By observing in the evening the position of the moon with regard to the fixed stars, she will appear about 13° farther cast than she was on the preceding evening, and will perform a complete sidereal revolution from one fixed star to another, or from one point in absolute space to the same point again, in 27d 43' 12". As the equi noxes during this period recede about 4", a space which the moon will pdss over in time, her periodic revolu tion, with regard to the equinoxes, will be 27d 7h 43'5". The nodes move backwards in the heavens 1° 26' 6" in the time of a revolution, and since the moon passes through this space in 2h 36' 49", her revolution, with re gard to her nodes, will be 27d 6' 23". The motion of the moon's apogee being about 3° 2' 38" direct in the time of a revolution, she will describe this space in 7h 43' 12", and will perform her anomalistic revolution in 27" 13" 15' 53". The revolution of the moon with regard to the sun, that is, the time which she takes to revolve from one conjunction to the next conjunction with the sun, is called her synodical revolution. While the moon is going round the earth, the earth, and consequently the sun, advance 'about 29° 6' 25", a space which the moon passes over in 2d 5h 1'. Hence the synodical revolution will be 29d 12" 44' 12".
As the earth revolves round the sun while the moon moves round the earth, her path in absolute space is very irregular. Like a point in the wheel of a carriage that is moving over a convex road, the moon will des cribe a succession of epicycloidal curves, which will al ways be concave towards the sun. A diagram of the moon's path in absolute space, and the account of a ma chine for describing it, will be seen in Ferguson's ?s tronomy, vol. 1. chap. xv.
While the moon performs her monthly revolution, she presents various appearances to a spectator on the earth. When she is seen near the sun in the western part of the horizon, she appears like a bow or crescent of light. As her distance from the sun increases, the enlightened part of her disc gradually augments, till she presents her fully illuminated disc to the earth. The enlightened portion again diminishes, till she is seen in the morning, a little belbre sunrise, in the form of a crescent ; and these phases are regularly repeated in the same order during every revolution. These different appearances will be understood from PLATE. XXXIX. Fig. 10. where S is the sun, Y. the earth, and ABCD, &c. the moon in dif ferent positions in her orbit round the earth, having one complete hemisphere always enlightened by the sun. When the moon is new, or is in conjunction with the sun at A, her dark side is turned to the earth, and she is invisible, as at a. When she reaches her first octant at B, or has gone through one-eighth of her orbit, one-fourth of her enlightened side is turned to the earth, and she ap pears like a crescent, as at b. When she reaches her first quarter or quadrature C, the half of her illumina ted disc is seen at the earth, and she appears a half moon, or dichotomised, as at c. In her second octant at
D, more of her enlightened hemisphere comes into view, and she appears gibbous, as at d. When she is in op position to the sun at E, her enlightened side is complete ly turned to the earth, and she appears full moon, as at e. At F, her third octant, a part of the enlightened hemis phere, is turned away from the earth, and the moon ap pears gibbous, as at f. In her third quarter at G, she again appears as a half moon at g. In her fourth octant at H, she has again the form of a crescent as at h, and at A she again disappears, having completed her synodi cal revolution round the earth. The moon is said to be in syzigy when she is in conjunction or opposition with the sun, and the line ElEAS is called the line of the syzigies. These different appearances are well illus trated by a white ball or globe, illuminated by the sun or by the light of a candle, and held in different positions with regard to the eye. The proportion between the enlightened and the obscure parts of the moon's disc, may be found for any given time, from the Table in p. 616, which has already been explained. By subtracting the longitude of the sun from that of the moon, we ob tain the moon's distance from the sun, which is the ar gument of the Table. With this argument enter the Table, and take out, by the method already mentioned, the proportion between the dark and illuminated parts of her disc.
By attending to the different positions of the earth with regard to the moon, it will appear, that the earth exhibits similar phases to an inhabitant of the moon, with this difference, that the phases of the earth are always opposite to those of the moon : When the moon is full, the earth is invisible ; when the moon is new, the earth is full ; and when the moon has of her diameter enlightened, the earth has 11- of its disc illuminated, The light, therefore, in the dark part of the moon, which has been explained in Section 4, p. 585, arises from the light reflected from the earth, which is nearly full at the time when the secondary light of the moon is vi sible.
If the moon moved in an orbit lying in the same plane with the earth and sun, she would obscure or eclipse the sun, when she came into the position A, PLATE XXXIX. Fig. 10 ; and the centre of the moon would pass over the centre of the sun. In like manner, when the moon comes into the position E, she would pass through the earth's shadow, and become invisible to an inhabitant upon its surface. But since the moon moves in an orbit inclined to the plane of the ecliptic, in which the sun and earth are always found, she will not obscure the sun in the position A, unless when she is in or near her nodes, or, what is the same thing, near the plane of the ecliptic at the time of new moon ; and for the same reason she will not pass through the earth's. shadow, unless she is in or near her nodes at the time of full moon.