the Fluid and that increas'd as the depth of the immers'd Body beneath the Surface of the Fluid increaseth 142 Par. 8. That water may be made as well to depress a Body lighter then it self as to buoy it up 160 Par. 9. That what ever is said of positive Levity a parcel of oyle lighter then water may be kept in water without ascending in it 165 Par. 10. That the cause of the Ascension of water in Syphom and of its flowing through them may be explicated without having a recourse to nature's abhorrency of a Vacuum 170 Par. 11. That a solid Body as ponderous as any yet known though near the Top of the water it will sinck by in own weight yet if it be plac'd at a greater depth then that of twenty times its own thickness it will not sinck if its descern be not assisted by the weight of the Incumbent water 184 Appendix 1. Containing an Answer to seven Objections propos'd by a late Learned Writer to evince that the upper parts of water press not upon the lower 193 Ap. 2. Concerning the Reason why Divers others who descend to the bottom of the sea are not oppress'd by the weight of the incumbent water 221 Imprimatur ROBERTUS SAY VICE-CANCELLARIUS OXON HYDROSTATICAL PARADOXES Made out by NEW EXPERIMENTS Presented to the ROYAL SOCIETY The Lord Viscount Brouncker being then President May 1664. My LORD TO obey the orders of the Society that forbid the making of Prefaces and Apologies in Accounts of the Nature of that which you expect from me I shall without any further preamble begin with taking notice that upon perusal of Paschall's small French Book which was put into my hands I find it to consist of two distinct Treatises The one of the AEquilibrium of Liquors as he calls it and the other of the weight of the Mass of the Air. As for this latter which I shall mention first because I can in very few words dispatch the little I have to say of it Though it be an ingenious discourse and containes things which if they had been published at the time when it is said to have been written would probably have been very wellcome to the Curious yet I have very little else to say of it in this place in regard that since that time such kind of Experiments have been so prosecuted that I presume it is needless and would not be acceptable to repeat what Monsieur Paschall has written in this Society which has seen the same Truths and divers others of the like Nature more clearly made out by Experiments which could not be made by Monsieur Paschall and those other Learned Men that wanted the advantage of such Engines and Instruments as have in this place been frequently made use of Wherefore having already at a former meeting given you by word of Mouth an account of Paschall's Ingenious Invention of a pair of Bellows without vent to measure the various Pressure of the Atmosphaere I remember nothing else that needs hinder me from proceeding to the other part of his Book The Treatise of the AEquilibrium of Liquors This I find so short and so worthy of the Author that to give you all that I judge worth taking notice of in it would obliege me to transcribe almost the whole Tract and therefore I shall rather invite you to read the whole then divert you from the designe by culling out any part of it yet if you will not be satisfied without something of more particular I shall be oblig'd to tell you That the Discourse consisting partly of Conclusions and partly of Experiments the former seemed to me to be almost all of them there being but few that I doubt of consonant to the Principles and Lawes of the Hydrostaticks But as for the latter the Experimental proofs he offers of his opinions are such that I confess I have no mind to make use of them And the Reasons why notwithstanding that I like most of Paschall's Assertions I decline imploying his way of proving them are principally these First Because though the Experiments he mentions be delivered in such a manner as is usual in mentioning matters of fact yet I remember not that he expresly says that he actually try'd them and therefore he might possibly have set them down as things that must happen upon a just confidence that he was not mistaken in his Ratiocinations And of the reasonableness of this Doubt of mine I shall ere long have occasion to give an instance Secondly Whether or no Monsieur Paschall ever made these Experiments himself he does not seem to have been very desirous that others should make them after him For he supposes the Phaenomena he builds upon to be produc'd fifteen or twenty foot under water And one of them requires that a Man should sit there with the End of a Tube leaning upon his Thigh But he neither teaches us how a Man shall be enabled to continue under water nor how in a great Cistern full of water twenty foot deep the Experimenter shall be able to discern the alterations that happen to Mercury and other Bodies at the Bottome And Thirdly These Experiments require not only Tubes twenty foot long and a great Vessel of at least as many feet in depth which will not in this Countrey be easily procured but they require Brass Cylinders or Pluggs made with an exactness that though easily supposed by a Mathematician will scarce be found obtainable from a Tradesman These difficulties making the Experiments propos'd by Monsieur Paschall more ingenious then practicable I was induc'd on this occasion to bethink my self of a far more Expeditious Way to make out not only most of the Conclusions wherein we agree but others that he mentions not and this with so much more ease and clearnesse That not only This Illustrious Assembly but persons no more than moderately vers'd in the Vulgar principles of the Hydrostaticks may easily enough apprehend what is design'd to be deliver'd if they will but bring with them a due Attention and minds dispos'd to preferre Reason and Experience to vulgar Opinions and Authors which last clause I annex because the following Discourse pretending to confute several of those challenges a right to except against their Authority It not being my present Task to deliver the Elements or a Body of Hydrostaticks but only ten or twelve Paradoxes which I conceive to be proveable by this new way of making them out I shall to avoid Confusion Deliver Them in as many distinct propositions After each of which I shall indeavour in a proof or an Explication to show both that it is true and why it ought to be so To all these I shall to avoid needless Repetitions premise a word or two by way either of postulatum or Lemma And because I remember to what Assembly I address This Discourse I shall make use of no other then an easie supposition I met with in a short Paper about a Mercuriall Phaenomenon
the Oyle will not fall down at the lower Orifice though that be open but will remain suspended at the same height or near there abouts that it rested at before Now Oyle of Turpentine being a heavy Fluid does as such tend downwards and not being stopp'd by the Glass it self whose lower Orifice is left open it would certainly fall down through the Pipe if it were not kept suspended by the pressure upwards of the water beneath it There appearing no other Cause to which the Effect can reasonably be ascrib'd and this being sufficient to give an Account of it as we shall presently see For that it is not any contrariety in Nature betwixt the oyle and the water as Liquors that will not mingle is evident from hence That if you had remov'd your finger when the Pipe was not so deeply immers'd in the Glass but that the Surface of the oyl in the Pipe was an Inch or two more elevated above that of the water in the Glass then in our present case we suppose it to be The Oyle notwithstanding its presum'd contrariety to water would have freely subsided in the Pipe till it had attain'd an aequipollency of pressure with the External Water The Reason therefore of the Phaenomenon seems to be plainly this Supposing the imaginary surface on which the Extremity Q of the pipe P Q leans to be G H. If that part of the Surface on which the Oyl leans at Q be as much and no more charged or press'd upon by the weight of the incumbent Cylinder of Oyle Q X then the other parts of the same imaginary Surface G H are by the water incumbent on Them there is no Reason why that part at Q should be displac'd either by being depress'd by the weight of the Cylinder of Oyle X Q or rais'd by the equal pressure of water upon the other parts of the Superficies G H. And that this Aequilibrium betwixt the Oyle and the Water is the true cause of the Phaenomenon may be confirm'd by observing what happens if the altitude of either of the two Liquors be alter'd in Relation to the other And First we have already taken notice That if the Cylinder of Oyle reach in the Pipe much higher then that of the Surface of the water the oyle will descend Of which the Reason is Because the designable Surface G H being more charg'd at Q then any where else the part Q being unable to resist so great a pressure must necessarily be thrust out of place by the descending oyle Secondly This subsiding will continue but till the Surface of the Oyle in the Pipe be fallen almost as low as that of the water without the Pipe because then and not before the parts at Q are but as much press'd by the oyle as the other parts of the Surface G H are by the water that leans upon them Thirdly 'T is a concluding Circumstance to our present purpose That if the Oyle and Water being in an Aequilibrium you gently lift up the Pipe as from Q to S the depth of the water being lessend the oyle in the Pipe will grow praeponderant and therefore will fall out in Drops or Globuls which by the greater Specifick Gravity of the water will be buoy'd up to the Top of the Liquor and there flote And still as you lift up the Pipe higher and higher towards the Surface L M more and more of the Oyle will run out But if you stop the Pipe any where in its Ascent as at S the Effluxion of the oyle will likewise be stopp'd And at the imaginary Superficies J K as by Reason of the shallowness of the water from L to J or M to K the pressure of the water upon the other parts of the Surface is not near so great as it was upon the Surface G H where the water had a greater depth So by reason of the proportionate Effluxion of the oyle whil'st the Pipe was lifted up from Q to S the remaining Cylinder of oyle incumbent on S is not able to press that part of the Superficies J K more strongly then the other parts of the same Superficies are prest by the water Incumbent on them And if the Pipe be lifted up till the lower Orifice be almost rais'd to V that is almost as high as the uppermost Surface of the water L M so much of the oyle will for the Reason already given run out that there will scarce be any left in the Pipe T V. Fourthly But if when the Pipe rests at the Surface G H where the oyle is in an Aequilibrium with the water you should instead of lifting it from Q to S thrust it down from Q to O then the External water would not only sustaine the oyle but make it ascend in the Pipe to a height equal to the distance E G and so the Pipe will containe besides a longer Cylinder of oyle AE W a shorter one of water AE O. For the pipe being transferr'd from the position P Q to the position O N there is a new Imaginary Surface E F that passes by the lower Orifice of the Pipe Now the part of this Surface at O will not by the Incumbent oyle alone be press'd as much as the other parts of the same Surface are by the Incumbent water For the oyl alone was but in Aequilibrium with the water when it was no deeper then L G or H M so that the other parts of the Superficies E F being more press'd upon by the water then the part at O by the oyle the oyle must give place and be buoy'd up by the water which if it were not for the weight of the oyle would be impell'd up into the pipe full as high as the Surface of the External water till the pressure of the admitted water O AE and the Cylinder of oyle AE W do both together gravitate as much upon the part O as the rest of the Incumbent water does upon the other parts of the same Superficies E F. Fifthly and lastly 'T is very agreeable to what has been delivered touching the Aequilibrium of the oyle and water in the pipe P Q that the Surface X of the oyle in the pipe will not be of the same level with L M that of the External water but a little higher than it For though the slenderness of the Pipe do somewhat contribute to this Effect yet there would be an inequality though not so great betwixt these Surfaces upon this Account That oyle of Turpentine being in Specie as they speak in the Schools that is bulk for bulk a lighter Liquor than Water it is requisite that the height of it incumbent on the part Q be greater than that of the water on the other parts of the same Surface G H to make the pressure of the oyle on the part it leans upon equal to the pressure of the water on the other parts of the Surface And if the inequality were greater betwixt the Specifick
Turpentine As will be obvious to them that have attentively consider'd the Explication of the former Paradox there being but this difference between this Experiment and that there Explain'd that here the water is in the Pipe and the oyle in the Vessel whereas there the oyle was in the Pipe and the water in the Vessel And if you either poure more oyle into the Glass or thrust the Pipe deeper into the oyle you shall see that the water will be buoyed up towards the top of the Pipe that is a heavier Liquor will be lifted up by a lighter And since by the Explication of the first Proposition it appears that the Reason why the Liquor is in this case rais'd in the Pipe is the Gravity of the Liquor that raises it we must allow that a lighter Liquor in specie may by its gravity press against a heavier And it agrees very well with our Explication both of this and of the first Experiment that as there the Surface of the oyle in the pipe was always higher than that of the water without it because the oyle being the lighter Liquor a greater height of it was requir'd to make an Aequilibrium so in our present Experiment the Surface of the Liquor in the Pipe will alwayes be lower than that of the oyle without it For in the imaginary plain E F the Cylinder of water J G contain'd in the Pipe J H will by reason of its greater gravity press as much upon the part J as the distill'd oyle K E J L being a lighter Liquor can do upon the other parts of the same suppos'd plain E F though the oyle reach'd to a greater height above it This second Paradox we have hitherto been discoursing of may be also prov'd by what we formerly deliver'd to make out the Truth of the third part of the Lemma premised to these Propositions But because this and the former Paradox are of importance not only in themselves but to the rest of this Treatise and are likely in most Readers to meet with indisposition enough to be receiv'd I will subjoyn in this place a couple of such Experiments as will not I hope be unacceptable that I devis'd the one to confirm this second Paradox and the other to prove the first Some of the Gentlemen now present may possibly remeber that about the end of the Year that preceded the two last I brought into this place a centain new Instrument of Glass whereby I made it appear that the upper parts of water gravitate upon the lower which I did by sincking a Body that was already under water by pouring more water upon it But that Experiment belonging to other papers I shall here substitute another perform'd by an Instrument which though it makes not so fine a shew may be more easily provided and will as well as that other though you were pleas'd to command that from me serve to make out the same Truth which I shall apply my self to do as soon as I have by an Improvement of the Expedient I am to propose made good my late promise of confirming the second Paradox And before I can well draw an Argument from these Experiments for either of the propositions to be prov'd by them I must briefly repeat what I have elsewhere deliver'd already on another occasion touching the cause of the sincking of such Bubbles Namely that the Bubble X. consisting of Glass which is heavier in specie then Water and Aire which is lighter in specie then Water and if you please also of Water itself which is of the same specifick Gravity with Water as long as this whole aggregate of several Bodys is lighter then an equal bulk of Water it will float but in case it grows heavier then so much water it must according to the known Laws of the Hydrostaticks necessarily sinck being not otherwise supported Now when there is any competent pressure whether produc'd by weight or otherwise upon the water in which this Bubble is for the most part immers'd because the glass is a firm Body the water though a Liquor either suffers no compression or but an inconsiderable one the Aire included in the Bubble being a springy and very compressible Body will be compell'd to shrink and thereby possessing less Room then it did before the contiguous water will succeed in its place which being a body above a thousand times heavier then aire the Bubble will thereby become heavier then an equall Bulk of water and consequently will sink but if that force or pressure be remov'd the Imprison'd Aire will by its own Spring free it self from the intruding water and the Aggregate of Bodys that makes up the Bubble being thereby grown lighter then an equal bulk of water the subsided bubble will presently emerge to the Top. This Explication of the Causes of the sinking of Bubbles agrees in some things with the Doctrine of the Learned Jesuites Kercher Shottus and some other writers in the Acount they give of those two Experiments that are commonly known by the name the one of the Romane the other of the Florentine Experiments But there are also particulars wherein I who have never a recourse to a fuoa Vacui dissent from their Doctrine the principles I go upon having invited and assisted me to make that Experiment afford me some new Phaenomena which agree not with their Opinions but do with mine but I forbear to mention them here because they belong to other Papers and for the same reason I omit some accession of Ludicrous Phaenomena as they call them which I remember I have sometimes added to those which our Industrious Authors have already deduc'd from those Experiments These things being premis'd I proceed to the confirmation of the second Paradox by the following Experiment Take a long glass pipe seal'd or otherwise exactly stop'd at one end and open at the other whose Orifice if it be no wider then that it may be conveniently stop'd with mans Thumb the Tube will be the fitter to exhibit some other Phanomena Into this pipe pour such a quantity of common water as that there may be a foot or half a yard or some other competent part left unfill'd for the use to be by and by mention'd Then having poiz'd a glass Bubble with a slender neck in such a manner as that though it will keep at the Top of the water yet a very little addition of weight will suffice to sinck it put this Bubble thus poiz'd into the Tube where it will swim in the upper part of the water as long as it is let alone but if you gently pour oyle of Turpentine upon it I say gently to avoid confounding the Liquors you will perceive that for a while the Bubble will continue where it was but if you continue pouring on oyl till it have attain'd a sufficient height above the water which 't will be easie to peceive because those two liquors will keep themselves distinct you shall
see the Bubble subside till it fall to the Bottom and continue there as long as the oyl remains at the height above the water The Reason of this Phanomenon according to our Doctrine is this That the oyl of Turpentine though a lighter Liquor then water yet gravitates upon the subjacent water and by its pressuce forces some of it into the cavity of the bubble at the open Orifice of its neck whereby the Buble which was before but very little less heavy then an equal Bulk of water being by this accession made a little more heavy must necessarily sinck and the cause of its submersion namely the pressure of the oyle continuing it must remain at the bottom And to confirm this explication I shall add that in case by inclining the Tube or otherwise you remove the Cylinder of oyl or a competent part of it in case it were longer then was necessary the Bubble will again emerge to the Top of the water for as for the oyle that is too light a Liquor to buoy it up which happens only because the pressure of the oyle upon the water being taken of the Aire by vertue of its own spring is able to recover its former Expansion and reduce the bubble to be as light as 't was before And now we may proceed to that other Experiment by which we lately promis'd to confirm the first Paradox And in some regard this following Experiment has been preferr'd as more strange to that I have been reciting For it seem'd much less improbable that of two Heterogeneous Liquors the inferior should be press'd upon by the incumbent which though lighter kept in an intire body above it then that in water which is a Homogeneous Liquor and whose parts mingle most freely and exquisitely with one another the upper part should press upon the lower and that they will do so may appear by the Experiment it is now time to sub joyn Provide a long Tube and a poiz'd Bubble as in the former Experiment then having pour'd water into the Tube till it reach above 5 or 6 Inches for a determinate height is no way necessary above the Bottome cast in the Bubble which will not only swim but if you thrust it down into the water it will of it self emerge to the upper part of it Wherefore take a slender Wand or a Wire or a slender glass pipe or any such Body that is long enough for your purpose and with it having thrust the bubble beneath the Surface of the water pour water slowly into the Tube whose Cavity will not be near fill'd by the rod or wire till it have attain'd a competent height which in my last Tryals was about a Foot or half a Yard above the bubble and you shall see that the bubble which before endeavour'd to emerge will by the additional weight of the incumbent water be depress'd to the bottom of the Tube After which you may safely remove the wire or other body that kept it from rising For as the weight of the Incumbent water was that which made it sinck so that weight continuing on it the bubble will continue at the bottom But yet it is not without cause that we imploy a wire or some such thing in this Experiment though we affirm it to be onely the weight of the Incumbent water that makes the Bubble sinck For if you should pour water into the Tube to the height lately mention'd or ev'n to a greater if you did not make use of the Wire it would not serve the turn because that as fast as you pour in the water the Bubble being left to it self will rise together with it and so keeping always near the upper part of the water it will never suffer the Liquor to be so high above it as it must be before it can depress it But to confirm that 't is the weight of the Superior water that sincks the Bubble and keeps it at the Bottom if you take out of the Tube a competent quantity of that Liquor and so take of the pressure of it from the Bubble this will presently without any other help begin to swim and regain the upper part of the water whence it may at pleasure be praecipitated by pouring back into the Tube the water that was taken out of it And these Confirmations added to the former Proofs of the first and second Paradoxes being we conceive sufficient to satisfie Impartial Readers of the Truth of them we should presently advance to the next Proposition if we did not think fit to interpose here a Scholium SCHOLIUM IT may perchance be wondred at why since we lately mention'd our having made some Tryals with oyle of Tartar per deliquium we did not in the present Experiment in stead of fair water make use of that it being a very much heavier Liquor and though it may be incorporated with express'd oyles unmingleable in such Tryals with oyle of Turpentine But to this I answer That ev'n in such slender pipes as those made use of about the first Experiment I found that oyle of Tartar was ponderous enough to flow down though slowly into the oyle of Turpentine at one side of the immers'd Orifice whilst the oyle pass'd upwards by it along the other side of the pipe And my knowledge of this could not but make me a little wonder That so Curious a person as Monsieur Paschall should somewhere teach That if a Tube of above 14 foot long and having its Orifice placed 14 foot under water be full of Quicksilver the fluid Metal will not all run out at the Bottom of the pipe though the Top of it be left open to the Aire but will be stop'd at a foot high in the pipe For the Impetus that its fall will give it must probably make it flow quite out of the pipe And not here to mention those Tryals of ours with Quicksilver and slender Tubes that made me think this very improbable if we consider that the Experiment will not succeed with much more favourable circumstances betwixt oyle of Turpentine and oyle of Tartar though the heavier of these two Liquors be many times lighter that quick silver It tempts me much to suspect that Monsieur Paschall never actually made the Experiment at least with a Tube as big as his Scheam would make one guess but yet thought he might safely set it down it being very consequent to those Principles of whose Truth he was fully perswaded And indeed were it not for the impetus the Quicksilver would acquire in falling from such a height the Ratiocanation were no way unworthy of him But Experiments that are but speculatively true should be propos'd as such and may oftentimes fail in practise because there may intervene divers other things capable of making there miscarry which are overlook'd by the peculator that is wont to compute only the consequences of that particullar thing which he principally considers As in this case our Author seems not to haue
not be amiss to add That it may easily be confirm'd by Experiment For if you take for instance a piece of Lead and hang it by a Horse haire that being suppos'd very near acquiponderant to water from one of the Scales of an exact Ballance and when you have put a just Connterpoize in the other Scale suffer the Lead to sinck in a ressel of water till it be perfectly covered with it but hangs freely in it the counterpoize will very much preponderance And part of the Counterpoize being taken out till the Ballatice be again reduc'd to an Aequilibrium you may easily by subducting what you have taken out and comparing it with the whole weight of the Lead in the aire find what part of its weight it looses in the water And then if you weigh any other piece of the same Lead suppose a Lump of 12 ounces and hang it by a Horse haire at one scale you may be sure that by puting into the other scale a weight less by a twelfth part supposing Lead to water to be as twelve to one that is eleven ounces though the weights be farr from an Aequilibrium in the Aire they will be reduc'd to it when the Lead it cover'd with water The pressure of water against the lower part of the Body immers'd in it may be confirmed by adding That we may thence deduce the cause of the emergency of wood and other Bodyes lighter then water which though a familiar Effect I have not found its cause to have been so much as enquired into by many nor perhaps to have been well rendred by any If we suppose then that the pipe be almost fill'd not with a sincking but a swimming oyle as oyle of Turpentine if as in the first Experiment the lower orifice be thrust under water to a far less depth then that of the oyle in the pipe and the upper be slovvly unstop'd the oyl vvill as vve formerly declar'd get out in drops at the bottom of the pipe But to determine vvhy these drops being quite cover'd and surrounded vvith vvater and press'd by it as vvell dovvnvvards as upvvards should rather emerge then descend I shall not content my self to say that vvater in specie heavier then this kind of oyle For besides that in some cases e're long to be mention'd I have made the water to depress ev'n this kind off oyle and besides that 't is not every piece of wood lighter in specie then water that will float upon water how shallow soever it be The Question is how this praepollent Gravity of the water comes to raise up the oyle though there be perchance much more water for it to break its way thorough above it then beneath it The Reason then of the emersion of Lighter Bodies in heavier fluids seems to be this That the endeavour upwards of the water contiguous to the lower part of the Body is stronger then the endeavour downwards of the same Body and the water incumbent on it As in the former Scheme supposing the Drop G to be the oyle of Turpentine and to touch the two imaginary and parallel plains H J K L 't is evident that upon the lower part of the Drop N there is a greater pressure of water then upon the upper part of the same Drop M because that upon all the surface K L there is but an uniform pressure of water A K B L and upon all the parts of the surface H I there is a greater weight of water A H B I except at the part N for there the oyle G being not so heavy as so much water the oyle being expos'd to a greater pressure from beneath then its own gravity and that of the water incumbent on it will enable it to resist must necessarily give way and be impell'd upwards And the case being the same between that and any other parallel plain wheresoever we suppose it to be in its ascent it must consequently be impell'd further and further upwards till it arrive at the Top and there it will float upon the water Or to Explicate the matter without Figures when a specifically lighter Body is immers'd under water it is press'd against by two pillars of water the one bearing against the upper and the other against the lower part and because the lengths of both these Pillars must be computed from the Top of the water the lower part of the immers'd body must be press'd upon by a Pillar longer then the upper part by the thickness of the immers'd Body and consequently must be press'd more upwards then downwards And by how much the greater disparity of specifick Gravity there is betwixt the water and the emerging Body by so much the swifter caeteris paribus it will ascend because so much the more will there be of pressure upon all the other parts of the imaginary surface then upon that part that happens to be contiguous to the Bottom of the ascending Body And upon the same Grounds we may give what we have not yet met with a good solution of that Probleme propos'd by Hydrostatical Writers why if a Cylindrical stick be cut in two parts the one as long again as the other and both of them having been detain'd under water at the same depth be let go at the same time and permitted to emerge the greater will rise faster then the lesser For suppose one of these Bodies as O P to be two foot high and the other Q R to be half so much and that the lowermost Surfaces of both be in the same imaginary plaine parallel to the uppermost surface of the water and three foot distant from it in this case there will be against the lower part of each of the wooden Bodies a pressure from the laterally superior water equal to that upon all the other parts of the Imaginary plain whereto those Bodies are contiguous But whereas upon the upper surface of the shorter Body Q R there will lean a pillar of water two foot high the pillar of the same Liquor that will lean upon the Top of the taller Body P O will be but one foot high as the attentive considerer will easily perceive So that the wooden Bodys being lighter in specie then water both of them will be impell'd upwards but that compounded pillar if I may so call it which consists of one foot of wood and two foot of water will by its gravity more resist the being rais'd then that which consists of two foot of wood and but one foot of water so that the cause of the unequal celerity in the Ascension of these Bodys consists chieflly for I would neither overvalue nor exclude Concomitant Causes that the difference of the pressure against the upper and lower part of each body respectively is greater in one then in the other And hence we may probably deduce a reason of what we often observe in the Distillation of the oyles of Annisseeds Cloves and diverse Aromatick vegetables in Lembecks by the
other parts of the same Superficies and consequently neither the one nor the other of those Liquors will subside but they will both rest in an Aequilibrium But here it will not he amiss to note First that it is not necessary that the Glass Cylinders L M N should be all of the same length since the lower Orifice being open the water will rise to the same height within them whether the parts immers'd under the water be exactly of the same length or no. And Secondly That throughout all this Discourse and particularly in the Explication of this Paradox we suppose either that the slenderest pipes that are imploy'd about these Experiments are of a moderate size and not exceeding small Or that in case they be very small allowance be made in such pipes for this property That water will rise in them to a greater height then can be attributed to the bare Counterpoize of either the water or the oyle that impels it upwards and keeps it suspended But this difference is of so little moment in our present Inquiries That we may safely neglect it as hereafter we mean to do now we have taken this notice of it for prevention of mistakes PARADOX VI. If a Body be plac'd under water with its uppermost Surface parallel to the Horizon how much water soever there may be on this or that side above the Body the direct pressure sustain'd by the Body for we now consider not the Lateral nor the recoyling pressure-to which the Body may be expos'd if quite environ'd with water is no more then that of a Columne of water having the Horizontal superficies of the Body for its Basis and the perpendicular depth of the water for its height And so likewise If the water that leans upon the Body be contain'd in pipes open at both ends the pressure of the water is to be estimated by the weight of a pillar of water whose Basis is equal to the lower Orifice of the pipe which we suppose to be parallel to the Horizon and its height equal to a perpendicular reaching thence to the top of the water though the pipe be much inclin'd towards the Horizon or though it be irregularly shap'd and much broader in some parts then the said Orifice STevinus in the tenth Proposition of his Hydrostatical Elements having propos'd in more general termes the former part of our Paradox annexes to se a Demonstration to this purpose If the Bottom E F be charged with a greater weight then that of the water G H F E that surplusage must come from the adjoyning water therefore if it be possible let it be from the water A G E D H B C F which granted the Bottom D E will likewise have a greater weight incumbent on it upon the score of the neigbouring water G H F E then that of the water A G E D. And the reason being the same in all the three cases the Basis F C must susteine a greater weight then that of the water H B C F. And therefore the whole bottom D C will have a greater weight incumbent on it then that of the whole water A B C D which yet A B C D being a rectangular Body would be absurd And by the same way of reasoning you may evince That the Bottom E F sustains no less a weight then that of the water G H F E. And so since it sustains neither a greater weight nor a less it must sustein just as much weight as the Columne of water G H F E. This Demonstration of the Learned Stevinus may well enough be admitted by a Naturalist though according to some Hypotheses touching the Cause and Nature of Gravity it may faile of Mathematical exactness and by it may be confirm'd the first part of our propos'd Paradox And some things annexed by Stevinus to this Demonstration may be also apply'd to countenance the second But because this is one of the noblest and usefullest Subjects of the Hydrostaticks we think it worth while to illustrate after our manner each of the two parts of our Paradox by a sensible Experiment First then Take a slender Glass pipe of an even Bore turn'd up at one end like the annexed Syphon Into this Syphon suck oyl of Turpentine till the Liquor have fill'd the shorter leg and be rais'd 2 or 3 Inches in the longer Then nimbly stopping the upper Orifice with your finger thrust the lower part of the Syphon so farre into a deep Glass full of water That the Surface of the oyle in the longer leg of the pipe may be but a little higher then that of the External water and upon the removal of your finger you will find the Surface of the oyle to vary but little or not at all its former Station And as if you then thrust the pipe a little deeper you will soe the oyle in the shorter leg to begin to be depress'd so if afterwards you gently raise the pipe toward the top of the water you shall see the oyle not only regain its former station but flow out by degrees in drops that will emerge to the Top of the water Now since the water was able at first to keep the oyl in the longer leg of the pipe suspended no higher then it would have been kept by a Cylinder of water equal to the Orifice of the shorter leg of the pipe and reaching directly thence to the Top of the water as may be easily cried by making a Syphon where the shorter leg may be long enough to contain such a Cylinder of water to conterpoize the oyl in the longer since when once by the raising of the pipe the height of the incumbent water was lessen'd the oyle did more then Counter-ballance it as appears by its flowing out of the Syphon we may well conclude That though thence were in the Vessel a great deal of water higher then the immers'd Orifice of the Syphon and it would be all one though the Syphon were placid at the same depth in a pond or lake yet of all that water no more did gravitate upon the Orifice then that which was plac'd directly over its which was such a pillat of water as the Paradox describes And by the way we may hence learn That though water be not included in pipes yet it may press as regularly upon a subjacent Body as if it were And therefore we may well enough conceive a pillar of water in the free water it self where there is nothing on any side but the contiguous water to bound the imaginary pillar But I had forgot to add That the first part of our Paradox will hold not only when the water superior to the Body it presses upon is free but also when it is included in Vessels of never so seemingly disadvantageous a shape For if you so frame the shorter leg of a Syphon that it may expand its self into a funnel like that of Fig. 6. employ'd about the proof of the foregoing
be kept from emerging to the Top of it being this That since the Surface of a Vessel full of standing water is Physically speaking Horizontal the water that presses against the lower part of the immers'd Body must needs be deeper then that which presses against the upper If I could so order the matter that the water that leans upon the upper part of the Body should be being higher then the level of the rest of the water have a height great enough to ballance that which presses against the lower and the Bodies not shift places by passing one by the other the oyle might be kept suspended betwixt two parcels of water To reduce this to practise I took the following course having suck'd into a slender pipe such as that imploy'd about the first experiment about an Inch of water and kept it suspended there by stopping the Orifice of the pipe I thrust the lower part of the pipe about two inches beneath the Surface of some oyl of Turpentitie which to make the effect the clearer I sometimes tinge deeply with Copper then removing my finger the oyle being press'd against the immers'd Orifice with a greater force then the weight of so little suspended water could resist that oyle was impell'd into the lower part of the pipe to the height of near an inch and then again I stopp'd the upper Orifice of the pipe with my finger and thereby keeping both the Liquors suspended in it I thrust the pipe into a Glass full of water three or four inches beneath the Surface of it and then for the Reason just now given the water upon the Removal of my finger will press in at the lower Orifice of the pipe and impell up the oyle till they come to such a station as that express'd in the annex'd Scheme where P Q is the water newly impell'd up into the pipe Q R is the oyl and R S the water that was at first suck'd into the pipe For in this station these three liquors do altogether as much gravitate upon the part P as the incumbent water alone does upon the other parts of the imaginary superficies G H and yet the oyle R Q does not ascend because the diffluence of the water R S being hindred by the sides of the pipe its superficies T S is higher then A D the Superficies of the rest of the water by which means the incumbent water may be brought to have upon the upper part R of the oleous Cylinder as great a pressure as that of the water that endeavours to impel upwards the lower part Q of the same suspended Cylinder of oyle PARADOX X. That the cause of the Ascension of water in Syphons and of its flowing through them may be explicated without having a recourse to natures abhorrency of a Vacuum BOth Philosophers and Mathematicians having too generally confest themselves reduc'd to fly to a fuga vacui for an account of the cause of the running of water and other Liquors through Syphons And ev'n those moderns that admit a Vacuum having as far as I have met with either left the Phaenomenon unexplicated or endeavour'd to explain it by disputable Notions I think the Curious much oblig'd to Monsieur Paschal for having ingeniously endeavour'd to shew That this difficult Probleme need not reduce us to have recourse to a fuga vacut And indeed his Explication of the motion of water in Syphons seems to me so consonant to Hydrostatical principles that I think it not necessary to alter any thing in it But as for the experiment he propounds to justifie his Ratiocination I fear his Readers will scarce be much invited to attempt it For besides that it requires a great quantity of Quicksilver and a new kind of Syphon 15 or 20 foot long the Vessels of Quicksilver must be plac'd 6 or 7 yards under water that is at so great a depth that I doubt whether men that are not divers will be able conveniently to observe the progress of the Tryal Wherefore we will substitute a way which may be try'd in a glass Tube not two foot deep by the help of another peculiarly contriv'd glass to be prepar'd by a skilful hand Provide then a glass Tube A B C D of a good wideness and half a yard or more in depth provide also a Syphon of two legs F K and K G whereunto is joyn'd at the upper part of the Syphon a pipe E K in such manner as that the Cavity of the pipe communicates with the cavities of the syphon so that if you should pour in water at E it would run out at F and G. To each of the two Legs of this new Syphon must be ty'd with a string a pipe of Glass I and H seal'd at one end and open at the other at which it admits a good part of the leg of the Syphon to which it is fastned and which leg must reach a pretty way beneath the Surface of the water wherewith the said pipe is to be almost fill'd But as one of these legs is longer then the other so the surface of the water in the suspended pipe I that is fastned to the shorter leg K F must be higher that is nearer to K or A B then the surface of the water in the pipe H suspended from the longer leg KG that according to what is usual in Syphons the water may run from a higher vessel to a lower All things being thus provided and the pipe E K being held or otherwise made fast that it may not be mov'd you must gently poure oyle of Turpentine into the Tube A B C D which if you have not much oyle you may before hand fill with water till the liquor reach near the Bottom of the suspended pipes as to the superficies X Y till it reach higher then the top of the Syphon F K G whose Orifice E you may if you please in the mean time close with your finger or otherwise and afterwards unstop and then the oyle pressing upon the water will make it ascend into the legs of the Syphon and pass through it out of the uppermost vessel J into the lowermost H and if the vessel J were supply'd with water the course of the water through the Syphon would continue longer then here by reason of the paucity of water it can do Now in this Experiment we manifestly see the water made to take its course through the legs of a Syphon from a higher vessel into a lower and yet the top of the Syphon being perforated at K the aire has free access to each of the legs of it through the hollow pipe E K which communicates with them both So that in our case where there is no danger of a Vacuum though the water should not run through the Syphon the fear of a Vacuum cannot with any shew of Reason be pretended to be the cause of its running Wherefore we must seek out some other And it will not be very difficult
by the seven following Arguments Object 1. Sayes he Because else the inferiour parts of the water would be more dense then the Superior since they would be compress'd and condens'd by the weight of them Ans But if the Corpuscles whereof water consists be suppos'd to be perfectly solid hard the inferior Corpuscles may be press'd upon by the weight of the superior without being compress'd or condens'd by them As it would happen if Diamond dust were lay'd together in a tall heap For though the upper parts being heavy and solid Corpuscles cannot be deny'd to lean and press upon the lower yet these by reason of their Adamantine hardness would not be thereby compress'd And 't is possible too that the Corpuscles of water though not so perfectly hard but that they may a little yield to an extream force be solid enough not to admit from such a weight as that of the incumbent water at least in such small heights as observations are wont to be made in any compression great enough to be sensible As besides some Tryals I have formerly mention'd in another place those made in the presence of this Illustrious Company seem sufficiently to argue viz. That water is not sensibly compressible by an ordinary force And I find not by those that make the Objection that they ever took pains to try whether in deep places of the Sea the lower parts are not more condens'd then the upper nor do I see any absurdity that would follow from admitting them to be so Object 2. Our Authors second Argument is Because Divers feel not under water the weight of the water that lyes upon them Ans But for Answer to this Argument I shall content my self to make a reference to the ensuing Appendix where this matter will be considered at large and where I hope it will be made to appear that the phaenomenon may proceed partly from the firm Texture of the Divers body and partly from the nature of that pressure which is exercis'd against bodyes immers'd in fluids which in that case as to sense presses every where equally against all the parts of the body expos'd to their Action Object 3. The third Argument is That ev'n the slightest Herbs growing at the bottom of the water and shooting up in it to a good height are not oppress'd or lay'd by the incumbent water Ans But the Answer to that is easie out of the foregoing Doctrine For the Plants we speak of sustain not the pressure of the water above them by their own strength but by the help of the pressure of water that is beneath which being it self press'd by the water that is though not perpendicularly over it superior to it presses them upwards so forcibly that if they were not by their Roots or otherwise fastned to the ground they being in specie lighter then water would be buoy'd up to the top of the water and made to float as we often see that weeds do which storms or other accidents have torn from their native soyle Object 4. A fourth Objection is this That a heavy Body ty'd to a string and let down under water is supported and drawn out with as much ease as it would be if it had no water incumbent on it nay with greater ease because heavy bodyes weigh less in water then out of it Ans But an Account of this is easie to be rendred out of our Doctrine For though the water incumbent on the heavy body do really endeavour to make it sinck lower yet that endeavour is rendred ineffectual to that purpose by the equal pressure of the water upon all the other parts of the Imaginary surface that is contiguous to the bottom of the immers'd body And that pressure upon the other parts of that suppos'd plain being equal not only to the pressure of the pillar of water but to that pillar and to the weight of as much water as the immers'd body fills the place of it must needs follow That not only the hand that susteins the body should not feel the weight of the incumbent water but should be able to lift up the Body more easily in the water then in the aire But though the pressure of the water incumbent on the stone can not for the reason assign'd be felt in the case propos'd yet if you remove that water as in the Experiment brought for the proof of the last Paradox it will quickly appear by the pressure against the lower part of the heavy body and its inability to descend by its own weight when it is any thing deep under water it will I say quickly appear by what will follow upon the absence of the Incumbent water how great a pressure it exercis'd upon the stone whilst it lean'd on it Object 5. The fifth Argument is propos'd in these words Because a Bucket full of water is lighter in the water then out of it nor does weigh more when full within the water then when empty out of it nay it weighs less for the reason newly assign'd in the fourth Objection therefore the water of the Bucket because it is within water does not gravitate nor consequently press downwards either the Bucket or the water under the Bucket This is the grand and obvious Experiment upon which the Schools and the generality of Writers have very confidently built this Axiom That the Elements do not gravitate in their proper place and particularly that water weighs not as they speak in its own Element Ans What they mean by proper or natural place I shall not stand to examine nor to enquire whether they can prove that water or any other sublunary body possesses any place but upon this account that the cause of gravity or some other movent enables it to expel other contiguous Bodies that are less heavie or less moved out of the place they possess'd before and gives it an incessant tendencie or endeavour towards the lowermost parts of the Earth But as to the Example propos'd it s very easie to give an account of it For suppose ABCD to be a Well wherein by the string E F the Bucket is suspended under water and has its Bottom contiguous to the imaginary plain I K. If now we suppose the Bucket to consist only of wood lighter then water it will not only not press upon the hand that holds the Rope at E but will be buoyd up till the upper parts of the Bucket be above the top of the water because the wood whereof the Bucket is made being lighter in specie then water the pressure of the water in the Bucket G and the rest of the water incumbent on that together with the weight of the Bucket it self must necessarily be unable to press the part H so strongly as the other parts of the imaginary plaine I K are press'd by the weight of the meer water incumbent on them But if as t is usual the Bucket consists partly of wood partly of iron the Aggregate
to this Doctrine I cannot admit our Authors reasoning that because a mans body is bulk for bulk heavier then water therefore the water does not endeavour to place its self beneath it For water being a heavy body derives from the cause of its gravity what ever that be an incessant endeavour towards the Center of the Earth nor is there any Reason why it s happening to be incumbent on a body heavier in specie then it self should destroy that endeavour And therefore though it may be said that the water does not endeavour to place it self beneath a humane body because indeed an inanimate Liquor cannot properly be said to act for this or any other end yet the water being a heavy body tends continually towards the lower part of the Earth and therefore will get beneath any body that is plac'd betwixt it and that without regard whether the inferior body be heavier or lighter in specie then it self as far as the degree of its gravity will enable it nor would it ever rest till it have reach'd the lowermost parts of the Earth if the greater ponderousness of the earth and other heavy bodies did not hinder not its endeavour downwards nor its pressure upon subjacent bodies but only its actual descent This Learned Author himself tells us as well as Stevinus and others that have written of the Hydrostaticks unanimously teach that if the bottom of a vessel be parallel to the Horizon the weight of water that rests upon it is equal to a pillar of water having that bottome for its Basis and for its height a perpendicular reaching thence to the uppermost Surface of the water Nor is it reasonable to conceive that there will be any difference in this pressure of the incumbent water whether the bottom be of Deale that will swimme or of Box that will sinck in water or to speak more generally whether it be of Wood in specie lighter then water or of Copper or some other Metal that is in specie heavier then it And since water being not a solid Body but a fluid consists as other fluids of innumerable Corpuscles that though extreamly minute have their own sizes and figures And since the pressure of water upon the bottom of a vessel is proportionate to its perpendicular height over the bottom 'T is manifest that the upper Corpuscles press the bottom as well as the lower which since they cannot do immediately they must do by pressing the intermediate ones And I have already shown discoursing one of the former Paradoxes that the Superior parts of water do not onely presse those that are directly under them but communicate a pressure to those that are aside of them and at a distance from them And if it be objected That water endeavours to get beneath a Bottome of Glass Vessels or other bodies heavier in specie then its self because under that bottome there is aire which is a body lighter in specie then water I say that this is precarious for the indisputable gravity of the water is alone sufficient to make it always tend downwards though it cannot always move downwards what ever body be beneath it And who can assure the makers of this Objection That there are not beneath even the bottome of Rivers or of the Sea where yet they say water is consistent and rests as in its own place vast spaces replenished but with aire fumes or fire or some other body lighter then water For not to mention that the Cartesians take the Earth we tread on to be but a thin Crust of the Terrestrial Globe whose inside as farre as the Center is replenish'd with a subtle fluid matter like that whereof the Sunne consists We know that in some places as particularly at a Famous Coal-mine in Scotland there are great Cavities that reach a good way under that ground that serves there for a bottome to the Sea So that for ought these Objectors know ev'n according to their own Doctrine the water ev'n in the Sea may endeavour to get beneath a body heavier in specie then it self But for my part I cannot but think that to imagine the water knows whether or no there be aire or some lighter body then it self beneath the body it leans on and the superior parts do accordingly exercise or suspend their pressure upon the inferior is to forget that it is a heavy Liquor and an inanimate Body Another Solution there is of this Hydrostatical problem we have been discoursing of which I met with in a Printed Letter of Monsieur Des Cartes in these terms Je ne me c. I remember not what reason 't is that Stevinus gives why one feels not weight of water when one is under it but the true one is that there can no more of water gravitate upon the body that is in it or under it then as much water as could descend in case that body left its place Thus for Example If there were a Man in the Barrel B that should with his Body so stop the hole A as to hinder the waters getting out he would feel upon himself the weight of the whole Cylinder of water A B C of which I suppose the Basis to be equal to the hole A for as much as if he sunck down through the hole all the Cylinder of water would descend too but if he be a little higher as about B so that he does no longer hinder the water from running out at the hole A he ought not to Feel any weight of the water which is over him betwixt B and C because if he should descend toward A that water would not descend with him but contrarywise a part of the water which is beneath him towards A of equal bulk to his Body would ascend into its place so that in stead of feeling the water to press him from the Top downward he ought to feel that it buoys him upward from the bottome which by Experience we see Thus far this subtil Philosopher for whose Ratiocinations though I am wont to have much respect yet I must take the liberty to confess my self unsatisfy'd with this For haveing already sufficiently prov'd That the upper parts of water press the lower and the bodies plac'd beneath them whether such bodies be lighter in specie then water or heavier we have subverted the Foundation upon which Monsieur Cartes's ingenious though unsatisfactory Explication is built And yet I shall add ex abundanti That supposing what he sayes That in case the solid B should descend towards A the incumbent water would not descend with it but a part of the subjacent water equal in bulk to the solid would ascend and succeed in its room yet that is but accidental by reason of the steinchness and fulness of the Vessel And though indeed the Superior water cannot actually desend upon the depression of the solid at B if at the same time while that body descends an equal bulk of water succeeds in its
your hand that you will imagine some ponderous weight is lay'd upon it And I remember by such an Experiment I have not onely had my hand put to much pain but have had the back of it so bent downward as if it were going to be broken But though such considerations as these may much lessen the difficulty of our phaenomenon whose cause is inquired into Yet still it seems somewhat odd to me That since 't is evident from the nature of the thing and by Stevinus's his confession that there is a vast pressure of water against every part of the body whose endeavour tends inward so exceedingly forcible a pressure which thrusts for instance the Muscles of the Arms and Thighs against the Bones the Skin and Flesh of the Thorax against the Ribs should not put the Dives to any sensible pain As I find not by one that I examin'd that it dos Though this man told me he stay'd a good while at the depth of betwixt 80 and 100 foot under the Sea water which is heavier then fresh water For that which Stevinus's Explication will only showis That there must be no manifest dislocation of the greater parts of the Body whereas the bare compression of two small parts one against another is sufficient to produce a sense of pain But it seems the Texture of the bodyes of Animals is better able to resist the pressure of an every way ambient fluid then if we were not taught by experience we should imagine And therefore to satisfie those that secluding the Question about the sense of pain think it an abundantly sufficient Argument to prove that bodyes immers'd under water are not compress'd by it That Divers are not oppress'd and ev'n crush'd by so vast a load of water amounting by Stevinus's computation to many thousands of pounds as is incumbent on them We will add that though an Experiment propos'd by Monsieur Paschal to this purpose were such that at first sight I said that it would not succeed and was not upon tryal mistaken in my conjecture yet it gave me the occasion to make another which will I hope fully make out the thing I design'd it for The Ingenious Monsieur Paschal would perswade his Readers that if into a glass Vessel with luke-warm water in it you cast a flie and by a Rammer forcibly press that water you shall not be able to kill or hurt the flie VVhich says he will live as well and walk up and down as lively in luke-warme water as in the aire But upon tryal with a strong flie the Animal was as we expected presently drowned and so made moveless by the luke-warm water Wherefore we substituted another Experiment that we knew would not only succeed as you will presently see it will do but teach us how great a pressure the included Animal must have been expos'd to VVe took then a somewhat slender Cylindrical pipe of Glass seal'd at one end and open at the other and to this we fitted a Rammer which by the help of some thongs of soft leather that were carefully wound about it did so exactly fill the pipe that it could not easily be mov'd to and fro and would suffer neither water nor aire to get by betwixt it and the internal surface of the Glass VVe also provided some small Tad-poles or Gyrini about an Inch long or less which sort of Animals we made choice of before any other partly because they could by reason of their smalness swim freely to fro in so little water as our pipe contain'd partly because those Creatures being as yet but in their Infancy were more tender and consequently far more expos'd to be injur'd by compression then other Animals of the same Bulk but come to their full age and growth would be as indeed such young Tad-poles are so soft and tender that they seem in comparison to the bigger sort of flies to be but organiz'd Gelly One of these Tadpoles being put into the water and some Inches of aire being left in the pipe for the use anon to be mention'd the water and aire and consequently the Tadpole were by the intrusion of the plug or rammer with as great a force as a man was able to imploy violently compress'd and yet though the Tadpole seem'd to be compress'd into a little less Bulk then it was of before it swom freely up and down the water without forbearing sometimes to ascend to the very top though the Instrument were held perpendicular to the Horizon Nor did it clearly appear to us That the little Animal was injur'd by this compression and most manifest it is he was not crush'd to death or sensibly hurt by it And having repeated this Experiment several times with Tadpoles of differing ages we may I presume safely conclude That the Texture of Animals is so strong that though water be allowed to weigh upon water yet a Diver ought not to be opprest by It Since whether or no water weighs in water 't is manifest that in our Experiment the water and consequently the Tadpole was very forcibly by an External Agent compress'd betwixt the violently condens'd aire and the rammer And by the notice we took of the quantity of aire before the compression began and that to which it was reduc'd by compression The moderatest estimate we could make was That it was reduc'd into an eighth or tenth part of it's former space and so according to what we have elswhere prov'd the pressure that was upon the aire and consequently upon the water and the included Tadpole was as great as that of a Cylinder of water of above 200 if not 300 foot high And yet all this weight being unable to oppress or so much as manifestly to hurt the tender Tadpole which a very small weight would suffice to have crush'd if it prest only upon one part of it and not upon the other we may thence learn the Truth of what we have been endeavouring to evince That though water be allowed to press against water and all immers'd Bodys yet a Diver may very well remaine unoppress'd at a great depth under water as long as the pressure of it is uniforme against all the parts expos'd thereunto FINIS * About this passage See the Publisher to the Reader * Chiefly in several places of the unpublish'd part of the Treatise of the osefulness of Experimental Philosophy * An Account of this passage also may be had from the Publishers Advertisement to the Reader * That excellent Mathematician the Learned Dr Wallis Savilian Professor of Geometry This Experiment and the Explication of it if to some they should here seem somewhat obscure will be easily understood by the Figures and Explications belonging to the first ensuing Paradoxe See the second Figure In certain Notes upon some of the Physics-mechanical Experiments touching the Aire Fig. 3. Fig. 1. 2. Fig. 4. Fig. 5. See PARADOX the sixth Fig. 6. Fig. 8. Figur 9. Fig. 10. Fig. 11. See Fig. 12. Fig. 13. Fig. 14. See the Proof of the 11. Paradox Fig. 15. Fig. 16. Fig. 17. Fig. 18. In the Physico-Mechanical Experiments Fig. 19. * The word about is added because indeed the Author as he elsewhere delivers did by exact scales find Brass to weigh between eight or nine times as much as water but judg'd it needless to his present Argument and inconvenient to take notice of the fraction Fig. 20. In the History of fluidity firmness Second Tome lettre 32. Fig. 22. Stevinus Hydrostat Lib. 5. pag. 149. Sed Exemple clarius ita intelliges este ABCD aqua cujus fundum D C in quo foramen E habeat Epistimeus sibi iesertum cui Dorso incumbat Homo F Quae cum ita fiat ab aqua pondere ipsi insidente nulla pars Corporis luxari poterit cum aqua ut dictus est undiquaque aqualiter urgeat Fig. 23. Si vero ejus veritatem explorare libeat eximito Epistemiun tumque tergum nulla re fultum sustinebitur ut in locis cateris ideoque istic tanto pressu afficietur quantus tertio exemple secunda propositionis hujus demonstratus est vidquantam efficit columna aquea cujus Basis sit foramica E altitudo autem eadem quae aqua ipsi insidentis Quo exemplo propositi veritas manifeste declaratur Fig. 24.