• According to him, the distance of the planets may be ex pressed nearly as follows, the earth's distance from the sun being considered as 10. Comparing these with the mean distances above given, we cannot but remark the near agreement, and scarcely hesitate to pronounce that their mean distances were assigned according to a law, although we are entirely ignorant of the exact law and of the reason for that law: See Dr. Brinkley's Elements of Astronomy. CHAPTER XIII. Of the Moon. C 1. The Moon, next to the Sun, is the most interesting to us, of all the heavenly bodies, and is particularly distinguished by the periodical changes to which her figure and light are subject. Among the ancients, Luna), or the Moon, was an object of very great respect. By the Hebrews she was more regarded than the Sun, and it appears they regulated their time by her motions and appearances, The new Moon was observed as a festival among them, which was celebrated with sound of trumpets, entertainments, and sacrifices. The ancient bards and poets have also celebrated the praises of the Moon under various appellations, as Cynthia, Cyllene, Phœbe, Silver Queen of Night, &c. 2. The Moon moves round the Earth in an elliptical orbit, of which the Earth is in one of the foci. The inclination of the Moon's orbit to the plane of 1 1 the ecliptic is about 5° 9'. The Moon performs her mean sidereal revolution in 27 days, 7 hours, 43 minutes and 11 seconds, at the mean distance of • 236,267 miles from the centre of the Earth. The Moon also accompanies the Earth in its annual revolution round the Sun. This necessarily follows, if the motion of the Earth be admitted, and is well illustrated by the motion of the satellites of Jupiter and Saturn. The inclination of the Moon's orbit is very variable: the greatest inequality sometimes extends to 8' 47". The motions of the Moon are exceedingly irregular, her sidereal revolution is not the same for every century. The comparison of modern with ancient observations, shows incontestibly an acceleration in the mean motion of the Moon; but this acceleration has been proved to be periodical. 3. The figure of the Moon is that of an oblate spheroid, like the Earth; her mean diameter is 2161 miles. The apparent diameter varies according to her distance from the Earth; when nearest to us, it is 33' 31", but at the greatest distance, it is about 29' 30"; so that the mean apparent diameter is about 31' 30". The magnitude or size of the Moon is .02, its mass .0146. and consequently its density .73; the size, mass, and density of the Earth being respectively considered as unity, or 1. TABLE, Showing the mean tropical revolution of the Moon, mean diurnal motion of the perigee, &c. Mean inclination of the orbit 5097 Greatest equation of the centre- 6 17 3" 9 to the equinoxes نا 13 10 35 Obs. 1. The line of the apsides has a motion according to the order of the signs when the Moon is in syzygies, and contrary, in quadratures. But in a whole revolution of the Moon, the progress exceeds the regress. They go forward with the greatest velocity, when the line of the apsides is in the nodes; and if they do go back when in the nodes, their regression is then slowest of all, in the same revolution. When the line of the apsides is in the quadratures, they are direct, with the least velocity when the Moon is in syzygies; but they return the swiftest in the quadratures; and in this case, the regress exceeds the progress, in one entire revolution of the Moon. 2. Considering one entire revolution of the Moon, cæteris paribus, the nodes move in antecendentia, with the greatest velocity, when she is in the syzygies; then slower and slower till they are at rest, when she is in the quadratures. In one whole revolution of the Moon, the nodes go back very fast when they are in quadratures; then slower till they come to rest, when the time of the nodes is in syzygies. 3. The inclination of the Moon's orbit is changed by the same force as that by which the nodes are moved; being increased as the Moon recedes from the node; and diminished as she approaches it. The inclination of the orbit is least of all when the nodes are come to the syzygies. For, in the motion of the nodes from the syzygies to the quadratures, and in one entire revolution of the Moon, the force which increases the inclination, exceeds that which diminishes it; therefore, the inclination is increased, and it is the greatest of all when the nodes are in quadratures. 4. The eccentricity of the Moon's orbit undergoes various changes every revolution. It is greatest of all when the line of the apsides is in the syzygies, and the least when that line is in the quadratures. This variation of the eccentricity affects the equation of the centre. 5. As to the inequality of the Moon's motion, she moves swifter, and, by the radius drawn from her to the Earth, (or radius vector of the Moon) describes a greater arc in proportion to the time, also has an orbit less curved, and by that means comes nearer to the Earth in her syzygies than in the quadratures: her motion is also swifter in the Earth's aphelion than in its perihelion. The Moon also perpetually changes the figure of her orbit, or the species of the ellipse in which she moves. 6. There are also a great many other inequalities in the motion of this satellite, which it is very difficult to reduce to any certain rule; and which render the calculations of her true place in the heavens a work of considerable labour. There are nearly thirty equations to be applied to the mean longitude to obtain the true, and about 24 for her latitude and parallax. 4. When the Moon is in conjunction with the Sun, it is then invisible; when moving from the Sun towards the east, it is first visible, it is then called the new Moon, and appears like a crescent; when 90 degrees from the Sun, it it is halved, or as it is usually called dichotomised; when more distant it is gibbous; and when in opposition, it shines with a full face, and is then called the full Moon: approaching the Sun towards the east, it becomes again gibbous, then halved, and lastly crescent, after which it disappears from the superior lustre of the Sun, and the smallness of the illuminated part which is turned towards the Earth. The phases of the Moon are particularly interesting; the luminous crescent being always turned towards the Sun, evidently indicates that the Moon receives its light from the Sun; and the law of the variation of its phases, which increase in a certain ratio of the angular distance of the Moon from the Sun, proves that the Moon is spherical. The enlightened part varies nearly as the versed sine of the angle of elongation from the Sun. The cause of the appearance of the whole Moon, observed a few days before and after the new Moon, is the reflection of light from the Earth. When the Moon becomes consi |