Chapter 26

Now supposing A B C D E to be a part of the great Orb of the _Annual_ motion, described by the Common Center of Gravity, in so long time as from a _Full-Moon_ at A to the next _New-Moon_ at E; (which, though an Arch of a _Circle_ or _Ellipse_, whose Center we suppose at a due distance below it; yet being put about 1/25 of the whole, may well enough be here represented by a streight Line:) the Center of the Earth at T, and that of the Moon at L, must each of them (supposing their common Center of Gravity to keep the Line A E) be supposed to describe a _Periphery_ about that Common Center, as the Moon describes her Line of _Menstrual_ motion (Of which I have (in the _Scheme_) onely drawn that of the _Earth_; as being sufficient to our present purpose; parallel to which, if need be, we may suppose one described by the Moon; whose distance is also to be supposed much greater from T than in the _figure_ is expressed, or was necessary to expresse.) And in like manner E F G H I, from that _New moon_ at E, to the next _Full-moon_ at I.

From A to E (from Full moon to New moon,) T moves (in its own _Epicycle_) upwards from the Sun: And from E to I, (from New moon to Full moon) it moves downwards, toward the Sun. Again, from C to G, (from last quarter to the following first quarter,) it moves _forwards according_ to the _Annual_ motion; But from G forward to C, (from the first Quarter to the ensuing last Quarter,) it moves _contrary_ to the _Annual_ motion.

It is manifest therefore, according to this Hypothesis, that from Last quarter to First quarter (from C to G, while T is above the Line of the _Annual_ motion) its _Menstrual_ motion in its Epicycle _adds_ somewhat of Acceleration to the _Annual_ motion, and most of all at E, the New-moon: And from the first to the last quarter (from G forward to C, while T is below the Line of the _Annual_ motion,) it _abates_ of the _Annual_ motion; and most of all at I, or A the Full-moon.

So that in pursuance of _Galilæo's_ Notion, the _Menstrual_ {274} adding to or detracting from the _Annual_ motion, should either leave behinde, or cast forward, the loose waters incumbent on the Earth, (and thereby cause a Tide, or accumulation of Waters) and most of all at the Full Moon and New-moon, where those Accelerations or Retardations are greatest.

Now this _Menstrual_ motion, if nothing else were superadded to the _Annual_, would give us two Tides in a moneth, and no more; (the one upon the Acceleration, the other on the Retardation;) at New moon and Full-moon; and two Ebbs, at the two Quarters; and in the Intervals, Rising and Falling water.

But the _Diurnal_ motion superadded, doth the same to this _Menstrual_, which _Galilæo_ supposeth it to do to the _Annual_; that is, doth _Add_ to, or _Subtract_ from, the _Menstrual_ Acceleration or Retardation; and so gives us Tide upon Tide.

For in whatsoever part of its Epicycle, we suppose T to be; yet because, while by its _Menstrual_ motion the Center moves in the Circle L T N; each point in its surface, by its diurnal motion moves in the Circle L M N: whatever effect (accelerative or tardative) the _Menstrual_ would give, that effect by the _Diurnal_ is increased in the parts L M N (or rather l M n. the Semicircle) and most of all at M: but diminished in the parts N O L (or rather n O l) and most of all at O. So that at M, and O, (that is when the Moon is in the _Meridian_ below or above the _Horizon_,) we are to have the Diurnal Tide or High-water, occasioned by the greatest Acceleration or Retardation, which the _Diurnal_ Arch gives to that of the _Menstrual_: which seems to be the true cause of the _Daily Tides_. And withall gives an account, not onely why it should be _every_ day; but like wise, why at _such a time_ of the day; and why this time should in a moneth run through the whole 24 hours; _viz._ because the Moons coming to the _Meridian_ above and below the _Horizon_, (or as the Seamen call it, the _Moons Southing_, and _Northing_,) doth so: As likewise of the _Spring tides_ and _Neap-tides_. For, when it so happens, that the _Menstrual_ and _Diurnal_ Accelerations or Retardations, be coincident, (as at New moons and Full-moons they are,) the effect must needs be the greater. And although (which is not to be dissembled) this happen {275} but to one of the two Tides; that is, the Night-tide at the New-moon (when both motions do most of all Accelerate,) and the Day-tide at Full-moon (when both do most Retard the _Annual_ motion;) Yet, this tide being thus raised by two concurrent causes; though the next Tide have not the same cause also, the _Impetus_ contracted will have influence upon the next Tide; Upon a like reason, as a _Pendulum_ let fall from a higher Arch, will (though there be no new cause to occasion it) make the Vibration on the other side (beyond the Perpendicular) to be also greater: Or, of water in a broad Vessel, if it be so jogged, as to be cast forward to a good height above its Levell, will upon its recoyling, by its own gravity, (without any additional cause) mount so much the higher on the hinder part.

But here also we are to take notice, that though all parts of the Earth by its _Diurnal_ motion do turn about its Axis, and describe _parallel_ Circles; yet not _equal_ Circles; but _greater_ neer the _Æquinoctial_, and _lesser_ near the _Poles_, which may be a cause why the Tides in some parts may be much greater than in others. But this belongs to the _particular_ considerations, (of which we are not now giving an Account:) not to the _general_ Hypothesis.

Having thus endeavoured to give an account of the _Diurnal_ and _Menstrual_ Periods of Tides; It remains that I endeavour the like as to the _Annual_. Of which there is, at least, thus much agreed; That, at some times of the year, the Tides are noted to be much higher, than at other times.

But here I have a double task; _First_, to rectify the Observation; and _then_, to give an account of it.

As to the _First_; It having been observed (grosly) that those high Tides have used to happen about the _Spring_ and _Autumn_; it hath been generally taken for granted (without any more nice observation) that the _two Æquinoxes_ are the proper times, to which these _Annual high Tides_ are to be referred; And such causes sought for, as might best sute with such a Supposition.

But it is now, the best part of twenty years, since I have had frequent occasions to converse with some Inhabitants of _Rumney-marsh_ in _Kent_; where the Sea being kept out with great Earthen walls, that it do not at high water overflow the Levell; {276} and the Inhabitants livelyhood depending most on grazing, or feeding Sheep; they are (as you may believe they have reason to be) very vigilant and observant, at what times they are most in danger of having their Lands drowned. And I find them generally agreed, by their constant Observations, (and Experience dearly bought) that their times of danger are about the beginning of _February_ and of _November_; that is, at those Spring Tides which happen near those times; to which they give the names of _Candlemass-stream_ and _Allhallond-stream_; And if they scape those Spring-tides, they apprehend themselves out of Danger for the rest of the year. And as for _March_ and _September_ (the two _Æquinoxes_) they are as little solicitous of them, as of any other part of the year.

This, I confess, I much wondred at, when I first heard it; and suspected it to be but a mistake of him, that first told me, though he were indeed a person not likely so to be mistaken, in a thing wherein he was so much concerned: But I soon found, that it was not onely his, but a general observation of others too; both there, and elsewhere along the Sea coast. And though they did not pretend to know any reason of it, (nor so much as to enquire after it;) Yet none made doubt of it; but would rather laugh at any that should talk of _March_ and _September_, as being the dangerous times. And since that time, I have my self very frequently observed (both at _London_ and elsewhere, as I have had occasion), that in those months of _February_ and _November,_ (especially _November_), the Tides have run much higher, than at other times: Though I confess, I have not been so diligent to set down those Observations, as I should have done. Yet this I do particularly very well remember, that in _November_ 1660. (the same year that his Majesty returned) having occasion to go by Coach from the _Strand_ to _Westminster_, I found the Water so high in the middle of _King-street_, that it came up, not onely to the Boots, but into the Body of the Coach; and the _Pallace-yard_ (all save a little place near the _West-End_) overflow'd; as likewise the Market-place; and many other places; and their Cellars generally filled up with Water. And in _November_ last, 1665. it may yet be very well remembred, what very high Tides there were, not onely on the Coasts of _England_, (where much hurt was {277} done by it) but much more, in _Holland_, where by reason of those Inundations, many Villages and Towns were overflow'd. And though I cannot so particularly name other years, yet I can very safely say, that I very often observed Tides strangely high about those times of the year.

This Observation did for divers years cause me much to wonder, not only because it is so contrary to the received opinion of the two _Æquinoxes_; but because I could not think of any thing signal at those times of the year: as being neither the two _Æquinoxes_, nor the two _Solstices_, nor the Sun's _Apogæum_ and _Perigæum_: (or Earths _Aphelium_ and _Perihelium_;) nor indeed, at contrary times of the year, which at least, would seem to be expected. From _Alhollandtide_ to _Candlemass_ being but three months; and from thence to _Alhollandtide_ again nine months.

At length it came into my mind, about four years since, that though there do not about these times happen any _single_ signal Accident, which might cast it on these times, yet there is a _compound of two_ that may do it; Which is the _Inequality_ of the _Natural day_ (I mean that of 24. hours, from noon to noon) arising at least from a double cause; either of which singly would cast it upon other times, but both joyntly on those.

It's commonly thought, how unequal soever the length be of the _Artificial_ dayes as contradistinguished to nights, yet that the _Natural_ Days, reckoning from noon to noon, are all _equal_: But _Astronomers_ know well, that even these dayes are _unequal_.

For, this _Natural_ Day is measured _not onely_ by one intire conversion of the _Æquinoctial_, or 24. _Æquinoctial_ hours, (which is indeed taken to be performed in equal times,) _but_ increases by so much, as answers to that part of the _Sun's_ (or _Earths_,) Annual motion as is performed in that time. For, when that part of the _Æquinoctial_, which (with the _Sun_) was the _Meridian_ yesterday at noon, is come thither again to day, it is not yet _Noon_ (because the Sun is not now at the place where yesterday he was, but is gone forward about one degree, more or less) but we must stay till that place, where the _Sun_ now is, comes to the _Meridian_ before it be now _Noon_.

Now this Additament (above the 24 _Æquinoctial_ hours, or intire conversion of the _Æquinoctial_) is upon a double account {278} 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 {279} 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 {280} 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 1-1/3 of the Earths Semidiameter) would scarce be sensible (if at all) to the remoter Planets; yet as to the nearer it might.

Now though what _Galilæo_ answers to a like Objection in his _Hypothesis_; (that its possible there may be some small difference, which _Astronomers_ have not yet been so accurate, as to observe) might here perhaps serve the turn; Yet my answer is much otherwise; to wit, that such difference hath been observed and hath very much puzzeled _Astronomers_ to give an account of. About which you will find Mr. _Horrocks_ (in some of his Letters, whereof I did formerly, upon the Command of the _Royal Society_, make an _Extract_) was very much perplexed; and was fain, for want of other relief, to have recourse to somewhat like _Keplers_ amicable _Fibres_, which did according to the several positions of the Moon, accelerate or retard the Moon's motion; which _amicable Fibres_ he had no affection to at all (as there appears) if he could any other waies give account of those little inequalities; and would much rather (I doubt not) have embraced this Notion of the Common Center of Gravity, to salve the _Phænomenon_, had it come to his mind, or been suggested to him. And you find, that other _Astronomers_ have been seen to bring in (some upon one supposition, some upon another) some kind of _Menstrual Æquation_, to solve the inequalities of the Moon's motion, according to her _Synodical_ Revolution, or different Aspects (of New-moon, Full Moon, &c.) beside what concerns her own _Periodical_ motion. {281}

For which, this consideration of the _Common Center of Gravity of the Earth and Moon_, is so proper a remedy (especially if it shall be found precisely to answer those _Phænomena_, which I have not Examined, but am very apt to believe) that it is so far from being, with me, an Objection against it, that it is one of the reasons, which make me inclinable to introduce it.

I must before I leave this, add one Consideration more, That if we shall upon these Considerations think it reasonable, thus to consider the _Common Center of Gravity of the Earth and Moon_; it may as well be thought reasonable, that the like Consideration should be had of _Jupiter_ and his four _Satellites_, which according to the Complication of their several motions, will somewhat change the position of _Jupiter_, as to that _Common center of Gravity_ of all these Bodies; which yet, because of their smallness, may chance to be so little, as that, at this distance, the change of his apparent place may not be discernable. And what is said of _Jupiter_, is in the like manner to be understood of _Saturne_ and his _Satelles_, discovered by _Hugenius_: For all these _Satellites_ are to their _Principals_, as so many Moons to the Earth. And I do very well remember, in the Letters forecited, Mr. _Horrocks_ expresseth some such little inequalities in _Saturnes_ motion, of which he could not imagine what account to give, as if (to use his Expression) this crabbed _Old Saturn_ had despised his _Youth_. Which, for ought I know, might well enough have been accounted for, if at that time the _Satelles_ of _Saturn_ had been discovered, and that Mr. _Horrocks_ had thought of such a notion as the _Common Center of Gravity_ of _Saturn_ and his _Companion_, to be considerable, as to the guiding of his motion.

You have now, in obedience to your Commands, an Account of my thoughts, as to this matter, though yet immature and unpolished: What use you will please to make of them, I shall leave to your prudence, &c.

* * * * *

_An _APPENDIX_, written by way of Letter to the _Publisher_; Being an answer to some Objections, made by several Persons, to the precedent Discourse._

I Received yours; and am very well contented, that _objections_ be made against my _Hypothesis_ concerning _Tydes_: being {282} proposed but as a conjecture to be examined; and, upon that Examination, rectified, if there be occasion; or rejected, if it will not hold water.

1. To the first objection of those you mention; _That it appears not how two Bodies, that have no tye, can have one common Center of Gravity:_ that is (for so I understand the intendment of the objection) can act or be acted in the same manner, as if they were connected: I shall onely answer, that it is harder to shew _How_ they have, than _That_ they have it. That the Load-stone and Iron have somewhat equivalent to a Tye; though we see it not, yet by the effects we know. And it would be easy to shew, that two Load-stones, at once applyed, in different positions, to the same Needle, at some convenient distance, will draw it, not to point directly to either of them, but to some point between both; which point is, as to those two, the _common Center of Attraction;_ and it is the same, as if some _one_ Load-stone were in that point. Yet have these two Load stones no connection or tye, though a _Common Center of Virtue_ according to which they joyntly act. And as to the present case, _How_ the Earth and Moon are connected; I will not now undertake to shew (nor is it necessary to my purpose;) but, That there is somewhat, that doth connect them, (as much as what connects the Load-stone, and the Iron, which it draws,) is past doubt to those, who allow them to be carryed about by the Sun, as one Aggregate or Body, whose parts keep a respective position to one another: Like as _Jupiter_ with his _four Satellites_, and _Saturn_ with his _one_. Some Tye there is, that makes those _Satellites_ attend their _Lords_, and move in a Body; though we do not _See_ that Tye; nor _Hear_ the Words of Command. And so here.