264. The Moon’s periodical and synodical revolution may be familiarly represented by the motions of the hour and minute hands of a watch round it’s dial-plate, which is divided into 12 equal parts or hours, as the Ecliptic is divided into 12 Signs, and the year into 12 months. Let us suppose these 12 hours to be 12 months, the hour hand the Sun, and the minute hand the Moon; then will the former go round once in a year, and the latter once in a month; but the Moon, or minute hand must go more than round from any point of the Circle where it was last conjoined with the Sun, or hour hand, to overtake it again: for the hour hand being in motion, can never be overtaken by the minute hand at that point from which they started at their last conjunction. The first column of the annexed Table shews the number of conjunctions which the hour and minute hand make whilst the hour hand goes once round the dial-plate; and the other columns shew the times when the two hands meet at every conjunction. Thus, suppose the two hands to be in conjunction at XII, as they always are; then, at the first following conjunction it is 5 minutes 27 seconds 16 thirds 21 fourths 49-1/11 fifths past I where they meet; at the second conjunction it is 10 minutes 54 seconds 32 thirds 43 fourths 38-1/2 fifths past II; and so on. This, though an easy illustration of the motions of the Sun and Moon, is not precise as to the times of their conjunctions; because, while the Sun goes round the Ecliptic, the Moon makes 12-1/3 conjunctions with him; but the minute hand of a watch or clock makes only 11 conjunctions with the hour hand in one period round the dial-plate. But if, instead of the common wheel-work at the back of the dial-plate, the Axis of the minute hand had a pinion of 6 leaves turning a wheel of 40, and this last turning the hour hand, in every revolution it makes round the dial-plate the minute hand would make 12-1/3 conjunctions with it; and so would be a pretty device for shewing the motions of the Sun and Moon; especially, as the slowest moving hand might have a little Sun fixed on it’s point, and the quickest a little Moon. Besides, the plate, instead of hours and quarters, might have a Circle of months, with the 12 Signs and their Degrees; and if a plate of 29-1/2 equal parts for the days of the Moon’s age were fixed to the Axis of the Sun-hand, and below it, so as the Sun always kept at the 1/2 day of that plate, the Moon-hand would shew the Moon’s age upon that plate for every day pointed out by the Sun-hand in the Circle of months; and both Sun and Moon would shew their places in the Ecliptic: for the Sun would go round the Ecliptic in 365 Days and the Moon in 27-1/3 days, which is her periodical revolution; but from the Sun to the Sun again, or from Change to Change, in 29-1/2 days, which is her synodical revolution.