Chapter D: E B O. A Rain-bow about the Sun, forming an entire Circle, but (4)

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.

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, _æquales {293} quatuor cubis_ DV; (_pag._ 43. _line_ 33.) into these (p. 44. l. 5.) _æqualia 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}

* * * * *

_Num._ 17.

PHILOSOPHICAL _TRANSACTIONS._

* * * * *

_Munday_, _Septemb._ 9. 1666.

* * * * *

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 Cometæ,_ 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. 39½ | 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 _Æstivall 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.

* * * * *

_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 _Æquinoxes_, 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_.)

* * * * *

_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 COMETÆ, Anno Æræ Christianæ MDCLXV. exorti; unà cum MANTISSA Prodromi Cometici, Observationes omnes prioris COMETÆ MDCLIV, ex iisque genuinum motum accuratè 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 _Æquator_) _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 1½ 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.