Page:Mathematical collections and translations, in two tomes - Salusbury (1661).djvu/443

 the Moon and Sun; neer, in a word, at the time of its conjun¦ction and change; remote, in its Full and Opposition; and the greatest vicinity differ the quantity of the Diameter of the Lunar Orb. Now if it be true that the virtue which moveth the Earth and Moon, about the Sun, be alwayes maintained in the same vigour; and if it be true that the same moveable moved by the same virtue, but in circles unequal, do in shorter times passe like arches of lesser circles, it must needs be granted, that the Moon when it is at a lesse distance from the Sun, that is in the time of conjunction, passeth greater arches of the Grand Orb, than when it is at a greater distance, that is in its OpppsitionOpposition [sic] and Full. And this Lunar inequality must of necessity be imparted to the Earth also; for if we shall suppose a right line produced from the centre of the Sun by the centre of the Terrestrial Globe, and prolonged as far as the Orb of the Moon, this shall be the semidiameter of the Grand Orb, in which the Earth, in case it were alone, would move uniformly, but if in the same semidiameter we should place another body to be carried about, placing it one while between the Earth and Sun, and another while beyond the Earth, at a greater distance from the Sun, it is necessary, that in this second case the motion common to both, according to the circumference of the great Orb by means of the distance of the Moon, do prove a little slower than in the other case, when the Moon is between the Earth and Sun, that is at a lesser distance. So that in this businesse the very same happeneth that befals in the time of the clock; that lead which is placed one while farther from the centre, to make the vibrations of the staffe or ballance lesse frequent, and another while nearer, to make them thicker, representing the Moon. Hence it may be manifest, that the annual motion of the Earth in the Grand Orb, and under the Ecliptick, is not uniform, and that its irregularity proceedeth from the Moon, and hath its Monethly Periods and Returns. And because it hath been concluded, that the Monethly and Annual Periodick alterations of the ebbings and flowings, cannot be deduced from any other cause than from the altered proportion between the annual motion and the additions and substractions of the diurnal conversion; and that those alterations might be made two wayes, that is by altering the annual motion, keeping the quantity of the additions unaltered, or by changing of the bignesse of these, reteining the uniformity of annual motion. We have already found the first of these, depending on the irregularity of the annual motion occasioned by the Moon, and which hath its Monethly Periods. It is therefore necessary, that upon that account the ebbings and flowings have a Monethly Period in which they do grow