unequal. First, because the Sun, by reason of its Apogæum and Perigæum, doth not at all times of the year dispatch in one day an equal Arch of the Ecliptick; but greater Arches neer the Perigæum, which is about the middle of December; and lesser neer the Apogæum, which is about the middle of June: As will appear sufficiently by the Tables of the Sun's Annual motion. Secondly, though the Sun should in the Ecliptick move alwaies at the same rate; yet equal Arches of the Ecliptick do not in all parts of the Zodiack answer to equal Arches of the Æquinoctial, by which we are to estimate time: Because some parts of it, as about the two Solsticial Points, lie nearer to a parallel position to the Æquinoctial, than others, as those about the two Æquinoctial points, where the Ecliptick and Æquinoctial do intersect; whereupon an Arch of the Ecliptick, neer the Solsticial points answers to a greater Arch of the Æquinoctial, than an Arch equal thereunto neer the Æquinoctial points: As doth sufficiently appear by the Tables of the Suns right Ascension.
According to the first of these causes, we should have the longest natural daies in December, and the shortest in June, which if it did operate alone, would give us at those times two Annual High-waters.
According to the second cause, if operating singly, we should have the longest daies at the two Solstices in June and December, and the two shortest at the Æquinoxes in March and September; which would at those times give occasion of four Annual High-waters.
But the true Inequality of the Natural Days, arising from a Complication of those two causes, sometimes crossing and sometimes promoting each each other: though we should find some increases or decreases of the Natural daies at all those seasons answerable to the respective causes (and perhaps of Tides proportionably thereunto:) yet the longest and shortest natural daies absolutely of the whole year (arising from this complication of Causes) are about those times of Allhallontide and Candlemas; (or not far from them) about which those Annual High-tides are found to be: As will appear by the Tables of Æquation of Natural daies. And therefore I think, we may with very good reason cast this Annual Period upon that cause, or rather
complication of causes. For (as we before shewed in the Menstrual and Diurnal) there will, by this inequality of Natural daies, arise a Physical Acceleration and Retardation of the Earths Mean motion, and accordingly a casting of the Waters backward or forward; either of which, will cause an Accumulation or High-water.
'Tis true, that these longest and shortest daies, do (according to the Tables, some at least) fall rather before, than after Alhallontide and Candlemas (to wit the ends of October and January;) but so do also (sometimes) those high Tydes: And it is not yet so well agreed amongst Astronomers, what are all the Causes (and in what degrees) of the Inequality of Natural daies; but that there be diversities among them, about the true time: And whether the introducing of this New Motion of the Earth in its Epicycle about this Common Center of Gravity, ought not therein also to be accounted for, I will not now determine: Having already said enough, if not too much, for the explaining of this general Hypothesis, leaving the particularities of it to be adjusted according to the true measures of the motions; if the General Hypothesis be found fit to be admitted.
Yet this I must add, (that I be not mistaken) that whereas I cast the time of the daily Tydes to be at all places, when the Moon is there in the Meridian; it must be understood of open Seas, where the water hath such free scope for its motions, as if the whole Globe of Earth were equally covered with water: Well knowing, that in Bayes and In land-Channels, the position of the Banks and other like causes must needs make the times to be much different from what we suppose in the open Seas: And likewise, that even in the Open Seas, Islands, and Currents, Gulfs and Shallows, may have some influence, though not comparable to that of Bays and Channels. And moreover, though I think, that Seamen do commonly reckon the time of High-water in the Open Seas, to be then, when the Moon is there in the Meridian (as this Hypothesis would cast it:) Yet I do not take my self to be so well furnished with a History of Tides, as to assure my self of it; much less to accommodate it to particular places and cases.
Having thus dispatched the main of what I had to say
concerning the Seas Ebbing and Flowing: Had I not been already too tedious, I should now proceed to give a further reason, why I do introduce this consideration of the Common Center of Gravity in reference to Astronomical Accounts. For indeed, that which may possibly seem at first to be an Objection against it, is with me one reason for it.
It may be thought perhaps, that if the Earth should thus describe an Epicycle about the Common Center of Gravity, it would (by this its change of place) disturbe the Cælestial motions; and make the apparent places of the Planets, especially some of them, different from what they would otherwise be. For though so small a removal of the Earth, as the Epicycle would cause (especially if its Semidiameter should not be above 1⅓ of the Earths Semidiameter) would scarce be sensible (if at all) to the remoter Planets; yet as to the nearer it might.