the pressure of the ambient Atmosphaere This bubble was like a Peare with its stemme furnish'd with a very slender pipe of Glass at which it was blown that it might be readily seald up and then the Aire within it being by the flame of the Lamp gradually rarified as much as conveniently could be whilst the Body of the Bubble was exceeding hot the newly mentioned stemme was nimbly put into the middle of the flame where by reason of its slenderness the Glass which was exceeding thin was immediately melted whereby the Bubble was Hermetically seal'd up This Glass being permitted leasurely to coole I could afterwards keep it by me an hour or a day or a week or longer if I thought fit and when I had a mind to shew the Experiment I put it in one of the scales of an exact ballance that would turn perhaps with the 30th or 50th or a lesse part of a grain and having carefully counterpois'd it I then warily broke off the seal'd end placing a sheet of paper just under the scale to receive the fragments of the Glass and putting in again those fragments that scale wherein the Glass was would considerably preponderate which it must do upon the account of the Weight of Aire there being no other cause either needful or justly assignable but the weight of the Aire that rush'd into the Cavity of the Glass as finding less resistance there then elsewhere by reason that the included Aire had it's spring much weakn'd by it's great expansion This Experiment I many times tryed sometimes before some Virtuosi and sometimes before others who all allowed it to be conclusive For here it could not be objected as against the weighing of Aire in a Bladder which objections yet I could easily answer if it were now proper that the aire which ponderates it stuff'd with the Effluvia of him that blows the Bladder and besides that is not aire in its Natural state but violently compress'd For here 't is the free aire and in it's wonted laxity that makes the Glass preponderate And that there is a great Ingress of the external aire is evident by these three Phaenomena The one that if you lend an attentive Ear you shall plainly heare a kind of whistling noise to be made by the external aire as it rushes violently in upon the breaking of the Glass The other that the Rarefaction of the aire seal'd up in the bubble being very great there is a great deal of space left for the ambient aire to fill upon its admission and the greatness of this Rarefaction may be guess'd at both by the breaking of such bubbles now and then by the pressure of the External aire which is not competently assisted by the Internal to resist and also by the third Phaenomenon I intended to take notice of namely That if instead of breaking off the seal'd end of the Glass in the aire you break it under water that Liquor will by the Pressure of the Atmosphaere be forc'd to spring up like an artificial Fountaine into the Cavity of the Bubble and fill about three quarters of it By which last circumstance I gather that the weight of the aire is more considerable then ev'n many who admit the aire to have weight seem to imagine For we must not suppose that all the aire contain'd in the Bubble when broken weighs no more then the weight requisite in the opposite Scale to reduce the Ballance to an Aequilibrium since this additional weight is onely that of the aire that intrudes on the breaking of the glass which aire by the Observations newly mention'd to have been made with water appears to be but about three quarters of the whole aire contain'd in the broken Bubble and yet according both to our Estimate and that of divers Virtuosi and some of them eminent Mathematicians when the capacity of the Bubble was short of two cubical Inches and so proportionably in other glasses the nice Ballance we us'd manifested the newly admitted Aire to amount to some times near halfe a grain and sometimes beyond it And because one of the last Experiments that I made to this purpose with seal'd Bubbles was none of the least accurate I shall conclude this Subject with the following account of it A thin glass Bubble blown at the flame of a Lamp and Hermetically seal'd when the contained aire was exceedingly rarified was Counterpoiz'd in a nice paire of Scales and then the seal'd apex being broken off and put again into the same Scale the weight appear'd to be increas'd by the re-admitted aire a pretty deal above 11 16 ths and consequently very near if not full ¾ of a graine Lastly having by some slight for 't is no very easie matter fill'd it with common water we weigh'd the glass and water together and found the latter besides the former to amount to 906 grains so that supposing according to our former Estimate countenanced by some Tryals that the re-admitted aire which amounted to ¾ of a grain fill'd but ¾ of the whole Cavity of the Bubble the aire that was in it when seal'd possessing one quarter of that Cavity the whole aire contain'd in the Bubble may be reasonably presum'd to weigh a whole grain in which case we might conclude abstracting from some little Niceties not fit to be taken notice of here as elsewhere that the water in our Experiment weighed very little more then nine hundred times as much as an equal quantity of Aire And therefore though we allow that in an Experiment so diligently made as this was the aire praexistent in the bubble did not adaequately possess so much as a fourth part but about a fifth or a sixth of its Cavity the aire will yet appear so heavy that this Experiment will agree well with those others recorded in another Treatise wherein we assign'd numero rotundo a thousand to one for the proportion wherein the specifick Gravity of water exceeds that of aire PARADOX I. That in Water and other Fluids the lower parts are press'd by the upper PRovide a Glass vessel of a convenient height and breadth A. B. C. D. fill'd with water almost to the Top Then take a glass Pipe open at both Ends Cylindrical and of a small Bore as about the eighth or sixth part of an Inch in Diameter Put the lower End of this Pipe into clear Oyle or Spirit of Turpentine and having by Suction rais'd the Liquor to what part of the Pipe you think fit as soon as it is there you must very nimbly removing your Lips stop the upper Orifice with the pulp of your finger that the rais'd Liquor may not fall back again Then taking the Pipe and that Liquor out of the Oyle of Turpentine place it perpendicularly in the Glass of water so as that the Surface of the Oyle in the Pipe be somewhat higher then that of the water without the Pipe and having so done though you take off your finger from the upper Orifice of the Pipe
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
of the imaginary Superficies that passes by the lower Orifice of it is the same with the pressure which other parts of that imaginary superficies sustaine from as much of the External water and of the Atmosphaere as come to lean upon it That there may be cases wherein water may be rais'd by suction not upon the Account of the weight of the aire but of its spring I have elsewhere shovvn and having likevvise in other places endeavour'd to explicate more particularly the ascension of vvater in Pumps vvhat has been said already may suffice to be said in this place where 't is sufficient for me to have shovvn That vvhither or no the Ascension of water may have other causes yet in the cases propos'd it needs no more then the competent vveight of an External Fluid as is the Aire vvhose not being devoid of gravity the Cogency of our Experiments has brought even our Adversaries to grant us For confirmation of this I will here add because it now comes into my mind what might perhaps be elsewhere somewhat more properly mention'd an Experiment that I did but lightly glance at in the Explication of the first and the Scholium of the second Paradox In order to this I must advertise That whereas I there took notice that some Ingenious men had complain'd that contrary to the Experiment propos'd by Monsieur Paschall they were not at all able to keep Mercury suspended in Tubes however very slender though the lower end were deeply immers'd in water if both their ends were open The Reasons of my doubting whether our Ingenious Author had ever made or seen the Experiment were not only that it had been unsuccesfully tryed and seem'd to me unlikely to succeed in Tubes more slender then his appear'd but because the Impetus which falling quick silver gains by the acceleration of motion it acquires in its descent must in all probability be great enough to make it all run out at the bottom of a Tube open at both ends and fill'd with so ponderous a Liquor though the Tube were very much shorter then that propos'd by Monsieur Paschall This advertisement I premise to intimate that notwithstanding the hopelessness of the Experiment as it had been propos'd and tried I might have reason not to think it impossible to perform by another way the main thing desir'd which was to keep Quicksilver suspended in a Tube open at both ends by the resistance of the subjacent water For by the Expedient I am going to propose I have been able to do it even with a Liquor much lighter then water Finding then that even a very short Cylinder of so ponderous a fluid as Mercury would if it were once in falling descend with an impetus not easy to be resisted by the subjacent Liquor I thought upon the following Expedient to prevent this inconvenience I took a slender pipe the Diameter of whose Cavity was little above the sixth part of an Inch and having suck'd in at the lower end of it somewhat lesse then half an inch of Quicksilver and nimbly stopp'd the upper Orifice with my finger I thrust the Quicksilver into a deep glass of oyle of Turpentine with a care not to unstop the upper Orifice till the small Cylinder of quicksilver was 18 or 20 times its depth beneath the Surface of the oyle For by this means when I unstopp'd the pipe the Quicksilver needed not as otherwise it would begin to fall as having a longer Cylinder then was requisite to make an Aequilibrium with the other fluid For by our Expedient the pressure of the oyle was already full as great if not greater against the lower part of the Mercurial Cylinder as that which the weight of so short a Cylinder could exercise upon the contiguous and subjacent oyle And accordingly upon the removal of my finger the Quicksilver did not run out but remain suspended in the lower part of the pipe And as if I rais'd it towards the Superficies of the oyle the Mercury would drop out for want of its wonted Counterpoize so if I thrust the pipe deeper into the oyle the increas'd pressure of the oyle would proportionably impell up the Mercury towards the higher parts of the pipe which being again a little and but a little rais'd the Quicksilver would fall down a little nearer the bottom of the pipe and so with a not unpleasant spectacle the ponderous Body of quick silver was made sometimes to rise and sometimes to fall but still to float up on the Surface of a Liquor lighter ther common Spirit of Wine it self But besides that the Experiment if the maker of it be not very careful may easily enough miscarry the divertisement it gives seldome proves lasting the oyle of Turpentine after a while insinuating it self betwixt the sides of the pipe and those of so short a Cylinder of Mercury and thereby disordering all And therefore though I here mention this Experiment as I tryed it in oyle of Turpentine because that is the Liquor I make use of all along these Paradoxes and because also I would shew that a lighter fluid then water and therefore why not aire if its height be greatly enough increas'd may by its weight and pressure either keep the Mercury suspended in pipes or even raise it in them Yet I found water wherewith I fill'd tall glasses a fitter Liquor then oyle for the Experiment in which though I sought and found some other Phaenomena yet because they more properly belong to another place I shall leave them unmention'd in this And since Experience shews us that a Cylinder of Mercury of about 30 Inches high is aequiponderant to a Cylinder of water of about 33 or 34 foot high it s very easie to conclude That the weight of the External aire which is able to raise and keep suspended 33 or 34 foot of water in a Pump may do the like to 29 or 30 Inches of Quicksilver in the Torricellian Experiment PARADOX V. That the pressure of an External Fluid is able to keep an Heterogeneous Liquor suspended at the same height in several Pipes though those Pipes be of very different Diameters THE contrary of this Proposition is so confidently asserted and believed by those Mathematicians and others that favour the Doctrine of the Schools That this perswasion of theirs seems to be the chief thing that has hinderd men from acknowledging that the Quicksilver in the Torricellian Experiment may be kept suspended by the Counterpoize of the external aire And a famous writer that has lately treated as well of the Hydrostaticks as of the 〈◊〉 of the Torricellian experiment 〈…〉 the falsehood of our Paradox That laying aside all other Arguments he contents himself to confute his Adversaries with one Demonstration as he calls it grounded on the quite contrary of what we here assert For his Objection runs to this sence That if it were the pressure of the External Aire that kept the Quicksilver suspended in the newly mention'd experiment 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
Angle with the superficies of the water A B though by this means the shorter and immers'd leg F G will in Situation sometimes respect the Bottom and sometimes the top of the Glass yet in all these oblique situations of this leg and the immers'd Orifice of it G the oblique pressure of the water will so much depend upon the height of the Surface of the Liquor above the Orifice and so much conform to the observations already deliver'd That you shall still see the surface of the oyle I K in the longer pipe to be a little and but a little superiour to that of the external water A B and so the AEquilibrium betwixt the Liquor or Liquors within the Syphon and the water without it will ev'n in this case also be maintain'd SCHOLIUM REmembring on this Occasion an Experiment which though it do not shew what the precise quantity of Lateral pressure is that the lower parts of the fluid may sustain from the more elevated yet it may confirm the foregoing Paradox and by its Phaenomena afford some hints that may render it not unacceptable I shall subjoyn it as I set it down not long after I devis'd it In the first place then there was made a glass Bubble with a slender neck and in a word of the figure express'd in the annex'd Scheme This Bubble I caus'd to be so poys'd That though it would float upon the water yet the addition of a weight small enough would suffice to make it sinck This done I provided a very large wide mouth'd Glass and caus'd to be fitted to it as exactly as I could a stopple of Cork which being strongly thrust in would not easily be listed up In the middle of this Cork there was burn'd with a heated instrument a round hole through which was thrust a long slender pipe of Glass so that the lower end of it was a pretty way beneath the Cork and the upper part of it was as near as could be at right Angles with the upper part of the said Cork And in an other part of the stopple near the edge there was made another round hole into which was likewise thrust another small pipe whose lower part reach'd also a pretty way beneath the Cork but its upper part was but about two or three Inches high and the Orifice of this upper part was carefully clos'd with a stopple and Cement Then the glass vessel being fill'd with water and the pois'd Bubble being made to float upon it the stopple or cover of the great glass vessel was put on and made fast with a close Cement that nothing might get in or out of the vessel but at the long slender pipe which was fastned into the Cork as was also the shorter pipe not only by its own fitness to the hole it pass'd through but by a sufficient Quantity of the same Cement carefully apply'd to stop all crevesses The Instrument thus prepar'd and inclin'd this or that way till the floating Bubble was at a good distance from that end of the long pipe which reached a pretty way downwards beneath the Surface of the water we began to pour in some of that Liquor at the open Orifice of the pipe E F and the mouth of the Vessel being exactly stopp'd the water for want of another place to receive it ascended into the pipe through which it had fallen before And if I held my hand when the water I had pour'd in was able to reach but to a small height in the Cylinder as for instance to the Superficies J the Bubble X would yet continue floating But if I continued pouring till the water in the pipe had attain'd to a considerable height above the Surface of that in the Vessel as if it reach'd to K then the Bubble X would presently sinck to the bottome of the Vessel and there continue as long as as the water continued at so great a height in the pipe E. F. This Experiment will not only teach us That the upper parts of the water gravitate upon those that are under them but which is the thing we are now to confirm That in a Vessel that is full all the lower parts are press'd by the upper though these lower be not directly beneath the upper but aside of them and perhaps at a good distance from the Line in which they directly press These things I say may be made out by our Experiment For the Addition of the Cylinder of water K J in the pipe E F makes the Bubble X subside as the force or pressure of any other heavy body upon the water in the vessel would do And since as may be gather'd from the Reason formerly given in the Proof of the second Paradox of the sincking of pois'd Bubbles the included aire in our Bubble was notably compress'd it will follow that the Cylinder of water KI did press the subjacent water in the Vessel For without so doing it could not be able to compress the aire in the Bubble And since the said Bubble did not swimme directly under or near the pipe E F but at one side of it and at a pretty distance from it nay and floated above the lower Orifice F of the pipe 't is evident that that Aqueous Cylinder JK does not only press upon the water or other Bodies that are directly under it but upon those also that are laterally situated in respect of it provided they be inferior to it And according to this Doctrine we may conceive that every assignable part of the sides of the Vessel does sustaine a pressure encreas'd by the encrease of that parts depth under water and according to the largness of the said part And therefore if any part were so weak as that it would be easily beaten out or broken by a weight equal to the Cylinder I K making always a due abatement for the obliquity of the pressure it would not be fit to be a part of our Vessel Nay the Cork it self though it be above the Surface of the water in the Vessel yet because the water in the pipe is higher then it each of its parts resists a considerable pressure proportionate to its particular bigness and to the height of the water in the pipe And therefore if the Cork be not well stopp'd in it may be lifted up by the pressure of the water in the pipe if that be fill'd to a good height And if the Cement be not good and close the water will not without noise make it self a passage through it And if the stopple G of the shorter pipe G H which is plac'd there likewise to illustrate the present conjecture do not firmly close the Orifice of it it may be forced out not without violence and noise And for further satisfaction if in stead of the stopple G you close the Orifice with your finger you shall find it press'd upwards as strongly as it would be press'd downwards by the weight of a Cylinder of water of
as imploy'd a round number as they call it when I said That no body yet known how ponderous soever will subside in water by its own weight alone if it were so plac'd under water that the depth of the water did above twenty times exceed the height of the Body not to mention here that though gold and water being weigh'd in the aire their proportion is above 19 to one yet in the water gold does as other sincking bodies loose as much of its weight as that of an equal bulk of water amounts too I was saying just now that in case the Brazen body were plac'd low eenough beneath the Surface of the water and kept from being depress'd by any incumbent water it would be supported by the subjacent water And this is that very thing that I am now to shew by an Experiment Let then the Brass body E F be the cover of a brass Valve as in the annexed figure and let the Valve be fastned with some strong and close Cement to a Glass pipe O P open at both ends and of a competent length and wideness For then the Body E F being the undermost part of the Instrument and not sticking to any other part of it will fall by its own weight if it be not supported Now then tying a thred to a Button Q that is wont to be made in the middle of the doors of Brass valves you must by pulling that string streight and upwards make the Body E F shut the orifice of the Valve as close as you can which is easily and presently done Then thrusting the Valve under water to the depth of a foot or more the Cement and the sides of the Glass O P which reaches far above the top of the water X Y will keep the water from coming to beare upon the upper part of the body E F and consequently the imaginary Surface V W that passes by the lower part of the said body will where it is contiguous thereunto be press'd upon only by the proper weight of the body E F but in its other parts by the much greater weight of the incumbent water So that though you let go the string that held the body E F close to the rest of the Instrument the said body will not at all sinck though there be nothing but water beneath it to support it And to manifest that 't is onely the pressure of the water of a competent depth that keeps the solid suspended if you slowly lift up the instrument towards X Y the top of the water you shall find that though for a while the parts of the Valve will continue united as they were before yet when once it is rais'd so near the Surface as between the plain J K and X Y that the single weight of E F upon the subjacent part of the imaginary plain that passes by it is greater then the pressure of the incumbent water upon other parts of the same plain that Body being no more supported as formerly will fall down and the water will get into the pipe and ascend therein to the level of the External water But if when the Valve is first thrust under water and before you let go the thred that keeps its parts together you thrust it down to a good depth as to the Superficies R S then though you should hang a considerable weight as L to the Valve E F as I am going to shew you a Tryal with a Massy Cylinder of stone broader then the Valve and of divers inches in length the surplusage of pressure on the other parts of the plain V W now in R S over and above what the weight of the body E F and that of the Cylindrical stone L to boot can amount to on that part of the Surface vvhich is contiguous to the said body E F will be great enough to press so hard against the lower part of the Valve that its own weight though assisted with that of the stone will not be able to disjoyne them By which to note that by the way you may see that though when two flat and polish'd marbles are joyn'd together we find it is impossible to sever them without force we need not have recourse to a fuga vacui to Explicate the cause of their Cohaesion whilst they are environ'd by the Aire which is a Fluid not devoid of Gravity and reaching above the Marbles no body knows how high And to evince That 't is only such a pressure of the water as I have been declaring that causes the Cohaesion of the parts of the Valve if you gently lift it up towards the top of the water you will quickly find the Brass body E F drawn down by the stone L that hangs at it as you will perceive by the waters getting in between the parts of the Valve and ascending into the pipe To which I shall only add what you will quickly see That in perfect Conformity to our Doctrine the pressure of the body E F upon the subjacent water being very much increased by the weight of the stone that hangs at it the Valve needs not as before be lifted up above the plain J K to overcome the resistance of the water being now enabled to do it before it is rais'd near so high APPENDIX I. 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 AFter I had this Morning made an end of reviewing the foregoing papers there came into my hands some questions lately publish'd among other things by a very recent Writer of Hydrostaticks In one of which Questions the Learned Author strongly defends the contrary to what has there been in some places prov'd and divers places suppos'd The Author of these Erotemata asserts That in consistent water the upper parts do not gravitate or press upon the lower And therefore I think it will be neither useless nor improper briefly to examine here the Arguments he produces Not useless because the Opinion he asserts both is and has long been very generally receiv'd and because too it is of so great importance that many of the Erroneous Tenets and Conclusions of those that whether professedly or incidentally treat of Hydrostatical matters are built upon it And not improper because our Learned Author seems to have done his Reader the favour to summe up into one page all the Arguments for his Opinions that are dispersedly to be found in his own or others mens Books So that in answering these we may hope to do much towards a satisfactory Decision of so important a Controversie And after what we have already deliver'd our Answers will be so seasonable that they will not need to be long The things they are built on having been already made out in the respective places whereto the Reader is referr'd Our Author then maintains that in Consistent water the Superiour do not actually press the Inferiour parts
brought in a year or two since to this Learned Society by a deservedly Famous Member of it For though his supposal be made upon occasion of an Experiment of another Nature then any of the ensuing it may be easily accomodated to my present purpose This postulatum or Lemma consists of three parts the first of them more and the two last less principal Suppose we then First That if a Pipe open at both Ends and held perpendicular to the Horizon have the lower of them under Water there passes an Imaginary plain or Surface which touching that Orifice is parallel to the Horizon and consequently parallel as to sense to the upper Surface of the water and this being but a help to the Imagination will readily be granted Secondly To this it will be consonant that each part of this designable surface will be as much and no more press'd as any other equal part of it by the water that is perpendicularly incumbent on it For the water or other Fluid being supposed to be of an homogeneous substance as to gravity and being of an equal height upon all the parts of the imaginary Surface there is no reason why one part should be more press'd by a perpendicular pillar of that incumbent fluid then any other equal part of the same Surface by another perpendicularly incumbent pillar of the same or equal Basis and height as well as of the same Liquor But Thirdly Though whilst our imaginary Surface is equally press'd upon in all parts of it the Liquor must retain its former position yet if any one part comes to have a greater weight incumbent on it then there is upon the rest that part must be displac'd or depress'd as it happens when a stone or other Body heavier then water sincks in water For wherever such a a Body happens to be underneath the water that part of the imaginary plain that is contiguous to the lower part of the stone having on it a greater weight then other parts of the same Surface must needs give way and this will be done successively till the stone arrive at the Bottom and if on the other side any part of the Imaginary Surface be less press'd upon then all the rest it will by the greater pressure on the other parts of the Surface be impell'd upwards till it have attain'd a height at which the pressure of the rais'd water and the lighter or floating Body if any there be that leans upon it and gravitates together with it upon the subjacent part of the Imaginary Surface will be equal to that which bears upon the other parts of the same Surface And because this seems to be the likeliest thing to be Question'd in our Assumption though he that considers it attentively will easily enough be induc'd to grant it Yet I shall here endeavour to evince it Experimentally and that by no other way of proof then the same I imploy all along this present discourse Take then a Cylindrical glass pipe of a convenient Bore open at both Ends let the Tube be steadily held perpendicular to the Horizon the lower end of it being two or three inches beneath the Surface of a convenient quantity of water which ought not to fill the Glass Vessel that contains it The pipe being held in this posture 't is manifest that the water within the pipe will be almost in a level with the Surface of the water without the pipe because the external and internal water as I am wont for Brevities sake to call them have free intercourse with one another by the open Orifice of the immers'd End of the pipe yet I thought fit to insert the word almost because if the pipe be any thing slender the Surface of the water in it will always be somewhat higher then that of the water without it for reasons that 't is not so necessary we should now inquire after as 't is that we should here desire to have this taken notice of once for all That mistakes may be avoided without a troublesome repetition of the difference in heights of the Surface of Liquors within pipes and without them in case they be any thing slender The pipe being held in the newly mention'd posture if you gently poure a convenient Quantity of Oyle upon the external water you shall see That as the Oyle grows higher and higher above the Surface of That water the water within it will rise higher and higher and continue to do so as long as you continue to poure on oyle Of which the Reason seems manifestly to be this That in the Imaginary plaine that passes by the Orifice of the immers'd end of the pipe all that is not within the Compass of the Orifice is expos'd to an additional pressure from the weight of the oyle which swims upon the water and that pressure must still be increas'd as there is more and more oyle poured on whereas a Circular part of the Imaginary plain equal to the Orifice of the Glasse is by the sides of the pipe fenc'd from the immediate pressure of the oyle so that all those other parts of the water being far more press'd then that part which is comprehended within the Cavity of the Tube and consequently the press'd parts of the external water are by the equal gravitation of the oyle upon the parts of the external water impell'd up into the Cavity of the pipe where they find less resistance then any where else till they arrive at such a height that the Cylinder of water within the pipe do's as much gravitate upon the subjacent part of the Imaginary Surface as the water and oyle together do upon every other equal part of the same Surface or plain But as well the former Lemma as this Experiment will be sufficiently both clear'd and confirm'd by the following Explications to which I should for that Reason forthwith proceed Were it not that since divers passages of the following Treatise suppose the Aire to be a Body not devoid of weight which yet divers Learned adherents to the Peripatetick Philosophy do resolutely deny it seems requisite to premise something for the proof of this Truth And though I think the Arguments we have imploy'd to that purpose already do strongly evince it yet if I may be allow'd to anticipate one of my own Experiments of the Appendix I shall give an instance of the weight of the Aire not lyable so much as to those invalid objections which some of the Aristotelians have made against those Proofs wherewith we have been so happy as to satisfie the learned'st even of our professed Adversaries We caus'd then to be blown at the flame of a Lamp a Bubble of glass of about the bigness of a small Hen-egge which that it might be light enough to be weigh'd in exact Scales ought to be of no greater thickness then is judged necessary to keep it from being when seal'd up with none but very much expanded aire in it broken by
Expedient alone I can decline several Difficulties and do many things which according to Paschal's way require a great deal of Trouble and Apparatus to be perform'd Lastly In such Experiments where it may be of use That there be a considerable disparity betwixt the two unmingled Liquors we may as is above intimated instead of fair water imploy Oleum Tartari per deliquium and tinge it with Brazill or Chochineele from either of which but especially from the latter it will obtaine an exceeding deep Redness and where one would avoid strong sents and oyliness he may if he will be at the Charge imploy oyle of Tartar per deliquium instead of fair water and highly Rectified Spirit of Wine instead of oyle of Turpentine For these two Liquors though they will both readily mingle with water will not with one another and if a great quantity of some other Liquor be to be substituted for simple water when these Chymical Liquors are not to be had in plenty one may imploy as we have done a very strong Solution made of Sea-salt and filtred through Cap-paper this Brine being near about as Limpid as common water and farre heavier than it And for a Curiosity we have added to the two lately mentioned Liquors oyle of Tartar and Spirit of Wine some oyl of Turpentine and thereby had three Liquors of different Gravities which will not by shaking be brought so to mingle as not quickly to part again retire each within its own Surface and by thrusting a Pipe with water in the bottom of it placing also ones finger upon the upper Orifice beneath the Surface of the lowermost of these Liquors and by opportunely raising or depressing it one may somewhat vary the Experiment in a way not unpleasant but explicable upon the same grounds with the rest of the Phaenomena mentioned in this Discourse PARADOX II. That a lighter Fluid may gavitate or weigh upon a heavier I Know that this is contrary to the common opinion not only of the Schools but ev'n of divers hodiern Mathematicians and Writers of Hydrostaticks some of whom have absolutely rejected this Paradox though they do but doubt of the truth of the former But when I consider that whether the cause of Gravity be the pulsion of any superior substance or the Magnetical attraction of the Earth or whatever else it be there is in all heavy Bodies as such a constant tendency towards the Centre or lowermost parts of the Earth I do not see why that tendency or endeavour should be destroy'd by the interposition of any other heavy Body Though what would otherwise be the effect of that endeavour namely an approach towards the Centre may be hindred by another Body which being heavier then it obtains by its greater gravity a lower place but then the lighter Body tending downwards must needs press upon the heavier that stands in its way and must together with that heavier press upon whatever Body it is that supports them both with a weight consisting of the united gravities of the more and the less heavy Body But that which keeps Learned Men from acknowledging this Truth seems to be this That a lighter Liquor or other Body being environ'd with a heavyer will not fall down but emerge to the Top whence they conclude that in such Cases it is not to be considered as a heavy but as a Light Body But to this I answer That though in Respect of the heavier Liquor the less heavy may in some sence be said to be light yet notwithstanding that relative or Comparative Levity it retains all its absolute Gravity tending downwards as strongly as before though by a contrary and more potent Endeavour upwards of the contiguous liquor whose lower parts if less resisted are pressed upwards by the higher elsewhere incumbent according to the Doctrine partly delivered already and partly to be cleared by the proof of the next proposition its endeavor downward is so surmounted that it is forcibly carry'd up Thus when a piece of some light wood being held under water is let go and suffer'd to emerge though it he buoy'd up by the water whose specifick Gravity is greater yet ev'n whilst it alcends it remains a heavy Body so that the aggregate of the water the ascending wood weighs more then the water alone would doe And when it floats upon the upper part of the water as part of it is extant above the surface so part of it is immerst beneath it which confirms what we were saying That a lighter Body may gravitate upon a heavier And thus there is little doubt to be made but that if a man stand in one of the scales of a Ballance with a heavy stone ty'd to his hand and hanging freely by his side if then he lift that weight as high above his head as he can notwithstanding that the stones motion upwards makes it seem a light Body in respect of the Man whose Body it leaves beneath it yet it dos not either during its ascent or after loose any thing of its connatural weight For the Man that lifts it up shall feel its tendency downwards to continue though his force being greater than that tendency be able notwithstanding that tendency to carry it up and when it is aloft it will so press against his hand as to offend if not also to bruise it and the Stone and the Man that supports it will weigh no less in the Scale he stands in then if he did not at all support it and they were both of them weigh'd apart Likewise if you put into one Scale a wide mouth'd Glass full of water and a good quantity of pouder'd common Salt and into the other Scale a Counterpoise to them both you may observe that though at the beginning the Salt will manifestly lie at the bottome and afterwards by degrees be so taken up into the Body of the Liquor that not a grain will appear there yet nevertheless as far as I can judge by my Experiments the weight in that Scale will not be diminished by the weight of as much Sale as is incessantly either carried up or supported by the restless motion of the dissolving Corpuscles of the water but both the one and the other allowing for what may evaporate will concurrently gravitate upon the Scale that the glass containing them leans on But of this more elsewhere Now to prove the proposiion by the New Method we have propos'd to our self in this Discourse Take a slender Glass pipe and having suck'd up into it fair water to the height of 3 or 4 Inches stop nimbly the upper Orifice with your finger and inmerse the lower into a Glass full of oyle of Turpenrine till the Surface of the oyle in the Vessel be somwhat higher than that of the water in the Pipe then removing your finger though the Pipe do thereby become open at both Ends the water will not fall down being hinder'd by the pressure of the oyle of
fisth Paradox for which purpose the legs must be at a pretty distance from each other though you fill that Funnel with water the oyle in the longer and slender leg of the Syphon will be able to resist the pressure of all the water notwithstanding the breadth of the upper part of the funnel So that ev'n in this case also the Surface of the oyle in the longer leg will be but a little higher then that of the water in the funnel For further Confirmation of this we caus'd to be made a Syphon so shap'd that one of the legs which were parallel and of the same Bore had in the midst of it a Sphaere of Glass save that it communicated with the upper and lower parts of the same leg In the uniform leg of the Syphon we put a convenient quantity of oyle of Turpentine and into the other as much water as fill'd not only the lower part of it but the Globular part too And yet we did not find that all this water was able to keep up the oyle in the uniform leg at a greater height then if the leg that contain'd the water had been uniform too as much of the water in the Globe as was not directly over the lower Orifice of it being supported by the lateral parts if I may so call them of the same Globe And if that leg were instead of water fill'd with oyle and the uniform leg with water notwithstanding the far greater quantity of oyl that was necessary to fill that leg whereof the hollow sphaere was but a part the water in the uniform leg would not be kept up so much as to the same height with the oyle in the mishapen leg But to make this matter yet the more clear we caus'd a Syphon to be made of the Figure express'd in the adjoyning Scheme into which having poured a convenient quantity of Mercury till it reach'd in the shorter leg C D almost to the bottom of the Clobulou part E and in the longer leg A B to an equal height We afterwards poured a sufficient quantity of water into the said longer leg A B which drove away the Quicksilver and impell'd it up in the shorter leg till it had half or more then half fill'd the Cavity of the Globular part E which yet we did not wholly fill with Quicksilver because the Tube A B was not long enough for that purpose and then we observ'd that notwithstanding the great weight of that Body which is of all Bodies save one the most Ponderous Quicksilver which was contain'd in the lower part of the same leg of the Syphon the surface of the Quicksilver H G was impell'd up as high by the water in the Leg A B as the disparity of the specifick weights of those two Liquors whereof one is about 14 times as heavy as the other did require So that it appear'd not that for all the great weight of Quicksilver contain'd in the Globulous Cavity E there press'd any more upon the slender and subjacent part E C of that leg then as much as was plac'd directly over the lower Orifice of the said Cavity E So that the other and lateral parts of that Mercury being supported by the concave sides of the Glass whereunto they were contiguous the water in the leg A B appear'd not any more press'd by the quicksilver then if the leg C D had been as well as the other of an uniform bigness and by this means if we had made the hollow Globe of a large Diameter a small quantity of water poured into the leg A B might have been able to raise a quantity of quicksilver exceedingly much heavier then it self But then so little water can raise the quicksilver in so broad a pipe but to an inconsiderable height To make out the second part of our Paradox by an Experiment we took three Glass-pipes the one made like a Bolt-head with a round Ball and two opposite Stemms the other was an irregular pipe blown with an Elbow wherewith it made an Angle and the third was as irregularly shap'd as I could get it blown being in some places much broader and in some much narrower then the lower Orifice of it And these two last nam'd pipes had their upper ends so inserted into holes made fit for them in a broad piece of Cork that when they were immers'd they made not right Angles but very oblique ones with the Horizontal Surface of the Liquor The other Glass likewise which consisted of a great Bubble and two opposite pipes was fastened to the same Cork which having before hand been made fit for a wide mouth'd glass of a good depth and half fill'd with water was thrust as a stopple into the mouth of the said glass so that the water a scended a pretty way into each of the three pipes by their lower Orifices which as well as the upper we left open Then a good quantity of oyle of Turpentine being pour'd into the same Vessel through a funnel the water was by the incumbent oyle impell'd up to the height of 2 or 3 Inches in each of the three pipes Which argues that notwithstanding their being so unequal in bigness and so irregular in shape insomuch that we guess'd one of them was 10 or 12 times greater in one part then in another or then it was even at the Orifice the water contain'd in each of them press'd upon its lower Orifice no more I do not add nor no less then it would have done if it had been a Cylinder having the Orifice for its Basis and the perpendicular depth of the water and oyle above for its height For in case each of the pipes had contein'd but such a Cylinder of water that water would nevertheless have had its uppermost Superficies at the same height and on the other side it would have been impell'd up beyond it if its weight did not as strongly endeavour to depress the immediately subjacent water as the pressure of the External fluids endeavour'd to impel it up And since the height of the water was about the same in the several pipes though two of them being very much inclin'd contain'd much more water then if they were erected yet by the same way of reasoning we may gather That the imaginary plain passing by the immers'd Orifice of either of these inclining pipes sustain'd no more of pressure then it would have done from a shorter Cylinder of water if erected And indeed in all these cases where a pipe either is broader in other places then at its lower Orifice or inclin'd any way towards the Horizon the weight of the contain'd Liquor is not all supported by the Liquor or the Body contiguous to the lower Orifice but partly by the sides of the pipe it self And therefore if when in a slender pipe you have brought a parcel of oyl of Turpentine to be in an Equilibrium with the External water as in the Experiment belonging to the first Paradox If I