Chapter 25

What is added, of the Manner of planting the _Sets_; of Dressing, Pruning, and Governing the Plantation; of the Ordering and Cultivating the Vine-yard after the first four years, till it needs renewing; as also of the _manner_ and _time_, how and when to manure the Vine-yard, with Compost, will be better understood from the Book it self, than can be here described; the Author pretending, that, those few observations of his, as the native production of his own Experience, being practised with care, the Vine-yards in _England_ may be planted, govern'd and perpetuated with undoubted success; and offering withall to furnish those, that have a desire to renew this Culture, and to store their grounds with _Sets_ and _Plants_ of all those sorts, which he recommends; he having a plentiful _stock_ of them all.

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Printed with Licence for _John Martyn_, and _James Allestry_, Printers to the Royal Society. 1666.

{263}

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_Num._ 16.

PHILOSOPHICAL _TRANSACTIONS._

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_Munday_, _August_ 6. 1666.

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The Contents.

_An essay of Dr. _John Wallis_, exhibiting his _Hypothesis_ about the _Flux and Reflux of the Sea_, taken from the consideration of the _Common Center of Gravity of the Earth and Moon_; together with an _Appendix_ of the same, containing an _Answer_ to some _Objections_, made by severall Persons against that _Hypothesis_. Some Animadversions of the same _Author_ upon Master _Hobs'_s late Book, _De Principiis & Ratiocinatione Geometrarum_._

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_An Essay of Dr. _John Wallis_, exhibiting his _Hypothesis_ about the _Flux and Reflux of the Sea_._

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

But this, though it might furnish us with the foundation of a _Menstrual_ Period of Accelerations and Retardations in the compound motion of several parts of the Earths surface; yet I am not at all inclined to admit this as a _true Hypothesis_, for divers Reasons, which if not demonstrative, are yet so consonant to the general Systeme of the World, as that we have no good ground to disbelieve them. For 1. The Earth being undeniably the greater Body of the two (whereof there is no doubt to be made) it cannot be thought probable, that this should be carried about by the Moon, lesser than it self: The contrary being seen, not onely in the _Sun_, which is bigger than any of the Planets, which it carryes about; but in _Jupiter_, bigger than any of his _Satellites_; and _Saturne_, bigger than his. 2. As the _Sun_ by it's motion about it's own Axis, is with good reason judged to be the _Physical_ cause of the _Primary_ Planets moving about it; So there is the like reason to believe, that _Jupiter_ and _Saturne_ moving about their Axes, are the Physical cause of their _Satellites_ moving about them, which motion of _Jupiter_ hath been of late discover'd, by the help of a _fixed_ Spot discern'd in him; and we have reason to believe the like of _Saturne:_ Whether _Venus_ and _Mercury_ (about whom no _Satellites_ have been yet observed) be likewise so moved; we have not yet the like ground to determine: But we have of _Mars_; from {271} the Observations of Mr. _Hook_ made in _February_ and _March_ last, and by him communicated to the _Royal Society_, and since Printed in the _Transactions_, published _Apr._ 2. 1666. consonant to the like observations of _Jupiter_, made by him in _May._ 1664, and since communicated to the same _Society_; and then published in the _Transactions_, of _March._ 6. then next following. Now that the Earth hath such a motion about its own _Axis_ (whereby it might be fitted to carry about the Moon) is evident by its _Diurnal_ motion. And it seems as evident that the Moon hath not; because of the same side of the Moon alwaies turned towards us; which could not be, if the Moon carried the Earth about: Unlesse we should say, that it carries about the Earth in just the same Period, in which it turnes upon its own Axis: Which is contrary to that of the Sun carrying about the Planets: the shortest of whose Periods, is yet longer than that of the Suns moving about its own Axis. And the like of _Jupiter_, shorter than the Period of any of his _Satellites_; if at least the Period of his conversion about his Axis, lately said to be observed, prove true. (Of _Saturn_ we have not yet any Period assigned; but it's likely to be shorter, than that of his _Satelles_.) And therefore we have reason to believe, not that by the Moons motion about its Axis the Earth should be carried by a contemporary Period (whereby the same face of the Moon should be ever towards us;) but that by the Earths revolution about its Axis in 24. hours, the Moon should be carried about it in about 29. dayes, without any motion on its own Axis: And accordingly, that the _Secondary_ Planets about _Jupiter_ and _Saturn_, are not (like their _Principals_) turned about their own Axis. And therefore I am not at all inclined to believe, that the _Menstrual_ Period of the Tides with us, is to be salved by such an Hypothesis.

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

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

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

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

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