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 Galilaeo'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 Galilaeo 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 Galilaeo'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 Galilaeo'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 Galilaeo 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 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 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 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 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 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 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 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 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 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 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 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 Solstitial 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 assert;) 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. 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.

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 Accumulation 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; assigning 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 12th 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 16th and 18th 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 Shoar (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 assent 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 prone 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.

And then as to Gassendus, in his discourse De AEstu Maris; I find him, after the relating of many other Opinions concerning the Cause of it, inclining to that of Galilaeo, ascribing it to the Acceleration & Retardation of the Earths motion, compounded of the Annual and Diurnal; And moreover attempting to give an account of the Menstrual Periods from the Earths carrying the Moon about it self, as Jupiter doth his Satellites; which together with them is carryed about by the Sun, as one Aggregate; (and that the Earth with its Moon is to be supposed in like manner to be carried about by the Sun, as one Aggregate, cannot be reasonably doubted, by those who entertain the Copernican Hypothesis, and do allow the same of Jupiter and his Satellites.) But though he would thus have the Earth and Moon looked upon as two parts of the same moved Aggregate, yet he doth still suppose (as Galilaeo had done before him) that the line of the Mean Motion of this Aggregate (or, as he calls, motus aequabilis et veluti medius) is described by the Center of the Earth (about which Center he supposeth both its own revolution to be made, and an Epicycle described by the Moons motion;) not by another Point, distinct from the Centers of both, about which, as the {288} common Center of Gravity, as well that of the Earth, as that of the Moon, are to describe several Epicycles. And, for that Reason fails of giving any clear account of this Menstrual Period. (And in like manner, he proposeth the Consideration as well of the Earths Aphelium and Perihelium as of the AEquinoctial and Solstitial Points, in order to the finding a Reason of the Annual Vicissitudes; but doth not fix upon any thing, in which himself can Acquiesce: And therefore leaves it in medio as he found it.)

It had been more agreeable to the Laws of Staticks, if he had, (as I do,) so considered the Earth and Moon as two parts of the same movable, (not so, as he doth, aliam in Centro et sequentem praecise revolutionem axis, aliam remotius ac velut in circumferentia, but,) so, as to make neither of them the Center, but both out of it, describing Epicycles about it: Like as, when a long stick thrown in the Air, whose one end is heavyer than the other, is whirled about, so as that the End, which did first fly foremost, becomes hindmost; the proper line of motion of this whole Body is not that, which is described by either End, but that, which is described by a middle point between them; about which point each end, in whirling, describes an Epicycle. And indeed, in the present case, it is not the Epicycle described by the Moon, but that, described by the Earth, which gives the Menstrual Vicissitudes of motion to the Water; which would, as to this, be the same, if the Earth so move, whether there were any Moon to move or not; nor would the Moons Motion, supposing the Earth to hold on its own course, any whit concern the motion of the Water.



But now, (after all our Physical, or Statical Considerations) the clearest Evidence for this Hypothesis (if it can be had) will be from Celestial Observations. As for instance; (see Fig. 5.) Supposing the Sun at S; the Earths place in its Annual Orb at T; and Mars (in opposition to the Sun, or near it) at M: From whence Mars should appear in the Zodiack at [gamma], and will at Full moon be seen there to be; the Moon being at C and the Earth at c; (and the like at the New-moon.) But if the Moon be in the First quarter at A, and the Earth at a: Mars will be seen, not at [gamma], but at [alpha]; too slow: And when the Moon is at B, and the Earth at b, Mars will be seen at [beta]; yet too slow: till at the {289} Full-moon, the Moon at C, the Earth at c, Mars will be seen at [gamma], its true place, as if the Earth were at T. But then, after the Full, the Moon at D, the Earth at d; Mars will be seen, not at [gamma], but at [delta], too forward: and yet more, when the Moon (at the last Quarter) is at E, the Earth at e, and Mars seen at [epsilon]. If therefore Mars (when in opposition to the Sun) be found (all other allowances being made) somewhat too backward before the Full moon, and somewhat too forward after the Full-moon, (and most of all, at the Quadratures:) it will be the best confirmation of the Hypothesis. (The like may be fitted to Mars in other positions, mutatis mutandis; and so for the other Planets.)

But this proof, is of like nature as that of the Parallaxis of the Earths Annual Orb to prove the Copernican Hypothesis. If it can be observed, it proves the Affirmative; but if it cannot be observed, it doth not convince the Negative, but only proves that the Semidiameter of the Earths Epicycle is so small as not to make any discernable Parallax. And indeed, I doubt, that will be the issue. For the Semidiameter of this Epicycle, being little more than the Semidiameter of the Earth it self, or about 1-1/3 thereof (as is conjectured, in the Hypothesis, from the Magnitudes and Distances of the Earth and Moon compared;) and there having not as yet been observed any discernable Parallax of Mars, even in his neerest position to the Earth; it is very suspicious, that here it may prove so too. And whether any of the other Planets will be more favourable in this point, I cannot say.

* * * * *

ANIMADVERSIONS of Dr. Wallis, upon Mr. Hobs's late Book, De Principiis & Ratiocinatione Geometrarum.

These were communicated by way of Letter, written in Oxford, July 24. 1666. to an Acquaintance of the Author, as follows:

Since I saw you last, I have read over Mr. Hobs's Book Contra Geometras (or De Principiis & Ratiocinatione Geometrarum) which you then shewed me. A New Book of Old matter: Containing but a Repetition of what he had before told us, more than once; and which hath been Answered long agoe.

In which, though there be Faults enough to offer ample {290} matter for a large Confutation; yet I am scarce inclined to believe, that any will bestow so much pains upon it. For, if that be true, which (in his Preface) he saith of himself, Aut solus insanio Ego, aut solus non insanio: it would either be Needless, or to no Purpose. For, by his own confession, All others, if they be not mad themselves, ought to think Him so: And therefore, as to Them a Confutation would be needless; who, its like, are well enough satisfied already: at least out of danger of being seduced. And, as to himself, it would be to no purpose. For, if He be the Mad man, it is not to be hoped that he will be convinced by Reason: Or, if All We be so; we are in no capacity to attempt it.

But there is yet another Reason, why I think it not to need a Confutation. Because what is in it, hath been sufficiently confuted already; (and, so Effectually; as that he professeth himself not to Hope, that This Age is like to give sentence for him; what ever Nondum imbuta Posteritas may do.) Nor doth there appear any Reason, why he should again Repeat it, unless he can hope, That, what was at first False, may by oft Repeating, become True.

I shall therefore, instead of a large Answer, onely give you a brief Account, what is in it; &, where it hath been already Answered.

The chief of what he hath to say, in his first 10 Chapters, against Euclids Definitions, amounts but to this, That he thinks, Euclide ought to have allowed his Point some Bigness; his Line, some Breadth; and his Surface, some Thickness.

But where in his Dialogues, pag. 151, 152. he solemnly undertakes to Demonstrate it; (for it is there, his 41th Proposition:) his Demonstration amounts to no more but this; That, unless a Line be allowed some Latitude; it is not possible that his Quadratures can be True. For finding himself reduced to these inconveniences; 1. That his Geometrical Constructions, would not consist with Arithmetical calculations, nor with what Archimedes and others have long since demonstrated: 2. That the Arch of a Circle must be allowed to be sometimes Shorter than its Chord, and sometimes longer than its Tangent: 3. That the same Straight Line must be allowed, at one place onely to Touch, and at another place to Cut the same Circle: (with others of like nature;) He findes it necessary, that these things may not seem Absurd, to allow his Lines some Breadth, (that so, as he speaks, While a Straight Line with its Out-side doth at one place {291} Touch the Circle, it may with its In-side at another place Cut it, &c.) But I shou'd sooner take this to be a Confutation of His Quadratures, than a demonstration of the Breadth of a (Mathematical) Line. Of which, see my Hobbius Heauton-timorumenus, from pag. 114. to p. 119.

And what he now Adds, being to this purpose; That though Euclid's [Greek: Semeion], which we translate, a Point, be not indeed Nomen Quanti; yet cannot this be actually represented by any thing, but what will have some Magnitude; nor can a Painter, no not Apelles himself, draw a Line so small, but that it will have some Breadth; nor can Thread be spun so Fine, but that it will have some Bigness; (pag. 2, 3, 19, 21.) is nothing to the Business; For Euclide doth not speak either of such Points, or of such Lines.

He should rather have considered of his own Expedient, pag. 11. That, when one of his (broad) Lines, passing through one of his (great) Points, is supposed to cut another Line proposed, into two equal parts; we are to understand, the Middle of the breadth of that Line, passing through the middle of that Point, to distinguish the Line given into two equal parts. And he should then have considered further, that Euclide, by a Line, means no more than what Mr. Hobs would call the middle of the breadth of his; and Euclide's Point, is but the Middle of Mr. Hobs's. And then, for the same reason, that Mr. Hobs's Middle must be said to have no Magnitude; (For else, not the whole Middle, but the Middle of the Middle, will be in the Middle: And, the Whole will not be equal to its Two Halves; but Bigger than Both, by so much as the Middle comes to:) Euclide's Lines must as well be said to have no Breadth; and his Points no Bigness.

In like manner, When Euclide and others do make the Terme or End of a Line, a Point: If this Point have Parts or Greatness, then not the Point, but the Outer-Half of this Point ends the Line, (for, that the Inner-Half of that Point is not at the End, is manifest, because the Outer-Half is beyond it:) And again, if that Outer Half have Parts also; not this, but the Outer part of it, and again the Outer part of that Outer part, (and so in infinitum.) So that, as long as Any thing of Line remains, we are not yet at the End: And consequently, if we must have passed the whole Length, before we be at the End; then that End (or Punctum terminans) has nothing of Length; (for, when the whole Length is past, there is nothing of it left.) And if Mr. Hobs tells us (as pag. 3.) that this {292} End is not Punctum, but only Signum (which he does allow non esse nomen Quanti) even this will serve our turn well enough. Euclid's [Greek: Semeion], which some Interpreters render by Signum, others have thought fit (with Tully) to call Punctum: But if Mr. Hobs like not that name, we will not contend about it. Let it be Punctum, or let it be Signum (or, if he please, he may call it Vexillum.) But then he is to remember, that this is only a Controversie in Grammar, not in Mathematicks: And his Book should have been intitled Contra Grammaticos, not, Contra Geometras. Nor is it Euclide, but Cicero, that is concern'd, in rendring the Greek [Greek: Semeion] by the Latine Punctum, not by Mr. Hobs's Signum. The Mathematician is equally content with either word.

What he saith here, Chap. 8. & 19. (and in his fifth Dial. p. 105. &c.) concerning the Angle of Contact; amounts but to thus much, That, by the Angle of Contact, he doth not mean either what Euclide calls an Angle, or any thing of that kind; (and therefore says nothing to the purpose of what was in controversie between Clavius and Peletarius, when he says, that An Angle of Contact hath some magnitude:) But, that by the Angle of Contact, he understands the Crookedness of the Arch; and in saying, the Angle of Contact hath some magnitude, his meaning is, that the Arch of a Circle hath some crookedness, or, is a crooked line: and that, of equal Arches, That is the more crooked, whose chord is shortest: which I think none will deny; (for who ever doubted, but that a circular Arch is crooked? or, that, of such Arches, equal in length, That is the more crooked, whose ends by bowing are brought nearest together?) But, why the Crookedness of an Arch, should be called an Angle of Contact, I know no other reason, but, because Mr. Hobs loves to call that Chalk, which others call Cheese. Of this see my Hobbius Heauton-timorumenus, from pag. 88. to p. 100.

What he saith here of Rations or Proportions, and their Calculus; for 8. Chapters together, (Chap. 11. &c,) is but the same for substance, what he had formerly said in his 4th. Dialogue, and elsewhere. To which you may see a full Answer, in my Hobbius Heauton-tim. from pag. 49. to p. 88. which I need not here repeat.

Onely (as a Specimen of Mr. Hobs's Candour, in Falsifications) you may by the way observe, how he deals a Demonstration of Mr. Rook's, in confutation of Mr. Hobs's Duplication of the Cube. Which when he had repeated, pag. 43. He doth then (that it might seem absurd) change those words, aequales {293} quatuor cubis DV; (pag. 43. line 33.) into these (p. 44. l. 5.) aequalia quatuor Lineis, nempe quadruplus Recta DV: And would thence perswade you, that Mr. Rook had assigned a Solide, equal to a Line. But Mr. Rook's Demonstration was clear enough without Mr. Hobse's Comment. Nor do I know any Mathematician (unless you take Mr. Hobs to be one) who thinks that a Line multiplyed by a Number will make a Square; (what ever Mr. Hobs is pleased to teach us.) But, That a Number multiplyed by a Number, may make a Square Number; and, That a Line drawn into a Line may make a Square Figure, Mr. Hobs (if he were, what he would be thought to be) might have known before now. Or, (if he had not before known it) he might have learned, (by what I shew him upon a like occasion, in my Hob. Heaut. pag. 142. 143. 144.) How to understand that language, without an Absurdity.

Just in the same manner he doth, in the next page, deal with Clavius, for having given us his words, pag. 45 l. 3. 4. Dico hanc Lineam Perpendicularem extra circulum cadere (because neither intra Circulum, nor in Peripherea;) He doth, when he would shew an errour, first make one, by falsifying his word, line 15. where instead of Lineam Perpendicularem, he substitutes Punctum A. As if Euclide or Clavius had denyed the Point A. (the utmost point of the Radius,) to be in the Circumference: Or, as if Mr. Hobs, by proving the Point A. to be in the Circumference, had thereby proved, that the Perpendicular Tangent A E had also lyen in the Circumference of the Circle. But this is a Trade, which Mr. Hobs doth drive so often, as if he were as well faulty in his Morals, as in his Mathematicks.

The Quadrature of a Circle, which here he gives us, Chap. 20. 21. 23. is one of those Twelve of his, which in my Hobbius Heauton-timorumenus (from pag. 104. to pag. 119) are already confuted: And is the Ninth in order (as I there rank them) which is particularly considered, pag. 106. 107. 108. I call it One, because he takes it so to be; though it might as well be called Two. For, as there, so here, it consisteth of Two branches, which are Both false; and each overthrow the other. For if the Arch of a Quadrant be equal to the Aggregate of the Semidiameter and of the Tangent of 30. Degrees, (as he would Here have it, in Chap. 20. and There, in the close of Prop. 27;) Then is it not equal to that Line, Whose Square is equal to Ten squares of the Semiradius, (as, There, he would have it, in Prop. 28. and, Here, in Chap. 23.) And if it be equal to This, then not to That. For This, and That, are not equal: As I then demonstrated; and need not now repeat it.

The grand Fault of his Demonstration (Chap. 20.) wherewith he would now New vamp his old false quadrature, lyes in those Words Page 49. line 30, 31. Quod Impossibile est nisi ba transeat per c. which is no impossibility at all. For though he first bid us draw the Line R c, and afterwards the Line R d; Yet, Because he hath no where proved (nor is it true) that these two are the same Line; (that is, that the point d lyes in the Line R c, or that R c passeth through d:) His proving that R d cuts off from ab a Line equal to the Sine of R c, doth not prove, that ab passeth through c: For this it may well do though ab lye under c. (vid. in case d lye beyond the line R c. that is, further from A:) And therefore, unless he first prove (which he cannot do) that A c ( a sixth part of A D) doth just reach to the line R c and no further, he only proves {294} that a sixth part of ab is equal to the Sine of B c. But, whether it lye above it, or below it, or (as Mr. Hobs would have it) just upon it; this argument doth not conclude. (And therefore Hugenius's assertion, which Mr. Hobs, Chap. 21. would have give way to this Demonstration, doth, notwithstanding this, remain safe enough.)

His demonstration of Chap. 23. (where he would prove, that the aggregate of the Radius and of the Tangent of 30. Degrees is equal to a Line, whose square is equal to 10 Squares of the Semiradius;) is confuted not only by me, (in the place forecited, where this is proved to be impossible;) but by himself also, in this same Chap. pag. 59. (where he proves sufficiently and doth confesse, that this demonstration, and the 47. Prop. of the first of Euclide, cannot be both true.) But, (which is worst of all;) whether Euclid's Proposition be False or True, his demonstration must needs be False. for he is in this Dilemma: If that Proposition be True, his demonstration is False, for he grants that they cannot be both True, page 59 line 21. 22. And again, if that Proposition be False, his Demonstration is so too; for This depends upon That, page 55. line 22. and therefore must fall with it.

But the Fault is obvious in His Demonstration (not in Euclid's Proposition:) the grand Fault of it (though there are more) lyes in those words, page 56. line 26. Erit ergo M O minus quam M R Where, instead of minus, he should have said majus. And when he hath mended that Error, he will find, that the major in page 56. line penult, will very well agree with majorem in page 57. line 4 (where the Printer hath already mended the Fault to his hand) and then the Falsum ergo will vanish.

His Section of an Angle in ratione data, Chap. 22 hath no other foundation, than his supposed Quadrature of Chap. 20. And therefore, that being false, this must fall with it. It is just the same with that of his 6. Dialogue, Prop. 46. which (besides that it wants a foundation) how absurd it is, I have already shewed, in my Hobbius Heauton-timor. page 119. 120.

His Appendix, wherein he undertakes to shew a Method of finding any number of mean Proportionals, between two Lines given: Depends upon the supposed Truth of his 22. Chapter; about Dividing an Arch in any proportion given: (As himself professeth: and as is evident by the Construction; which supposeth such a Section.) And therefore, that failing, this falls with it.

And yet this is other wise faulty, though that should be supposed True. For, In the first Demonstration; page 67. line 12. Producta L f incidet in I; is not proved, nor doth it follow from his Quoniam igitur.

In the second Demonstration; page 68. line 34. 35. Recta L f incidit in x; is not proved; nor doth it follow from his Quare.

In his third Demonstration; page 71: line 7. Producta Y P transibit per M; is said gratis; nor is any proof offered for it. And so this whole structure falls to the ground. And withall, the Prop. 47. El. 1 doth still stand fast (which he tells us, page 59, 61, 78. must have Fallen, if his Demonstrations had stood:) And so, Geometry and Arithmetick do still agree, which (he tells us, page 78: line 10.) had otherwise been at odds.

And this (though much more might have been said,) is as much as need to be said against that Piece.

* * * * *

Printed with Licence for John Martyn, and James Allestry, Printers to the Royal Society.

{295}

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Num. 17.

PHILOSOPHICAL TRANSACTIONS.

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Munday, Septemb. 9. 1666.

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The Contents.

Observations made in several places (at London, Madrid and Paris,) of the late Eclipse of the Sun, which hapned June 22. 1666. Some Enquiries and Directions, concerning Tides, proposed by Dr. Wallis. Considerations and Enquiries touching the same Argument, suggested by Sir Robert Moray. An Account of several Books lately publish't: Vid. 1. Johannis Hevelii Descriptio Cometae, A. 1665. exorti; una cum Mantissa Prodromi Cometici. 2. Isaacus Vossius de Nili & aliorum Fluminum Origine. 3. Le Discernement du Corps & de l'Ame, par Monsieur de Cordemoy.

* * * * *

Observations made in several places, Of the late Eclipse of the Sun, which hapned on the 22 of June, 1666.

The Observations that were made at London by Mr. Willughby, Dr. Pope, Mr. Hook, and Mr. Philips, are these:

The Eclipse began at 5h. 43' h. ' { 3/11 diam. at 6. 00 5 dig. at 7. 06 { 4 digits at 6. 07 4 dig. at 7. 13 It was { 5 dig. at 6. 13 3 dig. at 7. 20 darkned,{ 6 dig. at 6. 21 2 dig. at 7. 26 { 7 dig. at 6. 391/2 1 dig. at 7. 32 { 6 dig. at 6. 57 0 dig. at 7. 37

Its Duration hence appears to have been one hour and 54 m. Its greatest Obscurity somewhat more than 7. digits. About the middle, between the Perpendicular and Westward Horizontal Radius the Sun, viewing it through Mr. Boyle's 60. foot-Telescope, there was perceived a little of the Limb of the Moon without the Diske of the Sun: which seemed to some of the Observers to come from some shining Atmosphere about the Body either of the Sun or Moon.

They affirm to have observ'd the Figure of this Eclipse, and measured the {296} Digits, by casting the Figure through a 5 foot Telescope, on an extended paper, fix't at a certain distance from the Eye-glasse, and having a round figure; all whose Diameters were divided, by 6 Concentrick Circles, into 12 Digits.



The Observations made at Madrid by a Noble Member of the Royal Society, His Excellence the Earle of Sandwich, as they were sent to the Right Honourable, the Lord Vice-Count Brounker, are these;

The Eclipse began at Madrid about 5 of the Clock in the morning, at 5 h. 15', the Suns Altitude was 6 deg. 55'.

The Middle of it was at 6 h. 2', the Suns Altitude, 15. deg. 5'.

The End was exactly at 7 h. 5'; the Suns Altitude, 25. deg. 24'.

The Duration, 2h. 4'.

37. Parts of the Suns diameter remained light.

63. Parts of the same were darkened.



The Observations made at Paris by Monsieur Payen, assisted by several Astronomers, as they were printed in French, and addressed to Monsieur de Montmor, are these;

The Eclipse began there, at 5 h. 44'. 52". mane. It ended at 7 h. 43'. 6". So that its whole Duration was 1 h. 58'. 14". The greatest Obscuration they assign to have been 7. dig. 50. m. but they adde, that it seem'd to have been greater by 3 minuts; which M. Payen imputes to a particular motion of libration of the Suns Globe, which entertain'd that Luminary in the same Phasis for the space of 8. min. and some seconds, as if it had been stopped in the midst of its Course; rather than to a tremulous Motion of the Atmosphere, as Scheiner would have it.

They intimate that they took the time of each Phasis from half digit to half digit, as well by a Pendulum, as by the Altitudes of the Suns Center above the Horizon, corrected by the Verticall Paralaxes and AEstivall Refractions, by which they judged, that though the Time by the Pendulum may be sufficient for Mechanicall Operations, yet 'tis not exact enough for establishing the Grounds of true Astronomy.

They further conceive that the apparent Diameters were almost equal; seeing that in the Phasis of 6. Digits, the Circumference of the Moons disk passed through the Center of that of the Sun, so as that two Lines drawn through the two Horns of the Sun, made with the Common Semi-diameter two Equilateral Triangles.

Next, they affirm, That there was so great a Variation in the Parallaxes, by reason as well of the Refractions of the Air, which environs the Earth, as of the Alteration of the Air, which encompasses the Moon, that the Horns of the Sun, there formed by the Shaddow of the Moon, appeared in all kinds of Figures; Sometimes inclined to the Vertical, sometimes Perpendicular to the Horizon, and at last Parallel; the Convexe part respecting the Heaven, and the Concave, the Horizon. By the crossing (so they go on) of the {297} Horns with the Angles of Inclination, it will be easie to those, that have exactly observed them, and that are skill'd in the higher Astronomical Calculations, to compute the true Place of the Moon in her Orbite, that so it may be compared with that of the Tables, and with that, which has been observ'd in other places, for the more precise determinating of the Difference of Meridians (that being the way, esteem'd by Kepler the most certain) and for making a good Judgment of the defect or exactnesse of the Celestial Tables.

Then they observe, That the Beginning and the Middle of this Eclipse hapned to be in the North Eastern Hemisphere, and the End, in the South-Eastern. The first Contact (as 'twere) of the two Disks was observ'd in the Superior Limb of the Suns Disk in respect to the Vertical Line, and in the Inferior in respect to the Ecliptick: But the Middle, and the End were seen in the Superior Limb, in respect both to the Vertical and the Ecliptick: And (what to this Author seems extraordinary) both the Beginning and the End of this Eclipse hapned to be in the Oriental part of the Suns Disk.

Lastly, they take notice, that by their Observations it appears, that there is but little exactness in all the Astronomical Tables, predicting the Quantity, Beginning and Duration of this Eclipse; Those of Lansbergius importing, That the Obscuration should be of 10. dig. 48'; those of Ricciolo, of 9. dig. 1'; and those of Kepler, of 7. dig. 30'. 16": Again, that the Duration should be of 2h. 2'. Lastly, The Beginning did anticipate the Ricciolan Tables by 5 minuts, the End by 23; and the Middle, almost by 11. In the mean time the Author notes, that the Rudolphin Tables come nearest to the Truth; and withal assures the Reader of the goodnesse of the Instruments employed in his Observations, and of the singular care, he, together with his skilful Assistants, took in making them.

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Some Inquiries and Directions concerning Tides, proposed by Dr. Wallis, for the proving, or disproving of his lately publish't Discourse concerning them.

The Inquisitive Dr. Wallis, having in his lately printed Hypothesis of Tides intimated, that he had reason to believe, that the Annual Spring-tides happen to be rather about the beginnings of Febr. and Nov. than the two AEquinoxes, doth in a late Letter to the Publisher, written from Oxford in Aug. last, desire, that some understanding Persons at London, or Greenwich, but rather nearer the Sea, or upon the Sea-shore, would make particular Observation of all the Spring-Tides (New-Moon and Full-Moon) between this and the End of November; and take account of the Hour, and of the Perpendicular height: that we may see, whether those in September, or those of November be highest: And it were not amiss, the Low waters were observed too. Which may be easily done by a mark made upon any standing Post in the Water, by any {298} Water-man, or other understanding Person, who dwells by the Water-side.

It would also deserve (thinks he) to be inquired into, whether, when the Tides be highest, the Ebbs be ever lowest, & contra; (which is generally affirmed, and almost put out of question) or rather (which sutes best with this Hypothesis) whether, when the Tides are highest, both in the Annual and Menstrual Periods, the Low waters be not also highest; and at Neap Tides, the Ebbes also very low.

He adds, that he should expect, that the Spring Tides now coming, and those at the beginning of September, should not be so high, as those at the middle of September; and then lower again at the beginning of October, and after that, higher at the middle of October, and higher yet about the beginning of November (at the usual times of Spring-tides after the New and Full.)

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Considerations and Enquiries concerning Tides, by Sir Robert Moray; likewise for a further search into Dr. Wallis's newly publish't Hypothesis.

In regard that the High and Low waters are observed to increase, and decrease regularly at several seasons, according to the Moons age, so as, about the New and Full Moon, or within two or three daies after, in the Western parts of Europe, the Tides are at the highest, and about the Quarter-Moons, at the lowest, (the former call'd Spring-tides, the other Neap-tides;) and that according to the height and excesses of the Tides, the Ebbes in opposition are answerable to them, the heighest Tide having the lowest Ebbe, and the lowest Ebbe, the highest Tide; the Tides from the Quarter to the highest Spring-tide increasing in a certain proportion; and from the Spring tide to the Quarter-tide decreasing in like proportion, as is supposed: And also the Ebbes rising and falling constantly after the same manner: It is wished, that it may be inquired, in what proportion these Increases and Decreases, Risings and Fallings happen to be in regard of one another?

And 'tis supposed, upon some Observations, made in fit places, by the above-mentioned Gentleman, though, (as himself acknowledges) not thoroughly and exactly performed, that the Increase of the Tides is made in the Proportion of Sines; the first Increase exceeding the lowest in a small proportion; the next in a greater; the third greater than that; and so on to the mid-most, whereof the excess is greatest, diminishing again from that, to the highest Spring-Tide; so as the proportions, before and after the Middle, do greatly answer one another, or seem to do so. And likewise, from the highest Spring-tide, to the lowest Neap-tide, the Decreases seem to keep the like proportions; the Ebbes rising and falling in like manner and in like proportions. All which is supposed to fall out, when no Wind or other Accident causes an alteration. {299}

And whereas 'tis observed, that upon the main Sea-shore the Current of the Ebbings and Flowings is sometimes swifter, and sometimes slacker, than at others, so as in the beginning of the Floud the Tide moves faster but in a small degree, increasing its swiftness constantly till towards the Middle of the Floud; and then decreasing in velocity again from the Middle till to the top of the High water; it is supposed, that in Equal spaces of Time, the Increase and Decrease of velocity, and consequently the degrees of the Risings and Fallings of the same, in Equal spaces of time, are performed according to the Proportion of Sines.

But 'tis withall conceived, that the said Proportion cannot hold exactly and precisely, in regard of the Inequalities, that fall out in the Periods of the Tides, which are commonly observed and believed to follow certain Positions of the Moon in regard of the Equinox, which are known not to keep a precise and constant Course: so that, there not intervening equal portions of Time between one New Moon and another, the Moons return to the same Meridian, cannot be alwaies perform'd in the same Time; and consequently there must be a like Variation of the Tides in the Velocity, and in the Risings and Fallings of the Tides, as to equal spaces of time. And the Tides from New-moon to New-moon being not alwaies the same in number, as sometimes but 57, sometimes 58, and sometimes 59, (without any certain order of succession) is another evidence of the difficulty of reducing this to any great exactness. Yet, because 'tis worth while, to learn as much of it, as may be, the Proposer and many others do desire, That Observations be constantly made of all these Particulars for some Months, and, if it may be, years together. And because such Observations will be the more easily and exactly made, where the Tides rise highest, it is presumed, that a fit Apparatus being made for the purpose, they may be made about Bristol or Cheap-stow, best of any places in England, because the Tides are said thereabout to rise to ten or twelve fathoms; as upon the coast of Britanny in France, they do to thirteen and fourteen.

In order to which, this following Apparatus is proposed to be made use of. In some convenient place upon a Wall, Rock, or Bridge, &c. let there be an Observatory standing, as neer as may be to the brink of the Sea, or upon some wall; and if it cannot be well placed just where the Low water is, there may be a Channel cut from the Low water to the bottom of the Wall, Rock, &c. The Observatory is to be raised above the High water 18. or 20. foot; and a Pump, of any reasonable dimension, placed perpendicularly by the Wall, reaching above the High water as high as conveniently may be. Upon the top of the Pump a Pulley is to be fastned, for letting down into the Pump a piece of floating wood, which, as the water comes in, may rise and fall with it. And because the rising and falling of the water amounts to 60. or 70. foot, the Counterpoise of the weight, that goes into the Pump, is to hang upon as many Pulleys, as may serve to make it rise & fall within the space, by which the height of the Pump exceeds the height of the Water. And because by {300} this means the Counterpoise will rise and fall slower; and consequently by less proportions, than the weight it self, the first Pulley may have upon it a Wheele or two, to turn Indexes at any proportion required, so as to give the minute parts of the motion, and degrees of risings and fallings. All which is to be observed by Pendulum-watches, that have Minutes and Seconds, with Checks, according to Mr. Hugens's way.

And because if the Hole, by which the water is let into the Pump, be as large as the Bore of the Pump it self, the weight that is raised by the water, will rise and fall with an Undulalation, according to the inequality of the Sea's Surface, 'twill therefore be fit, that the Hole, by which the water enters, be less than half as bigg as the Bore of the Pump; any inconvenience that may follow thereupon, as to the Periods and Stations of the Floud and Ebb, not being considerable.

And to the end, that it may appear the better; what are the particular Observations, desired to be made, near Bristol or Cheap-stow bridg, it was thought not amiss, to set them down distinctly by themselves.

1. The degrees of the Rising and Falling of the water every quarter of an hour (or as often as conveniently may be) from the Periods of the Tides and Ebbs; to be observed night and day, for 2 or 3 months.

2. The degrees of the velocity of the Motion of the Water every quarter of an hour for some whole Tides together; to be observed by a second Pendul-watch: and a logg fastened to a line of some 50 fathoms, wound about a wheel.

3. The exact measures of the Heights of every utmost High-water and Low-water, from one Spring-tide to another, for some Months or rather Years.

4. The exact Heights of Spring-tides and Spring-Ebbs for some Years together.

5. The Position of the Wind at every observation of the Tides; and the times of its Changes; and the degrees of its Strength.

6. The State of the Weather, as to Rain, Hail, Mist, Haziness, &c, and the times of its Changes.

7. At the times of observation of the Tides, the height of the Thermometer; the height of the Baroscope; the height of the Hygroscope; the Age of the Moon, and her Azimuths; and her place in all respects; And lastly the Sun's place; all these to minutes.

And it would be convenient, to keep Journal Tables, for all these Observations, each answering to its day of the Month.

For the Apparatus of all these observations, there will be particularly necessary.

A good Pendulum-watch.

A Vane shewing Azimuths to minute parts.

An Intrument to measure the Strength of the Winde.

A large and good needle shewing Azimuths to degrees. {301}

Thermometers, Barometers, Hygroscopes.

These Observations being thought very considerable as well as curious, 'tis hoped, that those who have conveniency, will give encouragement and assistance for the making of them; and withall oblige the publick by imparting, what they shall have observed of this kind: The Publisher intending, that when ever such observations shall be communicated to him, he will give notice of it to the publick, and take care of the improvement thereof to the best use and advantage. A Pattern of the Table, proposed to be made for observing the Tides, is intended to be published the next opportunity, God permitting.

* * * * *

An Account of Several Books lately published

I. Johannis Hevelii DESCRIPTIO COMETAE, Anno AErae Christianae MDCLXV. exorti; una cum MANTISSA Prodromi Cometici, Observationes omnes prioris COMETAE MDCLIV, ex iisque genuinum motum accurate deductum, cum Notis & Animadversionibus, exhibens.

This Book (as the Title it self intimates) undertakes two things. First, To give an Account of the Second of the two late Comets, which appeared, when the other was scarce extinct; Concerning which, the Author doth, from the Observations made by himself with a Sextant of 6 foot, and divided into minutes and seconds, assign both its true place (as well in respect of the Ecliptick as the AEquator) and its proper motion; Adding a fair Delineation of its Course, together with the genuine Representations of its Head and Train, in each day of its apparition; and subjoyning a General Description and Discourse of some of the more notable Phenomena thereof. It was first seen at Dantzick by the Watchmen, the 5th of April st. n. 1665. and then observed by the Author from April 6, about 11/2 of the Clock in the morning, till April 20 at 3. in the morning. During which time, it went with a reasonable velocity; making 46 deg. in its Orb, according to the Order of the Signs, moving from the Breast of Pegasus, towards the Head of Andromeda, and the Left Horn of Aries; having, as 'tis presumed, taken its rise from above Sagittary, and run through the Breast of Antinous, under Aquila and the Dolphin, to the said Pegasus; and so on, as is already expressed.

The Head of it is in the Book described of a Colour like that of Jupiter, all along much brighter than that of the former Comet, though of a somewhat less magnitude; having in its middle onely one round, but very bright and big Kernel or Speck, resplendent like Gold, and encompassed with another more dilute and seemingly uniform matter: its Tail being at first, about 17. deg. and afterwards 20. and sometimes 25 deg. long, and divaricated towards the End.

Next, it is observed, that though this Star did afterwards slacken its pace, yet it retained the vividness of its Colour, both of the Head and Train; the Head especially, keeping at the time as well of the last observations, as of the {302} first, the brightness of its single kernel, though the environing more dilute matter were then almost all lost; it being, according to the Author, more and more attenuated, and grown narrow, the nearer the Star approached to the Sun.

Thirdly, 'tis noted, That this Comet did very much digress from the Hypothesis, delivered by M. Auzout, in regard that, whereas according to that Hypothesis, this Star should not arrive to the Ecliptick till after the space of 3 months, it arrived there the 28 of April. And then, that its first Conjunction with the Sun hapned between the 19 and 20 of April, and the second, the last of April, not (as M. Auzout, would have it) the 15 of May. So that he concludes, that this Comet never came down to the Pleiads and the Eye of Taurus, as the Hypothesis of M. Auzout requires, but that from April 20. it did immediately take its course towards the Ecliptick, deflecting every day more and more from the Section of a Great Circle, to the Lucida of Aries, arriving at the Ecliptick the last of April, about the 8th or 10th deg. of Taurus; not in July about the 8th of Gemini, and the Eye of Taurus.

Fourthly, He intimates, that if this Comet had appeared some weeks sooner, it would have confronted the former Comet, being yet in its vigour and of a conspicuous bigness, in the same place, where that was, viz. the Head of Aries.

Fifthly, He observes, that this Star in progress of time became Retrograde, whence it came to pass, that in the Months of June and July it did not appear again before the Rising of the Sun, though the Sun left it far behind: whereas, if it had proceeded toward the Eye of Taurus, it would have appeared again in the morning.

Sixthly, He maintains, that this Comet was not the same with the former; which he thinks may be demonstrated, onely by a due Delineation of both their Course upon the Globe; where he saith it to be evident, that the former could never come to the Head of Pegasus, as moving already in February in a streight Course about the Head of Aries; Besides, that the former went in the very beginning in a Retrograde motion; but this perpetually in a direct one: that, about the end, very slow, its Head lessning and growing dark; this swift enough, with its head conspicuous and bright. To which he adds, that the whole Course of the former was made under a quite different Angle of the Orbite and Ecliptick, and a different Motion of the Nodes from the latter: As also that their Faces differed very much from one another; the first exhibiting all along a matter, which as to its density and rarity, altered from day to day exceedingly, whereas the second retained (to the Authors admiration, who affirms, never to have observed the like) all the time he saw it, one and the same round, dense and bright Speck or Kernel.

All which he concludes 1, With an Intimation of his sense concerning two other Comets, pretended to have been lately seen, One at Rome, about the {303} Girdle of Andromeda, in the Months of February and March, 1664. the other in Germany in Capricorne, about Saturne in the head of Sagittary, during the Months of September and October, 1665. 2ly, With an Advertisement of what he has done in that important Work for the Advancement of Astronomy, the due Restitution of the Fixt Stars, vid. That he has almost finish't it; himself alone, without trusting to any other mans labour, that was not directed by him.

The Second Part of this Book (the Mantissa to the Prodromus Cometicus) endeavours to justifie the Authors Observations touching the former Comet, excepted against by M. Auzout, in several particulars; as 1. That it had not pass'd to the First, but Second Star in Aries, and had mov'd in quite another Line, than He had described. 2. That its proper motion about the end of January and the beginning of February, 1665. had not been rightly assigned. 3. That the Bignesse of its Diameter had not been truly delivered; Nor 4. The Faces of its Head in due manner represented.

To all which the Author endeavors to answer: 1. By delivering all his Observations of that Comet, thereby to shew, what care and diligence he had used, particularly to make out, how great its Diurnal motion had been; in what proportion, and how far, it decreased, and where and in what degree it increased again: Which being, as he conceives, duly and exactly deduced, and demonstrated, he esteems it afterwards to be easie for every one, versed in these matters, certainly to collect and to judge, what way the Comet, after it became invisible to the naked Eye, and could be no longer observed with Sextants and Quadrants, had taken, and what Line it had described. 2, By subjecting all those Observations, with great diligence and labour, to a rigid Calculus, thereby to obtain, for every day, the Longitudes, Latitudes, Right Ascensions, Declinations, Proper motion, Angle of the Ecliptick and the AEquator, and the Nodes of that Comet; for the construction of an Ephemerides of its whole Motion. From all which he pretends to prove, that he has not erred in his Observation of February 18, nor been prepossest by any Hypothesis, nor deluded by any Fixt Star, as M. Auzout thinketh; but that near the First Star of Aries there then appear'd a Phaenomenon, most like to that Comet, that was seen some dayes before, if compared with the Observations make thereof Febr. 12, 13, 14. Though he will not hitherto positively determine, whether that Phaenomenon, which appear'd to him February 18. was {304} indeed that very Comet, which he saw with his naked Eye, and observed with his Geometrical Instruments, the said 12, 13, and 14. dayes of February; or whether it was another, and whether he had lost that Comet, which moved towards the Second Star in Aries: but leaves it to the Learned World, and particularly to the Royal Society, after they shall have well examined and considered all his Observations, and the Calculus raised therefrom, to judge of this, and the other particulars in controversie.



II. Isaacus Vossius de NILI et ALIORUM FLUMINUM ORIGINE. It was Numb. 14. of these Transactions, that gave an account of the Cause of the Inundation of the Nile, as it was rendred by Monsieur de la Chambre: This is to give you another, not only of the Inundation, but also of the Origine of that, and of other Rivers, as it is delivered by Monsieur Isaac Vossius, who undertakes in this Book to shew;

1. That those Subterraneous Channels, through which several Philosophers teach, that the Sea discharges it self into the Rivers, are not only imaginary, but useless, in regard 'tis impossible for the water to rise from the Subterraneous places up to the Mountains, where commonly the Sources of Rivers are.

2. He explicates, why, if a Pipe be put into a Bason full of Water, the water is seen more raised in the Pipe, than in the Bason, and rises higher according as the Pipe is narrower; On the contrary, if the same Pipe be put into a Bason full of Quicksilver, the Quicksilver stayes lower in the Pipe, than in the Bason. The reason, which he renders hereof, is, That as the Water sticks easily to all it touches, it is sustain'd by the sides of the narrow Pipe wherein it is included: And indeed, if the Pipe be quite drawn out of the Water, the Water doth not all fall out, but so much of it remains, as the sides of the Pipe could sustaine: Whence it is, that the Water which is kept up by the Walls of the Tube, weighing no longer upon that which is in the Bason, is thrust upwards, and keeps it self raised above its Levell; but the Quicksilver not adhering so easily, as Water, to Bodies it touches, is not sustained by the sides of the Tube, and so mounts not above its Levell, but rather descends below it, because the Pipe, which is streight, hinders the endeavor that is in the Mercury to rise to its Level. He adds, that this Observation makes nothing for the Explication of the Origine of Rivers; because, though it be true, that the Water {305} by this means rises above its Levell, yet it does never run out at the top of the Pipe. Having said this, he answers to the other Arguments, commonly alledged to maintain this Opinion.

3. He pretends, that all Rivers proceed from a Colluvies or Rendevous of Rain-waters, and that, as the Water, that falls upon Hills, gathers more easily together, than that which falls in Plaines, therefore it is, that Rivers ordinarily take their Source from Hills. Thence also comes it (saies he) that there are more Rivers, than Torrents, in the Temperate Zones; and, on the contrary, more Torrents, than Rivers, in the Torrid Zone: For, as in hot Climats the Mountains are far higher, the Water, that descends from them with impetuosity, runs away in a little while, and formes such Collections of Water, as soon dry up, but in cold Climats, the Waters do not run away but slowly, and are renew'd and recruited by Rain, before they are quite dryed up; because the Hills are there lower, and so the Bed of Rivers hath lesse declivity.

Having thus discoursed of Rivers in General, he treats of the Nile in particular; and there

1. Observes, That the Order of the Seasons of the Year is quite inverted under the Torrid Zone. For, whereas it should be then Summer, when the Sun is near; and Winter, when the Sun is farther off: Under the Torrid Zone 'tis never lesse hot, than when the Sun is nearest; nor more hot, than when the Sun is farthest off: So that to the people that live between the AEquinoctial and the Tropicks, Summer begins about Christmass, and their Winter, about St. Johns day. The reason whereof is, (saith he) that when the Sun is directly over their Heads, it raises abundance of vapors, and draws them so high, that they are presently converted into Water by the coldnesse of the Air; whence it comes to passe, that then it rains continually, which does refresh the Air; but when the Sun is farther off, there falls no more rain, and so the Heat becomes insupportable.

2. He proves by many recent Relations, that the Sources of the Nile are on this side of the AEquinoctial in AEthiopia, of which he gives a very accurate Mappe, correcting many faults which Geographers are wont to commit in the Description of the Kingdom of the Abyssins, which they believe to be much greater than indeed it is. {306}

3. This supposed, he easily gives an account, why the Nile yearly overflows about the end of June: For, as at that time there falls much rain in AEthiopia, it must needs be, that the Nile, whose source is in that Country, should then overflow, when those rains begin, and subside, when they cease.

There are besides, in this Book, two other Tracts. In the first, M. Vossins endeavours to maintain the Doctrine, he had deliver'd in his Book De Lumine, and to shew, that the Soul of Animals is nothing but Fire, that there are no invisible Atoms; nor so much as any Pores, even in the Skin of man. Here he treats also of Refractions, and alledges the Examples of several persons, who have then seen the Sun by the means of Refraction, when really He was under the Horizon.