The Moon describes its orbit round the Earth in the Space of 27 days and 7 hours, which space of time is called a _Periodical Month_; yet from one conjunction to the next, the Moon spends 29 days and a half, which is called a _Synodical Month_; because while the Moon in her proper _Orbit_ finishes her course, the Earth advances near a whole sign in the ecliptic; which space the Moon has still to describe, before she will be seen in conjunction with the Sun. When the Moon is in conjunction with the Sun, note her place in the ecliptic; then turning the handle, you will find that 27 days and 7 hours will bring the Moon to the same place; and after you have made 2¼ revolutions more, the Moon will be exactly betwixt the Sun and the Earth. [Sidenote: _Phases of the Moon._] The Moon all the while keeps in her orbit, and so the wire that Supports her continually rises or falls in a socket, as she changes her latitude; the black cap shifts itself, and so shews the phases of the Moon, according to her age, or how much of her enlightened part is seen from the Earth. In one synodical month, the line of the nodes moves about 1½ degree from West to East, and so makes one entire revolution in 19 years. Let AB be an arch of the Earth’s orbit, and when the Earth is in T, let the Moon be in N, in conjunction with the Sun in S, while the Moon is describing her orbit NAFD, the Earth will describe the arch of her orbit T _t_; and when the Earth has got into the point _t_, the Moon will be in the point of her orbit _n_, having made one compleat revolution round the Earth. But the Moon, before she comes in conjunction with the Sun, must again describe the arch _n o_; which arch is similar to T _t_, because the lines FN, _f n_, are parallel; and because, while the Moon describes the arch _n o_, the Earth advances forward in the ecliptic; the arch described by the Moon, after she has finished her periodical month, before she makes a synodical month, must be somewhat greater than _n o_. To determine the mean length of a synodical month, find the diurnal motion of the Moon (or the space she describes round the Earth in one day) and likewise the diurnal motion of the Earth; then the difference betwixt the two motions, is the apparent motion of the Moon round the Earth in one day; then it will be, as this differential arch is to a whole circle; so is one day to that space of time wherein the Moon appears to describe a compleat circle round the Earth, which is about 29½ days. But this is not always a true _Lunation_, for the motion of the Moon is sometimes faster, and sometimes slower, according to the position of the Earth in her orbit.