the hole and put a final stop to the course of the water Nor was I able to take out the needle and put it in again so nimbly but that the aire found time to get into the Syphon and till the hole were again stopp'd render it useless notwithstanding that the water was by suction endeavour'd to be set a running PARADOX XI That a solid Body as ponderous as any yet known though near the Top of the water it will sinck by its 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 descent be not assisted by the weight of the incumbent water THis Paradox having never been that I know of propos'd as yet by any has seem'd so little credible to those to whom I have mention'd it without excepting Mathematicians themselves that I can scarce hope it should be readily and generally received in this Illustrious Company upon less clear Testimony then that of Experience And therefore though if I mistake not some part of this proposition may be plausibly deduc'd by the help of an Instrument ingeniously thought upon by Monsieur Paschal Yet I shall have recourse to my own Method for the making of it out for these two Reasons The one That a great part of the Paradox must be Explicated as well as prov'd by the Doctrine already setled in this paper The other That the Experiment propos'd by Monsieur Paschal being to be done in a deep River and requiring a Tube 20 foot long whose Bottome must be fitted with a Brass Cylinder made with an exactness scarce if at all to be hoped for from our Workmen If I should build any thing on this so difficult an Experiment which himself does not affirm to have ever been actually tryed I fear most men would rather reject the Experiment as a Chimaerical thing then receive for its sake a Doctrine that appears to them very Extravagant Let us then to imploy in this case also the method we have hitherto made use of Fill a Glass vessel A B C D almost full of water only in regard that there is a great depth of water requisite to some Circumstances of the Experiment This last must not be so shallow as those hitherto imploy'd but a deep Cylinder or Tube seal'd at one end whose depth must be at least two or three foot though its breadth need not be above 2 or 3 Inches and to keep it upright it may be plac'd in a socket of metal or wood of a size and weight convenient for such a purpose This Glass being thus fitted in water let us suppose E F to be a round and flat piece of solid Brass having about an Inch in Diameter and a fourth or sixth part of an inch in thickness This Cylinder being immers'd under water till it be just cover'd by the uppermost Surface of that Liquor and being let go must necessarily fall downwards in it because if we suppose the imaginary Superficies G H to pass along the Circle F which is the lower part of the Brass Body that metal being in specie far heavier then water the Brass that leans upon the part F must far more gravitate upon the said part F then the incumbent water does upon any other part of the Superficies G H and consequently the subjacent water at F will be thrust out of place by the descending Body And because that in what part soever of the water not exceeding nine times its thickness measured from the Top of the water A C the ponderous Body E F shall happen to be there will be still by reason of the specifick gravity of the Metal a greater pressure upon that part of the imaginary Superficies that passes along the bottome of the Body on which the part F shall happen to lean then upon any other part of the same imaginary Superficies the Brass Body would still descend by vertue of its own weight though it were not assisted by the weight of the water that is over it But let us suppose it to be plac'd under water on the designable plain J K and let this plain which as all other imaginary plains is as well as the real Surface of the water to be conceiv'd parallel to the Horizon and let the depth or distance of this plaine from the uppermost Surface of the water be some what above nine times the thickness of the Brass Body I say that in this case the body would not descend if it were not press'd downwards by the weight of the water it has over it For Brass being but about nine times as heavy as water of an equal bulk to it the Body E F alone would press upon the part F but as much as a Cylinder of water would which having an equal Basis were 8 or 9 times as high as the Brass is thick But now all the other parts of the Imaginary surfaces I K being press'd upon by the incumbent water which is as high above them as the newly mention'd Cylinder of water would be there is no reason why the part F should be depress'd rather then any other part of the Superficies J K But because it is true which we formerly taught namely that water retains its gravity in water and that too though a body heavier in specie then it be plac'd immediately under it it will necessarily happen That in what part soever the solid body be plac'd provided it be every way environ'd with the water it must for the Reason newly given be made to move downwards partly by its own weight and partly by that of the incumbent water and must continue to sinck till it come to the bottom or some other body that hinders its farther descent But in case the water above the solid body did not gravitate upon it and thereby assist its descent or in case that the incumbent water were by some Artifice or other so remov'd That none of the lateral water if I may so call it could succeed in its place to lean upon the solid then it will follow from what we have newly shown that the solid would be kept suspended And in case it were plac'd much deeper in the water as over against the point L or M Then if we conceive the incumbent water to be remov'd or fenc'd off from it the pressure of the solid alone upon the part F of the imaginary Superficies L M being very much inferior to that of the water upon the other parts of the same Surface the part F would be strongly impell'd upwards by a force proportionate to the difference of those two pressures And therefore since I have found by tryals purposely made in scales marvellously exact and with refined Gold purer then perhaps any that was ever weighed in water That Gold though much the ponderoufest of bodies yet known in the world is not full 20 times as heavy as water of the same Bulk I kept within compass as well
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
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
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