of the Phaenomena of Nature And as for the Peripateticks and other School-Philosophers though on some Occasions as when they tell us That water weighs not in water nor aire in aire they deliver assertions about matters belonging to the Hydrostaticks which term in this Treatise I often take in a large sense because most of the things delivered about the weight of Bodys may by easy variations be made applicable to other Fluids yet they are so far from having illustrated or improv'd them that they have but broach'd or credited divers of the most erroneous conceits that are entertain'd about them So that there being but few Treatises written about the Hydrostaticks and those commonly bound up among other Mathematical works and so written as to require Mathematical Readers this usefull part of Philosophy has been scarce known any farther then by name to the genèrality ev'n of those Learned men that have been inquisitive into the other parts of it and are deservedly reckoned among the ingenious Cultivators of the modern Philosophy But this is not all For some eminent men that have of late years treated of matters Hydrostatical having been prepossess'd with some errenous Opinions of the peripatetick School and finding it difficult to consult experience about the truth of their Conclusions have interwoven divers erroneous Doctrines among the sounder propositions which they either borrow'd from Archimedes and either circumspect Mathematicians or devis'd themselves and these mistakes being deliver'd in a Mathematical dress and mingled with Propositions demonstrably true the Reputation of such Learned Men from which I am far from desiring to detract and the unqualifiedness of most Readers to examine Mathematical things has procur'd so general an entertainment for those Errors that now the Hydrostaticks is grown a part of Learning which 't is not only difficult to attain but dangerous to Study Wherefore though neither the Occasion and designe of this Treatise exacted nor my want of skill and leasure qualified me to Write either a Body or Elements of Hydrostaticks yet I hop'd I might doe something both towards the illustrating and towards the rescue of so valuable a Discipline by Publishing the ensuing Tract where I endeavour to disprove the receiv'd errors by establishing Paradoxes còntrary to them and to make the Truths the better understood and receiv'd partly by away of Explicating them unimploy'd in Hydrostatical Books and partly by confirming the things I deliver by Physical and sensible Experiments And over and above this the more to recommend Hydrostaticks Themselves to the Reader I have besides the Paradoxes oppos'd to the Errors I would disprove taken occasion by the same way to make out some of the usefullest of those Hydrostatical Truths that are wont to seem strange to Beginners If it be here demanded why I have made some of my Explications so prolix and have on several occasions inculcated some things I answer That those who are not us'd to read Mathematical Books are wont to be so indispos'd to apprehend things that must be explicated by Schemes and I have found the generality of Learned men and ev'n of those new Philosophers that are not skill'd in Mathematicks so much more unacquainted then I before imagin'd both with the principles and Theorems of Hydrostaticks and with the ways of explicating and proving them that I fear'd that neither the Paradoxes themselves that I maintain nor the Hypotheses about the weight and pressure of the aire upon which little less then my whole Pneumatical Book depends would be throughly understood without such a clear Explication of some Hydrostatical Theorems as to a person not vers'd in Mathematical writings could scarce be satisfactorily deliver'd in few words And therefore though I do not doubt that those who are good at the most compendious ways of demonstrating will think I might in divers places have spar'd many words without injury to my proofs and though I am my self of the same mind I exspect to find them of yet I confess that 't was out of choice that I declind that close and concise way of writing that in other cases I am wont most to esteem For Writing now not to credit my self but to instruct others I had rather Geometricians should not commend the shortness of my Proofs then that those other Readers whom I chiefly design'd to gratifie should not throughly apprehend the meaning of them But this is not all for which I am to excuse my selfe to Mathematicall Readers For some of them I fear will not like that I should offer for Proofs such Physical Experiments as do not alwayes demonstrate the things they would evince with a Mathematical certainty and accuratenesse and much less will they approve that I should annex such Experiments to confirm the Explications as if Suppositions and Schemes well reason'd on were not sufficient to convince any rational man about matters Hydrostaticall In Answer to this I must represent that in Physical Enquiries it is often sufficient that our determinations come very near the matter though they fall short of a Mathematical Exactness And I choose rather to presume upon the equity of the Reader then to trouble him and my self with tedious Circumlocutions to avoid the possibility of being misunderstood or of needing his Candor And we see that even Mathematicians are wont without finding any inconvenience thereby to suppose all perpendicular Lines made by pendulous Bodies to be parallel to one another Though indeed they are not since being produc'd they would meet at the Centre of the Earth And to presume that the Surface of every calme water in a Vessel is parallel to the Horizon and consequently a Plain Though in strictness themselves think it the portion of a Sphere And though also I have usually observ'd it to be higher where 't is almost contiguous to the sides of the Vessel then 't is in other places Moreover since we find that though water will be uniformly rais'd in Pumps to several heights but not to thirty five foot and will in ordinary open pipes be almost of the same level within and without but not if the pipe be extraordinary slender Upon these and divers other such considerations I may have sometimes made use of expressions that seemed not positive and determinate enough to be employed about matters to which Mathematical Demonstrations are thought applicable But I elsewhere give an account of the scruples I have about such Demonstrations as they are wont to be apply'd to Physical matters And in the present Paradoxes I think I have not done nothing if in my Hydrostatical Explications I have made it appear That in Experiments made with such Liquors and Glasses as I employed the Rules will hold without any sensible or at least any considerable Error for thereby we may learn the Truth of many things for the main though in some we should not have attained to the exactness of measures and proportions which yet our endeavors may assist others to arrive at And as for my
yet being remov'd again into the same cold water it had been taken out of and duck'd as before to free it from adherent bubbles it lay quietly at the bottom and though rais'd several times to the upper part of the water would immediately subside again and fall to the very lowest Now that which invited me to promise an Experiment which seems to contradict the principles of the Hydrostaticks was not any distrust of those principles themselves but a conjecture that as by warmth the water would be made a little lighter in specie then 't was before so by the same warmth the spirituous and more agitable parts of the wax whose texture is loose enough would be somwhat though not visibly expanded and would by that expansion gain a greater advantage towards floating then the increas'd lightness of the water would give it disposition to sinck And I confirm'd this conjecture by a farther experiment which at first was it self somewhat surprising to the Beholders For when the wax was first taken out of the cold water immediately immers'd in the warm it would readily enough sinck being with a quill or a knife rais'd to the top of the water it would again fall down but more slowly then at the begining aftersome few minutes if it were rais'd to the upper parts of the water it would remain a float And I have known it when it had remain'd a while longer at the bottom so to emerge that if I were sure no unheeded bubbles had been newly generated and held it up it might be said to emerge of its own accord as on the other side being put into the cold water as soon as ever it was taken out of the warm it would at the very first float and being then knock'd downwards it would readily enough regain the upper part of the water but if I continu'd to send it downwards about 6 or 7 times more or fewer successively it would emerge every time more slowly then other and at length not emerge at all even when I try'd it in water made heavy by being highly infrigidated with salt aud snow plac'd about the Glass Which Phaenomena I had thought it reasonable to expect because I presum'd that the Wax being remov'd immediately out of the warm water into the cold must require some time to loose the adventitious expansion which the warmth had given it and must be depriv'd of it by degrees by the coldness of the water into which the wax was transferr'd As on the other side there must be some time necessary for so little a warmth as that of the tepid or little more then tepid water to give the wax that addition of dimensions which also it must receive by degrees that was necessary in spite of the rarefaction of the water to make it float I might add that these Tryals were repeated for the main with more Bullets of wax then one and that they succeeded far otherwise when instead of a piece of wax we imploy'd a pois'd glass bubble in which the temperature could make either no change at all or no considerable change of dimensions And to these I might add other circumstances if I did not remember that I mention these Tryals but occasionally and to make the caution formerly recommended to the Reader appear not to be impertinent since a Hydrostatical Experiment true in its self may easily miscarry by over-looking such Circumstances as 't is not easie to be aware of But by this Advertisement I would by no means divert Men from being diffident of Hydrostatical Traditions and Experiments For besides the many Erroneous Opinions there are matters of fact whose Truth thò not question'd but built upon I think ought to be brought to tryal For even whilst I was concluding this Preface I found that divers even of the Moderns particularly a very learned Man that has lately Writen of Hydrostaticks have much troubled themselves to render a reason why since according to their Doctrine water weighs not in water Wooden vessels though of a substance lighter then water being by leaks or otherwise fil'd with water should sinck and remain at the bottom of the water whereas judging this Phaenomenon disagreable to what I look upon as the Laws of the Hydrostaticks I was confirm'd in that opinion by having had the curiosity to make some tryals of it wtth 4 or 5 vessels of differing shapes and sizes whereof two were of wax which though a matter but very little lighter then water I could not sinck or keep sunck by pouring water into them or suffering them to fill themselves at leaks made near the bottom and if they were depressed by force or weights they as also the wooden Vessels would upon the removal of the impediment and sometimes with the cavity upwards emerge And I am the more solicitous to have things in the Hydrostaticks duly ascertain'd because the weighing of bodies in Liquors may hereafter appear to be one of the general ways I have employ'd and would recommend for the examining of almost all sorts of tangible Bodies THE CONTENTS PAradox 1. That in Water and other Fluids the lower parts are press'd by the upper 24 Par. 2. That a lighter Fluid may gravitate or weigh upon a heavier 43 Par. 3. That if a Body contignous to the water be altogether or in part lower than the highest level of the said water the lower part of the Body will be press'd upward by the water that touches it beneath 67 Par. 4. That in the ascension of water in Pumps c. there needs nothing to raise the Water but a competent weight of an External Fluid 94 Par. 5. That the pressure of an Externall Fluid is able to keep an Heterogeneous Liquor suspended at the same height in several Pipes though those Pipes be of very different Diameters 106 Par. 6. 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 aboyd 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 Colomne of water having the Horizontal superficies of the Body for its Basis and the perpendicular depth of the water for it's 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 thought it be irregularly shap'd and much broader in some parts then the said Orifice 117 Par. 7. That a Body immers'd in a Fluid sustains a lateral pressure from
consider'd that in such Tubes as the Torricelliah Experiment is wont to be made in the largness of them would make them unfit for this Tryal And I have known Ingenious men that are very well exercis'd in making such Experiments complaine that they could never make this of Paschall's to succeed In which attempts that the size of the Tubes much contributed to the unsuccesfulness of the Tryals I shall without repeating what has been already intimated to that purpose in the following part of this Discourse have opportunity to manifest and withal to adde as Illustrious a proof of this our second Paradox as almost any we have yet given PARADOX III. That if a Body contiguous to the water be altogether or in part lower than the highest level of the said water the lower part of the Body will be press'd upward by the water that touches it beneath THis may be prov'd by what has been already delivered in the Explication of the first Experiment For where ever we conceive the lowest part of the Body which is either totally or in part immers'd in water to be there the imaginary Superficies being beneath the true Superficies every part of that imaginary Superficies must be press'd upwards by vertue of the weight of the water incumbent on all the other parts of the same Superficies and so that part of it on which the immers'd Body chances to leane must for the same Reason have an endeavour upwards And if that Endeavour be stronger then that wherewith the weight of the Body tends downwards then supposing there be no Accidental Impediment the Body will be buoy'd or lifted up And though the Body be heavier then so much water and consequently will subside yet that Endeavour upwards of the water that touches its lower part is onely rendred ineffectual to the raising or supporting the body but not destroyed the force of the heavy Body being from time to time resisted and retarded by the water as much as it would be if that Body were put into One Scale and the weight of as much water as is equal to it in bulk were put into the other To confirm this we may have recourse to what we said in the Explication of the second Experiment For in case the slender pipe wherein the water is kept suspended be thrust deeper into the oyl or in case these be more oyle pour'd into the Vessel the water will be impell'd up higher into the pipe which it would not be if the oyle though bulk for bulk a lighter Body did not press against the lower Surface of the vvater where alone the two Liquors are contiguous more forcibly then the water by its gravity tends dovvnvvards And even vvhen the Liquors rest in an Aequilibrium the oyle continually presses upvvards against the lower Surface of the water since in that continual endeavour upvvards consists its constant resistance to the continual endeavour that the gravity of the water gives it to descend And since the same Phaenomenon happens whether we suspend water in oyle as in the second Experiment on oyle in water as in the first it appears that the proposition is as well applicable to those cases where the sustein'd Body is specifically heavier as to those where 't is specifically lighter then the subjacent fluid But a further and clearer proof of this Doctrine will appear in the Explication of the next proposition In the mean time to confirm that part of out Discourse where we mention'd the Resistance made by the water to Bodies that sinck in it Let us suppose in the annexed Figure That the pipe E F contains an oyle specifically heavier then water as are the oyls of Guaisteum of Cinnamon or Cloves and some others and then That the oyle in the pipe and the water without being at rest in an Aequilibrium the pipe be slowly rais'd towards the Top of the Vessel 'T is evident from our former Doctrine and from Experience too that there will run out drops of oyle which will fall from the bottom of the pipe to that of the Vessel but far more slowly then if they fell out of the same pipe in the Aire Now to compute how much the pressure of the water against the lower parts of the drop amounts too let us suppose the drop to be G to whose lowermost part there is contigueus in any assignable place where it falls the imaginary Superficies H J. 'T is evident That if the drop of oyle were not there its place would be supplied by an equal bulk of water which being of the same specifick Gravity with the rest of the water in the Vessel the Surface H J would be laden every where alike and consequently to part of it would be displac'd But now the drop of oyle being heavier then so much water that part of the imaginary superficies on which that drop leans has more weight upon it then any other equal part of the same Superficies and consequently will give place to the descending drop And since the case of every other suppos'd Surface at which the drop can be conceiv'd to arrive in its descent will be the same with that of the Superficies H J it will for the Reason newly given continue falling till it comes to the bottom of the Vessel which will suffer it to fall no further And in case the drop G were not as we suppose it of a substance heavier in specie then water but just equal to it the contiguous part of the Superficies H J would be neither more nor less charged then the other parts of the same Supeficies and the part lean'd on would be neither depress'd nor rais'd but the drop G would continue in the same place And so we may prove what is affirm'd by Archimedes and other Hydrostatical Writers That a Body acquiponderant in specie to water will rest in any assignable place of the water where 't is put And to proceed further since if the drop G were of a matter but acquiponderant to water it would not sinck lower at all no more then emerge it follows that though being heavier in specie then water it will fall yet the gravity upon whose account it falls is no more then that by which it surmounts an equal bulk of water since if it were not for that over plus the resistance of the water would hinder it from falling at all and consequently it looses in the water just as much of the weight it would have in the aire as so much water weigh'd likewise in the same aire would amount to Which is a Physicall Account of that grand Theorem of the Hydrostaticks which I do not remember that I have seen made out in any Printed Book both solidly and clearly The Learned Stevinus himself to whom the later Writers are wont to refer having but an obscure and not Physical demonstration of it And because this Theorem is not only very noble but as we else where manifest very useful 't will
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
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
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
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
may often indeed be heavier then an equal bulk of water But then the hand that draws up the Bucket by the Rope F E ought not according to our Doctrine to feel the weight of all the Bucket much less that of the water contein'd in it For though that aggregate of wood and iron which we here call the Bucket be heavier then so much water yet it tends not downwards with its whole weight but only with that surplusage of weight whereby it exceeds as much water as is equal to it in Bulk which surplusage is not wont to be very considerable And as for the water in the Cavity G of the Bucket there is no reason why it should at all load the hand at E though really the water both in the Bucket and over it do tend downwards with their full weight because that the rest of the water L I and M K do full as strongly press upon the rest of the imaginary Superficies I K as the Bucket aud the incumbent water do upon the part H and consequently the bottom of the Bucket is every whit as strongly press'd upwards by the weight of the water upon all the other parts of the plain I K as it tends downwards by virtue of the weight of the Incumbent water that is partly in the Bucket and partly above it and so these pressures ballancing one another the hand that draws the Rope at E has no more to lift up then the surplusage of weight whereby the empty Bucket exceeds the weight of as much water as is equall in bulk I say not to the Bucket as 't is a hollow Instrument but to the wood and iron whereof the Bucket consists And because this Example of the lightness of fil'd Buckets within the water has for so many Ages gain'd credit to if it have not been the only ground of the assertion That water weighs not in its own Element or in its proper place I shall add though I can scarse present it to such a company as this without smiles an Experiment that I made to convince those that were through unskilfulness or prejudice indispos'd to admit the Hydrostatical account I have been giving of the phaenomenon I took then a round wooden Box which I substituted in the room of a Bucket and having fill'd it with melted Butter into which when it was congeal'd some small bitts of lead were put to make it a little heavier then so much water I caus'd a small string of twin'd silk to pass through two small holes made in the opposite parts of the upper edge of the box and to be suspended at one end of the beam of a pair of Gold-smiths Scales and then putting it into a vessel full of water till it was let down there to what depth I pleas'd it appear'd that not only the least endeavour of my hand would either support it or transport to and fro in the water or draw it up to the top of it and this whether the box were made use of or whether the butter and lead alone without the box were suspended by the silken string but to evince that it was not the strength of my hand or the smallness of the immers'd body that kept me from feeling any considerable resistance I cast some grains into the scale that hung at the other end of the above mention'd Beame and presently rais'd the Lead and Butter to the surface of the water So that unless the Schoolmen will say that the butter lead were in their own Element we must be allow'd to think that the easie sustentation and elevation of the box did not proceed from hence That those bodyes weigh'd not because they were in their natural place And yet in this case the effect is the same with that which happens when a bucket is drawing out of a well And to manifest that 't was the pressure of the water against the lower part of the surface of our suspended body that made it so easie to be supported in the water or rais'd to the top of it I shall add that though a few grains suffic'd to bring the upper surface of the butter to the top of the water yet afterwards there was a considerable weight requisite to raise more more of its parts above the waters surface a considerabler yet to lift the whole body quite out of the water Which is very consonant to our Doctrine For suppose the bucket to be at the part N half in and half out of the water the hand or counterpoise that supports it in that posture must have a far greater strength then needed to sustein it when it was quite under water because that now the imaginary plain P Q passing by the bottom of the bucket has on its other parts but a little depth of water as from L to P or M to Q and consequently the bottom of the bucket H will searce be press'd upwards above half as strongly as when the bucket was quite under water And if it be raised to O consequently quite out of the water that liquor reaching no longer to the bottom of the bucket can no longer contribute to its supportation and therefore a weight not only equal but somewhat superiour to the full weight of the bucket and all that it contains being all suppos'd to be weighd in the aire will be necessary to lift it clear out of the water But to dwell longer on this subject cannot but be tedious to those that have been any thing attentive to the former Discourses I proceed therefore to our Authors sixth Argument which is Object 6. That Horse-hairs which are held to be of the same gravity with water keep whatever place is given them in that Liquor nor are depress'd by the weight of the super-incumbent water Answ Whether the matter of fact bestrictly and universally true is scarce worth the examining especially since we find the difference in point of specifick gravity betwixt most Horse-haires and most waters to be inconsiderable enough But the phaenomenon supposing the truth of it is very easily explicable according to the Doctrine above deliver'd For supposing in the last Scheme the body R to be bulk for bulk exactly equiponderant to water 't is plain there is no reason why that body should press the part S of the imaginary Superficies I K either more or less then that part S would be press'd if the body R being annihilated or remov'd it were succeeded by parcel of water of just the same bulk and weight And consequently though all the water directly above the solid R do really lean upon that body and endeavour to depress it yet that endeavour being resisted by an equal and contrary endeavour that proceeds as we have been but too often faine to declare from the pressure exercis'd upon the other parts of the Superficies I K by the water incumbent on them the body R will be neither depress'd nor rais'd And its case being the same in what
confirmation of Hydrostatical propositions by Physical Experiments if some Readers dislike that way I make no doubt but that the most will not only approve it but thank me for it For though in pure Mathematicks he that can demonstrate well may be sure of the Truth of a Conclusion without consulting Experience about it Yet because demonstrations are wont to be built upon Suppositions or Postulates and some things though not in Arithmetick or Geometry yet in Physical matters are wont to be taken for granted about which men are lyable to slip into mistakes even when we doubt not of the Ratiocination we may doubt of the conclusion because we may of the Truth of some of the things it supposes And this Consideration if there were no other will I hope excuse me to Mathematicians for ventring to confute some reasonings that are given out for Mathematical demonstrations For I suppose it will be consider'd that those whose presum'd Demonstrations I examine though they were some of them Professours of Mathematicks yet did not Write meerly as Mathematicians but partly as Naturalists so that to question their Tenets ought not to disparage those as well certain as excellent and most useful Sciences pure Mathematicks any more then that the Mathematicians that follow the Ptolemaick the Copernican the Tichonian or other Systemes of the world Write Books to manifest one anothers Paralogismes in Astronomical matters And therefore to proceed to what I was about to say it cannot but be a satisfaction to a wary man to consult sense about those things that fall under the Cognisance of it and to examine by Experiences whether men have not been mistaken in their Hypotheses and Reasonings and therefore the Learned Stevinus himself the chief of the Moderne Writers of Hydrostaticks thought fit after the end of his Hydrostatical Elements to add in an Appendix some Pragmatical Examples as he calls them that is Mechanical Experiments how cogent I now inquire not to confirm the Truth of his Tenth Proposition to which he had not far from the beginning of his Book annexed what he thinks a Mathematical Demonstration And about the very Subjects we are now upon the following Paradoxes will discover so many mistakes of eminent Writers that pretend to have Mathematically demonstrated what they teach that it cannot but make wary Naturalists and 't is chiefly to gratifie such that I publish this be somewhat diffident of Conclusions whose proofs they do not well understand And it cannot but to such be of great satisfaction to find the things that are taught them verified by the visible testimony of Nature her self The importance of this Subject and the frequent Occasion I have to make use of this kind of Apology will I hope procure me the Readers pardon if I have insisted somewhat long upon it After what has been hitherto discours'd 't wil be easie for me to give an Account why I premised these Hydrostatical Paradoxes to the rest of the Appendix wherewith they are now publish'd For since a great part of my work in that Appendix was to be a further Explication of some things delivered in the Book it is subjoyn'd to and the vindication of then from invalid objections And since I have generally observ'd that the objections that have bin either publickly or privately made against the explications reasonings contain'd in that Book were wont to proceed from unacquaintedness either with the true notion of the weight and spring of the aire as I maintain them or with the Principles and Theorems of Hydrostaticks or else from erroneous Conceits about them I thought it would much conduce to both the forementioned ends of my Appendix If I clear'd up that Doctrine to which my Experiments and reasonings have been all along Consonant whos 's being either not known or misunderstood seems to have occasion'd the objections that have been hitherto made against the Hypotheses I have propos'd or the Explications I have thence given And however since the Proofs I offer for my opinions are for the most part drawn from Experiments new easie and that my aim is but to discover Truths or make them out by clearer explications without supposing like those I dissent from any thing that is either precarious or scarce if at all intelligible I hope that if I should not prove happy enough to reach my ends yet the Ingenious and Equitable Reader will approve my Designe and be advantaged by my Experiments Of which some of the chiefest and some of the most difficult having been seen divers of them more then once by the Royal Society it self or by inquisitive Members of it it will I presume be but a reasonable request if the Reader that shall have the curiosity to try them over again be desired not to be hasty in distrusting the matters of fact in case he should not be able at first to make every thing succeed according to expectation For as easie as I have endeavour'd to make these Experiments yet I dare not promise my self that they will all of them be priviledg'd from the fate whereto I have observ'd other Physico-Mathematical ones to be not seldome obnoxious from some unheeded Physical Circumstance by which those that are not acquainted with the subtleties of Nature or at least for the time do not sufficiently consider them are apt to be imposed upon This Advertisement will perhaps be best illustrated recommended by an instance And therefore I shall subjoyne one that will possibly seem somewhat odd It has been taken notice of by two or three Ingenious modern Mathematicians and I have had occasion to make it out by particular Experiments that warm water is lighter in specie then cold whence it has been deduc'd that wax and other Bodies very near aequiponderant with common water will swim in that which is cold and sinck in that which is hot or luke-warm Which Experiment though as it may be and perhaps it has been tryed I readily allow to be agreeable to the known Laws of the Hydrostaticks Yet I have sometimes undertaken that the Tryal should have a quite contrary event To this purpose having taken some yellow Bees-wax which was formed into a Pellet of the bigness of a Cherry and by the help of a little Lead was made so near aequiponderant to cold water that being but a very little heavier a very small diminution of its weight would make it emerge I remov'd it out of the very cold water into some that had bin purposely made lukewarm or a little more then so where it quickly somewhat to the wonder of the lookers on appeard to swim on the top of the water And that it might not be suspected that it was supported by any visible bubbles which I have observed in some cases to buoy up even heavy Bodies and deceive the unskilful or unattentive I briskly enough duck'd the bullet 2 or 3 times under water to throw them off notwithstanding which it constantly return'd to float and
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
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
Gravities of these two Liquors the inequalities betwixt the Surface X and the Surface L M would be also greater as may be try'd by substituting for common water oyle of Tartar per deliquium which is a saline Liquor much heavier than it And that in case the Pipe containe not a lighter Liquor then the External fluid the Surface of the Liquor in the Pipe will not be higher than that of the Liquor without it we shall by and by have opportunity to manifest by Experience From what has been hitherto shewen we may safely infer the Proposition upon whose occasion all this has been delivered For since the oyle in a Pipe open at both Ends may be kept suspended in any part under water as at Q because it is there in an Aequilibrium with the External water and since being lifted up in the water as from Q to S the oyle can no longer be kept suspended but by its own gravity will runne out And since in a word the deeper the water is the greater weight and pressure is requir'd in the Cylinder of oyle to be able to countervail the pressure of the water and keep it self from being lifted up thereby there seems no cause to doubt but that the parts of the water incumbent on the Superficies G H do more press that Superficies than the parts of the water contiguous to the Superficies J K do press that and consequently that the parts of the water that are under the uppermost Surface of it are press'd by those of the same Fluid that are directly over them As we saw also that the upper parts of the oyle whil'st the pipe was in raising from Q to S depress'd the lower so much as to force them quite out of the Pipe there being in these cases no reason why the lowermost parts of a Liquor should press more or have a stronger Endeavour against any other Liquor or any other Body the higher the Liquor incumbent reaches if these inferiour parts deriv'd their pessure only from their own particular Gravity which is no greater then that of the other Homogeneous parts of the Liquor and therefore they must derive the great force wherewith they press from the weight of the Incumbent parts which consequently must be allow'd to press upon them But before I proceed to the following propositions it will not be amiss to mention here once for all a few advertisements to avoid the necessity of repeating the same things in the sequel of the Discourse And First What is here said of the pressure of the parts of water upon one another and the other Affections that we shall attribute to it in the following paper are to be apply'd to heavy Fluids in general unless there shall appear some particular Cause of excepting some of them in particular Cases Secondly Whereas I lately intimated That the inequality betwixt the Surfaces of the oyle in the Pipe and of the External water was in part to be ascrib'd to the slenderness of the Pipe to be imploy'd in these Experiments I did it for this cause that whatever the Reason of it be which we need not here inquire after we are assur'd by Experience as we have elsewhere shewn That when Glass pipes come to be slender water and many other Liquors though not Quicksilver will have within them a higher Surface then that of the same Liquor without them and this inequality of Surfaces as far as we have yet try'd increases with the slenderness of the pipe But this as to our present Experiment is a matter of so little moment That it may suffice to have intimated that we did not oversee it Thirdly Wherefore notwithstanding this little inconvenience of slender Glasses we think it Expedient to imploy such in the following Experiments because we found that in those of a wide Bore upon such little inequalities of pressure as are not easily to be avoided the oyle and water will pass by one another in the Cavity of the pipe and so spoile the Experiment which requires that the oyle within the pipe be kept in an intire and distinct Body Fourthly Common oyle and water or any other two Liquors that will not mingle may serve the turn in most of these Experiments but we rather chuse oyle of Turpentine because it is light and thin clear and colourless and may be easily had in quantities and is not so apt to spot ones Cloaths or obstinately to adhere to the porous Bodies it chances to fall on as Common and other express'd oyles And for their sakes to whom the odour is offensive we presently correct it by mingling with it a convenient quantity of oyle of Rhodium or some other Chymical oyle that is odoriferous Fifthly Oyle of Turpentine though it be not reckon'd among the saline Menstruums will yet as we elsewhere note work upon Copper and so by digesting it upon crude filings of that Metal we obtaine a deep green Liquor which may be made use of instead of the Limpid oyle to make the Distinction of the Liquors more conspicuous Sixthly And for the same purpose we often use instead of clear water a strong Decoction of Brazill or Logg-wood or else Red Inck it self I say a strong Decoction because unless the Liquor be so deeply ting'd as to appear Opacous in the Glass when it comes into the slender pipe its Colour will be so diluted as to be scarce discernable Seventhly In the shape of the Glass Vessel we need not be Curious though that of a wide Mouth'd Jarr express'd in the Scheme be for some uses more convenient than other shapes The depth of these Glasses and the length of the Pipes must be determin'd by the Experiments about which one means to imploy them To make out the first Paradox already prov'd a Glass of about five or six Inches deep and a Pipe about as many Inches long will serve the turn but for some others of the following Experiments tall Cylindrical Glasses will be requisite and for some Broad ones likewise will be Expedient Eighthly One must not be discourag'd by not being able at the first or second time to suck up oyle of Turpentine to the due height and stop it with ones finger from relapsing but one must try again and again especially since many Tryals of this kind may be made in a few Minutes and for Beginners 't is a safe and good though not the shortest way to suck up rather more Liquor then one judges will be needful because having fill'd the Pipe to that height you may by letting in the Aire warily and slowly between the Orifice of the Glass and the pulp of your finger suffer so much Liquor to run out of the Pipe as will reduce it to the height you desire and there by close stopping the Orifice with your finger you may keep it suspended as long as you please and immerse it into any Heterogeneous Liquor and take it out again at pleasure without spilling any of it By which slight
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
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
intervention of water for oftentimes when the fire has not been well regulated there will come over besides the floating Oyle a whitish water which will not in a long time become cleare And as we have elswhere taught That whiteness to proceed from the numerous reflections from the oyly substance of the Concrete ' by the heat of the fire broken into innumerable little Globuls and dispers'd through the Body of the water so the reason why this whiteness continues so long seems to be chiefly for I mention not such things as the great surfaces that these little Globuls have in respect of their Bulk that because of the exceeding minuteness of these Drops the height of the water that presses upon the upper part is almost equal to that of the water that presses against the lower part so that the difference between these two pressures being inconsiderable it has power to raise the Drops but very slowly insomuch that upon this ground I devis'd a Menstruum wherewith I could mingle oyle in drops so exceedingly minute that ev'n when there was but a few spoonfuls of the mixture it would continue whitish for divers whole days together though at length they will emerge and the sooner because whilst they swim up and down as they frequently chance to meet and run into one another they compose greater Drops which are for the Reason already given less slowly impell'd up by the water at the Top of which the Chymist after a due time is wont to find new oyl floating But whether this be any way applicable to the swimming of the insensible particles of corroded metals in Aquaflortis and other saline Menstruums I must not now stay to enquire One thing more there is that I would point at before I dismiss this Paradox Namely that for the same Reason we have all this while deduc'd when the emergent drop or any other Body floats upon the Top of the water it will sinck just so far no farther till the immers'd part of the floating Body be equal in Bulke to as much water as is equal in weight to the whole Body For suppose in the annexed figure Y to be a Cube of wood three foot high and six pound in weight this wood being much heavier then Aire will sinck into the water till it come to an imaginary superficies X W where having the position newly describ'd it will necessarily acquiesce For all the other equal parts of the Superficies X W Q being lean'd upon by pillars of water equal in height to the part X A or W B if the whole weight of the wooden Cube be greater then that of as much water as is equal to the immers'd part it must necessarily sinck lower because the subjacent part of the Surface at V will be more charg'd then any of the Rest And on the other side if the Cube were lighter then as much water as that whose place the immers'd part takes up it must by the greater pressure of the water upon the other parts of the imaginary superficies X W then upon that contiguous to the wood as at V be impell'd upward til the pressure of the whole wood upon the part it leans on be of the same degree with that of the rest of the water upon the rest of the superficies and consequently be the same with the water whose place the immers'd part of it takes up The lightness of that immers'd part in respect of so much water being recompenc'd by the weight of the unimmers'd part which is extant above the Superficies of the water And we see that when a piece of wood fals into water though by the impetus it acquires in falling it passes through divers imaginary plains that lye beneath its due station yet the greater pressure to which each of those plains is expos'd in all its other parts then in that which is contiguous to the Bottom of the wood dos quickly impel it up again till after some emersions and subsidings it rests at length in such a position as the newly explicated Hydrostatical Theorem assignes it SCHOLIUM THis Ingenious Proposition about floating Bodys is taught and prov'd after the manner of Mathematicians by the most subtle Archimedes and his Commentators and we have newly been endeavouring to manifest the Physical reason why it must be true But partly because the Proposition ought to hold not only in such intire and homogeneous Bodyes as men exemplifie it in such as a piece of wood or a Lump of wax but in all Bodyes though of a concave figure and made up of many Bodys of never so differing natures and perhaps some of them joyn'd together only by their superincumbency upon one another and partly because that a Truth which is one of the main and usefullest of the Hydrostaticks and may be of so much importance to Navigation has noyet that I know of been attemtpted to be demonstrated otherwise then upon Paper it will not be amiss for the satisfaction of such of those whom it may concern as are not vers'd in Mathematical Demonstrations to add an Experiment which I made to prove it Mechanically as exactly as is necessary for the satisfaction of such persons After then having imploy'd several Vessels some of wood some of Laton and some of other materials to compass what I desir'd we found glasses to be the most commodious we could procure And therefore filling a large and deep glass to a convenient height with fair water we plac'd in it another deeper glass shap'd like a Goblet or Tumbler that it might be the fitter for swimming and having furnish'd it first with Ballast and then for merryment sake with a wooden Deck by which a tall Mass with a Sayle fusten'd to it was kept upright we fraughted with wood and by degrees pour'd Sand into it till we had made it sâ—â—â—k just to the Tops of certaine conspicuous marks that we had fasten'd on the outside of the Glass to opposite parts thereof Then observing how high the water reach'd in the larger Glass which by reason of the Vessels Transparency was easie to be seen we carefully plac'd two or three markes in the same level with the Horizontal Surface of the water and taking out the floating Vessel as it was with all that belong'd to it and wiping the outside dry we put it into a good paire of scales and having found what it amounted to we weigh'd in a competently large Viol first counterpoiz'd apart so much water to a graine or thereabouts and pouring this water into the large Glass above mentioned we found it to reach to the marks that we had fastened to the outside of the Glass and consequently to reach to the same height to which the weight of the floating glass and all that was added to make it resemble a Ship had made it arise to By which Experiment which we tried as to the essential parts of it with Vessels of differing sizes shapes and ladings too as Wood
Stone Quick-silver c. it appears that the floating Vessel it self with all that was in it or supported by it was equal in weight to as much water as was equal in bulk to that part of the Vessel which was under water suppos'd to be cut off from the extant part of the same vessel by a plain continuing the Horizontal Surface of the water since the weight of the floating Vessel which rais'd up the water in the larger Vessel to the greatest height it attain'd was the same with the weight of the water which being pour'd into the larger vessel when the other was taken out rais'd the water therein to the same height We may also obtaine the same end by a somewhat differing way which is the best way in case the Vessels be too great viz. to observe first by pouring in water out of a Bowle or Paile or other Vessel of known capacity as often as is necessary to fill the great Vessel or Cistern or Pond to the Top or to any determinate height requir'd and next letting out or otherwise removing all that water to put in its place the Vessel whose weight is to be found out Thirdly to let or poure in water till the Vessel be afloat and by its weight raise the External water to the height it had before And lastly to examine how much this water that was last pour'd in falls short in weight of the water that was in it at first and afterwards remov'd For this difference will give us the weight of as much water as is aequiponderate to the whole floating Vessel whither small or great with all that it either carries or susteins The Hydrostatical Theorem we have been considering and the Experiments whereby we have endeavour'd to confirm or illustrate it may Mutatis mutandis be apply'd to a Ship with all her Ballast Lading Guns and Company it holding generally true That to express the sence of the Proposition more briefly the weight of a floating Body is equal to as much water as its immers'd part takes up the room of Whence we might draw some Arguments in favour of the Learned Stevinus for whose sake it partly was that I annexed this Scholium who if I mis-remember not does somewhere deduce as a Corollary from certain Hydrostatical Propositions That a whole Ship and all that belongs to it and leans upon it presses no more nor less upon the Bottome it swims over then as much water as is equal in bulk to that part of the Ship which is beneath the Surface of the water PARADOX IV. That in the Ascension of water in Pumps c. there needs nothing to raise the Water but a competent weight of an External Fluid THis Proposition may be easily enough deduc'd from the already mention'd Experiments But yet for further illustration and proof vve vvill add that vvhich follovvs Take a slender Glass-pipe such as vvas us'd about the first Experiment and suck into it about the height of an Inch of deeply tincted vvater and nimbly stopping the upper Orifice immerse the lovver part of the pipe into a Glass half fill'd vvith such tincted vvater till the Surface of the Liquor in the pipe be an inch or as low as you would have it beneath that of the External water Then pouring on oyle of Turpentine till it swim 3 or 4 Inches or as high as you please above the vvater loosen gently your finger from the upper Orifice of the pipe to give the inclosed Aire a little intercourse vvith the External and you shall see the tincted vvater in the pipe to be impell'd up not only higher then the Surface of the External vvater but almost as high as that of the External oyl through vvhich it being transparent and colourless the Red Liquor may be easily discern'd Novv in this case it cau't be pretended That the ascent of the water in the pipe proceeds from Natures abhorrency of a Vacuum since the pipe being full of aire and its Orifice unstopp'd though the vvater should not ascend no danger of a Vacuum vvould ensue the aire and the vvater remaining contiguous as before The true Reason then of the ascent of the water in our case is but this That upon all the other parts of the Imaginary Superficies that passes by the immers'd Orifice of the pipe there is a pressure partly of water and partly of the oyle swimming upon that water amounting to the pressure of 4 or 5 inches of water whereas upon that part of the same superficies whereon the Liquor contain'd in the pipe leans there is but the pressure of one inch of water so that the parts near the immers'd Orifice must necessarily be thrust out of place by the other parts of water that are more press'd till so much Liquor be impell'd up into the pipe as makes the pressure on that part of the Imaginary Superficies as great as that of the oyle and water on any other equal part of it and then by Vertue of the Aequilibrium often mention'd the water will rise no further and by vertue of the same Aequilibrium it will rest a little beneath the Surface of the External oyle because this last nam'd Liquor is lesse heavy bulk for bulk then water And by this we may be assisted to give a reason of the Ascension of water in ordinary sucking Pumps For as the oyle of Turpentine though a lighter Liquor then water and not mingleable with it does by leaning upon the Surface of the External water press up the water within the pipe to a far greater height then that of the External water it self so the Aire which though a far lighter Liquor then oyle of Turpentine reaches I know not how many Miles high leaning upon the Surface of the water in a Well would press it up into the Cylindrical Cavity of the Pump much higher then the External water it self reaches in the Well if it were not hinder'd Now that which hinders it in the Pump is either the Sucker which fences the water in the Pump from the pressure of the External aire or that pressure it self And therefore all that the drawing up of the Sucker needs to do is to free the water in the Pipe from the impediment to its Ascent which was given it by the Suckers leaning on it or the pillar of the Atmosphaeres being incumbent on it as in our Experiment the sides of the pipe do sufficiently protect the water in the pipe from any pressure of the External oyle that may oppose its ascent And lastly as the water in our pipe was impell'd up so high and no higher that the Cylinder of water in the pipe was just able to ballance the pressure of the water and oyle without the pipe so in Pumps the water does rise but to a certain height as about 33 or 34 foot and though you pump never so long it will be rais'd no higher because at that height the pressure of the water in the Pump upon that part
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
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
what the reading of Stevinus might make a man expect yet may deserve to be further prosecuted that whether or no the Paradox of Stevinus which not only some others but the Learned Dr. Wallis himself question wil hold the Inquiry he has started may be so persued as to occasion some improvement of this part of Hydrostaticks where to define things with certainty will perhaps be found a difficulter Task then at first glance one would think both because divers speculative things must be taken into consideration whose Theory has not perhaps yet been clear'd and because of the difficulty that will be found in practice by them that shall go about to make Stevinus's Experiments or others of that sort with all requisite Accurateness As indeed it is far easier to propose Experiments which would in likelyhood prove what we intend in case they could be made then to propose practicable Expedients how they may be made PARADOX VII That a Body immers'd in a Fluid sustains a lateral pressure from the Fluid and that increas'd as the depth of the immers'd Body beneath the Surface of the Fluid increaseth THough I shall not wonder if this proposition seems strange enough to most Readers yet I think I could make it out by several wayes and particularly by one that is plain and easie being but that which follows Take then a slender Glass pipe like that imployd about the first Experiment and cause it to be bent within two or three Inches of one end so that the longer and the shorter legs E F and F G may make as near as can be a right Angle at F then dipping the Orifice of the shorter leg F G in oyle of Turpentine suck into the Syphon if I may so call it as much of the Liquor as will fill the shorter leg and reach two or three Inches high in the longer then nimbly stopping the upper Orifice with your finger immerse the lower part of the Glass under water in such manner as that the longer leg E F may make as to sense right Angles with A B the Horizontal Surface of the water and the shorter leg F G may be so far depress'd under that Surface That I K the Superficies of the oyle in the longer leg be but a little higher then A B that of the external water Then removing your finger you may observe That the oyle in the Syphon will continue with little or no change in its former station By which it appears that there is a lateral pressure of the water against the oyle contiguous to G the Orifice of the shorter leg of the pipe since it is only that pressure that hinders the efflux of the oyl at that Orifice notwithstanding the pressure of the perpendicular Cylinder of oyle that would drive it out And that this pressure of the perpendicular Cylinder doth really urge the oyle in the shorter leg to flow out you may learn by slowly lifting the Syphon without changing its former posture towards the Surface of the water For as the lower leg comes nearer and nearer to that Surface to which as I newly intimated it is still to be kept parallel the oyle in the Horizontal leg will be driven out in drops by the pressure of the other oyle in the perpendicular leg That likewise before you begin to raise the Syphon the lateral pressure of the water against the lower Orifice of it is at least in such Experiments near about the same with what would be the perpendicular pressure of a Cylinder of water reaching from the same Orifice G or some part of it to the top of the water may be gather'd from hence That the Surface of the oyle in the longer leg will be a litle higher then that of the external water as by reason of the often mention'd comparative levity of the oyl it would be if we suppose That a pipe of Glass of the same bore and reaching to the top of the water being fitted to the Orifice of the Horizontal Leg as in the annex'd figure the Cylinder G H were fill'd with water And to make out the latter part of our proposition we need add no more then that if you plunge the Syphon deeper into the water you shall find the oyle by the Lateral pressure of the water driven by degrees quite out of the shorter leg into the longer and if you thrust it yet deeper you may observe that the longer leg will admit a Cylinder of water upon which that of oyle will swim the whole oyle alone being unable to counterballance the lateral pressure of the water at so great a depth By which last circumstance it appears that water has also a lateral pressure against water it self and that increas'd according to its depth since otherwise the external water could not impel that in the Horizontal leg of the Syphon into the perpendicular leg though to doe so it must surmount the weight or resistance of the whole cylinder of oyl that must be hereby violently rais'd in the said perpendicular leg But if you gently raise the Syphon again the lateral pressure of the water against the immers'd Orifice being diminish'd according as the distance of that Orifice G from the Horizontal Surface A B comes to be lessen'd the prevalent oyle will drive out the water first out of the Longer leg and then out of the shorter and will at length flow out in drops at the immers'd Orifice and thence emerge to the Top of the water Besides when the oyle in the Syphon does just counterballance the external water if you keep the shorter leg parallel to the Surface of the water and move the Orifice of it this way or that way and place it nearer or further off from the middle or from the sides of the Glass provided you keep it always at the same depth under the water you 'l find the oyl in the longer Leg to continue as to sense at the same height Whence we may learn what I have not yet found mention'd by any Writer That ev'n in the mid'st of the water we may suppose a pillar of water of a Basis equal to the side of an immers'd Body and reaching to the lowest part of it And that though this Imaginary aqueous pillar such as in our figure G H be not included in any solid Body or stable superficies nevertheless it s lower parts will have a lateral pressure tending outwards against the imaginary sides from the weight of the water that is above these subjacent and lateral parts and will have that pressure increas'd proportionably to the height to which the imaginary pillar reaches above them Which observation being duely noted and apply'd may be of no mean use in the explication of divers Hydrostatical phaenomena And lastly if in stead of holding E F the longer leg of our Syphon perpendicular and consequently the shorter parallel to the Horizon you variously incline the former so as to bring it to make an obtuse or an Acute
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
the breadth of the pipe and of a not inconsiderable height for 't is not easie to determine precisely what height so that to be short in the fluid Body we made our tryal with the pressure of the Superior parts was communicated not onely to those that were plac'd directly under them but ev'n to those that were but obliquely so and at a distance from them I had forgot to confirm that it was the pressure of the superiour parts of the water that made our floating bubble sinck by such another circumstance as I took notice of in some of the former Experiments viz. that when it lay quietly at the bottom of the Vessel if by inclining the Instrument we pour'd off as much of the water in the pipe E F as suffic'd competently to diminish its height above the water in the Vessel A B C D the air in the bubble finding its former pressure alleviated would presently expand it self and make the bubble emerge And to show That the very oblique pressure which the bubble sustain'd from the water in the pipe was not overmuch differing from that which it would have sustain'd from an External force or from the weight of water plac'd directly over it I caus'd two such bubbles to be pois'd and having put each of them into a long Cylindrical Glass open above and fill'd with water upon which it floated if we thrust it down a little way it would agreeably to what hath been above related ascend again so that we were forc'd to thrust it down to a good depth before the pressure of the incumbent water was great enough to make it subside And perhaps it will not be impertinent to take notice before we conclude how the pressure of such differing fluids as aire and water may be communicated to one another For having sometimes forborn to fill the Vessel A B C D quite full of water so that when the Cork was fitted to it there remain'd in it a pretty quantity of aire as between the Surface L M and the Cork nevertheless if the stopple or cork were very closely put in the pressure of the water that was afterwards poured into the pipe E F from J to K would make the bubble sinck little otherwise for ought I took notice of then if the Vessel had been perfectly fill'd with water the aire above L M that was both imprisoned and compress'd communicating the pressure it receiv'd to the water contiguous to it PARADOX VIII That water may be made as well to depress a Body lighter then it self as to buoy it up HOw strange soever this may seem to those that are prepossess'd with the vulgar Notions about gravity and levity It need not be marvail'd at by them that have consider'd what has been already deliver'd For since in Fluid Bodies the upper parts press upon the lower and upon other bodies that lie beneath them And since when a Body is unequally press'd by others whether lighter or heavier then it self it must necessarily be thrust out of that place where it is more press'd to that where 't is less press'd If that a parcel of oyle be by a contrivance so exposed to the water as that the water presses against its upper Superficies and not against the undermost or lateral parts of it If we suppose that there is nothing whose pressure is not inferiour to that of the water to hinder its descent supposing withal that the oyle and water cannot pass by one another for which cause we make use of a slender pipe the oyle must necessarily give way downwards and consequently be depress'd and not buoy'd up This is easily exemplified by the following Experiment Take a slender Glass Syphon E F G H of the bore we have often mention'd whose shorter leg G H may be about 3 or 4 Inches long and as parallel as the Artificer can make it to the longer E F dip the shorter leg in oyle of Turpentine till the oyle quite fill the shorter leg and reach to an equal height in the longer as from F to J. Then stopping the Orifice E of the longer leg with your finger and immersing the replenish'd part of the Syphon about an inch under water you shall perceive that as you thrust it lower and lower upon the removal of your finger the oyle in the shorter leg will be made to sinck about an inch or somewhat more and as afterwards you thrust the pipe deeper the oyle in the shorter leg will by the weight of the incumbent water H K be driven downward more and more till it come to the very bottom of the shorter leg whence by continuing the immersion you may impel it into the longer The cause of which Phaenomenon I suppose to be already clearly enough assign'd to make it needless to add any thing here about it It remains that before I proceed to the next proposition I add That to Exemplifie at once three Paradoxes both this and the next foregoing and the second I caus'd to be made a slender Glass-pipe of the Figure express'd in the annexed Scheme and having by the lower Orifice L suck'd into it as much oyle of Turpentine as reach'd in the longest leg N O as high as the Top of the other part of the Glass namely to the part P in the same level with the Orifice L I first stopp'd the upper Orifice of it O with my finger And then thrusting it as before under water to a convenient depth upon the removal of my finger the External water did first drive away the oyle that was in L M that part of the crooked pipe which was parallel to the Horizon then it depress'd the same oyle to the bottom of the shorter leg that is from M to N And lastly it impell'd it all up into the longer leg N P O to what height I thought fit So that the oyle was press'd by the water both laterally downwards and upwards the causes of which are easily deducible from the Doctrine already deliver'd PARADOX IX That what ever is said of positive Levity a parcel of oyle lighter then water may be kept in water without ascending in it TO make out what I have to represent about this Paradox the more intelligible the best way perhaps will be to set down the Considerations that induc'd me to judge the thing it pretends to feasible And in order to this it would be expedient to consider why it is that a Body lighter in specie then water being plac'd never so much beneath the Superficies of that Liquor will rather emerge to the Top then sinck to the bottom of it if we had not already consider'd that problem in the Explication of the third Paradox But being now allow'd to apply to our present purpose what hath been there deliver'd I shall forthwith subjoyne That 't was easie enough for me to collect from hence that the Reason why it seems not possible That a parcel of oyle lighter then water should without violence
part of the water soever it be plac'd provided it be perfectly environ'd with that Liquor it must keep in the water which in this whole Discourse we suppose to be Homogeneous as to gravity the place you please to give it And to add That on this occasion though Mathematicians have hitherto contented themselves to prove that in case a Body could be found or provided that were exactly equiponderant to water it would retaine any assignable place in it yet the Curiosity we had to give an Experimental proof of this Truth at length produc'd some glass Bubbles which some Gentlemen here present have not perhaps forgot that were by a dexterous hand we employ'd about it so exquisitely pois'd as to the wonder of the Beholders to retain the places given them sometimes in the middle sometimes near the top sometimes near the bottom of the water though that were Homogeneous for a great while till some change of consistence or gravity in the water or some of its parts made the bubble rise or fall The Application of this to what has been objected concerning Horse-hairs being too easie to need to be insisted on there remains to be dispatched our Authors seventh and last Argument which is this Object 7. That otherwise all the inferiour parts of the water would be in perpetual motion and perpetually expell'd by the Superior Answ But if by the inferior parts he means such portions as are of any considerable bulk the Answer newly made to the last objection where we shew'd that the body R would retain its place any where in the water and consequently near the bottome will shew the invalidity of this Objection And unless we knew of what bignesse and shape the Corpuscles of water are it would perhaps be to little purpose to dispute how far it may be granted or may be true in the particles that water is made up of Onely this I shall add That whereas this Learned Authour mentions it as an absurdity that the lower parts of water should be in perpetual motion And Stevinus himself in the beginning of his Hydrostatical Elements seems to me to speak somewhat inconsiderately of this matter and though as I lately said I allow such sensible bodies as those whose gravity in water Writers are wont to dispute of to be capable of retaining their places in water if they be in specie equiponderant to it Yet I am so far from thinking it absurd that the inferiour Corpuseles of water should be perpetually in motion that I see not how otherwise they could constitute a Fluid body That restless Motion of their parts being one of the generalest Attributes of Liquors and being in water though not immediately to be seen yet to be easily discover'd by its Effects As when Salt being cast into water the aqueous parts that are contiguous to it and consequently near to the bottom do soon carry up many of the faline ones to the very top of the water where after a while they are wont to disclose themselves in little floating grains of a Cubical shape But of this restless motion of the parts of Liquors having professedly treated elsewhere already I shall add nothing at present But rather take notice of what our Authour subjoyns to the last of his Arguments as the Grand thing which they suppose in these words Ratio porro a priori hujus sententiae videtur esse quia res non dicitur gravitare nisi quatenus habet infra se Corpus levius se in specie The erroniousness of which conceit if I should now go about solemnly to evince I as well fear it would be tedious as I hope it will be needless to those that have not forgot what may concern this subject in the former part of the now at length finish'd discourse and especially where I mention those Experiments which show That neither a stone nor Gold it self when plac'd deep under water would sinck in it if the Superiour water that gravitates on it did not contribute to its depression APPENDIX II. Concerning the Reason why Divers and others who descend to the Bottome of the Sea are not oppress'd by the weight of the incumbent water AMongst the difficulties that belong to the Hydrostaticks there is one which is so noble and which does still so much both exercise and pose the wits of the Curious That perchance it will not be unacceptable if to the former Experiments we add by way of Appendix one that may conduce to the solving of this difficult problem viz. Why men deep under water feel no inconvenience by the pressure of so great a weight of water as they are plac'd under The common Answer of Philosophers and other Writers to this puzling Question is That the Elements do not gravitate in their own proper places and so water in particular has no gravitation upon water nor consequently upon bodies every way surrounded with water But that this Solution is not to be admitted may be easily gather'd from our proofs of the first Paradox and from divers other particulars applicable to the same purpose that may be met with in the foregoing papers A famous VVriter and for ought I know the Recentest except Monsieur Paschal that has treated of Hydrostaticks having rendred this Reason of the Phaenomenon The Superior parts of consistent water as he speaks press not the inferior unless beneath the inferior there be a Body lighter in specie then water and therefore since a humane Body is heavier in specie then water it is not press'd by the incumbent water because this does not endeavor to be beneath a humane Body He subjoyns contrary to his Custome this confident Epiphonema Qui aliam causam hujus rei assignant errant alios decipiunt But by his favour notwithstanding this confidence I shall not scruple to seek another Reason of the Phaenomenon For I have abundantly prov'd that contrary to the Assertion on which his Explication is built the upper parts of water press against the lower whether a body heavier or lighter in specie then water be underneath the lower And the contrary of which being the 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 in this Controversie perhaps the matter may be somewhat cleard by mentioning here a distinction which I sometimes make use of I consider then a body may be said to gravitate upon another body in two senses For sometimes it actually sincks into or gets beneath the body that was under it as a sincking stone gravitates upon water and which I call Praevalent or successful Gravitation sometimes it does not actually at least not visibly descend but only exercises its gravitation by pressing against the subjacent body that hinders its descent as when a VVoman carries a Paile of water on her head though the weight do not actually get nearer the Center of the Earth yet actually presses with its whole gravity upon the Womans head and back and other subjacent parts that hinder its actual descent and according
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
place Yet both the solid about C and the water that succeeds it do in their turns hinder the descent of the Superior water which therefore must gravitate upon which soever of the two it be that actually comes to be plac'd directly under it if there be nothing before the displacing of the solid capable to take away the natural gravity upon whose account the water over B and C does incessantly tend downwards And though Monsieur Des Cartes does not so clearly express himselfe whether he supposes the hole at A to be stopp'd with some other body when the solid is plac'd about B yet because he is wont to speak consistently I presume he means that when the solid is remov'd to B the hole at A is otherwise sufficiently stopp'd I say then that the reason why the solid which whilst at A sustain'd a great pressure from the incumbent water feels not the weight of it when plac'd at B is not that which Monsieur des Cartes gives but this That the solid being environ'd with water the subjacent water does as we have often had occasion to manifest press it upwards full as strongly and somewhat more as the weight of the incumbent water presses it downwards So that a mans body in stead of sincking would be buoy'd up if as it is a little heavier it were a little lighter in specie then water Whereas when the solid was that alone which cover'd and stop'd the hole there was a manifest Reason why it should be forcibly thrust downwards by the weight of the incumbent water B C. For in that case there was no water underneath it at A to support the solid and by its pressure upward to enable it to resist so great a weight And this to hint that upon the by may perchance help us to guess at the reason of what Geographers relate of the Lake Asphaltites in Judea in case the matter of fact be true That this dead Sea as they also call it will not suffer any living creature to sinck in it For the Body of a Man and for ought we know of other Animals is not much heavier in specie then common fresh water Now if in this Lake that stands where Sodom and Gomorrah did before those impious Regions were destroy'd by fire from Heaven we suppose which the nature of the Soyle and the Sacred Story makes probable enough That the water abounds with Saline or Sulphurous Corpuscles the former helping the later to associate with the water as we see in sope consisting of salt and oyle and in Chymical mixtures of Alcalis and Brimstone dissoluble in water the Liquor may have its gravity so augmented as to become heavier in specie then the body of an animal For I have learned of a Light Swimmer that he could hardly begin to Dive in salt water though he easily could in fresh And 't is not difficult to make a Brine or Lixivium which are but Solutions of salt in water heavy enough to keep up an egg from sincking And not only barely by dissolving a metalline body in a saline Menstruum without otherwise thickning the Liquor I have brought solid pieces of Amber it self to swim upon it but I have try'd that certain saline Solutions which I elsewhere mention nay and a distill'd Liquor I us'd defleam'd oyle of Vitriol without any thing dissolv'd in it would do the same thing by reason of the numerous though minute Corpuscles of salt and sulphur that it abounds with There remains but one solution more of our Hydrostatical probleme that I think worth mentioning and that is given by the Learned Stevinus in these words Omni pressu quo Corpus dolore afficitur pars aliqua Corporis luxatur sed isto pressu nulla Corporis pars luxatur isto igitur pressu Corpus dolore nullo afficitur Assumptio syllogismi manifesta est nam si pars aliqua ut caro sanguis humor aut quodlibet denique membrum luxaretur in alium locum concedat necesse esset atqui locus ille non est extra Corpus cum aqua undiquaque aequali pressu circumfusa sit quod vero pars ima per 11. propositionem Hydrostaticorum paulo validius prematur superiori id hoc casu nullius momenti est quia tantula differentia partem nullam sua sede dimovere potest neque item intra ipsum Corpus concedit cum istic Corpore omnia oppleta sint unde singulae partes singulis partibus aequaliter resistunt namque aqua undiquaque eadem ratione Corpus totum circumstat Quare cum locus is nec intra nec extra Corpus sit absurdum imo impossibile fuerit partem ullam suo loco emoveri ideoque nec Corpus hic afficitur dolore This Solution of Stevinus I esteem preferrible by farr to those that are wont to be given of this difficult Probleme But yet the Phaenomenon seems to me to have still somewhat in it of strange 'T is true that if the Question were only that which some put viz. Why the body of a Diver when it is near the bottom of the Sea is not press'd down by so vast a weight of water as is incumbent on it It might be rationally answer'd That the weight of so much water as leans upon the body is not sustein'd by the force of the body it self but by that of the water which is under it For by the Experiments and Explications we have annexed to some of the foregoing Paradoxes it appears That the subjacent water by its pressure upwards is able not only to support the weight of the incumbent water but so far to exceed it that it would not only support the immers'd body and the incumbent water but buoy up the body if it were never so little lighter in specie then water And as for what Stevinus insinuates That when the water presses the body every way that pressure is not felt though it would be in case it press'd upon some parts and not upon others I am of the same opinion too and to prove it shall not make use of the example he proposes in the words immediately following those of his I just now recited For I doubt that example is rather a supposition then a try'd thing but by an Experiment which may be easily made and has diverse times been so in our Pneumatical Engine For though the aire be a heavy fluid and though whilst it uniformely presses the whole superficies of the body we feel not the pressure of it And though for this reason you may lay the palm of your hand upon the open orifice of a small brass Cylinder apply'd to the Engine instead of a Receiver without any hurt Yet when by pumping the aire that was before under the palm of your hand is withdrawn and consequently can no longer help to support your hand against the pressure of the external and incumbent aire the external aire will lean so heavy upon the back of
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.
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
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
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
height would not as Experience shews it is be the same in all Cylindrical pipes though of very differing Bâ—â—es For supposing the height of the Mercurial Cylinder in a Tube of half an Inch Diameter to be 29 Inches 't is plain that a Mercurial Cylinder of the same height and three Inches in Diameter must weigh divers times as much as the former and therefore the pressure of the External aire being but one and the same if it be a just Counterpoize to the greater Cylinder it cannot be so to the less and if it be able to keep the one suspended at 29 Inches it must be able to keep the other suspended at a far greater height which yet is contrary to experience And indeed this Objection is so specious That though I elsewhere have already answer'd it both by reason and Experience as far forth as it concerns the Torricellian Experiment Yet to shew the mistake on which it is grounded it may be very well worth while to make out our proposed Paradox as that whose truth will sufficiently disprove that errour by shewing both that the Assertion is true and why it must be so Provide then a more then ordinarily wide mouth'd Glass cleer and of a Convenient depth into which having put a convenient quantity of water deeply ting'd with Brazil or some other Pigment fit to the Orifice a broad but thin Cork in which by burning or cutting make divers round holes of very differing widenesses into each of which you may thrust a glass Cylinder open at both ends and of a size fit for the hole that is to receive it that so the several pipes may be imbrac'd by these several holes And as neare as you can make them parallel to one another and perpendicular to the superficies of the water into which they are to be immers'd But we must not forget that besides these holes there is an aperture to be made in the same Corke it matters not much of what figure or whereabouts to receive the slender end of a glass Funnel by which oyl may be convey'd into the vessel when it is stopp'd with the Cork And in the slender part of this Funnel we use to put some Cotton-week to break the violence of the oyl that is to be pour'd in which might else disorder the Experiment All this being thus provided and the Cork furnish'd with its pipes being fitted to the Orifice of the Vessel if at the Funnel you pour in oyl of Turpentine and place the Glass betwixt your eye and the Light you may through that transparent Liquor perceive the Tincted water to be impell'd up into all the pipes and to rise uniformly in them And when this tincted Liquor has attain'd to the height of two or three or more Inches above the lowermost Surface of the External oyl if you remove the Funnel which yet you need not do unless there be yet oyl in it you may plainly perceive the water to reach as high in one of the smaller pipes as in another three or four times as great and yet the water in the several pipes as 't is evident is sustain'd at that height above the level of the other water by the pressure or counterprize of the external oyle which then if one being lighter in specie then water will have its Surface somewhat higher without the pipes then that of the Tincted water within them And if by the Aperture that receives the Funnel you immerse almost to the Bottom of the oyle the shorter leg of a slender glass Syphon at whose longer Leg you procure by Suction the oyle to run out you shall perceive That according as the depth and pressure of the External third decreases so the water in the pipe will subside and that uniformely as well in the lesser as in the greater pipes The Reason of this is not difficult to be render'd by the Doctrine already deliver'd For suppose E F to be the Surface of the water both within and without the pipes before any oyle was poured on it if we then suppose the oyle to be poured in through the Funnel its lightness in respect of water wherewith it will not mingle will keep it from getting into the cavity of the pipes L M N and therefore spreading it self on the outside of them above it must necessarily by its gravity press down the Superficies of the external water and impell up that liquor into the cavities of the pipes And if we suppose the pouring on of the oyl to be continued till the uppermost surface of the oyl be raised to G H and that of the external water depress'd to I K or thereabouts an imaginary plain passing along the lower Orifices of the pipes I say the tincted waters in the pipes ought to have their uppermost Surfaces in the same level notwithstanding the great inequality of their Bores For that part of the Surface IK which is comprehended within the Circular Orifice of the greatest pipe L is no more charged by the incumbent water then any other part equal to that Circle of the same Imaginary Superficies is by the water or oyle incumbent on it and consequently no more then the part comprehended within the circle of the finall pipe N is by the water contain'd in that small pipe the external oyle having as much a greater height upon the Superfices I K then the water within the pipe as is requisite to make the two Liquors Counter-ballance each other notwithstanding the difference of their specifick Gravities And though the pipe L were twice as bigg it would Charge the subjacent plain I K no more then the pressure of the oyle on the other parts of the same imaginary Surface is able to resist And yet this pressure of the External oyle ought not to be able to raise the water in the slender pipe N higher then the Surface Q in the same Level with the Surface O. For if the water were higher in the small pipe being a heavier Liquor then oyle it must press upon that part of the Surface I K it leans on with greater force then the external oyle upon the other parts of the same plain I K and therefore with greater force then the weight of the External oyle could resist And consequently the water in the slender pipe must subside till its Surface be inferiour to that of the External oyle since till then the difference of their specifick gravities cannot permit them to rest in an Aequilibrium To be short It is all one to the resistance of the external oyl how wide the Cylinder is that it supports in the pipe provided the height of it be not greater in respect of the height of the oyl then the difference of the respective Gravities of those two Liquors requires For so long the pressure of the Cylinder of water-will be no greater on that part of the Imaginary Superficies which it leans upon then the pressure of the external oyle will be on all the
say when this is done you incline the pipe towards the sides of the Glass You may indeed observe the Surface of the oyle in the pipe to be as before a little higher then that of the water without it But you shall likewise see That though the Orifice of the pipe were not thrust deeper into the water yet therewill be a pretty deal of water got up into the pipe because the oyle not leaning now upon the water only as it did before but partly upon the water and partly upon the pipe its pressure upon the subjacent water is considerably lessen'd and there by the external water whose pressure is not diminish'd too is able to impel up the oyl and intrude for a little way into the pipe But if you re-erect the pipe the pressure of the oyle being then again exerted upon the subjacent water it will be able to depress and drive it again out of the Cavity of the pipe And to this agrees very well what we further try'd as follows We caused 3 pipes to be blown shap'd as the adjoyning Figures one having in it divers acute Angles the other being of a winding form like a scrue or worm of the Limbeck and the third very irregularly crooked and yet each of these pipes having all its crooked parts and some of its streight erected parts fil'd with oyl of Turpentine being thrust to a convenient depth under water and unstopp'd there after the manner already often declar'd we found that according to our Paradox the surface of the oyle in the pipe was higher than that of the water without it as much as it would have been in case the pipe had been streight as we try'd by placing by the crookedest of them a streight pipe with oyle in it though the quantity of the oyle in one of these pipes were perhaps three times as much as would have suffic'd if the pipe had been strait So that this surplusage of oyle did not press upon the subjacent water for if it had done so the oyle would have run out of the pipe And I remember that lifting up as much of one of these crooked pipes as I thought fit somewhat above the Surface of the water when the Superficies of the oyle in the pipe was not above half an inch higher then that of the water without it I estimated that the crooked pillar of oyl contain'd in that part of the pipe which was above the Surface of the water was about 7 or 8 Inches long So true it is that the pressure of Liquors contain'd in pipes must be computed by the perpendicular that measures their height what ever be their length or bigness SCHOLIUM THE Learned Stevinus having demonstrated the Proposition we lately mention'd out of him subjoyns divers consectaries of which the truth hath been thought more questionable then that of the Theorem it self And therefore he thought fit to add a kind of Appendix to make good a Paradox which seems to amount to this That If in the Cover of a large Cylindrical Box exactly closed there be perpendicularly erected a Cylindrical Pipe open at both ends and reaching to the Cavity of the Box this Instrument being fill'd with water the circular Basis of it will susteine a pressure equal to that of the breadth of the Basis and height of the Pipe I chose thus to express this Theorem which might be according to Stevinus propos'd in more general terms because this way of expressing it will best suit with the subsequent Experiment and may consequently facilitate the understanding of the Paradox But though the Learned Stevinus's aims were to be commended who finding this Proposition doubted seems to have had a great mind to give an Experimental Demonstration of it and therefore proposes no less then five pragmatical Examples as he calls them to make out the truth of what he asserts yet in this he hath been somewhat unhappy that that Experiment which alone for ought I can find has been try'd of all the five is rejected as incompetent by those that profess to have purposely made tryal of it And indeed by reason of the difficulty of bringing them to a practical examen I have somewhat doubted whether or no this useful writer did ever make all those Tryals himself rather then set down the events he suppos'd they must needs have as presuming his conjectures rightly deduc'd from a Demonstrative Truth Wherefore though another of the Experiments he proposes be not free from difficulty yet having by the help of an Expedient made it practicable we are induc'd by its plainness and clearness to prefer it to what else he proposes to the same purpose We provided then a vessel of Laton of the figure express'd in the Scheme and furnished it with a loose Bottom C D made of a flat piece of wood cover'd with a soft Bladder and greas'd on the lower side neer the edges that leaning on the rim of wood G H contiguous every where to the inside of the Laton it might be easily lifted from off this Rim and yet lye so close upon it that the water should not be able to get out between them And to the midst of this loose bottom was fastned a long string of a good strength for the use hereafter to be declared The Instrument thus fitted the water was poured in apace at the Top A B which by its weight pressing the false Bottom C D against the subjacent Rim G H contributed to make the Vessel the more tight and to hinder its own passing The Vessel being fill'd with water we took the forementioned string one of whose ends was fastned to I the middle part of the loose Bottom and tying the other end K to the extremity of the Beam of a good pair of Scales we put weights one after another into the opposite scale till at length those weights lifted up the false Botom C D from the Rim G H and consequently lifted up the Incumbent water which presently after ran down between them And having formerly before we poured in any water try'd what water would suffice to raise the Bottom C D when there was nothing but its own proper weight that was to be surmounted we found by deducting that weight from the weight in the scale and comparing the Residue with the weight of as much water as the cavity of the broad but very shallow Cylinder B E C H G D F would have alone if there had been no water in the pipe A I amounted to we found I say by comparing these particulars that the pressure upon C D was by so very great odds more then could have been attributed to the weight of so little water as the Instrument pipe and all contain'd in case the water had been in an uniform Cylinder and consequently a very shallow one of a Basis as large as that of our Instrument That we could not but look upon the success as that which though it did not answer
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
to find that 't is partly the pressure of the oyle and partly the contrivance and situation of the vessels if we will but consider the matter somewhat more atentively For the oyle that reaches much higher then K and consequently then the leggs of the Syphon presses upon the surface of the External water in each of the suspended pipes I and H. I say the External water because the oyle floating upon the water and the Orifice of both the legs F and G being immers'd under the water the oyle has no access to the cavity of either of those legs Wherefore since the oyle gravitates upon the water without the legs and not upon that within them and since its height above the water is great enough to press up the water into the Cavity of the legs of the Syphon and impel it as high as K the water must by that pressure be made to ascend And this raising of the water happening at first in both legs for the cause is in both the same there will be a kind of conflict about K betwixt the two ascending portions of water and therefore we will now examine which must prevaile And if we consider That the pressure sustein'd by the two parcels of water in the suspended pipes I and H depends upon the height of the oyle that presses upon them respectively it may seem at the first view That the water should be driven out of the lower vessel into the higher For if we suppose that part of the shorter leg that is unimmers'd under water to be 6 Inches long the unimmers'd part of the longer leg to be seaven Inches because the surface of the water in the vessel I is an Inch higher then that of the water in the vessel H it will follow That there is a greater pressure upon the water whereinto the longer leg is dip'd by the weight of an Inch of oyle so that that liquor being an inch higher upon the surface of the water in the pipe H then upon that in the pipe I it seems that the water ought rather to be impell'd from H towards K then from I towards K. But then we must consider That though the descent of the water in the leg G be more resisted then that in the other leg by as much pressure as the weight of an Inch of oyle can amount to Yet being longer by an Inch then the water in the leg F it tends downwards more strongly by the weight of an Inch of water by which length it exceeds the water in the opposite leg So that an inch of water being ceteris paribus heavier then an Inch of oyle the water in the longer leg notwithstanding the greater resistance of the external oyle has a stronger endeavour downwards then has the water in the shorter leg though the descent of this be resisted but by a depth of oyl less by an Inch. So that all things computed the motion must be made towards that way where the endeavour is most forcible and consequently the course of the water must be from the upper vessel and the shorter leg into the longer leg and so into the lower vessel The application of this to what happens in Syphons is obvious enough For when once the water is brought to run through a Syphon the aire which is a fluid and has some gravity and has no access into the cavity of the Syphon must necessarily gravitate upon the water whereinto the legs of the Syphon are dip'd and not upon that which is within the Syphon and consequently though the incumbent aire have somewhat a greater height upon the water in the lower vessel then upon that in the upper yet the gravitation it thereby exercises upon the former more then upon the latter being very inconsiderable the water in the longer leg much preponderating by reason of its length the water in the shorter leg the efflux must be out of that leg and not out of the other And the pressure of the External aire being able to raise water as we find by sucking Pumps to a far greater height then that of the shorter leg of the Syphon the efflux will continue for the same reason till the exhaustion of the water or some other circumstance alter the case But if the legs of the Syphon should exceed 34 or 35 foot of perpendicular altitude the water would not flow through it the pressure of the external aire being unable as has been elsewhere declared to raise water to such a height And if a hole being made at the top of a Syphon that hole should be unstopp'd while the water is running the course of it would presently cease For in that case the aire would gravitate upon the water as well within as without the cavity of the Syphon and so the water in each leg would by its own weight fall back into the vessel belonging to it But because this last circumstance though clearly deducible from Hydrostatical principles and Experiments has not that I know of been verified by particular Tryals I caus'd two Syphons to be made the one of Tin the other of Glass each of which had at the upper part of the flexure a small round hole or socket which I could stop and unstop at pleasure with the pulp of my finger So that when the water was running through the Syphon in case I remov'd my finger the water would presently fall partly into one of the subjacent vessels and partly into the other And if the legs of the Syphon were so unequal in length that the water in the one had a far greater height or depth then in the other there seem'd to be when the liquor began to take its course through the Syphon some light pressure from the external aire upon the finger wherewith I stopp'd the Orifice of the socket made at the flexure And on this occasion I will add what I more then once try'd to shew at how very minute a passage the pressure of the External aire may be communicated to Bodyes fitted to receive it For having for this purpose stopp'd the orifice of one of the above mentioned Syphons insteed of doing it with my finger with a piece of oyl'd paper carefully fastned with Cement to the sides of the socket I found as I expected that though hereby the Syphon was so well clos'd that the water ran freely through yet if I made a hole with the point of a needle the aire would at so very little an orifice insinuate it self into the cavity of the Syphon and thereby gravitating as well within as without make the water in the legs to fall down into the vessels And though if I held the point of the needle in the hole I made and then caus'd one to suck at the longer leg this small stopple without any other help from my hand suffic'd to make the Syphon fit for use Yet if I remov'd the needle the aire would not without some noise presently get in at