Part 27

2. To the second objection; _That, at Chatham and in the Thames, the Annual Spring-tydes, happen about the Æquinoxes; not (as this Hypothesis doth suppose elsewhere to have been observed) about the beginning of February and November._ If their meaning be, that Annual High Tydes, do then happen, and then onely: If this prove true, it will ease me of half my work. For it is then easily answered, that it depends upon the _Obliquity of the Zodiack_; the parts of the Æquinoctial answering to equal parts of the {283} _Zodiack_, being neer the Solstitial points greatest, and near the Æquinoctial points least of all. But beside this _Annual Vicissitude of the Æquinoxes_, not to say, of the 4. Cardinal Points (which my Hypothesis doth allow and assert;) I believe it will be found, that there is _another Annual vicissitude_ answering to the Suns _Apogæum_ and _Perigæum_. And that the greatest Tydes of all, will be found to be upon a result of these two causes Cooperating: which (as doth the Inequality of Natural dayes, depending on these same causes) will light nearer the times, I mention. To what is said to be observed at _Chatham_ and in the _Thames_, contrary to that I allege as observed in _Rumney marsh_: I must at present [Greek: apechein], and refer to a _melius inquirendum_. If those who object this contrary observation, shall, after this notice, find, upon new Observations heedfully taken, that the _Spring-tydes_ in _February_ and _November_, are not so high, as those in _March_ and _September_; I shall then think the objection very considerable. But I do very well remember, that I have seen in _November_, very high Tydes at _London_, as well as in _Rumney Marsh_. And, the time is not yet so far past, but that it may be remembered (by your self or others then in _London_) whether in _November_ last when the Tydes were so high at _Dover_, at _Deal_, at _Margate_, and all along the Coast from thence to _Rumney Marsh_, as to do in some of those places much hurt, (and, in _Holland_, much more;) whether, I say, there were not also at the same time, at _London_, (upon the _Thames_) very high Tydes. But a good _Diary_ of the Height and time both of High-water, and Low-water, for a year or two together, even at _Chatham_, or _Greenwich_; but rather at some place in the _open_ Sea, or at the _Lands end_ in _Cornwal_, or on the _West parts of Ireland_; or at St. _Hellens_, or the _Bermodas_, &c. would do more to the resolving of this point, than any verbal discourse without it.

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

4. To the fourth Objection, _That the highest Tydes are not at all places, about the New Moon and Full Moon; and particularly, that, in some places of the East Indies, the Highest Tydes are at the Quadratures_: I must first answer in _general_; That as to the particular varieties of Tydes in several parts of the World, I cannot pretend to give a satisfactory account, for want of a competent History of Tydes, &c. Because (as is intimated in what I wrote in the _general_) the various positions of Chanels, Bays, Promontories, Gulfs, Shallows, Currents, Trade-winds, &c. must needs make an innumerable variety of Accidents in particular places, of which no satisfactory account is to be given from the general _Hypothesis_ (though never so true) without a due consideration of all those. Which is a task too great for me to undertake, being so ill furnished with materials for it. And then as to the particular instance of some places in the _East Indies_, where the highest Tydes are at the _Quadratures_: I suppose, it may be chiefly intended of those about _Cambaia_, and _Pegu_. At which places, beside that they are situate at the inmost parts of Vast Bayes, or Gulfs (as they are called) they have also vast In-draughts of some hundred Miles within Land; which when the Tydes are out, do lye (in a manner) quite dry: And may therefore very well be supposed to participate the effect of the Menstrual Tydes many dayes after the {285} cause of them happens in the open Sea, upon a like ground as in Straights and narrow Channels the Diurnall Tydes happen some hours later than in the Ocean. And a like account must be given of particular accidents in other places, from the particular situation of those places, as _Bays_, _Chanels_, _Currents_, &c.

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 12_th_ Chapter.) Or that there is no other connexion between the Moons motion, and the Tydes _menstrual_ period, than a _casual Synchronism_ (which seems to be the doctrine of his 16_th_ and 18_th_ Chapters;) Beside many other things in his Philosophy, which I cannot allow: Yet I am well enough pleased with what is Historical in it, of the matter of Fact: Especially if I may be secure, that he is therein accurate and candid, not wresting the _Phænomena_ 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 _Galilæo_ long since, from the Earths _Diurnal_ motion: (which, neare the _Æquator_, 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 Phænomena are much better salved by mine, than his.

And then as to _Gassendus_, in his discourse _De Æstu Maris_; I find him, after the relating of many other Opinions concerning the Cause of it, inclining to that of _Galilæo_, 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 _Galilæo_ had done before him) that the line of the Mean Motion of this Aggregate (or, as he calls, _motus æquabilis 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 _Æquinoctial_ 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 præcise 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: Sêmeion], 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: Sêmeion], 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: Sêmeion] by the Latine _Punctum_, not by Mr. _Hobs_'s _Signum_. The Mathematician is equally content with either word.