An Essay of Dr. John Wallis, Exhibiting His Hypothesis about the Flux and Reflux of the Sea, Taken from the Consideration of the Common Center of Gravity of the Earth and Moon; Together with an Appendix of the Same, Containing an Answer to Some Objections, Made by Severall Persons against That Hypothesis

PHILOSOPHICAL TRANSACTIONS. Monday, August 6, 1667. The Contents. An Essay of Dr. John Wallis, exhibiting his Hypothesis about the Flux and Reflux of the Sea, taken from the Consideration of the Common Center of Gravity of the Earth and Moon; together with an Appendix of the same, containing an Answer to some Objections, made by severall Persons against that Hypothesis. Some Animadversions of the same Author upon Master Hobs's late Book, De Principiis & Ratiocinatione Geometricarum. An Essay Of Dr. John Wallis, exhibiting his Hypothesis about the Flux and Reflux of the Sea. 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 Phenomenon, taken from the Consideration of the Common Center of Gravity of the Earth and Moon. This being by several Learned Men looked 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 yourself and others concerning the Common Center of Gravity of the Earth and Moon, in order to salving the Phanomena 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 Galileo, 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 Aeon; which either by some occult quality, or or particular influence, which it hath on moist Bodies, or by some Magnetick virtue, 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 should 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 exclude the consideration of the Moon's 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 Galileo; who in his Systeme of the World, hath a particular discourse on this subject: Which, from the first time that 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 Phenomenon was to be referred to the Earth's 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 Galileo, 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 be 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. And what I say of Galileo, 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 only 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 myself, how well the Hypothesis would answer Observation: Having for divers years neglected to do it, waiting a time when I might be at leisure thoroughly 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 therupon, to be the first Inventors 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 (publicly 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 contemptible) 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 do do it; as to bring it to perfection, I cannot determine. And therefore, if as to myself any thing should humanitatis 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 yourself, 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 strangely high Tides do follow, (which yet perhaps may prove not to be so merely 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 Nuxium, 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 Autumn; or the two Equinoxes; but I have reason to believe (as well from my own Observations, for many years, as of others who have been much 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 Equinoxes. 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 hindered 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 Galileo'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 to 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. 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 Earth's 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 Earth's surface being compounded of those two motions; the Annual and Diurnal; (the Annual in B E C being, as Galileo there supposeth, about three times as fast as a diurnal motion in a great Circle, as D E F;) while a Point in the Earth's 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, 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 daytime there is abated, in the night time is added to the Annual motion, about as much as is G E, the Earth's 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 Galileo's Discourse holds well enough; But then in this it comes short; that as it gives an Account of two Tides; so those two Tides are always to be at F and D; that is, at Noon and Midnight; whereas Experience tells us, that the Time of Tides, moves in a month's 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 only as to the Quantity of the Tides; greater or less; not as to the Time of the Tides, sooner or later. *Vid. Riccioli Almagest. novum, Tom. 1. lib. 4. cap. 10. n. 111. pag. 216.* 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 Earth's 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 itself: The contrary being seen, not only 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 its motion about its 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 the 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 always turned towards us; which could not be, if the Moon carried the Earth about: Unless we should say, that it carries about the Earth in just the same Period, in which it turns 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. days, 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. Instead 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 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 straight 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 proportions; 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 $\frac{4}{5}$ or $\frac{3}{5}$ of a Semidiameter; that is about $\frac{1}{5}$ of a Semidiameter of the Earth, above its surface, in the Air, directly between the Earth and Moon. Now supposing the Earth and Moon, jointly 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 Secondary Secondary Planet, against which we were before disputing: But by the Common Center of Gravity of the Bodies, Earth and Moon, as one Aggregate. 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 but about $\frac{1}{3}$ of the whole, may well enough be here represented by a straight 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) only 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 express.) 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 Galileo's Notion, the Menstrual add- ing to or detracting from the Annual motion, should either leave behind, 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 month, 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 Galileo supposeth is to do to that Annual; that is, doth Add to, or Subtract from, the Menstrual Acceleration or Retardation; and so gives us Tide upon Tide. See For in whatsoever part of its Epicycle, we suppose Fig. 4. T to be; yet because, while by its Menstrual motion the Center moves in the Circle LTN; each point in its surface, by its diurnal motion moves in the Circle LMN: whatever effect (accelerative or tardative) the Menstrual would give, that effect by the Diurnal is increased in the parts LMN (or rather LMn. the Semicircle) and most of all at M: but diminished in the parts NOL (or rather nOl) 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 only why it should be every day; but likewise, why at such a time of the day; and why this time should in a month 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 but 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 alike 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 recouling, 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 near the Equinoctial, 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 (grossly) 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 Equinoxes are the proper times, to which these Annual high Tides are to be referred. And such causes sought for, as might best suit 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 Romney-marsh in Kent; where the Sea being kept out with great Earthen walls, that it do not at high water overflow the Hevell; 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 escape those Spring-tides, they apprehend themselves out of Danger for the rest of the year. And as for March and September (the two Equinoxes) they are as little solicitous of them, as of any other part of the year. This, I confess, I much wondered 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 only 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 myself 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 only 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 remembered, what very high Tides there were, not only on the Coasts of England, (where much hurt was done 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 Equinoxes; but because I could not think of any thing signal at those times of the year: as being neither the two Equinoxes, nor the two Solstices, nor the Sun's Apogeeum and Perigeum; (or Earths Aphelium and Perihelium;) nor indeed, at contrary times of the year, which at least, would seem to be expected. From Albollandtide to Candlemas being but three months; and from thence to Albollandtide 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 jointly on those. It's commonly thought, how unequal soever the length be of the Artificial dayes as contradistinguished to nights, yet that the Natural Day, 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 only by one entire conversion of the Equinoctial, or 24 Equinoctial 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 Earth's,) Annual motion as is performed in that time. For, when that part of the Equinoctial, which (with the Sun) was at 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 Equinoctial hours, or entire conversion of the Equinoctial) is upon a double account unequal; First, because the Sun, by reason of its Apogeeum and Perigeeum, doth not at all times of the year dispatch in one day an equal Arch of the Ecliptick; but greater Arches near the Perigeeum, which is about the middle of December; and lesser near the Apogeeum, 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 Equinoctial, 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 Equinoctial, than others, as those about the two Equinoctial points, where the Ecliptick and Equinoctial do intersect; whereupon an Arch of the Ecliptick, near the Solsticial points answers to a greater Arch of the Equinoctial, than an Arch equal thereunto near the Equinoctial points: As doth sufficiently appear by the Tables of the Sun's 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 Equinoxes 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 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 Equation of Natural daies. And therefore I think, we may with very good reason cast this Annual Period upon that cause, or rather complication plication 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 Earth's 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 Allhallontide 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 Bays and Inland-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 myself to be so well furnished with a History of Tides, as to assure myself of it; much less to accommodate it to particular places and cases. Having thus dispatched the main of what I had to say concerning cerning 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) disturb the Celestial 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 \( \frac{1}{3} \) of the Earth's Semidiameter) would scarce be sensible (if at all) to the remoter Planets; yet as to the nearer it might. Now though what Galileo 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 puzzled 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 Kepler's 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 Phenomenon, 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 Equation, 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. 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 this 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 motion 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