any other. Flamstead himself soon after furnished observations, by which Sir Isaac Newton was enabled to investigate, by the theory of gravity, the lunar irregularities, which he has given in his ever memorable work. Notwithstanding the field opened by the publication of the "Principia," and the known necessity of exact tables of the moon for the discovery of the longitude at sea, seventy years elapsed from the publication of that great work, before any tables were formed for the moon, which gave its place within one minute. Clairaut made, after Newton, the first considerable advances in the improvement of the lunar theory from the principles of gravitation. Professor Mayer, of the university of Gottingen, first published tables, by which the moon's place might be computed to one minute. The ingenuity exhibited in his theory and tables, and the incredible labour exerted in their computation and verification, will always render his memory distinguished. He died in 1762, at the early age of thirty-nine, worn out by his great and incessant exertions. His widow received from the British parliament a reward of £3000. About the year 1780, Mr. Mason, under the direction of Dr. Maskelyne, to whom modern astronomy is so much indebted, improved, by considerable alterations and additions, the tables of Mayer. Till very lately these were the tables generally used. Improved tables have now been furnished by M. Burg of Vienna, which appear to give the place of the moon to less than twenty seconds. The improvements in these tables were founded entirely on the observations of Dr. Maskelyne, for which purpose 3600 places of the moon, observed at Greenwich in the space of about thirty years, were used.

The tables of M. Burg have been superseded by those of M. Burckhardt, which are now used in computing the Nautical Almanac, and Conn. des Temps. They are probably more accurate, and certainly more convenient than those of M. Burg.