Philosophical Transactions of the Royal Society Part 29

1666. consonant to the like observations of _Jupiter_, made by him in _May._ 1664, and since communicated to the same _Society_; and then published in the _Transactions_, of _March._ 6. then next following. Now that the Earth hath such a motion about its own _Axis_ (whereby it might be fitted to carry about the Moon) is evident by its _Diurnal_ motion. And it seems as evident that the Moon hath not; because of the same side of the Moon alwaies turned towards us; which could not be, if the Moon carried the Earth about: Unlesse we should say, that it carries about the Earth in just the same Period, in which it turnes upon its own Axis: Which is contrary to that of the Sun carrying about the Planets: the shortest of whose Periods, is yet longer than that of the Suns moving about its own Axis. And the like of _Jupiter_, shorter than the Period of any of his _Satellites_; if at least the Period of his conversion about his Axis, lately said to be observed, prove true. (Of _Saturn_ we have not yet any Period a.s.signed; but it's likely to be shorter, than that of his _Satelles_.) And therefore we have reason to believe, not that by the Moons motion about its Axis the Earth should be carried by a contemporary Period (whereby the same face of the Moon should be ever towards us;) but that by the Earths revolution about its Axis in 24. hours, the Moon should be carried about it in about 29. dayes, without any motion on its own Axis: And accordingly, that the _Secondary_ Planets about _Jupiter_ and _Saturn_, are not (like their _Princ.i.p.als_) turned about their own Axis. And therefore I am not at all inclined to believe, that the _Menstrual_ Period of the Tides with us, is to be salved by such an Hypothesis.

In stead of this, that _Surmise_ of mine, (for I dare not yet, with confidence give it any better name,) of what I have spoken to you heretofore, (and which hath occasioned this present account which I am now giving you,) is to this purpose.

The Earth and Moon being known to be Bodies of so great connexion (whether by any Magnetick, or what other Tye, I will not determine; nor need I, as to this purpose;) as that {272} the motion of the one follows that of the other; (The Moon observing the Earth as the Center of its _period.i.c.k_ motion:) may well enough be looked upon as _one Body_, or rather _one Aggregate of Bodies_, which have _one common center of Gravity_; which Center (according to the known Laws of _Staticks_) is in a streight Line connecting their respective Centers, so divided as that its parts be in reciprocal proportion to the Gravities of the two Bodies. As for Example; Suppose the Magnitude (and therefore probably, the Gravity) of the Moon to be about an _One and fourtieth part_ of that of the Earth; (and thereabouts _Hevelius_ in his _Selenography_ page 203. doth out of _Tycho_, estimate the proportion; and an exact certainty is not necessary to our present businesse.) And the distance of the Moons Center from the Center of the Earth, to be about _fifty six Semidiameters_ of the Earth, (as thereabouts he doth there estimate it, in its middle distance; and we need not be now very accurate in determining the numbers; wherein Astronomers are not yet very well agreed.) The distance of the Common Center of Gravity of the two Bodies, will be from that of the Earth, about a two and fourtieth part of fifty six Semidiameters; that is, about 56/42 or 4/3 of a Semidiameter; that is about 1/3 of a Semidiameter of the Earth, above its surface, in the Air, directly between the Earth and Moon.

Now supposing the Earth and Moon, joyntly as one Body, carried about by the Sun in the great Orb of the _Annual_ motion; this motion is to be estimated, (according to the Laws of _Staticks_, in other cases,) by the motion of the common Center of Gravity of both Bodies. For we use in _Staticks_, to estimate a Body, or Aggregate of Bodies, to be moved upwards, downwards, or otherwise, so much as its Common Center of Gravity is so moved, howsoever the parts may change places amongst themselves.

And accordingly, the Line of the _Annual_ motion, (whether _Circular_ or _Elliptical_; of which I am not here to dispute,) will be described, not by the Center of the Earth (as we commonly estimate it, making the Earth a Primary and the Moon a Secondary Planet,) nor by the Center of the Moon, (as they would do, who make the Moon the Primary and the Earth a {273} Secondary Planet, against which we were before disputing:) But by the _Common Center of Gravity of the Bodies, Earth and Moon_, as one Aggregate.

[Sidenote: See Fig. 2. and 3.]

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.

[Ill.u.s.tration]

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 _Galilaeo's_ Notion, the _Menstrual_ {274} adding to or detracting from the _Annual_ motion, should either leave behinde, or cast forward, the loose waters inc.u.mbent on the Earth, (and thereby cause a Tide, or acc.u.mulation of Waters) and most of all at the Full Moon and New-moon, where those Accelerations or r.e.t.a.r.dations 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 r.e.t.a.r.dation;) 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 _Galilaeo_ supposeth it to do to the _Annual_; that is, doth _Add_ to, or _Subtract_ from, the _Menstrual_ Acceleration or r.e.t.a.r.dation; and so gives us Tide upon Tide.

[Ill.u.s.tration]

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 r.e.t.a.r.dation, 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 r.e.t.a.r.dations, 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 r.e.t.a.r.d 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 _aequinoctial_, 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 aequinoxes_ 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 _Candlema.s.s-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 _aequinoxes_) 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 _aequinoxes_; but because I could not think of any thing signal at those times of the year: as being neither the two _aequinoxes_, nor the two _Solstices_, nor the Sun's _Apogaeum_ and _Perigaeum_: (or Earths _Aphelium_ and _Perihelium_;) nor indeed, at contrary times of the year, which at least, would seem to be expected. From _Alhollandtide_ to _Candlema.s.s_ 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 _aequinoctial_, or 24. _aequinoctial_ 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 _aequinoctial_, 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 _aequinoctial_ hours, or intire conversion of the _aequinoctial_) is upon a double account {278} unequal. _First_, because the Sun, by reason of its _Apogaeum_ and _Perigaeum_, doth not at all times of the year dispatch in one day an equal Arch of the _Ecliptick_; but greater Arches neer the _Perigaeum_, which is about the middle of _December_; and lesser neer the _Apogaeum_, 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 _aequinoctial_, 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 _aequinoctial_, than others, as those about the two _aequinoctial_ points, where the _Ecliptick_ and _aequinoctial_ do intersect; whereupon an Arch of the _Ecliptick_, neer the _Solsticial_ points answers to a greater Arch of the _aequinoctial_, than an Arch equal thereunto neer the _aequinoctial_ 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 _aequinoxes_ 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 aequation_ 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 r.e.t.a.r.dation of the Earths _Mean_ motion, and accordingly a casting of the Waters backward or forward; either of which, will cause an Acc.u.mulation 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 a.s.sure 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 _Caelestial_ 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 _Galilaeo_ 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 r.e.t.a.r.d 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 _Phaenomenon_, 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 aequation_, 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 _Phaenomena_, 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 _Princ.i.p.als_, 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.

2. To the second objection; _That, at Chatham and in the Thames, the Annual Spring-tydes, happen about the aequinoxes; not (as this Hypothesis doth suppose elsewhere to have been observed) about the beginning of February and November._ If their meaning be, that Annual High Tydes, do then happen, and then onely: If this prove true, it will ease me of half my work. For it is then easily answered, that it depends upon the _Obliquity of the Zodiack_; the parts of the aequinoctial answering to equal parts of the {283} _Zodiack_, being neer the Solst.i.tial points greatest, and near the aequinoctial points least of all. But beside this _Annual Vicissitude of the aequinoxes_, not to say, of the 4. Cardinal Points (which my Hypothesis doth allow and a.s.sert;) I believe it will be found, that there is _another Annual vicissitude_ answering to the Suns _Apogaeum_ and _Perigaeum_. And that the greatest Tydes of all, will be found to be upon a result of these two causes Cooperating: which (as doth the Inequality of Natural dayes, depending on these same causes) will light nearer the times, I mention. To what is said to be observed at _Chatham_ and in the _Thames_, contrary to that I allege as observed in _Rumney marsh_: I must at present [Greek: apechein], and refer to a _melius inquirendum_. If those who object this contrary observation, shall, after this notice, find, upon new Observations heedfully taken, that the _Spring-tydes_ in _February_ and _November_, are not so high, as those in _March_ and _September_; I shall then think the objection very considerable. But I do very well remember, that I have seen in _November_, very high Tydes at _London_, as well as in _Rumney Marsh_.

And, the time is not yet so far past, but that it may be remembered (by your self or others then in _London_) whether in _November_ last when the Tydes were so high at _Dover_, at _Deal_, at _Margate_, and all along the Coast from thence to _Rumney Marsh_, as to do in some of those places much hurt, (and, in _Holland_, much more;) whether, I say, there were not also at the same time, at _London_, (upon the _Thames_) very high Tydes. But a good _Diary_ of the Height and time both of High-water, and Low-water, for a year or two together, even at _Chatham_, or _Greenwich_; but rather at some place in the _open_ Sea, or at the _Lands end_ in _Cornwal_, or on the _West parts of Ireland_; or at St. _h.e.l.lens_, or the _Bermodas_, &c. would do more to the resolving of this point, than any verbal discourse without it.

3. To the third Objection, _That supposing the Earth and Moon to move about a Common center of gravity; if that the highest Tydes be at the New-moon, when the moon being nearest to the Sun, the Earth is farthest from it, and its compound motion at the swiftest; and that the Tydes abate as the Earth approacheth nearer; till it comes into the supposed Circle of her Annual motion: It may be demanded, why do they not still abate as the Earth comes yet nearer to the Sun; and the_ {284} _swiftnesse of its compound motion still slackens? And so, why have we not Spring tides at the New Moon (when the motion is swiftest) and Neap tides at Full Moon (when the motion is slowest) but Spring tides at both?_ The answer (if observed) is already given in my _Hypothesis_ it self. Because the effect is indifferently to follow, either upon a suddain Acceleration, or a suddain r.e.t.a.r.dation. (Like as a loose thing, lying on a moving body; if the body be thrust suddainly forward, that loose thing is cast back, or rather left behind, not having yet obtained an equal _impetus_ with that of the body, on which it lyes; but if stopped, or notably r.e.t.a.r.ded, that loose inc.u.mbent is thrown forward, by its formerly contracted _impetus_ not yet qualified or accomodated to the slowness of the Body, on which it lyes.) Now both of these happening, the one at the New Moon, the other at the Full Moon, do cause high Tides at both.

4. To the fourth Objection, _That the highest Tydes are not at all places, about the New Moon and Full Moon; and particularly, that, in some places of the East Indies, the Highest Tydes are at the Quadratures_: I must first answer in _general_; That as to the particular varieties of Tydes in several parts of the World, I cannot pretend to give a satisfactory account, for want of a competent History of Tydes, &c. Because (as is intimated in what I wrote in the _general_) the various positions of Chanels, Bays, Promontories, Gulfs, Shallows, Currents, Trade-winds, &c.

must needs make an innumerable variety of Accidents in particular places, of which no satisfactory account is to be given from the general _Hypothesis_ (though never so true) without a due consideration of all those. Which is a task too great for me to undertake, being so ill furnished with materials for it. And then as to the particular instance of some places in the _East Indies_, where the highest Tydes are at the _Quadratures_: I suppose, it may be chiefly intended of those about _Cambaia_, and _Pegu_. At which places, beside that they are situate at the inmost parts of Vast Bayes, or Gulfs (as they are called) they have also vast In-draughts of some hundred Miles within Land; which when the Tydes are out, do lye (in a manner) quite dry: And may therefore very well be supposed to partic.i.p.ate the effect of the Menstrual Tydes many dayes after the {285} cause of them happens in the open Sea, upon a like ground as in Straights and narrow Channels the Diurnall Tydes happen some hours later than in the Ocean. And a like account must be given of particular accidents in other places, from the particular situation of those places, as _Bays_, _Chanels_, _Currents_, &c.

5. To the 5. Objection, _That the Spring-Tydes happen not, with us, just at the Full and Change, but two or three daies after_. I should with the more confidence attempt an Answer, were I certain, whether it be so in the _Open_ Seas, or onely in our Channels. For the Answers will not be the same in both cases. If onely in our Channels, where the Tydes find a large in-draught; but not in the Open Seas: we must seek the reason of it from the particular position of these places. But if it be so generally in the wide Open Seas: We must then seek a reason of it from the general Hypothesis. And, till I know the matter of Fact, I know not well, which to offer at; lest whilst I attempt to salve one, I should fall foul of the other. I know that Marriners use to speak of Spring-Tydes at the New and Full of the Moon; though I have still had a suspition that it might be some daies after, as well in the open Seas, as in our narrower Channels; (and therefore I have chosen to say, in my Papers, _About_ the New and Full, rather than _At_ the New and Full; and even when I do say _At_, I intend it in that laxer sense in which I suppose the Marriners are to be understood, for _Neer_ that time:) Of which suspition you will find some intimations even in my first Papers: But this though I can admit; yet, because I was not sure of it, I durst not build upon it. The truth is, the Flux and Reflux of water in a vessel, by reason of the jogging of it, though it follow thereupon; yet is, for the most part, discernable some time after.

For there must, upon that jog, be some time for Motion, before the Acc.u.mulation can have made a Tyde. And so I do not know but that we must allow it in all the Periods. For as the _menstrual_ High Tyde, is not (at least with us) till some Daies after the Full and Change; so is the _Diurnal_ High water, about as many Hours, after the Moons comming to South; (I mean, At Sea: for in Chanels it varies to all Hours, according as they are neerer or further from the open Sea:) And the _Annual_ High-Tydes of _November_ and _February_; somewhat later than {286} (what I conjecture to be from the same causes) the greatest Inequalities of the natural Days, happening in _January_ and _October_. But this though I can admit, yet (till I am sure of the matter of Fact) I do not build upon. And since it hath hitherto been the custome to speak with that laxness of expression; a.s.signing the times of New-moon, Full-moon, and Quadratures, with the Moons comming to South, for, what is neer those times: I did not think myself obliged in my conjectural Hypothesis (while it is yet but a _Candidate_) to speak more nicely. If the Hypothesis for the maine of it be found Rational; the Niceties of it are to be adjusted, in time, from particular Observation.

Having thus given you some Answers to the Objections you signifie to have been made by several persons to my Hypothesis, and that in the same order your Paper presents them to me; I shall next give you some account of the two _Books_, which you advised me to consult; so far as seems necessary to this business; Which, upon your intimation, I have since perused, though before I had not.

And first, as to that of _Isaac Vossius, De motu Marium & Ventorum_; Though I do not concur with him in his Hypothesis; That all the _Great motions of the Seas_, &c. should arise onely from _so small a warming of the water_ as to raise it (where most of all) _not a Foot_ in perpendicular, (as in his 12_th_ Chapter.) Or that there is no other connexion between the Moons motion, and the Tydes _menstrual_ period, than a _casual Synchronism_ (which seems to be the doctrine of his 16_th_ and 18_th_ Chapters;) Beside many other things in his Philosophy, which I cannot allow: Yet I am well enough pleased with what is Historical in it, of the matter of Fact: Especially if I may be secure, that he is therein accurate and candid, not wresting the _Phaenomena_ to his own purpose. But I find nothing in it, which doth induce me to vary from my Hypothesis. For, granting his Historicals to be all true; the account of the constant Current of the Sea Westward, and of the constant Eastern Blasts, &c. within the _Tropicks_, is much more plausibly, and (I suppose) truly rendered by _Galilaeo_ long since, from the Earths _Diurnal_ motion: (which, neare the _aequator_, describing a greater Circle, than nearer the {287} _Poles_, makes the Current to be there more conspicuous and swift, and consequently, the Eddy, or recurrent motion, nearer the Poles, where this is, more remiss:) than can easily be rendered by so small a Tumor, as he supposeth. Not to adde; that his account of the Progressive motion, which he fansieth to follow upon this Tumefaction, and by Acceleration to grow to so great a height near the Sh.o.a.r (as in Chap. 13. and 14.) is a Notion, which seems to me too extravagant to be salved by any laws of _Staticks_. And that of the Moons motion onely Synchronizing with the Tydes, casually, without any _Physical_ connexion; I can very hardly a.s.sent to. For it can hardly be imagined, that any such constant _Synchronisme_ should be in Nature; but where, either the one is the cause of the other, or both depend upon some _Common_ cause. And where we see so fair a foundation for a _Physical_ connection. I am not p.r.o.ne to ascribe it to an Independent Sychronism. In sum; His History doth well enough agree with my Hypothesis; and I think, the Phaenomena are much better salved by mine, than his.