PHILOSOPHICALTRANSACTIONS.

Punctum.Linea.Terminus.Linea Recta.Superficies.Superficiei Termini.Superficies Plana,Angulus(Where he is large upon theAngulus Contactus.)Petitio prima Elem. 1. Euclidis.Ratio.Radix & Latus.Prop. 16. El. 3.Dimensio Circuli.Magnitudo Circuli Hugeniana.Sectio Anguli.Ratio, quam habet recta composita ex Radio & Tangente 30. grad, ad Radium ipsum.Propos. 47æ. Elem. 1. Demonstratio.Addita est Appendix de Mediis proportionalibus in genere.

Punctum.

Linea.

Terminus.

Linea Recta.

Superficies.

Superficiei Termini.

Superficies Plana,

Angulus(Where he is large upon theAngulus Contactus.)

Petitio prima Elem. 1. Euclidis.

Ratio.

Radix & Latus.

Prop. 16. El. 3.

Dimensio Circuli.

Magnitudo Circuli Hugeniana.

Sectio Anguli.

Ratio, quam habet recta composita ex Radio & Tangente 30. grad, ad Radium ipsum.

Propos. 47æ. Elem. 1. Demonstratio.

Addita est Appendix de Mediis proportionalibus in genere.

KING SALOMONS POUTRAITURE OF OLD AGE; byJohn Smith, M.D. This Treatise being aPhilosophicalDiscourse, though upon aSacredTheme, may certainly claim a place amongPhilosophicalTransactions. Not here to mention the many other learned Notes, this Worthy Author gives upon that Hieroglyphical Description of Old Age, made by that Royal Pen-man ofEcclesiastes, cap. 12. We shall onely take notice of that surprizingly Ingenious one, there to be met with, concerning the Antiquity of the Doctrine of theBlood's Circulation: KingSalomon, who lived neer 2700 years agoe, using such expressions, as may, to a considering Reader, very probably denote the same Doctrine, which the Sagacious Dr.Harveyhas of late years so happily brought to light, and introduced into all the most Ingenuous Societies of Learned men: ThePitcher, mention'd in the quoted place, being Interpreted for theVeines, and theFountainfor theRight Ventricle of the Heart, as theCisternfor theLeft; theWheele, there spoken off, manifestly importing aCirculation, made by theGreat Arterywith its Branches, the principal Instrument thereof.

Printed with Licence forJohn Martyn, andJames Allestry, Printers to the Royal Society. 1666.

Num.15.

Wednesday,July18. 1666.

A new Experiment, shewing, How a considerable degree of Cold may be suddenly produced without the help ofSnow,Ice,Haile,Wind, orNiter, and that at any time of the year. An Account of two Books, lately printed inLondon; whereof the one is entituled,EUCLIDIS ELEMENTA GEOMETRICA, novo ordine ac Methodo demonstrata; the AuthorAnonymus. The other,THE ENGLISH VINE-YARD VINDICATED, byJOHN ROSE.

This subject will it self, 'tis presumed, without any otherPreamble, speak the Cause, why this present Paper is publish't at this (unusual) time of the Month: though, by the by, it may not be amiss to add on this occasion, that the Publisher of theseTractsnever meant so to confine himself to aSettime, as not to retain the Liberty of taking any other, when there is occasion. And there being one given him, before another Month is come in, he does without any scruple or delay comply therewith, presenting the Curious with an Experiment which he thinks is both seasonable, and will not be unwellcome to them; furnish't out of the Ample Magazin of that Philosophical Benefactor, the Noble Mr.Boyle; Concerning which, thus much is further thought requisite to intimate on this occasion, that it, and some others of the same Gentlemans, that have been, and may be, mentioned in theTransactions, belong to certain Treatises, the Author hath lying by him; but that yet he denys notto communicate them to his Friends, and to allow them to dispose thereof, upon a hope, that equitable Readers will be ready to excuse, if hereafter they should appear also in the Treatises they belong to, since he consents to this Anticipation, but to comply with those, that think the imparting of real and practical Experiments, may do the Publick some Service, by exciteing and assisting mens Curiosity in the interim.

As for the Experiment, you saw the other day at my Lodgings, though it belongs to some Papers aboutCold, that (you know) could not be Publish't, when the rest of theHistorycame forth, and therefore was reserved for the nextEditionof that Book; yet the Weather having been of late very hot, and threatning to continue so, I presume, that to give you here in compliance with your Curiosity an Account of the Main and Practical part of the Experiment, may enable you to gratify not onely the Curious among your Friends, but those of the Delicate, that are content to purchase a Coolness of Drinks at a somewhat chargeable rate.

You may remember, that the Spring before the last, I shew'd you a particular Account of a way, wherein by a certain substance obtain'd fromSal Armoniack, I could presently produce a considerable degree ofCold, and that with odd Circumstances, without the help ofSnow,Ice,Niter&c. But that Experiment being difficult and costly enough, and design'd to afford menInformation, notAccomodations, I afterwards tryed, what some more cheap and facile mixtures of likely Bodies withSal Armoniackwould do towards the Production of Cold, and afterwards I began to consider, whether to that purpose alone (for my first experiment was design'd to exhibite otherPhænomenatoo) those mixtures might not without inconvenience be omitted: and I was much confirm'd in my conjecture, by an accident, which was casually related to me by a very Ingenious Physician of my acquaintance, but not to be repeated to you in few words, though he complain'd, he knew not what to make of it.

Among the several ways, by which I have made infrigidating Mixtures withSal Armoniack, the most simple and facile is this; Take one pound of powder'dSal Armoniackand about three Pints (or pounds) of Water, put the Salt into the Liquor,eitheraltogether, if your design be to produce an intense, thoughbut a short coldness;orat two, three, or four several times, if you desire, that the produced coldness should rather last somewhat longer than be so great. Stirre the powder in the Liquor with a stick or whalebone (or some other thing that will not be injur'd by the fretting Brine, that will be made) to hasten the dissolution of the Salt; upon the quickness of which depends very much the intensity of the Cold, that will ensue upon this Experiment. For the clearing up whereof, I shall annex the following particulars.

1. That a considerable degree of Cold is really produced by this operation, is very evident:Firstto the touch;Secondly, by this, that if you make the Experiment (as for this reason I sometimes chuse to do) in a Glass-Body or a Tankard, you*In the History of Cold.may observe, that, whilst the Solution of the Salt is making, the outside of the Metalline Vessel will, as high as the mixture reaches within, be bedew'd (if I may so speak) with a multitude of little Drops of Water as I have * elsewhere shown that it happens, when mixtures of Snow and Salt, being put into Glasses or other Vessels, the aqueous vapors that swim to and fro in the Air, and chance to glide along the sides of the Vessels, are by the coldness thereof condens'd into Water. And in our Armoniack Solution you may observe, that if you wipe off the Dew from any particular part of the outside of the Vessel, whilst the solution does yet vigorously goe on, it will quickly collect fresh Dew, which may be sometimes copious enough to run down the sides of the Vessel. ButThirdly, the best and surest way of finding out the Coldness of our Mixture is that, which I shew'd you by plunging into it a good seal'd Weatherglass furnish't with tincted Spirit of Wine. For the Ball of this being put into our frigorifick mixture, the Crimson Liquor will nimbly enough descend much lower, than when it was kept either in the open Air, in common Water, of the same temper with that, wherein theSal Armoniackwas put to dissolve. And if you remove the Glass out of our Mixture into common water, the tincted Spirit will, (as you may remember, it did) hastily enough reascend for a pretty while, according to the greater or lesser time, that it continued in theArmoniackSolution. And this has succeeded with me, when instead of removing the Mixture intoCommonWater, I removed it into water newly impregnated withSalt-peter.

2. TheDurationof the Cold, produc'd by this Experiment, depends upon several Circumstances; asFirst, upon the Season of the year, and present temperature of the Air; For, in Summer and Hot weather the Cold will sooner decay and expire.Secondly, upon the Quantity of Salt and Water: For, if both these be great, the effect will be as well more lasting, as more considerable.Thirdly, for ought I yet know, we may here add the Goodness & Fitness of the particular parcel of Salt, that is imploy'd; for, though it be hard to discern beforehand, which will be the more, and which the less proper; yet some trials have tempted me to suspect, that there may be a considerable disparity, as to their fitness to produce Cold, betwixt parcels of Salt, that are without scruple look't upon as Sal Armoniack: Of which difference it were not perhaps very difficult to asign probable reasons from the Nature of the Ingredients of this compound Concrete, and the wayes of preparing it. But the Duration of the Cold may be conceived to depend also.Fourthly, upon the Way of putting in the Salt into the Water. For, if you cast it in all at once, the Water will sooner acquire an intense degree of Coldness, but it will also the sooner return to its former temper; Whereas, if you desire but an inferiour degree of that Quality, but that may last longer (which wil usually be the most convenient for the Cooling of Drinks), then you may put in the Salt by little and little. For, keeping a long Weather-glass for a good while in our impregnated Mixture, I often purposely try'd, that, when the tincted liquor subsided but slowly, or was at a stand, by putting in, from time to time, 2 or 3. spoonfuls of fresh Salt, and stirring the Water to quicken the Dissolution, the Spirit of Wine would begin again to descend, if it were at a stand or rising, or subside much more swiftly than it did before. And if you would lengthen the Experiment, it may not be amiss, that part of the Sal Armoniack be but grosly beaten, that it may be the longer in dissolving, and consequently in Cooling the Water. Whilst there are dewy drops produced on the outside of the Vessel, 'tis a sign, that the Cold within continues pretty strong; for when it ceases, these drops especially in warm weather, will by degrees vanish. But asurerway of measuring the duration of the Cold, is, by removing from time to time the Seal'd Weather-glass out of the Saline Mixture into the same common Water, with part of which it was made. And though it be not easie to determin any thing particularly about this matter; yet it may somewhat assist you in your Estimates, to be inform'd, That I have in the Spring by a good Weather-glass found a sensible adventitious Cold made by a pound of Sal Armoniack at the utmost, to last about 2 or 3 hours.

3. To cool Drinks with this Mixture, you may put them inthinGlasses, the thinner the better; which (their orifices being stopp'd, and still kept above the Mixture) may be moved to and fro in it, and then be immediately pour'd out to be drunk: Though when in the Glass, I imployed, was conveniently shap'd as, like a Sugar-loaf, or with a long Neck, I found it not amiss to drink it out of that, without pouring it into any other; which can scarce be done without lessning the Coolness. The refrigeration, if the Glass viall be convenient, is quickly perform'd: And if one have a mind to cool his hands, he may readily do it by applying them to the outside of the Vessel, that contains the refrigerating Mixture; by whose help, pieces of Chrystal, or Bullet for the cooling ofthe Mouths or Hands of those patients, to whom it may be allow'd, may be potently cool'd, and other such refreshments may be easily procur'd.

4. How far Sal Armoniack, mingl'd with Sand or Earth, and not dissolv'd, but only moistn'd with a little Water sprinkl'd on it, will keep Bottles of Wine or other liquors more coole, than the Earth or that Sand alone will do, I have not yet had opportunity by sufficient trials fully to satisfie my self, and therefore resign that Enquiry to the Curious.

5. For the cooling of Air, and Liquors, to adjust Weather-glasses (to be able to do which at all times of the year, was one of the chief aimes, that made me bethink my self of this Experiment;) or to give a small quantity of Beer &c. a moderate degree of coolness, it will not be requisite, to employ neer so much as a whole pound of Sal Armoniack at a time. For, you may easily observe by a seal'd Weather-glass, that a very few ounces, well pouder'd and nimbly dissolv'd in about 4. times the weight of Water, will serve well enough for many purposes.

6. And that you may the less, scruple at this, I shall tell you, that even before and after Midsummer, I have found the Cold producible by our Experiment to be considerable and useful for refrigerating of Drinks, &c. but if the Sal Armoniack be of the fittest sort (for I intimated above, that I suspected, 'tis not equally good) and if the season of the year do make no disadvantagious difference, the degree of Cold, that may be produced by no more than one pound (if not by less) of Sal Armoniack, may, within its own Sphere of Activity, be much more vehement, than, I presume, you yet imagine, and may afford us excellent Standards to adjust seal'd Weather glasses by; and for several other purposes, For I remember that in the Spring, about the end ofMarch, or beginning ofApril, I was able with one pound of Sal Armoniack, and a requisite proportion of Water, to produce a degree of Cold much greater, than was necessary the preceding Winter, to make it frosty Weather abroad; nay I was able to produce real Ice in a space of time, almost incredibly short. To confirm which particulars, because they will probably seem strange to you, I will here annex the Transcript of an entry, that I find in a Note book of thePhænomenaand success of one of those Experiments, as I then tryed it; though I should be asham'd to expose to your perusal a thing so rudely pen'd; if I did not hope, you would consider, that 'twas hastily written onely for my own Remembrance. And that you may not stop at any thing in the immediately annext Note, or the two, that follow, it will be requisite to premise this Account of the seal'd Thermoscope; (which was a good one) wherewith these Observations were made; That the length of the Cylindrical pipe was 16. Inches; the Ball, about the bigness of a somewhat large Walnut, and the Cavity of the Pipe by guess about an eight or ninth part of an inch Diameter.

The First Experiment is thus registered.Marchthe 27th, in the Seal'd Weather glass, when first put into the Water, the tincted Spirit rested at 8⅝ inches; being suffered to stay there a good while, and now and then stirr'd to and fro in the Water; it descended at length a little beneath 7⅝ inches; then theSal Armoniackbeing put in, within about a quarter of an hour or a little more it descended to 211/16inches, but before that time, in half aquarter of an hour it began manifestly to freeze the vapours and drops of water on the outside of the Glass. And when the frigorifick power was arriv'd at the height, I several times found, that water, thinly plac'd on the outside, whilst the mixture within was nimbly stirr'd up and down, would freeze in a quarter of a minute (by a Minute-watch.) At about ¾ of an hour after the infrigidating Body was put in, the Thermoscope, that had been taken out a while before, and yet was risen but to the lowest freezing mark, being again put in the liquor, fell an inch beneath the mark. At about 2½ houres from the first Solution of the Salt I found the tincted liquor to be in the midst between the freezing marks, whereof the one was at 5½ inches (at which height when the Tincture rested, it would usually be, some, though but a small, frost abroad;) and the other at 4¾ inches; which was the height, to which strong and durable Frosts had reduced the liquor in the Winter. At 3 hours after the beginning of the Operation, I found not the Crimson liquor higher than the upper Freezing mark newly mention'd; after which, it continued to rise very slowly for about an hour longer; beyond which time I had not occasion to observe it.

Thus far theNote-book; wherein there is mention made of a Circumstance of some former Experiments of the like kind, which I remember was very conspicuous in this newly recited. For, the frigorifick mixture having been made in a Glass body (as they call it) with a large and flattish bottom, a quantity of water, which I (purposely) spilt upon the Table, was by the operation of the mixture within the Glass, made to freeze, and that strongly enough, the bottom of the Cucurbite to the Table; that stagnant liquor being turn'd into solid ice, that continued a considerable while unthaw'd away, and was in some places about the thickness of a half Crown piece.

Another Observation, made the same Spring, but less solemn, as meant chiefly to shew the Duration of Cold in a high degree, is recorded in these terms: The first time, the Seal'd Weather-glass was put in, before it touch'd the common water, it stood at 8⅛, having been left there a considerable while, and once or twice agitated the water, the tincted liquor sunk but to 7⅞, or at furthest, 76/8; then the frigorifick liquor being put into the water with circumstances disadvantagious enough in (about) half a quarter of an hour the tincted liquor fell beneath 3¾, and the Thermoscope, being taken out, and then put in again, an hour after the water had been first infrigidated subsided beneath 5 inches, and consequently within ¼ of an inch of the mark of the strongly freezing weather.

7. Whereas the grand thing, that is like to keep this Experiment from being as generallyUseful, as perhaps it will proveLuciferous, is the Dearness of Sal Armoniack, two things may be offered to lessen this Inconvenience. Forfirst, Sal Armoniack might be made much cheaper, if instead of fetching it beyond-sea, our Country-men made it here at home; (which it may easily be and I am ready to give you the Receipt, which is no great Secret.) Butnext, I considered, that probably the infrigidating vertue of our mixture might depend upon the peculiar Texture of the Sal Armoniack whereby, whilest the Water is dissolving it, either some Frigorifick particles are extricated and excited or (rather) some particles which did before more agitate the minute parts of the water, are expell'd (or invited out by the ambient Bodies) orcome to be clogg'd in their motion: Whence it seem'd reasonable to expect that upon the Reunion of the Saline particles into such a Body, as they had constituted before, the redintegrated Sal Armoniack having, neer upon, the same Texture, would, upon its being redissolv'd, produce the same, or a not much inferior degree of Coldness: And hereupon, though I well enough foresaw that an Armoniack solution, being boyl'd up in Earthen vessels (for Glass ones are too chargeable) would, by piercing them, both lose some of the more subtle parts, and thereby somewhat impaire the texture of the rest; yet I was not deceiv'd in Expecting, that the dry Salt, remaining in the pipkins, being redissolv'd in a due proportion of water, would very considerably infrigidate it; as may further appear by the Notes, which for your greater satisfaction you will find here subjoyn'd, as soon as I have told you, that, though for want of other vessels I was first reduc'd to make use of Earthen ones, and the rather, because some Metallin Vessels will be injur'd by the dissolv'd Sal Armoniack, if it be boyl'd in them; yet I afterwards found some conveniencies in Vessels of other Mettall, as of Iron; whereof you may command a further Account.

Marchthe 29th, the Thermoscope in the Air was at 8⅞ inches; being put into a somewhat large evaporating glass, fill'd with water, it fell (after it staid a pretty while, and had been agitated in the liquor) to 8. inches: then about half the Salt, or less, that had been usedtwicebefore, and felt much less cold than the water, being put in and stirr'd about, the tincted Spirit subsided with a visible progress, till it was faln manifestly beneath 4. inches; and then, having caused some water to be freshly pump'd and brought in; though the newly mention'd Solution were mixt with it, yet it presently made the Spirit of Wine manifestly to ascend in the Instrument, much faster, than one would have expected,&c.

And this much may suffice for this time concerning ourFrigorifickExperiment; which I scarce doubt but theCartesianswill lay hold on as very favourable to some of their Tenents; which you will easily believe, it isnotto the Opinion, I have elsewhere oppos'd, of those Modern Philosophers, that would haveSalt-petreto be thePrimum Frigidum: (though I found by trial, that, whilst 'tis actually dissolving, it gives a much considerabler degree of Cold, than otherwise.) But about the Reflexions, that may be made on this Experiment, and the Variations, and Improvements & Uses of it, though I have divers things lying by me; yet, since you have seen several of them already, and may command a sight of the rest, I shall forbear the mention of them here, not thinking it proper, to swell the bulk of this Letter with them.

I.EUCLIDIS ELEMENTA GEOMETRICA, novo ordine ac methodo demonstrata.In this compendious and pretty Edition, the Anonymous Author pretends to have rendred these Elements more expeditious; by bringing all together into one place, what belongs to one and the same subject: Comprising 1. whatEuclidhath said ofLines, Streight, Intersecting one another, and Parallel. 2. What he hath demonstrated of aSingle Triangle, and ofTriangles Comparedone with another. 3. What of theCircle, and its Properties. 4. What ofProportionsin Triangles and other Figures. 5. What ofQuadratsandRectangles, made of Lines diverslycut. 6. What ofPlane Superficies's. 7. What ofSolids. After which follow theProblems. TheDefinitionsare put to eachChapteras need requireth. TheAxioms, because they are few, and almost every where necessary, are not thus distributed inChapters. ThePostulata, are not subjoyn'd to theAxioms, but reserv'd for theProblems, the Author esteeming, that they beingpracticalPrinciples, had only place inProblems.

This for theOrder:As to theMannerof Demonstrating, One and the same is observ'd in most Propositions; all with much brevity; to the end, that what is not of it self difficult, may not be made so, by multitude of Words and Letters.

II.THE ENGLISH VINE-YARD VINDICATED.The Author (Mr.John Rose, his Majesties Gardener at his Royal Garden in St.James's) makes it his business in this small Tract (a very thin Pocket-book) by a few short Observations made by himself, to directEnglishmenin theChoiceof theFruit, and thePlantingof Vine-yards; heretofore very frequently cultivated, though of late almost quite neglected by them.

He discourses skilfully, 1. Of theseverall sortsofVines, and whatGrapesare most sutable to theClimateofEngland; where he chiefly commends the smallBlack-grape, orCluster-grape; theParsley-grape; the WhiteMuscadine; theFrontiniack; and a newWhite-grape, with a red Wood and a dark green Leaf: All these being early ripe fruit. 2. Of theSoyle, andScituationof a Vine-yard inEngland: Where, as to theFirst, he pitches upon aLight Soile, having a bottom ofChalkorGravel, and given toBramblesobserving, that no Plant whatsoever is so connatural to the Vine for Soyl, as theBramble. As for theScituationhe chooses that side or declivity of a Hill, that lies to theSouthorSouthwest; and is favoured withother Hillssomewhat higher, orWoodson theNorthandEast, to break the rigour of those quarters. This direction he thinks of that importance, that he affirms, that the discouragement of the Culture of Vines inEnglandhas only proceeded from men's misinformation on this material article ofChoiceofSoyleandScituation. 3. How topreparethe Ground for the Plantation,vid.by plowing up theSwarthinJuly, and by disposing theTurfinsmallheaps, and so burning them, and spreading the ashes over the Land; care being taken, that by heaping too much materials together, the Earth be not over-burnt by the excessive heat and fire, which they require to reduce them to ashes.

What is added, of the Manner of planting theSets; 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 themannerandtime, 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 inEnglandmay 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 withSetsandPlantsof all those sorts, which he recommends; he having a plentifulstockof them all.

Printed with Licence forJohn Martyn, andJames Allestry, Printers to the Royal Society. 1666.

Num.16.

Munday,August6. 1666.

An essay of Dr.John Wallis, exhibiting hisHypothesisabout theFlux and Reflux of the Sea, taken from the consideration of theCommon Center of Gravity of the Earth and Moon; together with anAppendixof the same, containing anAnswerto someObjections, made by severall Persons against thatHypothesis. Some Animadversions of the sameAuthorupon MasterHobs's late Book,De Principiis & Ratiocinatione Geometrarum.

How abstruse a subject in Philosophy, theFlux and Reflux of the Seahath proved hitherto, and how much the same hath in all Ages perplexed the Minds even of the best ofNaturalists, 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 theTheoriesorHypotheses, formerly invented for that End, have not been able to deterre the Ingenious ofthisAge from making farther search into that Matter: Among whom that Eminent Mathematician Dr.John Wallis, following his happyGeniusfor advancing reall Philosophy, hath made it a part of his later Inquiries and Studies, to contrive and deduce a certain Hypothesis concerning thatPhænomenon, takenfrom the Consideration of theCommon 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 theConjecture(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 theProposerhimself expressly desires in the Discourse, we now, without any morePreamble, are going to subjoyn, as it was by him addressed, by way of Letter, fromOxfordto Mr.Boyle, April25. 1666. and afterwards communicated to theR. 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 theCommon Center of Gravity of the Earth and Moon, in order to salving thePhænomenaas well of theSeas Ebbing and Flowing; as of some perplexities inAstronomical Observationsof thePlacesof the Celestial Bodies.

How much the World, and the great Bodies therein, are manag'd according to theLaws of Motion, andStatick Principles, and with how much more of clearness and satisfaction, many of the more abstrusePhænomenahave 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 thatGalilæoand (after him)Torricellio, and others, have appliedMechanickPrinciples to the salving ofPhilosophicalDifficulties;Natural Philosophyis 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.

TheSeas Ebbing and Flowing, hath so great a connexion with theMoonsmotion, that in a manner all Philosophers (whatever other Causes they have joyned with it), have attributed much of its cause to theMoon, which either by someoccult quality,orparticular influence, which it hath on moyst Bodies, or by someMagnetick vertue, drawing the water towards it, (which should therefore make the Water therehighest, where the Moon isvertical) or by its gravity and pressure downwards upon the Terraqueous Globe (which would make itlowestwhere the Moon isvertical) 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: ThePeriods 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 theEarth'smotion, (DiurnalandAnnual) wasGalilæo; who in hisSysteme 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 greatPhænomenonwas to be referred to the Earths motion, as thePrincipalcause of it: Yet that of the Moon (for the reasons above mentioned) not to be excluded, as to the determining thePeriods of Tides, and other circumstances concerning them. And though it be manifest enough, thatGalilæo, 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 themain Hypothesis: For that Discourse is to be looked upon onely as anEssayof thegeneral Hypothesis; which as toparticularswas to afterwards adjusted, from a goodGeneral 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 Waterthenandthereat the Highest,whereandwhenthe other makes it at the Lowest; as when the Moon is Vertical to the place.

And what I say ofGalilæo, 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 mygeneral Hypothesisto theparticular cases; or that I will indeed undertake for the certainty of it, but onely as anEssaypropose 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 theEnglish, 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 theLymphatick VesselsinAnatomy; theInjection of Liquors into the veins of Living animals; theExhibiting of a straight line equal to a crooked; thespot in Jupiter, whence his motion about his own Axis may be demonstrated; and many other the like considerable Inventions.

TheotherReason (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 sodo it, as to bring it to perfection, I cannot determine. And therefore, if as to my self any thing shouldhumanitus 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 thesethreenotorious Observations made of the Reciprocation of Tides.First, theDiurnalReciprocation; whereby twice in somewhat more than 24. hours, we have a Floud and an Ebbe; or a High-water and Low-water.Secondly, theMenstrual; whereby in oneSynodicalperiod of the Moon, suppose from Full-moon to Full-moon, the Time of those Diurnal Vicissitudes doth move round through the whole compass of theΝυχθήμερον, 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, theAnnual; 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 beenmuch concerned to heed it, whereof more will be said by and by;) that we should rather assign the beginnings ofFebruaryandNovember, than the twoÆquinoxes.

Now in order to the giving account of these three Periods, according to theLaws of MotionandMechanick Principles; We shallfirsttake 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 anImpetusto 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 equalImpetuswith it) will be left behind, or seem to fly backward upon it. Or, (which isGalilæo'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 ofImpetuswith 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.

Fig. 1.

Now this premised, We are next, with him, to suppose the Earth carried about with a double motion; The oneAnnual, 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 otherDiurnal, whereby the whole moves upon its ownAxis, 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 equalImpetusthereunto, 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, theAnnualandDiurnal; (theAnnualin B E C being, asGalilæothere supposeth, about three times as fast as adiurnalmotion 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 themotion of B above the Center; G. is alsoput forward as much as from G to E; and E put backward as much as from E to G:) so that theDiurnalmotion, in that part of the Earth, which is next the Sun, as E F G, doth abate the progress of theAnnual, (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 theAnnualmotion, about as much as is G E, the EarthsDiameter. 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 farGalilæo's Discourse holds well enough; But thenin 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, atNoonandMidnight; whereas Experience tells us, that the Time of Tides, moves in amoneths spacethrough 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 theQuantityof the Tides; greater or less; not as to theTimeof theTides, sooner or later.

*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 theEarthto be but asecondaryPlanet; 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 aMenstrualPeriod 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 atrue 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 theSun, which is bigger than any of the Planets, which it carryes about; but inJupiter, bigger than any of hisSatellites; andSaturne, bigger than his. 2. As theSunby it's motion about it's own Axis, is with good reason judged to be thePhysicalcause of thePrimaryPlanets moving about it; So there is the like reason to believe, thatJupiterandSaturnemoving about their Axes, are the Physical cause of theirSatellitesmoving about them, which motion ofJupiterhath been of late discover'd, by the help of afixedSpot discern'd in him; and we have reason to believe the like ofSaturne:WhetherVenusandMercury(about whom noSatelliteshave been yet observed) be likewise so moved; we have not yet the like ground to determine: But we have ofMars; fromthe Observations of Mr.Hookmade inFebruaryandMarchlast, and by him communicated to theRoyal Society, and since Printed in theTransactions, publishedApr.2. 1666. consonant to the like observations ofJupiter, made by him inMay.1664, and since communicated to the sameSociety; and then published in theTransactions, ofMarch.6. then next following. Now that the Earth hath such a motion about its ownAxis(whereby it might be fitted to carry about the Moon) is evident by itsDiurnalmotion. 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 ofJupiter, shorter than the Period of any of hisSatellites; if at least the Period of his conversion about his Axis, lately said to be observed, prove true. (OfSaturnwe have not yet any Period assigned; but it's likely to be shorter, than that of hisSatelles.) 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 theSecondaryPlanets aboutJupiterandSaturn, are not (like theirPrincipals) turned about their own Axis. And therefore I am not at all inclined to believe, that theMenstrualPeriod of the Tides with us, is to be salved by such an Hypothesis.

In stead of this, thatSurmiseof 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 thatthe motion of the one follows that of the other; (The Moon observing the Earth as the Center of itsperiodickmotion:) may well enough be looked upon asone Body, or ratherone Aggregate of Bodies, which haveone common center of Gravity; which Center (according to the known Laws ofStaticks) 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 anOne and fourtieth partof that of the Earth; (and thereaboutsHeveliusin hisSelenographypage 203. doth out ofTycho, 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 aboutfifty six Semidiametersof 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, about56/42or4/3of a Semidiameter; that is about ⅓ 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 theAnnualmotion; this motion is to be estimated, (according to the Laws ofStaticks, in other cases,) by the motion of the common Center of Gravity of both Bodies. For we use inStaticks, 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 theAnnualmotion, (whetherCircularorElliptical; 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 aSecondary Planet, against which we were before disputing:) But by theCommon Center of Gravity of the Bodies, Earth and Moon, as one Aggregate.

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