Chapter D: E B O. A Rain-bow about the Sun, forming an entire Circle, but (3)

How abstruse a subject in Philosophy, the _Flux and Reflux of the Sea_ hath proved hitherto, and how much the same hath in all Ages perplexed the Minds even of the best of _Naturalists_, when they have attempted to render an Account of the Cause thereof, is needless here to represent. It may perhaps be to more purpose, to take notice, that all the deficiencies, found in the _Theories_ or _Hypotheses_, formerly invented for that End, have not been able to deterre the Ingenious of _this_ Age from making farther search into that Matter: Among whom that Eminent Mathematician Dr. _John Wallis_, following his happy _Genius_ for advancing reall Philosophy, hath made it a part of his later Inquiries and Studies, to contrive and deduce a certain Hypothesis concerning that _Phænomenon_, taken {264} from the Consideration of the _Common Center of Gravity of the Earth and Moon_, This being by several Learned Men lookt upon, as a very rational Notion, it was thought fit to offer it by the Press to the Publick, that other Intelligent Persons also might the more conveniently and at their leisure examine the _Conjecture_ (the Author, such is his Modesty, presenting it no otherwise) and thereupon give in their sense, and what Difficulties may occur to them about it, that so it may be either confirm'd or laid aside accordingly; As the _Proposer_ himself expressly desires in the Discourse, we now, without any more _Preamble_, are going to subjoyn, as it was by him addressed, by way of Letter, from _Oxford_ to Mr. _Boyle, April_ 25. 1666. and afterwards communicated to the _R. Society_, as follows:

You were earnest with me, when you last went from hence, that I would put in writing somewhat of that, which at divers times, these three or four years last past, I have been discoursing with your self and others concerning the _Common Center of Gravity of the Earth and Moon_, in order to salving the _Phænomena_ as well of the _Seas Ebbing and Flowing_; as of some perplexities in _Astronomical Observations_ of the _Places_ of the Celestial Bodies.

How much the World, and the great Bodies therein, are manag'd according to the _Laws of Motion_, and _Statick Principles_, and with how much more of clearness and satisfaction, many of the more abstruse _Phænomena_ have been salved on such Principles, within this last Century of years, than formerly they had been; I need not discourse to you, who are well versed in it. For, since that _Galilæo_ and (after him) _Torricellio_, and others, have applied _Mechanick_ Principles to the salving of _Philosophical_ Difficulties; _Natural Philosophy_ is well known to have been rendered more intelligible, and to have made a much greater progress in less than an hundred years, than before for many ages.

The _Seas Ebbing and Flowing_, hath so great a connexion with the _Moons_ motion, that in a manner all Philosophers (whatever other Causes they have joyned with it), have attributed much of its cause to the _Moon_, which either by some _occult quality_, {265} or _particular influence_, which it hath on moyst Bodies, or by some _Magnetick vertue_, drawing the water towards it, (which should therefore make the Water there _highest_, where the Moon is _vertical_) or by its gravity and pressure downwards upon the Terraqueous Globe (which would make it _lowest_ where the Moon is _vertical_) or by whatever other means (according to the several Conjectures of inquisitive persons,) hath so great an influence on, or at least a connexion with, the Sea's Flux and Reflux, that it would seem very unreasonable, to seclude the consideration of the Moons motion from that of the Sea: The _Periods of Tides_ (to say nothing of the greatness of them near the New moon and Full moon) so constantly waiting on the Moon's motion, that it may be well presumed, that either the one is governed by the other, or at least both from some common cause.

But the first that I know of, who took in the consideration of the _Earth's_ motion, (_Diurnal_ and _Annual_) was _Galilæo_; who in his _Systeme of the World_, hath a particular discourse on this subject: Which, from the first time I ever read it, seemed to me so very rational, that I could never be of other opinion, but that the true Account of this great _Phænomenon_ was to be referred to the Earths motion, as the _Principal_ cause of it: Yet that of the Moon (for the reasons above mentioned) not to be excluded, as to the determining the _Periods of Tides_, and other circumstances concerning them. And though it be manifest enough, that _Galilæo_, as to some particulars, was mistaken in the account which there he gives of it; yet that may be very well allowed, without any blemish to so deserving a person, or prejudice to the _main Hypothesis_: For that Discourse is to be looked upon onely as an _Essay_ of the _general Hypothesis_; which as to _particulars_ was to afterwards adjusted, from a good _General History of Tides_; which it's manifest enough that he had not; and which is in a great measure yet wanting. For were the matter of Fact well agreed on, it is not likely, that several Hypotheses should so far differ, as that one should make the Water _then_ and _there_ at the Highest, _where_ and _when_ the other makes it at the Lowest; as when the Moon is Vertical to the place. {266}

And what I say of _Galilæo_, I must in like manner desire to be understood of what I am now ready to say to you. For I do not profess to be so well skilled in the History of Tides, as that I will undertake presently to accommodate my _general Hypothesis_ to the _particular cases_; or that I will indeed undertake for the certainty of it, but onely as an _Essay_ propose it to further consideration; to stand or fall, as it shall be found to answer matter of Fact. And truly had not your importunity (which is to me a great Command) required me to do it, I should not so easily have drawn up any thing about it, till I had first satisfied my selfe, how well the Hypothesis would answer Observation: Having for divers years neglected to do it, waiting a time when I might be at leisure throughly to prosecute this design.

But there be two reasons, by which you have prevailed with me, at least to do something. _First_, because it is the common Fate of the _English_, that out of a modesty, they forbear to publish their Discoveries, till prosecuted to some good degree of certainty and perfection; yet are not so wary, but that they discourse of them freely enough to one another, and even to Strangers upon occasion; whereby others, who are more hasty and venturous, comming to hear of the notion, presently publish something of it, and would be reputed thereupon, to be the first Inventers thereof: though even that little, which they can then say of it, be perhaps much less, and more imperfect, than what the true Authors could have published long before, and what they had really made known (publikely enough, though not in print) to many others. As is well known amongst us as to the business of the _Lymphatick Vessels_ in _Anatomy_; the _Injection of Liquors into the veins of Living animals_; the _Exhibiting of a straight line equal to a crooked_; the _spot in Jupiter_, whence his motion about his own Axis may be demonstrated; and many other the like considerable Inventions.

The _other_ Reason (which, with me, is more really of weight, though even the former be not cotemptible) is, because, as I have been already for at least three or four years last past diverted from prosecuting the inquiry or perfecting the Hypothesis, as I had thoughts to do; so I do not know, but like Emergencies may divert me longer; and whether I shall ever so {267} do it, as to bring it to perfection, I cannot determine. And therefore, if as to my self any thing should _humanitus accidere_; yet possibly the notion may prove worth the preserving to be prosecuted by others, if I do it not. And therefore I shall, at least to your self, give some general account of my present imperfect and undigested thoughts.

I consider therefore, that in the Tides, or the Flux and Reflux of the Sea, besides extraordinary Extravagancies or Irregularities, whence great Inundations or strangly high Tides do follow, (which yet perhaps may prove not to be so meerly accidental as they have been thought to be, but might from the regular Laws of Motion, if well considered, be both well accounted for and even foretold;) There are these _three_ notorious Observations made of the Reciprocation of Tides. _First_, the _Diurnal_ Reciprocation; whereby twice in somewhat more than 24. hours, we have a Floud and an Ebbe; or a High-water and Low-water. _Secondly_, the _Menstrual_; whereby in one _Synodical_ period of the Moon, suppose from Full-moon to Full-moon, the Time of those Diurnal Vicissitudes doth move round through the whole compass of the [Greek: Nuchthêmeron], or Natural day of twenty four hours: As for instance, if at the Full-moon the full Sea be at such or such a place just at Noon, it shall be the next day (at the same place) somewhat before One of the clock; the day following, between One and Two; and so onward, till at the New moon it shall be at midnight; (the other Tide, which in the Full moon was at midnight, now at the New-moon coming to be at noon;) And so forward till at the next Full-moon, the Full sea shall (at the same place) come to be at Noon again: Again, That of the Spring-tides and Neap-tides (as they are called;) about the Full-moon and New-moon the Tides are at the Highest, at the Quadratures the Tides are at the Lowest: And at the times intermediate, proportionably. _Thirdly_, the _Annual_; whereby it is observed, that at sometimes of the year, the Spring-tides are yet much higher than the Spring-tides at other times of the year: Which Times are usually taken to be at the Spring and Autumne; or the two Æquinoxes; but I have reason to believe (as well from my own Observations, for many years, as of others who have been {268} much concerned to heed it, whereof more will be said by and by;) that we should rather assign the beginnings of _February_ and _November_, than the two _Æquinoxes_.

Now in order to the giving account of these three Periods, according to the _Laws of Motion_ and _Mechanick Principles_; We shall _first_ take for granted, what is now adayes pretty commonly entertained by those, who treat of such matters; _That a Body in motion is apt to continue its motion, and that in the same degree of celerity, unless hindred by some contrary Impediment_; (like as a Body at rest, to continue so, unless by some sufficient mover, put into motion:) And accordingly (which daily experience testifies) if on a Board or Table, some loose incumbent weight, be for some time moved, & have thereby contracted an _Impetus_ to motion at such a rate; if that Board or Table chance by some external obstacle, or otherwise, to be stopped or considerably retarded in its motion, the incumbent loose Body will shoot forward upon it: And contrarywise, in case that Board or Table chance to be accelerated or put forward with a considerably greater speed than before, the loose incumbent Body, (not having yet obtained an equal _Impetus_ with it) will be left behind, or seem to fly backward upon it. Or, (which is _Galilæo_'s instance,) if a broad Vessel of Water, for some time evenly carried forward with the water in it, chance to meet with a stop, or to slack its motion, the Water will dash forward and rise higher at the fore part of the Vessel: And, contrarywise, if the Vessel be suddenly put forward faster than before; the Water will dash backwards, and rise at the hinder part of the Vessel. So that an Acceleration or Retardation of the Vessel, which carries it, will cause a rising of the Water in one part, and a falling in another: (which yet, by its own weight, will again be reduced to a Level as it was before.) And consequently, supposing the Sea to be but as a loose Body, carried about with the Earth, but not so united with it, as necessarily to receive the same degree of _Impetus_ with it, as its fixed parts do: The acceleration or retardation in the motion of this or that part of the Earth, will cause (more or less, according to the proportion of it) such a dashing of the Water, or rising at one part, with a Falling at another, as is that, which we call the Flux and Reflux of the Sea. {269}

Now this premised, We are next, with him, to suppose the Earth carried about with a double motion; The one _Annual_, as (_Fig._ 1.) in B E C the great Orb, in which the Center of the Earth B, is supposed to move about the Sun A.

The other _Diurnal_, whereby the whole moves upon its own _Axis_, and each point in its surface describes a Circle, as D E F G.

It is then manifest, that if we suppose, that the Earth moved but by any one of these motions, and that regularly, (with an equal swiftness;) the Water, having once attained an equal _Impetus_ thereunto, would still hold equal pace with it; there being no occasion, from the Quickening or Slackening of the Earths motion, (in that part where the Water lyeth) for the Water thereon either to be cast Forward or fall Backward; and thereby to accumulate on the other parts of the Water: But the true motion of each part of the Earths surface being compounded of those two motions, the _Annual_ and _Diurnal_; (the _Annual_ in B E C being, as _Galilæo_ there supposeth, about three times as fast as a _diurnal_ motion in a great Circle, as D E F;) while a Point in the Earths surface moves about its Center B. from G. to D. and E. and at the same time, its Center B. be carried forwards to C; the true motion of that Point forwards, is made up of both those motions; to wit, of B to C, and of G to E; but while G moves by D to E, E moves backward by F to G, contrary to the motion of B to C; so that the true motion of E, is but the difference of B C, and E G: (for, beside the motion of B above the Center; G. is also put forward as much as from G to E; and E put backward as much as from E to G:) so that the _Diurnal_ motion, in that part of the Earth, which is next the Sun, as E F G, doth abate the progress of the _Annual_, (and most of all at F;) and in the other part, which is from the Sun, as G D E, it doth increase it, (and most of all at D.) that is, in the day time there is abated, in the night time is added to the _Annual_ motion, about as much as is G E, the Earths _Diameter_. Which would afford us a Cause of two Tides in twenty four hours; the One upon the greatest Acceleration of motion, the Other upon its greatest Retardation.

And thus far _Galilæo_'s Discourse holds well enough; But then {270} in this it comes short; that as it gives an Account of two Tides; so those two Tides are alwayes to be at F and D; that is, at _Noon_ and _Midnight_; whereas Experience tells us, that the Time of Tides, moves in a _moneths space_ through all the 24. hours. Of which he gives us no account. For though he do take notice of a Menstrual Period; yet he doth it onely as to the _Quantity_ of the Tides; greater or less; not as to the _Time_ of the _Tides_, sooner or later.

[Sidenote: * _Vid. Riccioli Almagest. novum_, Tom. 1, lib. 4. cap. 10. n. 111. pag. 216. 2.]

To help this, there is one (_Vid.* Jo. Baptista Balianus_) who makes the _Earth_ to be but a _secondary_ Planet; and to move, not directly about the Sun, but about the Moon, the Moon meanwhile moving about the Sun; in like manner as we suppose the Earth to move about the Sun, and the Moon about it.

But this, though it might furnish us with the foundation of a _Menstrual_ Period of Accelerations and Retardations in the compound motion of several parts of the Earths surface; yet I am not at all inclined to admit this as a _true Hypothesis_, for divers Reasons, which if not demonstrative, are yet so consonant to the general Systeme of the World, as that we have no good ground to disbelieve them. For 1. The Earth being undeniably the greater Body of the two (whereof there is no doubt to be made) it cannot be thought probable, that this should be carried about by the Moon, lesser than it self: The contrary being seen, not onely in the _Sun_, which is bigger than any of the Planets, which it carryes about; but in _Jupiter_, bigger than any of his _Satellites_; and _Saturne_, bigger than his. 2. As the _Sun_ by it's motion about it's own Axis, is with good reason judged to be the _Physical_ cause of the _Primary_ Planets moving about it; So there is the like reason to believe, that _Jupiter_ and _Saturne_ moving about their Axes, are the Physical cause of their _Satellites_ moving about them, which motion of _Jupiter_ hath been of late discover'd, by the help of a _fixed_ Spot discern'd in him; and we have reason to believe the like of _Saturne:_ Whether _Venus_ and _Mercury_ (about whom no _Satellites_ have been yet observed) be likewise so moved; we have not yet the like ground to determine: But we have of _Mars_; from {271} the Observations of Mr. _Hook_ made in _February_ and _March_ last, and by him communicated to the _Royal Society_, and since Printed in the _Transactions_, published _Apr._ 2. 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 assigned; 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 _Principals_) 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 _periodick_ 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.

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.

2. To the second objection; _That, at Chatham and in the Thames, the Annual Spring-tydes, happen about the Æquinoxes; 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 Æquinoctial answering to equal parts of the {283} _Zodiack_, being neer the Solstitial points greatest, and near the Æquinoctial points least of all. But beside this _Annual Vicissitude of the Æquinoxes_, not to say, of the 4. Cardinal Points (which my Hypothesis doth allow and assert;) I believe it will be found, that there is _another Annual vicissitude_ answering to the Suns _Apogæum_ and _Perigæum_. 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. _Hellens_, 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 Retardation. (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 retarded, that loose incumbent 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 participate 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.