HYDROSTATICAL PARADOXES, Made out by New EXPERIMENTS, (For the most part PHYSICAL and Easy.)  
By the Honourable ROBERT boil, Fellow of the Royal Society.  
OXFORD, Printed by William Hall, for Richard Davis, Anno Dom. M.DC.LXVI.   

THE PUBLISHERS ADVERTISEMENT TO THE READER.  
WHen the Author Writ the following Treatise, he had a design, as appears by some passages in the Preface, to publish together with it some things, which he had divers years before provided for an Appendix to the Physicomechanical Treatise about the Air: But part of the Appendix consisting of Experiments, which the Author has several times made, but trusting to his memory, did not think it necessary to Record, when he came to recollect particulars, he found that some years which had passed since divers of them were tried, and variety of intervening occurrents, had made it unsafe for him to rely absolutely upon his Memory for all the circumstances fit to be set down in the Hystorical part of the designed Appendix. And therefore he resolved to repeat divers Experiments and Observations, that he might set down their Phaenomena whilst they were fresh in his Memory, if not objects of his sense. But though, when he Writ the following Preface▪ he did it upon a probable supposition, that he should seasonably be able to repeat the intended Trials, yet his Expectation was sadly disappointed by that heavy, as well as just, Visitation of the Plague which happened at London whilst the Author was in the Country: and which much earlier than was apprehended, began to make havoc of the People, at so sad a rate that not only the Glassmen there were scattered, and had, as they themselves advertised him, put out their Fires, but also Carriers, and other ways of Commerce (save by the Post) were strictly prohibited betwixt the parts he resided in and London; which yet was the only place in England whence he could furnish himself with peculiarly shaped Glasses, and other Mechanical Implements requisite to his purposes; And the same Calamity continuing still, without yet affording us any certain ground of determining when it will end: The Author chooses rather to suffer the following Paradoxes to come abroad without the Appendix, (which is no way necessary to them, whatever they may be to It,) then any longer put off those Ingenious persons that solicited the publication of them.   

The PREFACE.  
THe Rise of the following Treatise being a Command imposed on me by the Royal Society, the Reader will, I hope, need no more than this intimation, to keep him from wandering to find some passages Worded as parts of a Discourse pronounceed before an Assembly, it being not unusual (though not necessary) to present either in writing or by word of mouth, together with the Experiments made before that Illustrious Company, an Historical account of Them.  
But because 'tis probable, that some Readers will desire to be satisfied about other particulars, relating to the publication of this Treatise, I presume it will not be amiss, both to say something of the Reasons, why I publish it as the first part of the present Appendix to my Physicomechanical Experiments, and to give some account of the manner of writing it.  
I had quickly both an opportunity and an Invitation to enlarge the papers I was to read, beyond the Limits of a bare description of the Phaenomena, and matters of fact, by my having been through some intervening Accidents so hindered from exhibiting them altogether, that I was desired to bring in an Account in Writing, that might be Registered (how little soever worthy of such Company) in the Societies Collection of Philosophical Papers, for the sake of those Members who could not be present at all the Experiments: So that finding some enlargements expected from me, I was easily induced to add the Explications of the Phaenomena I described, whilst I perceived that by a small addition of pains I might much gratify divers Ingenious Friends that were not so well versed in hydrostatics as in the other parts of real Learning.  
Having thus been induced to enlarge the Account of my Experiments till it had attained the bulk 'tis now arrived at, I confess I was without much difficulty persuaded, that to suffer it to pass abroad 
* About this passage, See the Publisher, to the Reader.  in the Company of the Appendix wherewith 'tis published, would not prove unacceptable to the Curious, no more than an improper introduction to the rest of my Appendix, and that for several Reasons.  
For (first) the hydrostatics is a part of Philosophy, which I confess I look upon as one of the ingeniousest Doctrines that belong to it. Theorems and Problems of this Art, being most of them pure and handsome productions of Reason duly exercised on attentively considered Subjects, and making in them such Discoveries as are not only pleasing, but divers of them surprising, and such as would make one at first wonder by what kind of Ratiocination men came to attain the knowledge of such unobvious Truths. Nor are the delightfulness, and the subtlety of the hydrostatics, the only things for which we may commend Them: For there are many, as well of the more familiar, as of the more abstruse Phaenomena of Nature; that will never be throughly understood, nor clearly explionted by those that are strangerste the hydrostatics; upon whose Principles depend, besides many other things, the Explications of most of the Physico. Mechanical Experiments, we have ventured to present the Public, and the Decision of those many Coutroversies, which they, and the Phaenomena of the Torrecellian Experiment have occasioned among the Modern Inquirers into Nature.  
But the use of this Art is not alone Speculative, but Practical, since not only the propositions it teaches, may be of great importance to Navigation, and to those that inquire into the magnitudes and gravities of Bodies, as also to them that deal in Salt works: But that the hydrostatics may be made divers ways serviceable to the Chemists themselves, to whose Art that Doctrine seems to be so little of Kin, I might here manifest, if I could think it fit to transcribe, what I have 
* Chiefly, in several places of the unpublished part of the Treatise of the osefulness of Experimental Philosophy.  elsewhere delivered to that purpose.  
But that which invited me to Write something of this part of Philosophy, is, not only that I think it considerable, but that, notwithstanding its being so, I find it but very little, and not very happily cultivated. For being not looked upon as a Discipline purely Mathematical, the generality of Mathematicians have not in their Writings so much as taken notice of it, much less improved It. And since the admirable Archimedes, who, in his little Tract De insidentibus humido, has left us three or four very excellent propositions, (but proved by no very easy Demonstrations) among divers others that have more of Geometrical Subtlety, than usefulness, Those Mathematicians, that, (like Marinus Ghetaldus, Stevinus, and Galileo) have added anything considerable to the hydrostatics have been (that I know of) very few, and those too, have been wont to handle them, rather as Geometricians, then as Philosophers, and without referring them to the explication of the Phaenomena of Nature. And as for the Peripatetics, and other School-Philosophers, though on some Occasions, as when they tell us, That water weighs not in water, nor air in air, they deliver assertions about matters belonging to the hydrostatics, (which term, in this Treatise, I often take in a large sense because most of the things delivered about the weight of bodies may by easy variations, be made applicable to other Fluids) yet they are so far from having illustrated, or improved them, that they have but broached or credited, divers of the most erroneous conceits, that are entertained about them. So that, there being but few Treatises written about the hydrostatics, and those commonly bound up among other Mathematical works, and so written, as to require Mathematical Readers, this useful part of Philosophy, has been scarce known any farther than by name, to the genèrality even 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 prepossessed with some errenous Opinions of the peripatetic 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 borrowed from Archimedes, and either circumspect Mathematicians, or devised themselves, and these mistakes being delivered 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 procured so general an entertainment for those Errors, that now the hydrostatics is grown a part of Learning, which 'tis not only difficult to attain, but dangerous to Study.  
Wherefore, though neither the Occasion and design of this Treatise exacted, nor my want of skill and leisure qualified me to Write either a Body or Elements of hydrostatics: yet I hoped I might do 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 received errors, by establishing Paradoxes còntrary to them, and to make the Truths the better understood and received, partly by away of Explicating them unemployed 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 hydrostatics Themselves to the Reader, I have, besides the Paradoxes, opposed 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 used to read Mathematical Books, are wont to be so indisposed to apprehend things, that must be explicated by Schemes, and I have found the generality of Learned men, and even of those new Philosophers that are not skilled in Mathematics, so much more unacquainted, than I before imagined both with the principles and Theorems of hydrostatics, and with the ways of explicating and proving them, that I feared, that neither the Paradoxes themselves, that I maintain, nor the Hypotheses about the weight and pressure of the air, upon which, little less than my whole Pneumatical Book depends, would be throughly understood without such a clear Explication of some Hydrostatical Theorems, as to a person not versed in Mathematical writings, could scarce be satisfactorily delivered 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 spared many words without injury to my proofs, and though I am myself, of the same mind I expect to find them of; yet, I confess that 'twas 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 myself, but to instruct others, I had rather Geometricians should not commend the shortness of my Proofs, then that those other Readers, whom I chiefly designed to gratify, should not throughly apprehend the meaning of them.  
But this is not all for which I am to excuse myself to Mathematical Readers. For some of them, I fear, will not like that I should offer for Proofs such Physical Experiments, as do not always demonstrate the things, they would evince, with a Mathematical certainty and accurateness; and much less will they approve, that I should annex such Experiments to confirm the Explications, as if Suppositions and Schemes, well reasoned on, were not sufficient to convince any rational man about matters Hydrostaticall.  
In Answer to this I must represent, that in Physical Inquiries 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 myself with tedious Circumlocutions, to avoid the possibility of being misunderstood, or of needing his Candour. 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 produced, they would meet at the Centre of the Earth: And to presume, that the Surface of every calm 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 observed it to be higher, where 'tis almost contiguous to the sides of the Vessel, then 'tis in other places.  
Moreover, since we find that though water will be uniformly raised 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 applied 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 endeavours may assist others to arrive at.  
And as for my 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 Mathematics, 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 Arithmetic or Geometry, yet in Physical matters, are wont to be taken for granted, about which men are liable 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 venturing to confute some reasonings that are given out for Mathematical demonstrations. For I suppose it will be considered, that those whose presumed Demonstrations I examine, though they were some of them Professors of Mathematics, yet did not Write merely 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 Mathematics, any more than that the Mathematicians that follow the Ptolemaick, the Copernican, the Tichonian, or other Systemes of the world, Write Books to manifest one another's 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 Modern Writers of hydrostatics) 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 'tis chiefly to gratify 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 herself. 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 discoursed, 'twil be easy for me to give an Account, why I premised these Hydrostatical Paradoxes to the rest of the Appendix, wherewith they are 
* An Account of this passage also, may be had from the Publishers Advertisement to the Reader.  now published: 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 subjoined to, and the vindication of then from invalid objections: And since I have generally observed, that the objections that have been, either publicly or privately▪ made against the explications & reasonings contained in that Book, were wont to proceed from unacquaintedness, either with the true notion of the weight and spring of the air, as I maintain them, or with the Principles and Theorems of hydrostatics, or else from erroneous Conceits about them; I thought it would much conduce to both the forementioned ends of my Appendix, If I cleared up that Doctrine to which my Experiments and reasonings have been all along Consonant, & whose being either not known, or misunderstood, seems to have occasioned the objections that have been hitherto made against the Hypotheses I have proposed, 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 & easy, and that my aim is but to discover Truths, or make them out by clearer explications, without supposing, like those I descent 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 Design, 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 than once) by the Royal Society itself, 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 easy as I have endeavoured to make these Experiments, yet I dare not promise myself that they will all of them be privileged from the fate whereto I have observed other Physico-Mathematical ones to be not seldom 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 subjoin 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 deduced, that wax, and other Bodies, very near aequiponderant with common water, will swim in that which is cold, and sink in that which is hot, or lukewarm. Which Experiment, though as it may be (and perhaps it has been) tried, I readily allow to be agreeable to the known Laws of the hydrostatics; Yet I have sometimes undertaken that the Trial should have a quite contrary event. To this purpose having taken some yellow Bees-wax, which was form 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 removed it out of the very cold water, into some that had been purposely made lukewarm, (or a little more than so) where it quickly, somewhat to the wonder of the lookers on, appeared 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 ducked the bullet 2 or 3 times under water to throw them off, notwithstanding which it constantly returned to float, and yet being removed again into the same cold water it had been taken out of, and ducked as before to free it from adherent bubbles, it lay quietly at the bottom, and, though raised 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 hydrostatics, 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 'twas before; so by the same warmth the spirituous and more agitable parts of the wax, whose texture is loose enough, would be somewhat (though not visibly) expanded, and would by that expansion gain a greater advantage towards floating, than the increased lightness of the water would give it disposition to sink. And I confirmed this conjecture by a farther experiment, which at first was itself somewhat surprising to the Beholders. For when the wax was first taken out of the cold water, & immediately immersed in the warm, it would readily enough sink, & being (with a quill or a knife) raised to the top of the water, it would again fall down, but more slowly then at the beginning, & aftersome few minutes, if it were raised to the upper parts of the water, it would remain a float. (And I have known it, when it had remained 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 knocked downwards, it would, readily enough, regain the upper part of the water, but if I continued to send it downwards about 6 or 7 times (more or fewer) successively, it would emerge every time more slowly than other, and at length not emerge at all, even when I tried it in water made heavy, by being highly infrigidated with salt and snow placed about the Glass. Which Phaenomena I had thought it reasonable to expect, because I presumed, that the Wax being removed immediately out of the warm water, into the cold, must require some time, to lose the adventitious expansion, which the warmth had given it, and must be deprived of it by degrees, by the coldness of the water into which the wax was transferred. As on the other side, there must be some time necessary for so little a warmth, as that of the tepid (or little more than 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 Trials 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 employed a poised 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 Trials 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 overlooking such Circumstances as 'tis not easy 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 questioned, but built upon, I think aught to be brought to trial. For, even whilst I was concluding this Preface, I found that divers even of the Moderns, & particularly a very learned Man that has lately Written of hydrostatics, 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 than water, being by leaks, or otherwise, filled with water, should sink and remain at the bottom of the water: whereas judging this Phaenomenon disagreeable to what I look upon as the Laws of the hydrostatics, I was confirmed in that opinion, by having had the curiosity to make some trials 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 than water, I could not sink, or keep sunk 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 hydrostatics duly ascertained, because the weighing of bodies in Liquors may hereafter appear to be one of the general ways I have employed, 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 pressed 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 pressed upward by the water that touches it beneath. 67  
Par. 4. That in the ascension of water in Pumps, etc. there needs nothing to raise the Water, but a competent weight of an External Fluid. 94  
Par. 5. 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. 106  
Par. 6. If a Body be placed 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 sustained by the Body (for we now consider not the Lateral nor the recoiling pressure, to which the Body may be expos'd& if quite environed with water) is no more than that of a Colomne 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 contained 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 inclined towards the Horizon, or thought it be irregularly shaped, and much broader in some parts, than the said Orifice. 117  
Par. 7. That a Body immersed in a Fluid, sustains a lateral pressure from the Fluid▪ and that increased, as the depth of the immersed Body, beneath the Surface of the Fluid, increaseth. 142  
Par. 8. That water may be made as well to depress a Body lighter than itself, as to buoy it up. 160  
Par. 9 That, what ever is said of positive Levity, a parcel of oil lighter than 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 sink by in own weight; yet if it be placed at a greater depth then that of twenty times its own thickness▪ it will not sink, if its discern be not assisted by the weight of the Incumbent water. 184  
Appendix. 1. Containing an Answer to seven Objections, proposed 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 oppressed by the weight of the incumbent water. 221    

Imprimatur,  
ROBERTUS SAY, VICECANCELLARIUS OXON.   

HYDROSTATICAL PARADOXES, Made out by NEW EXPERIMENTS: Presented to the ROYAL SOCIETY, (The Lord Viscount Brouncker being then Precedent.) 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 Monsieur 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 contains things, which if they had been published at the time, when it is said to have been written, would probably have been very welcome 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 Monsieur 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 oblige me to transcribe almost the whole Tract; and therefore I shall rather invite you to read the whole, then divert you from the design by culling out any part of it; yet if you will not be satisfied without something of more particular, I shall be obliged 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 Laws of the hydrostatics. 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 Monsieur Paschall's Assertions, I decline employing 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 expressly says that he actually tried 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 produced 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 Bottom.  
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 Country 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 proposed by Monsieur Paschall more ingenious than practicable, I was induced on this occasion to bethink myself▪ 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 clearness, That not only This Illustrious Assembly, but persons no more than moderately versed in the Vulgar principles of the hydrostatics, may easily enough apprehend what is designed to be delivered, if they will but bring with them a due Attention, and minds disposed to prefer 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 hydrostatics, but only ten or twelve Paradoxes, which I conceive to be provable 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 endeavour 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 than an easy supposition I met with in a short Paper (about a Mercurial Phaenomenon) brought in a year or two since to this Learned Society, by a deservedly Famous Member of it 
* That excellent Mathematician the Learned Dr Wallis, Savilian Professor of Geometry. , For though his supposal be made upon occasion of an Experiment of another Nature, than any of the ensuing, it may be easily accommodated 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 pressed, 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 pressed by a perpendicular pillar of that incumbent fluid, than 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 pressed 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, than there is upon the rest, that part must be displaced, or depressed, as it happens, when a stone or other Body heavier than water sinks 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 than 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 pressed upon then all the rest; it will by the greater pressure on the other parts of the Surface be impelled upwards, till it have attained a height, at which the pressure (of the raised 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 Questioned in our Assumption, 
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 Paradox.  though he that considers it attentively, will easily enough be induced to grant it: Yet I shall here endeavour to evince it Experimentally, and that by no other way of proof, than the same I employ all along this present discourse.  
Take then a Cylindrical glass pipe▪ of a convenient Boar 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, 'tis 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 Brevity's sake to call them) have free intercourse with one another by the open Orifice of the immersed 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 than that of the water without it, for reasons that 'tis not so necessary we should now inquire after, as 'tis, 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 mentioned posture, if you gently pour a convenient Quantity of Oil upon the external water, you shall see, That as the Oil 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 pour on oil; Of which the Reason seems manifestly to be this; That in the Imaginary plain that passes by the Orifice of the immersed end of the pipe, all that is not within the Compass of the Orifice, is exposed to an additional pressure from the weight of the oil which swims upon the water, and that pressure must still be increased, as there is more and more oil poured on; whereas a Circular part of the Imaginary plain, equal to the Orifice of the Glass, is by the sides of the pipe fenced from the immediate pressure of the oil; so that all those other parts of the water, being far more pressed, than that part which is comprehended within the Cavity of the Tube: and consequently the pressed parts of the external water, are by the equal gravitation of the oil, upon the parts of the external water, impelled up into the Cavity of the pipe, where they find less resistance, than any where else, till they arrive at such a height, that the Cylinder of water, within the pipe, does as much gravitate upon the subjacent part of the Imaginary Surface, as the water and oil 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 cleared and confirmed 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 Air to be a Body not devoid of weight, which yet divers Learned adherents to the Peripatetic Philosophy do resolutely deny, it seems requisite to premise something for the proof of this Truth.  
And though I think the Arguments we have employed to that purpose already, do strongly evince it: yet if I may be allowed to anticipate one of my own Experiments of the Appendix, I shall give an instance of the weight of the Air, not liable 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 satisfy the learned'st even of our professed Adversaries.  
We caused 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 weighed in exact Scales, aught to be of no greater thickness, then is judged necessary to keep it from being (when sealed up with none but very much expanded air in it) broken by the pressure of the ambient Atmosphaere. This bubble was (like a Pear with its stem) furnished with a very slender pipe of Glass, at which it was blown, that it might be readily sealed up; and then (the Air 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 stem 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 sealed up. This Glass being permitted leisurely to cool, 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 show the Experiment, I put it in one of the scales of an exact balance, that would turn, perhaps with the 30th, or 50th, or a less part of a grain; and having carefully counterpoised it, I then warily broke off the sealed 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 Air, there being no other cause, either needful, or justly assignable, but the weight of the Air that rushed into the Cavity of the Glass, as finding less resistance there then elsewhere, by reason that the included Aire had its spring much weakened by its great expansion.  
This Experiment I many times tried, sometimes before some Virtuosos, and sometimes before others; who all allowed it to be conclusive. For here it could not be objected as against the weighing of Air in a Bladder, (which objections yet I could easily answer, if it were now proper) that the air which ponderates, it stuffed with the Effluvia of him that blows the Bladder, and (besides that) is not air in its Natural state, but violently compressed. For here 'tis the free air, and in its wont laxity, that makes the Glass preponderate.  
And that there is a great Ingress of the external air, is evident by these three Phaenomena. The one, that if you lend an attentive Ear, you shall plainly hear a kind of whistling noise to be made by the external air, as it rushes violently in upon the breaking of the Glass; The other, that the Rarefaction of the air, sealed up in the bubble, being very great, there is a great deal of space left for the ambient air to fill upon its admission; and the greatness of this Rarefaction may be guessed at, both by the breaking of such bubbles now and then by the pressure of the External air, 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 sealed end of the Glass in the air, you break it under water, that Liquor will, by the Pressure of the Atmosphaere, be forced to spring up like an artificial Fountain into the Cavity of the Bubble, and fill about three quarters of it. By which last circumstance I gather, that the weight of the air is more considerable than even many, who admit the air to have weight, seem to imagine. For we must not suppose, that all the air contained in the Bubble, when broken, weighs no more than the weight requisite in the opposite Scale, to reduce the Balance to an Aequilibrium; since this additional weight is only that of the air, that intrudes on the breaking of the glass; which air, by the Observations newly mentioned to have been made with water, appears to be but about three quarters of the whole air contained in the broken Bubble; and yet, according both to our Estimate, and that of divers Virtuosos, 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 Balance we used, manifested the newly admitted Air to amount to some times near half a grain, and sometimes beyond it.  
And because one of the last Experiments that I made to this purpose, with sealed 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 sealed when the contained air was exceedingly rarified, was Counterpoised in a nice pair of Scales, and then the sealed apex being broken off, and put again into the same Scale, the weight appeared to be increased by the readmitted air, a pretty deal above 11/16; this, and consequently very near, if not full ¾ of a grain: Lastly, having by some slight (for 'tis no very easy matter) filled it with common water, we weighed 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 Trials, that the readmitted air, which amounted to ¾ of a grain, filled but ¾ of the whole Cavity of the Bubble, the air that was in it, when sealed, possessing one quarter of that Cavity, the whole air contained in the Bubble, may be reasonably presumed 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 than nine hundred times as much as an equal quantity of Air. And therefore, though we allow, that in an Experiment so diligently made, as this was, the air 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 air will yet appear so heavy, that this Experiment will agree well with those others, recorded in another Treatise, wherein we assigned (numero rotundo) a thousand to one, for the proportion wherein the specific Gravity of water exceeds that of air.  

PARADOX I.  
That in Water, and other Fluids, the lower parts are pressed by the upper.  
PRovide a Glass vessel of a convenient height and breadth A. B. C. D. filled with water almost to the Top; Then take a glass Pipe, open at both Ends, Cylindrical, and of a small Boar, (as about the eighth or sixth part of an Inch in Diameter.) Put the lower End of this Pipe into clear Oil or Spirit of Turpentine; and having by Suction raised 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 raised Liquor may not fall back again: Then taking the Pipe and that Liquor out of the Oil of Turpentine, place it perpendicularly in the Glass of water, so as that the Surface of the Oil in the Pipe be somewhat higher than 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 Oil 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 Oil of Turpentine, being a heavy Fluid, does, as such, tend downwards, and not being stopped by the Glass itself, 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 ascribed, 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 oil and the water, as Liquors that will not mingle, is evident from hence, That if you had removed your finger when the Pipe was not so deeply immersed in the Glass, but that the Surface of the oil 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 Oil, notwithstanding its presumed contrariety to water, would have freely subsided in the Pipe, till it had attained 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 Oil leans at Q, be as much, and no more charged, or pressed upon by the weight of the incumbent Cylinder of Oil Q X, than 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 displaced, either by being depressed by the weight of the Cylinder of Oil X Q, or raised by the equal pressure of water upon the other parts of the Superficies G H.  
And that this Aequilibrium, betwixt the Oil and the Water, is the true cause of the Phaenomenon, may be confirmed by observing what happens, if the altitude of either of the two Liquors be altered in Relation to the other.  
And (First,) we have already taken notice, That if the Cylinder of Oil reach in the Pipe, much higher than that of the Surface of the water, the oil will descend: Of which the Reason is, Because the designable Surface G H, being more charged 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 oil.  
Secondly, This subsiding will continue but till the Surface of the Oil 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 pressed by the oil, as the other parts of the Surface G H are by the water that leans upon them.  
Thirdly, 'Tis a concluding Circumstance to our present purpose, That if the Oil and Water being in an Aequilibrium, you gently lift up the Pipe, as from Q to S, the depth of the water being lessened, the oil in the Pipe will grow praeponderant, and therefore will fall out in Drops or Globuls, which by the greater Specific Gravity of the water, will be buoyed up to the Top of the Liquor, and there float: And still as you lift up the Pipe higher and higher, towards the Surface L M, more and more of the Oil will run out. But if you stop the Pipe any where in its Ascent, as at S, the Effluxion of the oil will likewise be stopped. And at the imaginary Superficies▪ I K, as by Reason of the shallowness of the water from L to I, 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 oil, whilst the Pipe was lifted up from Q to S, the remaining Cylinder of oil incumbent on S, is not able to press that part of the Superficies I K more strongly than the other parts of the same Superficies, are pressed by the water Incumbent on them. And if the Pipe be lifted up till the lower Orifice be almost raised to V; that is, almost as high as the uppermost Surface of the water L M, so much of the oil 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 oil 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 sustain the oil, but make it ascend in the Pipe to a height equal to the distance E G; and so the Pipe will contain besides a longer Cylinder of oil A W, a shorter one of water A O. For the pipe being transferred 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 oil alone, be pressed as much as the other parts of the same Surface are by the Incumbent water. For the oil alone was but in Aequilibrium with the water, when it was no deeper than L G, or H M; so that the other parts of the Superficies E F, being more pressed upon by the water, than the part at O by the oil, the oil must give place, and be buoyed up by the water, (which, if it were not for the weight of the oil, would be impelled up into the pipe full as high as the Surface of the External water) till the pressure of the admitted water O A, and the Cylinder of oil A 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, 'Tis very agreeable to what has been delivered, touching the Aequilibrium of the oil and water in the pipe P Q, that the Surface X of the oil 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 oil 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 oil 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 Specific Gravities of these two Liquors, the inequalities betwixt the Surface X, and the Surface L M would be also greater, as may be tried by substituting for common water, oil of Tartar per deliquium, which is a saline Liquor much heavier than it. And that, in case the Pipe contain not a lighter Liquor than 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 shown, we may safely infer the Proposition, upon whose occasion all this has been delivered. For since the oil 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 oil can no longer be kept suspended, but by its own gravity will run out. And since, in a word, the deeper the water is, the greater weight and pressure is required in the Cylinder of oil, to be able to countervail the pressure of the water, and keep itself 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 I K do press that; and consequently, that the parts of the water that are under the uppermost Surface of it, are pressed by those of the same Fluid that are directly over them: As we saw also that the upper parts of the oil, whilst the pipe was in raising from Q to S, depressed 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 inferior parts derived their pessure only from their own particular Gravity, (which is no greater than 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 allowed 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 applied 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 oil in the Pipe, and of the External water, was in part to be ascribed to the slenderness of the Pipe, to be employed 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 assured by Experience, as we have elsewhere shown, 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 tried) 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 employ such in the following Experiments, because we found, that in those of a wide Boar, upon such little inequalities of pressure as are not easily to be avoided, the oil and water will pass by one another in the Cavity of the pipe, and so spoil the Experiment, which requires that the oil within the pipe be kept in an entire and distinct Body.  
Fourthly, Common oil and water, or any other two Liquors that will not mingle, may serve the turn in most of these Experiments; but we rather choose oil 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 one's clothes, or obstinately to adhere to the porous Bodies it chances to fall on, as Common, and other expressed oils. And for their sakes to whom the odour is offensive, we presently correct it, by mingling with it a convenient quantity of oil of Rhodium, or some other Chemical oil that is odoriferous.  
Fifthly, Oil of Turpentine, though it be not reckoned 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 obtain a deep green Liquor, which may be made use of instead of the Limpid oil, 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 Ink itself, I say, a strong Decoction, because unless the Liquor be so deeply tinged, as to appear Opacous in the Glass, when it comes into the slender pipe, its Colour will be so diluted, as to be scarce discernible.  
Seventhly, In the shape of the Glass Vessel, we need not be Curious; though that of a wide Mouthed Jar, expressed 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 determined by the Experiments, about which one means to employ them. To make out the first Paradox already proved, 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 discouraged by not being able at the first or second time, to suck up oil of Turpentine to the due height, and stop it with one's finger from relapsing; but one must try again, and again; especially since many Trials of this kind may be made in a few Minutes: and for Beginners 'tis a safe and good, though not the shortest way, to suck up rather more Liquor than one judges will be needful; because having filled the Pipe to that height, you may by letting in the Air 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 Monsieur Paschal's way, require a great deal of Trouble and Apparatus to be performed.  
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, employ Oleum Tartari per deliquium, and tinge it with Brazill or Chochineele; from either of which, but especially from the latter, it will obtain an exceeding deep Redness: and where one would avoid strong scents and oiliness, he may, if he will be at the Charge, employ oil of Tartar per deliquium, instead of fair water, and highly Rectified Spirit of Wine, instead of oil 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 Chemical Liquors are not to be had in plenty, one may employ (as we have done) a very strong Solution made of Sea-salt, and filtered through Cap-paper: this Brine being near about as Limpid as common water, and far heavier than it. And for a Curiosity, we have added to the two lately mentioned Liquors (oil of Tartar, and Spirit of Wine) some oil 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 even of divers hodiern Mathematicians, and Writers of hydrostatics; 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 destroyed 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 hindered by another Body, which being heavier than 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 environed 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 sense 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 endeavour downward is so surmounted that it is forcibly carried up. Thus when a piece of some light wood being held under water, is let go and suffered to emerge, though it he buoyed up by the water, whose specific Gravity is greater, yet even whilst it alcends it remains a heavy Body; so that the aggregate of the water & the ascending wood weighs more than the water alone would do; 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 immersed 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 Balance with a heavy stone tied 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 does not, either during its ascent or after, lose 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 weighed apart.  
Likewise, if you put into one Scale a wide mouthed Glass full of water, and a good quantity of powdered 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 bottom, 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 proposed to ourselves in this Discourse.  
Take a slender Glass pipe, and having sucked 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 oil of Turpenrine, till the Surface of the oil in the Vessel be somewhat 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 hindered by the pressure of the oil of Turpentine. As will be obvious to them that have attentively considered the Explication of the former Paradox; there being but this difference between this Experiment and that there Explained, that here the water is in the Pipe, and the oil in the Vessel, whereas there the oil was in the Pipe, and the water in the Vessel. And if you either pour more oil into the Glass, or thrust the Pipe deeper into the oil, 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 raised 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 oil in the pipe was always higher than that of the water without it, because the oil being the lighter Liquor, a greater height of it was required to make an Aequilibrium; so in our present Experiment, the Surface of the Liquor in the Pipe will always be lower than that of the oil without it.  
For in the imaginary plain E F, 
See the second Figure.  the Cylinder of water I G, contained in the Pipe I H, will, by reason of its greater gravity, press as much upon the part I, as the distilled oil (K E, I L,) being a lighter Liquor, can do upon the other parts of the same supposed plain E F, though the oil reached to a greater height above it.  
This second Paradox, we have hitherto been discoursing of, may be also proved by what we formerly delivered, 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 received, I will subjoin in this place a couple of such Experiments, as will not, I hope, be unacceptable; that I devised, 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 sinking 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 performed by an Instrument, which though it makes not so fine a show, may be more easily provided, and will as well as that other (though you were pleased to command that from me) serve to make out the same Truth; which I shall apply myself 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 proved by them, 
In certain, Notes upon some of the Physics-mechanical Experiments, touching the Air.  I must briefly repeat what I have elsewhere delivered already (on another occasion) touching the cause of the sinking of such Bubbles. Namely that the Bubble X. consisting▪ of Glass, 
Fig. 3.  which is heavier in specie then Water; and Air, which is lighter in specie then Water; and, if you please, also of Water itself, which is of the same specific Gravity with Water; as long as this whole aggregate of several bodies is lighter than an equal bulk of Water, it will float; but in case it grows heavier than so much water, it must, according to the known Laws of the hydrostatics, necessarily sink, (being not otherwise supported.) Now when there is any competent pressure (whether produced by weight or otherwise,) upon the water, in which this Bubble is for the most part immersed, because the glass is a firm Body & the water, though a Liquor, either suffers no compression, or but an inconsiderable one; the Air included in the Bubble, being a springy and very compressible Body, will be compelled to shrink, and thereby possessing less Room, than it did before, the contiguous water will succeed in its place; which being a body above a thousand times heavier than air, the Bubble will thereby become heavier than an equal Bulk of water, and consequently will sink: but if that force or pressure be removed, the Imprisoned Air will by its own Spring free itself from the intruding water; and the Aggregate of bodies, that makes up the Bubble, being thereby grown lighter than 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 Jesuits 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 Roman, the other of the Florentine Experiments. But there are also particulars wherein I (who have never a recourse to a fuoa Vacui,) descent 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 deduced from those Experiments.  
These things being premised, I proceed to the confirmation of the second Paradox, by the following Experiment.  
Take a long glass pipe, sealed or otherwise exactly stopped at one end and open at the other (whose Orifice if it be no wider, then that it may be conveniently stopped with man's. 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 unfilled, for the use to be by and by mentioned. Then having poised 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 sink it, put this Bubble thus poised 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 oil 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 oil, till it have attained a sufficient height above the water, (which, 'twill be easy to overthrow, 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 oil remains at the height above the water.  
The Reason of this Phanomenon, according to our Doctrine, is this, That the oil of Turpentine, though a lighter Liquor than 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 Bubble, which was before but very little less heavy than an equal Bulk of water, being by this accession made a little more heavy must necessarily sink; and the cause of its submersion, namely the pressure of the oil, 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 oil, or a competent part of it, (in case it were longer than was necessary,) the Bubble will again emerge to the Top of the water (for, as for the oil, that is too light a Liquor to buoy it up;) which happens only because the pressure of the oil upon the water being taken of the Air, by virtue of its own spring, is able to recover its former Expansion, and reduce the bubble to be as light as 'twas before.  
And now we may proceed to that other Experiment, by which we lately promised to confirm the first Paradox. And in some regard this following Experiment has been preferred, as more strange, to that I have been reciting. For it seemed much less improbable, that of two Heterogeneous Liquors, the inferior should be pressed upon by the incumbent, which, though lighter, kept in an entire body above it; then that in water, which is a Homogeneous Liquor; and whose parts mingle most freely and tightly 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 join.  
Provide a long Tube and a poised Bubble, as in the former Experiment, then having poured water into the Tube, till it reach above 5 or 6 Inches (for a determinate height is no way necessary) above the Bottom, cast in the Bubble, which will not only swim, but if you thrust it down into the water it will of itself 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 filled by the rod or wire) till it have attained a competent height, (which, in my last Trials, was about a Foot, or half a Yard above the bubble:) and you shall see, that the bubble, which before endeavoured to emerge, will by the additional weight of the incumbent water, be depressed 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 sink, so that weight continuing on it, the bubble will continue at the bottom.  
But yet it is not without cause, that we employ a wire, or some such thing, in this Experiment, though we affirm it to be only the weight of the Incumbent water, that makes the Bubble sink. For if you should pour water into the Tube, to the height lately mentioned, or even 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 itself, 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 'tis the weight of the Superior water that sinks 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 precipitated, 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 satisfy 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 wondered at, why, since we lately mentioned our having made some Trials with oil 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 expressed oils) unmingleable in such Trials with oil of Turpentine. But to this I answer, That even in such slender pipes, as those made use of about the first Experiment, I found that oil of Tartar was ponderous enough to flow down, though slowly, into the oil of Turpentine at one side of the immersed Orifice, whilst the oil passed 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 Air, but will be stopped 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 Trials 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 oil of Turpentine and oil 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 persuaded. 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 proposed as such, and may oftentimes fail in practice; because there may intervene divers other things capable of making there miscarry, which are overlooked 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 have considered, that in such Tubes, as the Torricelliah Experiment is wont to be made in the largeness of them would make them unfit for this Trial.  
And I have known Ingenious men, that are very well exercised in making such Experiments, complain, that they could never make this of Monsieur Paschall's to succeed. In which attempts, that the size of the Tubes much contributed to the unsuccesfulness of the Trials, 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 add 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 pressed upward by the water that touches it beneath,  
THis may be proved 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, immersed in water, to be there the imaginary Superficies being beneath the true Superficies, every part of that imaginary Superficies must be pressed upwards, by virtue 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 immersed Body chances to lean, must for the same Reason have an endeavour upwards. And if that Endeavour be stronger than that wherewith the weight of the Body tends downwards, then (supposing there be no Accidental Impediment) the Body will be buoyed or lifted up. And though the Body be heavier than so much water, and consequently will subside, yet that Endeavour upwards of the water, that touches its lower part, is only rendered 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. 
Fig. 1. 2.  For in case the slender pipe, wherein the water is kept suspended, be thrust deeper into the oil or in case these be more oil poured into the Vessel, the water will be impelled up higher into the pipe; which it would not be, if the oil, though bulk for bulk a lighter Body, did not press against the lower Surface of the water, (where, alone, the two Liquors are contiguous,) more forcibly than the water by its gravity tends downward. And even when the Liquors rest in an Aequilibrium, the oil continually presses upwards, against the lower Surface of the water; since in that continual endeavour upwards 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 oil, as in the second Experiment, on oil in water, as in the first: it appears, that the proposition is as well applicable to those cases, where the sustained Body is specifically heavier, as to those where 'tis specifically lighter than 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 mentioned the Resistance made by the water to Bodies that sink in it, Let us suppose, in the annexed Figure, That the pipe E F contains an oil specifically heavier than water, 
Fig. 4.  (as are the oils of Guaisteum, of Cinnamon, or Cloves, and some others,) and then, That the oil in the pipe, and the water without, being at rest in an Aequilibrium, the pipe be slowly raised towards the Top of the Vessel. 'Tis evident, from our former Doctrine, and from Experience too, that there will run out drops of oil, which will fall from the bottom of the pipe, to that of the Vessel; but far more slowly than if they fell out of the same pipe in the Air.  
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. 'Tis evident, That if the drop of oil were not there, its place would be supplied by an equal bulk of water; which being of the same specific Gravity with the rest of the water in the Vessel, the Surface H I would be laden every where alike; and consequently to part of it would be displaced▪ But now, the drop of oil being heavier than so much water, that part of the imaginary superficies, on which that drop leans, has more weight upon it, than any other equal part of the same Superficies; and consequently, will give place to the descending drop. And since the case of every other supposed Surface, at which the drop can be conceived to arrive in its descent, will be the same with that of the Superficies H I; 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 I would be neither more nor less charged than the other parts of the same Supeficies; and the part leaned on would be neither depressed nor raised, but the drop G would continue in the same place. And so we may prove, (what is affirmed by Archimedes, and other Hydrostatical Writers) That a Body acquiponderant in specie to water, will rest in any assignable place of the water where 'tis put.  
And (to proceed further) since, if the drop G were of a matter but acquiponderant to water it would not sink lower at all, no more than 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 than 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 loses in the water just as much of the weight it would have in the air, as so much water, weighed likewise in the same air, would amount to.  
Which is a Physical Account of that grand Theorem of the hydrostatics, 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, 'twill not be amiss to add, That it may easily be confirmed by Experiment.  
For if you take (for instance) a piece of Lead, and hang it by a Horse hair (that being supposed very near acquiponderant to water) from one of the Scales of an exact Balance; and, when you have put a just Connterpoize in the other Scale, suffer the Lead to sink in a ressel of water, till it be perfectly covered with it, but hangs freely in it, the counterpoise will very much preponderance, And, part of the Counterpoise being taken out till the Ballatice be again reduced 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 air) find what part of its weight it loses 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 hair at one scale, you may be sure that by putting 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 far from an Aequilibrium in the Air, they will be reduced to it when the Led it covered with water.  
The pressure of water against the lower part of the Body immersed in it may be confirmed by adding; That we may thence deduce the cause of the emergency of wood and other Bodies lighter than 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 rendered by any. If we suppose then that the pipe be almost filled, not with a sinking but a swimming oil, as oil of Turpentine, if, as in the first Experiment, the lower orifice be thrust under water, (to a far less depth then that of the oil in the pipe) and the upper be slowly unstopped, the oil will (as we formerly declared) get out in drops at the bottom of the pipe. But to determine why these drops, being quite covered and surrounded with water, and pressed by it as well downward as upwards, should rather emerge then descend, I shall not content myself to say, that water in specie heavier than this kind of oil; For, besides that in some cases (ere long to be mentioned) I have made the water to depress even this kind off oil, and besides that 'tis 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 oil, though there be perchance much more water, for it to break its way through, 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 than 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 oil of Turpentine, and to touch the two imaginary and parallel plains H I, K L; 'tis 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 oil G, being not so heavy as so much water, the oil being exposed to a greater pressure from beneath, than its own gravity (and that of the water incumbent on it) will enable it to resist, must necessarily give way and be impelled 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 impelled 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 immersed under water, it is pressed 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 immersed body must be pressed upon by a Pillar longer than the upper part by the thickness of the immersed Body; and consequently must be pressed more upwards then downwards. And by how much the greater disparity of specific 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 Problem, proposed 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 detained under water at the same depth, be let go at the same time and permitted to emerge, the greater will rise faster than 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 plain, 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 bodies being lighter in specie then water, both of them will be impelled 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 raised, 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 bodies consists chiefly, (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 oils of Annisseeds, Cloves, and divers▪ Aromatic vegetables, in Lembecks by the intervention of water; for oftentimes, when the fire has not been well regulated, there will come over, besides the floating Oil, a whitish water, which will not in a long time become clear. And as we have elsewhere taught, That whiteness to proceed from the numerous reflections from the oily substance of the Concrete ' by the heat of the fire broken into innumerable little Globuls, and dispersed 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 devised a Menstruum, wherewith I could mingle oil in drops so exceedingly minute, that, even 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 impelled up by the water: at the Top of which, the Chemist; after a due time, is wont to find new oil 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 inquire.  
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 deduced, when the emergent drop, or any other Body, floats upon the Top of the water, it will sink just so far, (& no farther) till the immersed part of the floating Body be equal in Bulk to as much water as is equal in weight to the whole Body. 
Fig. 5.  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 than Air, will sink into the water, till it come to an imaginary superficies, X W, where, having the position newly described, it will necessarily acquiesce. For all the other equal parts of the Superficies, X, W, Q, being leaned 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 than that of as much water as is equal to the immersed part, it must necessarily sink lower, because the subjacent part of the Surface (at V,) will be more charged than any of the Rest. And, on the other side, if the Cube were lighter than as much water as that whose place the immersed 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 impelled upward, till 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 immersed part of it takes up. The lightness of that immersed part, in respect of so much water, being recompensed by the weight of the unimmersed part, which is extant above the Superficies of the water. And we see, that when a piece of wood falls into water, though, by the impetus it acquires in falling, it passes through divers imaginary plains that lie beneath its due station; yet the greater pressure, to which each of those plains is exposed in all its other parts, then in that which is contiguous to the Bottom of the wood, does 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 assigns it.  

SCHOLIUM.  
THis Ingenious Proposition (about floating bodies) is taught and proved 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 entire and homogeneous Bodies as men exemplify it in, (such as a piece of wood, or a Lump of wax) but in all Bodies, though of a concave figure, and made up of many bodies of never so differing natures; (and perhaps some of them joined together only by their superincumbency upon one another) and partly because that a Truth, which is one of the main and usefullest of the hydrostatics, 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 versed 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 employed several Vessels, some of wood, some of Laton, and some of other materials, to compass what I desired; 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 placed in it another deeper glass, shaped like a Goblet or Tumbler, that it might be the fitter for swimming; and having furnished it first with Ballast, and then, for merriment sake, with a wooden Deck, by which a tall Mass, with a Sail fustened to it, was kept upright; we fraughted with wood, and by degrees poured Sand into it, till we had made it s●●●k just to the Tops of certain conspicuous marks, that we had fastened on the outside of the Glass to opposite parts thereof. Then observing how high the water reached in the larger Glass, (which by reason of the Vessels Transparency was easy to be seen) we carefully placed two or three marks in the same level with the Horizontal Surface of the water; and taking out the floating Vessel, as it was, with all that belonged to it, and wiping the outside dry, we put it into a good pair of scales, and having found what it amounted to, we weighed in a competently large Viol (first counterpoised apart) so much water, (to a grain, 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, Quicksilver, etc.) it appears, that the floating Vessel itself, 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, supposed 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 raised up the water in the larger Vessel to the greatest height it attained, was the same with the weight of the water, which being poured into the larger vessel (when the other was taken out) raised the water therein to the same height. We may also obtain 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 Bowl or Pail, 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 required) 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 pour 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 poured in, falls short in weight of the water that was in it at first, and afterwards removed. 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 endeavoured to confirm, or illustrate it, may (Mutatis mutandis) be applied to a Ship with all her Ballast, Lading, Guns, and Company; it holding generally true, That (to express the sense of the Proposition more briefly) the weight of a floating Body, is equal to as much water, as its immersed 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, 
See PARADOX the sixth.  That a whole Ship, and all that belongs to it, and leans upon it, presses no more nor less upon the Bottom 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 IU.  
That in the Ascension of water in Pumps, etc. there needs nothing to raise the Water, but a competent weight of an External Fluid.  
THis Proposition may be easily enough deduced from the already mentioned Experiments. But yet, for further illustration and proof, we will add that which follows.  
Take a slender Glass-pipe, (such as was used about the first Experiment) and suck into it about the height of an Inch of deeply tincted water; and, nimbly stopping the upper Orifice, immerse the lower part of the pipe into a Glass half filled with such tincted water, 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 oil of Turpentine till it swim 3 or 4 Inches, or as high as you please above the water; loosen gently your finger from the upper Orifice of the pipe, to give the enclosed Air a little intercourse with the External, and you shall see the tincted water in the pipe, to be impelled up, not only higher than the Surface of the External water, but almost as high as that of the External oil, through which (it being transparent and colourless) the Red Liquor may be easily discerned.  
Now in this case it caved be pretended, That the ascent of the water in the pipe proceeds from Nature's abhorrency of a Vacuum; since the pipe being full of air, and its Orifice unstopped, though the water should not ascend, no danger of a Vacuum would ensue; the air and the water 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 immersed Orifice of the pipe, there is a pressure partly of water, and partly of the oil 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 contained in the pipe leans, there is but the pressure of one inch of water, so that the parts near the immersed Orifice must necessarily be thrust out of place by the other parts of water that are more pressed; till so much Liquor be impelled up into the pipe as makes the pressure on that part of the Imaginary Superficies, as great as that of the oil and water on any other equal part of it: and then, by Virtue of the Aequilibrium, (often mentioned) the water will rise no further; and, by virtue of the same Aequilibrium, it will rest a little beneath, the Surface of the External oil, because this last named Liquor is less heavy, bulk for bulk, than water.  
And by this we may be assisted to give a reason of the Ascension of water in ordinary sucking Pumps. For as the oil of Turpentine, though a lighter Liquor than 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 itself: so the Air, which, though a far lighter Liquor than oil 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 than the External water itself reaches in the Well, if it were not hindered.  
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 air, or that pressure itself. 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 oil, that may oppose its ascent.  
And lastly, as the water in our pipe was impelled up so high, and no higher, that the Cylinder of water in the pipe was just able to balance the pressure of the water and oil 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 raised no higher; because at that height the pressure of the water in the Pump, upon that part 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▪ sustain 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 raised by suction, not upon the Account of the weight of the air, but of its spring, I have elsewhere shown; and having likewise in other places; endeavoured to explicate more particularly the ascension of water in Pumps; what has been said already may suffice to be said in this place, where 'tis sufficient for me to have shown, That whither or no the Ascension of water may have other causes, yet in the cases proposed, it needs no more than the competent weight of an External Fluid, as is the Air; whose 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 mentioned) 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 complained, that, contrary to the Experiment proposed by Monsieur Paschall, they were not at all able to keep Mercury suspended in Tubes, however very slender, though the lower end were deeply immersed 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 unsuccessfully tried, and seemed to me unlikely to succeed in Tubes more slender than his appeared; 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 filled with so ponderous a Liquor, though the Tube were very much shorter than that proposed by Monsieur Paschall.  
This advertisement I premise to intimate, that, notwithstanding the hopelessness of the Experiment, as it had been proposed and tried, I might have reason not to think it impossible to perform, by another way, the main thing desired; 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 than 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 sucked in at the lower end of it somewhat less than half an inch of Quicksilver, and nimbly stopped the upper Orifice with my finger; I thrust the Quicksilver into, a deep glass of oil 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 oil. For by this means, when I unstopped the pipe, the Quicksilver needed not (as otherwise it would) begin to fall, as having a longer Cylinder than was requisite to make an Aequilibrium with the other fluid. For by our Expedient the pressure of the oil 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 oil. 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 raised it towards the Superficies of the oil, the Mercury would drop out for want of its wont Counterpoise; so, if I thrust the pipe deeper into the oil, the increased pressure of the oil would proportionably impel up the Mercury towards the higher parts of the pipe, which being again a little, and but a little, raised, 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 there common Spirit of Wine itself.  
But, besides that the Experiment, if the maker of it be not very careful; may easily enough miscarry, the divertisement it gives seldom proves lasting; the oil of Turpentine after a while insinuating itself 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 tried it in oil of Turpentine; because that is the Liquor I make use of all along these Paradoxes; and because also I would show that a lighter fluid than water, (and therefore why not air, if its height be greatly enough increased:) 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 filled tall glasses) a fitter Liquor than oil 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 unmentioned in this.  
And since Experience shows 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 easy to conclude, That the weight of the External air, 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 persuasion of theirs seems to be the chief thing, that has hindered men from acknowledging, that the Quicksilver in the Torricellian Experiment may be kept suspended by the Counterpoise of the external air. And a famous writer, that has lately treated, as well of the hydrostatics, 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 sense. That if it were the pressure of the External Aire, that kept the Quicksilver suspended in the newly mentioned experiment, the height would not (as Experience shows it is) be the same in all Cylindrical pipes, though of very differing B●●es. For, supposing the height of the Mercurial Cylinder, in a Tube of half an Inch Diameter, to be 29 Inches; 'tis 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 air, being but one and the same, if it be a just Counterpoise 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 answered it, both by reason and Experience, as far forth as it concerns the Torricellian Experiment; Yet, to show 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 error) by showing both that the Assertion is true, and why it must be so.  
Provide then a more then ordinarily wide mouthed Glass, 
Fig. 6.  clear, and of a Convenient depth; into which having put a convenient quantity of water, deeply tinged 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 embraced by these several holes; And, as near as you can, make them parallel to one another, and perpendicular to the superficies of the water, into which they are to be immersed. But we must not forget, that, besides these holes, there is an aperture to be made in the same Cork (it matters not much of what figure or whereabouts) to receive the slender end of a glass Funnel; by which oil may be conveyed into the vessel, when it is stopped with the Cork. And in the slender part of this Funnel we use to put some Cotton-week, to break the violence of the oil that is to be poured in, which might else disorder the Experiment. All this being thus provided, and the Cork (furnished with its pipes) being fitted to the Orifice of the Vessel; if at the Funnel you pour in oil of Turpentine, and place the Glass betwixt your eye and the Light; you may, through that transparent Liquor; perceive the Tincted water, to be impelled up into all the pipes, and to rise uniformly in them. And, when this tincted Liquor has attained to the height of two or three, or more Inches, above the lowermost Surface of the External oil; if you remove the Funnel, (which yet you need not do, unless there be yet oil 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 'tis evident) is sustained, at that height above the level of the other water, by the pressure or counterprize of the external oil; which than 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 oil, the shorter leg of a slender glass Syphon, at whose longer Leg you procure by Suction the oil 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 uniformly, as well in the lesser as in the greater pipes.  
The Reason of this is not difficult to be rendered, by the Doctrine already delivered. For suppose, E F to be the Surface of the water, both within and without the pipes, before any oil was poured on it: if we then suppose the oil 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 itself on the outside of them above, it must necessarily, by its gravity, press down the Superficies of the external water, and impel up that liquor into the cavities of the pipes. And if we suppose the pouring on of the oil to be continued till the uppermost surface of the oil be raised to G H, and that of the external water depressed 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 Boars. 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, than any other part, equal to that Circle of the same Imaginary Superficies, is by the water or oil incumbent on it; (and consequently, no more than the part comprehended within the circle of the final pipe N, is by the water contained in that small pipe;) the external oil having as much a greater height upon the Superfices I K, than the water within the pipe, as is requisite to make the two Liquors Counterbalance each other, notwithstanding the difference of their specific Gravities. And though the pipe L were twice as big, it would Charge the subjacent plain I K no more than the pressure of the oil on the other parts of the same imaginary Surface is able to resist. And yet this pressure of the External oil ought not to be able to raise the water in the slender pipe N, higher than 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 than oil, it must press upon that part of the Surface I K, it leans on, with greater force than the external oil upon the other parts of the same plain I K; and therefore with greater force than the weight of the External oil could resist. And consequently, the water in the slender pipe must subside, till its Surface be inferior to that of the External oil; since, till then, the difference of their specific gravities cannot permit them to rest in an Aequilibrium. To be short; It is all one, to the resistance of the external oil, 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 oil, than 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, than the pressure of the external oil will be on all the other parts of the same Superficies; and consequently, neither the one, nor the other of those Liquors will subside, but they will both rest in an Aequilibrium,  
But here it will not he amiss to note; First, that it is not necessary that the Glass Cylinders L, M, N, should be all of the same length; since, the lower Orifice being open, the water will rise to the same height within them, whether the parts immersed 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 employed 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 Counterpoise of either the water or the oil, 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 placed 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 sustained by the Body (for we now consider not the Lateral nor the recoiling pressure-to which the Body may be exposed if quite environed with water,) is no more than that of a Column 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 contained 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 inclined towards the Horizon, or though it be irregularly shaped, and much broader in some parts, than the said Orifice.  
STevinus, in the tenth Proposition of his Hydrostatical Elements, having proposed in more general terms the former part of our Paradox; annexes to see 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 adjoining 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 neighbouring 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 sustain 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 sustain just as much weight as the Column 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 fail of Mathematical exactness;) and by it may be confirmed the first part of our proposed Paradox. And some things annexed by Stevinus to this Demonstration, may be also applied to countenance the second. But because this is one of the noblest and usefullest Subjects of the hydrostatics, 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 Boar, turned up at one end like the annexed Syphon. 
Fig. 8.  Into this Syphon suck oil of Turpentine till the Liquor have filled the shorter leg, and be raised 2 or 3 Inches in the longer. Then nimbly stopping the upper Orifice with your finger, thrust the lower part of the Syphon so far into a deep Glass full of water, That the Surface of the oil in the longer leg of the pipe, may be but a little higher than that of the External water; and, upon the removal of your finger, you will find the Surface of the oil to vary but little, or not at all, its former Station. And as, if you then thrust the pipe a little deeper, you will so the oil in the shorter leg to begin to be depressed; so, if afterwards you gently raise the pipe toward the top of the water, you shall see the oil 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 oil, in the longer leg of the pipe, suspended no higher, than 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 oil in the longer;) & since, when once, by the raising of the pipe, the height of the incumbent water was lessened, the oil did more than Counterbalance 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 than the immersed 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 placed 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 itself, where there is nothing on any side, but the contiguous water, to bond 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. employed 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 oil 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, even in this case also, the Surface of the oil in the longer leg, will be but a little higher than that of the water in the funnel.  
For further Confirmation of this; we caused to be made a Syphon, so shaped, that one of the legs (which were parallel, and of the same Boar,) had in the midst of it a Sphere 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 oil of Turpentine, and into the other, as much water as filled 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 oil in the uniform leg, at a greater height then if the leg that contained 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, filled with oil, and the uniform leg with water; notwithstanding the far greater quantity of oil, that was necessary to fill that leg, whereof the hollow sphere was but a part; the water in the uniform leg would not be kept up▪ so much as to the same height with the oil in the misshapen leg.  
But to make this matter yet the more clear, we caused a Syphon to be made of the Figure expressed in the adjoining Scheme; 
Figur. 9  into which having poured a convenient quantity of Mercury, till it reached 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 impelled it up in the shorter leg till it had half, or more than half, filled 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 observed, that, notwithstanding the great weight of (that Body, which is of all Bodies, save one, the most Ponderous) Quicksilver, which was contained in the lower part of the same leg of the Syphon, the surface of the Quicksilver H G, was impelled up as high by the water in the Leg A B, as the disparity of the specific weights of those two Liquors (whereof one is about 14 times as heavy as the other) did require: So that it appeared not, that, for all the great weight of Quicksilver, contained in the Globulous Cavity E, there pressed any more upon the slender and subjacent part E C of that leg, then as much as was placed 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, appeared not any more pressed 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 than itself. 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, 
Fig. 10.  with a round Ball and two opposite Stems; the other was an irregular pipe, blown with an Elbow, wherewith it made an Angle; and the third was as irregularly shaped, as I could get it blown; being in some places much broader, and in some much narrower than the lower Orifice of it. And these two last named pipes had their upper ends so inserted into holes, made fit for them in a broad piece of Cork; that, when they were immersed, 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 mouthed glass of a good depth, and half filled with water, was thrust as a stopple into the mouth of the said glass, so that the water ascended 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 oil of Turpentine being poured into the same Vessel, through a funnel, the water was by the incumbent oil impelled 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 guessed 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, contained in each of them, pressed upon its lower Orifice no more (I do not add, nor no less) than it would have done if it had been a Cylinder, having the Orifice for its Basis, and the perpendicular depth of the water and oil above, for its height. For in case each of the pipes had contained 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 impelled up beyond it, if its weight did not as strongly endeavour to depress the immediately subjacent water, as the pressure of the External fluids endeavoured 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 inclined, contained much more water than if they were erected: yet by the same way of reasoning we may gather, That the imaginary plain, passing by the immersed Orifice of either of these inclining pipes, sustained no more of pressure, than 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 inclined any way towards the Horizon, the weight of the contained Liquor is not all supported by the Liquor or the Body contiguous to the lower Orifice, but partly by the sides of the pipe itself. And therefore if, when in a slender pipe you have brought a parcel of oil of Turpentine to be in an Equilibrium with the External water, as in the Experiment belonging to the first Paradox; If, I say, when this is done, you incline the pipe towards the sides of the Glass, You may indeed observe the Surface of the oil in the pipe to be, as before, a little higher than 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 oil 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 lessened; and there by the external water, whose pressure is not diminished too, is able to impel up the oil, and intrude for a little way into the pipe. But if you re-erect the pipe, the pressure of the oil 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 tried as follows: We caused 3 pipes to be blown (shaped as the adjoining Figures; 
Fig. 11. ) one having in it divers acute Angles; the other being of a winding form, like a screw 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 straight & erected parts, filled with oil of Turpentine; being thrust to a convenient depth under water and unstopped there, (after the manner already often declared) we found, that, according to our Paradox, the surface of the oil 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 straight, (as we tried by placing by the crookedest of them a straight pipe with oil in it) though the quantity of the oil, in one of these pipes, were perhaps three times as much as would have sufficed, if the pipe had been straight: So that this surplusage of oil did not press upon the subjacent water, (for if it had done so, the oil 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 oil in the pipe was not above half an inch higher than that of the water without it, I estimated that the crooked pillar of oil, contained 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, contained 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 mentioned out of him, subjoins divers consectaries of which the truth hath been thought more questionable, then that of the Theorem itself. 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 filled with water, the circular Basis of it will sustain 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, proposed 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' 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 than 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 aught I can find) has been tried of all the five, is rejected as incompetent, by those that profess to have purposely made trial 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 Trials himself; rather then set down the events, he supposed they must needs have; as presuming his conjectures rightly deduced 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 induced 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 expressed in the Scheme, 
See Fig. 12.  and furnished it with a loose Bottom C D, made of a flat piece of wood covered with a soft Bladder and greased on the lower side near 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 lie 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 fastened 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 tied, and to hinder its own passing. The Vessel being filled with water we took the forementioned string, one of whose ends was fastened 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 bottom 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, tried 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, than could have been attributed to the weight of so little water, as the Instrument pipe and all contained, 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 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) will hold; the Inquiry he has started, may be so pursued, as to occasion some improvement of this part of hydrostatics: 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 cleared, and because of the difficulty that will be found in practice by them that shall go about to make Stevinus' Experiments, or others of that sort with all requisite Accurateness: As indeed, it is far easier to propose Experiments, which would in likelihood prove what we intent, in case they could be made, then to propose practicable Expedients how they may be made.    

PARADOX VII.  
That a Body immersed in a Fluid, sustains a lateral pressure from the Fluid; and that increased, as the depth of the immersed 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 ways, and particularly by one that is plain and easy, being but that which follows.  
Take then a slender Glass pipe (like that employed about the first Experiment;) 
Fig. 13.  and cause it to be bend 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 oil 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 depressed under that Surface, That I K, the Superficies of the oil in the longer leg, be but a little higher than A B, that of the external water. Then, removing your finger, you may observe, That the oil 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 oil contiguous to G, the Orifice of the shorter leg of the pipe, since it is only that pressure that hinders the efflux of the oil at that Orifice, notwithstanding the pressure of the perpendicular Cylinder of oil that would drive it out.  
And that this pressure of the perpendicular Cylinder doth really urge the oil 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 oil in the Horizontal leg will be driven out in drops, by the pressure of the other oil 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 gathered from hence, That the Surface of the oil in the longer leg will be a little higher than that of the external water, as (by reason of the often mentioned comparative levity of the oil) 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 annexed figure the Cylinder, G H) were filled 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 oil, 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 oil will swim; the whole oil alone being unable to counterbalance 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 itself, and that increased 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 do so, it must surmount the weight or resistance of the whole cylinder of oil, that must be hereby violently raised in the said perpendicular leg.  
But if you gently raise the Syphon again, the lateral pressure of the water against the immersed Orifice being diminished, (according as the distance of that Orifice G from the Horizontal Surface, A B, comes to be lessened,) the prevalent oil 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 immersed Orifice, and thence emerge to the Top of the water.  
Besides, when the oil in the Syphon does just counterbalance 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'll find the oil in the longer Leg to continue (as to sense) at the same height: Whence we may learn (what I have not yet found mentioned by any Writer,) That, even in the midst of the water, we may suppose a pillar of water, of a Basis equal to the side of an immersed 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 increased proportionably to the height to which the imaginary pillar reaches above them. Which observation, being duly noted and applied, 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 immersed 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 immersed 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 delivered, That you shall still see the surface of the oil I K, in the longer pipe, to be a little, and but a little superior 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 even in this case also be maintained.  

SCHOLIUM.  
Remembering on this Occasion an Experiment, which though it do not show 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 subjoin it, as I set it down not long after I devised it.  
In the first place then, there was made a glass Bubble with a slender neck; and (in a word) of the figure expressed in the annexed Scheme; 
Fig. 14.  This Bubble I caused to be so poised, That, though it would float upon the water, yet the addition of a weight small enough would suffice to make it sink.  
This done, I provided a very large wide mouthed Glass, and caused 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 burned, 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 reached 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 closed with a stopple and Cement. Then the glass vessel being filled with water, and the poised 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 fastened into the Cork▪ (as was also the shorter pipe) not only by its own fitness to the hole, it passed through, but by a sufficient Quantity of the same Cement, carefully applied to stop all crevesses.  
The Instrument thus prepared, (and inclined 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 stopped, 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 poured in was able to reach but to a small height in the Cylinder, as for instance, to the Superficies I; the Bubble X would yet continue floating. But if I continued pouring till the water in the pipe had attained to a considerable height above the Surface of that in the Vessel, as if it reached to K; then the Bubble X would presently sink to the bottom 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 pressed 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 I, 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 gathered from the Reason formerly given (in the Proof of the second Paradox) of the sinking of poised Bubbles) the included air in our Bubble was notably compressed; 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 air in the Bubble. And since the said Bubble did not swim 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; 'tis 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 sustain a pressure, increased by the increase of that parts depth under water, and according to the largeness 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 ay 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 itself, though it be above the Surface of the water in the Vessel; yet because the water in the pipe is higher than 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 stopped in, it may be lifted up by the pressure of the water in the pipe, if that be filled to a good height. And if the Cement be not good and close, the water will (not without noise) make itself a passage through it. And if the stopple G, of the shorter pipe G H, (which is placed 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 pressed upwards as strongly, as it would be pressed downwards by the weight of a Cylinder of water of the breadth of the pipe, and of a not inconsiderable height, (for 'tis not easy to determine precisely, what height:) so that (to be short) in the fluid Body, we made our trial with, the pressure of the Superior parts was communicated, not only to those that were placed directly under them, but even 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 superior parts of the water, that made our floating bubble sink, 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 poured off as much of the water in the pipe, E F, as sufficed 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 itself, and make the bubble emerge. And to show, That the very oblique pressure which the bubble sustained from the water in the pipe, was not overmuch differing from that which it would have sustained from an External force, or from the weight of water placed directly over it; I caused two such bubbles to be poised, and having put each of them into a long Cylindrical Glass, open above, and filled 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; 
See the Proof of the 11. Paradox.  so that we were forced 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 air 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 remained in it a pretty quantity of air, (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 I to K, would make the bubble sink, little otherwise, for aught I took notice of, then if the Vessel had been perfectly filled with water; the air (above L M,) that was both imprisoned and compressed, communicating the pressure it received to the water contiguous to it:    

PARADOX VIII.  
That water may be made as well to depress a Body lighter than itself, as to buoy it up.  
HOw strange soever this may seem, to those that are prepossessed with the vulgar Notions about gravity and levity: It need not be marvail'd at, by them that have considered what has been already delivered. 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 pressed by others, whether lighter or heavier than itself, it must necessarily be thrust out of that place, where it is more pressed, to that where 'tis less pressed; If that a parcel of oil 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 inferior to that of the water) to hinder its descent, (supposing, withal, that the oil and water cannot pass by one another; for which cause, we make use of a slender pipe;) the oil must necessarily give way downwards, and consequently be depressed and not buoyed up. This is easily exemplified by the following Experiment.  
Take a slender Glass Syphon E F G H, of the bore we have often mentioned, 
Fig. 15.  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 oil of Turpentine, till the oil 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 replenished 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 oil in the shorter leg will be made to sink about an inch or somewhat more; and as afterwards you thrust the pipe deeper, the oil 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 assigned, 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 Exemplify at once three Paradoxes, (both this, and the next foregoing, 
Fig. 16.  and the second) I caused to be made a slender Glass-pipe, of the Figure expressed in the annexed Scheme, and having, by the lower Orifice L, sucked into it as much oil of Turpentine, as reached 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 stopped 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 oil that was in L M, that part of the crooked pipe which was parallel to the Horizon; than it depressed the same oil to the bottom of the shorter leg, that is from M to N: And lastly, it impelled it all up into the longer leg N P O, to what height I thought fit. So that the oil was pressed by the water both laterally, downwards, and upwards: the causes of which are easily deducible from the Doctrine already delivered.   

PARADOX IX.  
That, what ever is said of positive Levity, a parcel of oil lighter than 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 induced 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 placed never so much beneath the Superficies of that Liquor, will rather emerge to the Top, then sink to the bottom of it; if we had not already considered that problem in the Explication of the third Paradox. But being now allowed to apply to our present purpose what hath been there delivered, I shall forthwith subjoin, That 'twas easy enough for me to collect from hence, that, the Reason why it seems not possible, That a parcel of oil lighter than water, should without violence 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 immersed Body, must needs be deeper than 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 than the level of the rest of the water have a height great enough to balance that which presses against the lower, (and the Bodies not shift places by passing one by the other) the oil might be kept suspended betwixt two parcels of water.  
To reduce this to practise, I took the following course; having sucked into a slender pipe▪ (such as that employed 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 oil of Turpentitie (which, to make the effect the clearer, I sometimes tinge deeply with Copper:) then removing my finger, the oil being pressed against the immersed Orifice with a greater force, than the weight of so little suspended water could resist, that oil was impelled into the lower part of the pipe to the height of near an inch; and then again I stopped 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 impel up the oil, 
Fig. 17.  till they come to such a station, as that expressed in the annexed Scheme: where P Q is the water, newly impelled up into the pipe, Q R is the oil, and R S the water that was at first sucked 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 oil, R Q, does not ascend, because the diffluence of the water, R S, being hindered by the sides of the pipe, its superficies, T S, is higher than 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 oil.   

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 nature's abhorrency of a Vacuum.  
BOth Philosophers and Mathematicians, having too generally confessed themselves reduced to fly to a fuga vacui, for an account of the cause of the running of water and other Liquors through Syphons. And even those moderns, that admit a Vacuum, having (as far as I have met with) either left the Phaenomenon unexplicated, or endeavoured to explain it by disputable Notions: I think the Curious much obliged to Monsieur Paschal, for having ingeniously endeavoured to show▪ That this difficult Problem 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 justify 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 placed 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 Trial.  
Wherefore we will substitute a way, which may be tried in a glass Tube, not two foot deep, by the help of another peculiarly contrived glass, to be prepared 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 joined (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; 
Fig. 18.  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 tied with a string a pipe of Glass, I and H, sealed 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 fastened, and which leg must reach a pretty way beneath the Surface of the water, wherewith the said pipe is to be almost filled. But as one of these legs is longer than the other, so the surface of the water in the suspended pipe I, that is fastened to the shorter leg K F, must be higher (that is, nearer to K or A B) than 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 moved; you must gently pour oil of Turpentine into the Tube A B C D, (which, if you have not much oil, 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 than 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 oil pressing upon the water will make it ascend into the legs of the Syphon; and pass through it, out of the uppermost vessel I, into the lowermost H; and if the vessel I were supplied with water, the course of the water through the Syphon would continue longer, than 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 air 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 show 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 'tis partly the pressure of the oil, and partly the contrivance and situation of the vessels; if we will but consider the matter somewhat more atentively. For the oil, that reaches much higher than K, and consequently then the legs 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 oil floating upon the water, and the Orifice of both the legs F and G being immersed under the water, the oil has no access to the cavity of either of those legs. Wherefore, since the oil 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 prevail.  
And if we consider, That the pressure, sustained by the two parcels of water in the suspended pipes I and H, depends upon the height of the oil 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 unimmersed under water to be 6 Inches long, & the unimmersed part of the longer leg to be seven 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 dipped, by the weight of an Inch of oil: 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 impelled 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 than that in the other leg, by as much pressure as the weight of an Inch of oil can amount to; Yet being longer by an Inch than 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 oil; the water in the longer leg, notwithstanding the greater resistance of the external oil, 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 oil 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 air (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 dipped, and not upon that which is within the Syphon: and consequently, though the incumbent air 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 than 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 air 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; 
In the Physicomechanical Experiments.  the pressure of the external air 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 unstopped while the water is running, the course of it would presently cease. For, in that case, the air 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 Trials, I caused 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 removed 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 seemed to be, when the liquor began to take its course through the Syphon, some light pressure from the external air upon the finger, wherewith I stopped the Orifice of the socket made at the flexure.  
And on this occasion I will add, what I more than once tried; to show, at how very minute a passage the pressure of the External air may be communicated, to Bodies fitted to receive it. For, having for this purpose stopped the orifice of one of the above mentioned Syphons, (instead of doing it with my finger,) with a piece of oiled paper, carefully fastened with Cement to the sides of the socket; I found, as I expected, that though hereby the Syphon was so well closed, that the water ran freely through: yet, if I made a hole with the point of a needle, the air would at so very little an orifice insinuate itself 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 caused one to suck at the longer leg; this small stopple, without any other help from my hand, sufficed to make the Syphon fit for use: Yet if I removed the needle, the air would (not without some noise) presently get in at 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 air found time to get into the Syphon; and, till the hole were again stopped, render it useless, notwithstanding that the water was by suction endeavoured 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 sink by its own weight; yet if it be placed at a greater depth then that of twenty times its own thickness, it will not sink, if its descent be not assisted by the weight of the incumbent water.  
THis Paradox, having never been (that I know of) proposed as yet by any, has seemed so little credible to those to whom I have mentioned 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 deduced 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 proved, by the Doctrine already settled in this paper. The other, That the Experiment proposed by Monsieur Paschal, being to be done in a deep River, and requiring a Tube 20 foot long, whose Bottom 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 tried,) 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 employ in this case also the method we have hitherto made use of, Fill a Glass vessel, A B C D, almost full of water; 
Fig. 19  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 employed: but a deep Cylinder, or Tube sealed 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 placed 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 immersed under water till it be just covered 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 than water, the Brass that leans upon the part F, must far more gravitate upon the said part F, than 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 specific gravity of the Metal, a greater pressure upon that part of the imaginary Superficies that passes along the bottom 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 virtue 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 placed under water on the designable plain I K; and let this plain, which (as all other imaginary plains) is, as well as the real Surface of the water, to be conceived parallel to the Horizon; and let the depth or distance of this plain, 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 pressed downwards by the weight of the water it has over it. For Brass being but about nine times 
* 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 judged it needless to his present Argument, and inconvenient to take notice of the fraction.  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 pressed upon by the incumbent water, which is as high above them as the newly mentioned Cylinder of water would be; there is no reason why the part F should be depressed, rather than any other part of the Superficies I 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 placed immediately under it; it will necessarily happen, That in what part soever the solid body be placed, provided it be every way environed 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 sink, 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 removed, That none of the lateral water (if I may so call it) could succeed in its place to lean upon the solid; than it will follow, from what we have newly shown, that the solid would be kept suspended. And in case it were placed much deeper in the water, as over against the point L or M; Then, if we conceive the incumbent water to be removed or fenced 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 impelled upwards, by a force proportionate to the difference of those two pressures. And therefore, since I have found by trials, purposely made in scales marvellously exact, and with refined Gold, (purer than 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 employed 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 placed 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 weighed in the air, their proportion is above 19 to one, yet in the water, gold does, as other sinking 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 placed low eenough beneath the Surface of the water, and kept from being depressed by any incumbent water, it would be supported by the subjacent water. And this is that very thing that I am now to show by an Experiment.  
Let then the Brass body E F, be the cover of a brass Valve; 
Fig. 20.  (as in the annexed figure:) and let the Valve be fastened 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 thread 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 straight 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 bear 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 pressed 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 sink, though there be nothing but water beneath it to support it.  
And to manifest that 'tis only 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 raised so near the Surface, (as between the plain I 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 than 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 thread 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 show you a Trial with a Massy Cylinder of stone broader than 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 which 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 disjoin them.  
By which (to note that by the way) you may see, that though, when two flat and polished marbles are joined 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 environed by the Air, which is a Fluid not devoid of Gravity, and reaching above the Marbles no body knows how high.  
And to evince, That 'tis 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 I K, to overcome the resistance of the water, being now enabled to do it before it is raised near so high.   

APPENDIX I.  
Containing an Answer to seven Objections, proposed 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 published, among other things, by a very recent Writer of hydrostatics. In one of which Questions. the Learned Author strongly defends the contrary to what has there been in some places proved, and divers places supposed.  
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 received; 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 sum up into one page all the Arguments for his Opinions that are dispersedly to be found in his own or others men's Books. So that in answering these, we may hope to do much towards a satisfactory Decision of so important a Controversy. And, after what we have already delivered, 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 referred.  
Our Author then maintains, that, in Consistent water, the Superior do not actually press the Inferior parts, by the seven following Arguments.  
Object. 1. Says he, Because else the inferior parts of the water would be more dense than the Superior, since they would be compressed and condensed by the weight of them.  
Ans. But if the Corpuscles, whereof water consists, be supposed to be perfectly solid & hard; the inferior Corpuscles may be pressed upon by the weight of the superior, without being compressed or condensed by them. As it would happen, if Diamond dust were laid together in a tall heap: For though the upper parts, being heavy and solid Corpuscles, cannot be denied to lean and press upon the lower; yet these, by reason of their Adamantine hardness, would not be thereby compressed. And 'tis possible too, that the Corpuscles of water, though not so perfectly hard, but that they may a little yield to an extreme 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 Trials I have formerly mentioned 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 condensed than the upper: nor do I see any absurdity, that would follow from admitting them to be so.  
Object. 2. Our Author's second Argument is, Because Divers feel not, under water, the weight of the water that lies upon them.  
Ans. But for Answer to this Argument, I shall content myself 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 exercised against bodies immersed in fluids; which, in that case, (as to sense) presses every where equally, against all the parts of the body, exposed to their Action.  
Object. 3. The third Argument is, That even the slightest Herbs growing at the bottom of the water, and shooting up in it to a good height, are not oppressed or laid by the incumbent water.  
Ans. But the Answer to that is easy, 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 itself pressed 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 fastened to the ground, they, being in specie lighter than water, would be buoyed 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 soil.  
Object. 4. A fourth Objection is this, That a heavy Body tied 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 bodies weigh less in water then out of it.  
Ans. But an Account of this is easy to be rendered out of our Doctrine; For, though the water incumbent on the heavy body do really endeavour to make it sink lower, yet that endeavour is rendered 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 immersed body. And that pressure upon the other parts of that supposed 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 immersed 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 air. But though the pressure of the water incumbent on the stone can not, for the reason assigned, be felt in the case proposed; 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 exercised upon the stone whilst it leaned on it.  
Object. 5. The fifth Argument is proposed in these words, Because a Bucket full of water, is lighter in the water, than 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 assigned (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 inquire 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 heavy or less moved,) out of the place they possessed before; and gives it an incessant tendency, or endeavour towards the lowermost parts of the Earth.  
But as to the Example proposed, it's very easy 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 than 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 itself, must necessarily be unable to press the part H so strongly, as the other parts of the imaginary plain I K are pressed by the weight of the mere water incumbent on them. But if, as 'tis usual, the Bucket consists partly of wood, partly of iron; the Aggregate may often indeed be heavier than 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 contained in it. For though that aggregate of wood and iron, which we here call the Bucket, be heavier than 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 and the incumbent water do upon the part H: and consequently the bottom of the Bucket is every whit as strongly pressed 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 balancing 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 equal in bulk (I say, not to the Bucket as 'tis a hollow Instrument, but) to the wood and iron whereof the Bucket consists.  
And because this Example of the lightness of filled Buckets within the water has for so many Ages gained 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 scarce present it to such a company as this without smiles) an Experiment that I made to convince those, that were, through unskilfulness or prejudice, indisposed 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 filled it with melted Butter, into which, when it was congealed, some small bits of lead were put, to make it a little heavier than so much water,) I caused a small string of twined 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 Goldsmith's Scales; and then putting it into a vessel full of water, till it was let down there, to what depth I pleased, it appeared 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 immersed 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 mentioned Beam, and presently raised 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 allowed to think, that the easy sustentation, and elevation of the box, did not proceed from hence, That those bodies weighed 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 'twas the pressure of the water against the lower part of the surface of our suspended body, that made it so easy to be supported in the water, or raised to the top of it; I shall add, that though a few grains sufficed 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 than needed to sustain 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 pressed 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 superior to the full weight of the bucket, and all that it contains, (being all supposed to be weighed in the air,) 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 Horsehairs, which are held to be of the same gravity with water, keep whatever place is given them in that Liquor; nor are depressed 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 specific 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 delivered. For supposing in the last Scheme the body, R, to be bulk for bulk exactly equiponderant to water; 'tis plain there is no reason why that body should press the part S, of the imaginary Superficies ay▪ K, either more or less than that part S would be pressed, if, the body R being annihilated or removed, 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 fain to declare) from the pressure exercised upon the other parts of the Superficies, I K, by the water incumbent on them; the body, R, will be neither depressed nor raised. And its case being the same in what part of the water soever it be placed, provided it be perfectly environed 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 retain any assignable place in it; yet the Curiosity we had, to give an Experimental proof of this Truth, at length produced some glass Bubbles, which some Gentlemen here present have not perhaps forgot, that were (by a dexterous hand we employed about it) so tightly poised, 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 Horsehairs, being too easy to need to be insisted on, there remains to be dispatched our Author's seventh and last Argument, which is this.  
Object. 7. That, otherwise, all the inferior parts of the water would be in perpetual motion, and perpetually expelled 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 showed that the body, R, would retain its place any where in the water, and consequently near the bottom) will show the invalidity of this Objection. And unless we knew of what bigness 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. Only this I shall add▪ That, whereas this Learned Author 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 inferior 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 discovered 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; 
In the History of fluidity & firmness  I shall add nothing at present: But rather take notice of what our Author subjoins 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 finished discourse; and especially where I mention those Experiments, which show, That neither a stone, nor Gold itself, when placed deep under water, would sink in it, if the Superior water, that gravitates on it, did not contribute to its depression.   

APPENDIX II.  
Concerning the Reason why Divers, and others who descend to the Bottom of the Sea, are not oppressed by the weight of the incumbent water.  
AMongst the difficulties that belong to the hydrostatics, 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 placed under?  
The common Answer of Philosophers and other Writers to this puzzling 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 gathered 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 Writer, and, for aught I know, the Recentest (except Monsieur Paschal) that has treated of hydrostatics, having rendered 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 pressed by the incumbent water, because this does not endeavour to be beneath a humane Body.] He subjoins, contrary to his Custom, this confident Epiphonema, Qui aliam causam hujus rei assignant, errand & alios decipiunt.  
But, by his favour, notwithstanding this confidence, I shall not scruple to seek another Reason of the Phaenomenon. For I have abundantly proved, 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 Controversy, perhaps the matter may be somewhat cleared, 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 sinks into, or gets beneath the body that was under it, as a sinking 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 Woman carries a Pail of water on her head, though the weight do not actually get nearer the Centre of the Earth; yet actually presses with its whole gravity upon the Woman's 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 man's body is bulk for bulk heavier than 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 Centre of the Earth; nor is there any Reason, why it's happening to be incumbent on a body heavier in specie then itself, should destroy that endeavour. And therefore, though it may be said that the water does not endeavour to place itself 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 placed betwixt it and that, (without regard whether the inferior body be heavier or lighter in specie then itself) as far as the degree of its gravity will enable it; nor would it ever rest, till it have reached 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 hydrostatics, 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 bottom 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 Deal that will swim, or of Box that will sink in water; or to speak more generally, whether it be of Wood, in specie lighter than water, or of Copper, or some other Metal, that is in specie heavier than it. And since water, being not a solid Body, but a fluid, consists (as other fluids) of innumerable Corpuscles, that, though extremely 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; 'Tis 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 only press 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 Bottom of Glass Vessels, or other body's heavier in specie then its self, because under that bottom there is air, 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 bottom 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 air, fumes, or fire, or some other body lighter than 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 far as the Centre, is replenished with a subtle fluid matter, like that whereof the Sun 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 bottom to the Sea: So that, for aught these Objectors know, even according to their own Doctrine, the water even in the Sea, may endeavour to get beneath a body heavier in specie then itself.  
But, for my part, I cannot but think, that, to imagine the water knows, whether or no there be air or some lighter body than itself 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, etc. I remember not what reason 'tis that Stevinus gives, 
Second Tom lettre 32.  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: 
Fig. 22.  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 sunk 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 contrariwise 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 bottom; which by Experience we see.  
Thus far this subtle Philosopher: for whose Ratiocinations though I am wont to have much respect, yet I must take the liberty to confess myself unsatisfied with this. For having already sufficiently proved, That the upper parts of water press the lower, and the bodies placed beneath them, whether such bodies be lighter in specie then water or heavier; we have subverted the Foundation, upon which Monsieur Cartes' ingenious, though unsatisfactory, Explication is built. And yet I shall add ex abundanti, That supposing what he says, 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 fullness of the Vessel. And though indeed the Superior water cannot actually descend 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 placed 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 himself, whether he supposes the hole at A▪ to be stopped with some other body, when the solid is placed about B: yet, because he is wont to speak consistently, I presume he means, that when the solid is removed to B, the hole at A is otherwise sufficiently stopped; I say then, that the reason why the solid, which, whilst at A, sustained a great pressure from the incumbent water, feels not the weight of it, when placed at B, is not that which Monsieur des Cartes gives, but this, That the solid being environed 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 man's body, in stead of sinking, would be buoyed 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 covered and stopped 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 guests 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 sink in it. For the Body of a Man (and for aught 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 destroyed by fire from Heaven,) we suppose, (which the nature of the Soil, 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 soap consisting of salt and oil, and in Chemical mixtures of Alcalis and Brimstone dissoluble in water) the Liquor may have its gravity so augmented, as to become heavier in specie than 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 'tis not difficult to make a Brine or Lixivium (which are but Solutions of salt in water,) heavy enough to keep up an egg from sinking. And, not only barely by dissolving a metalline body in a saline Menstruum, without otherwise thickening the Liquor, I have brought solid pieces of Amber itself to swim upon it: but I have tried that certain saline Solutions, which I elsewhere mention; nay, and a distilled Liquor, (I used defleamed oil of Vitriol) without any thing dissolved 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 problem, 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, humour, aut quodlibet denique membrum luxaretur, 
Stevinus Hydrostat. Lib. 5. pag. 149.  in alium locum concedat necesse esset: 
Sed Exemple clarius ita intelliges, este ABCD aqua, cujus fundum  atqui locus ille non est extra Corpus; 
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.  cum aqua undiquaque aequali pressu circumfusa sit (quod vero pars ima, 
Fig. 23.  per 11. propositionem Hydrostaticorum, 
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.  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 far, to those that are wont to be given of this difficult Problem: But yet, the Phaenomenon seems to me to have still somewhat in it of strange. 'Tis 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 pressed down by so vast a weight of water, as is incumbent on it; It might be rationally answered, That the weight of so much water, as leans upon the body, is not sustained by the force of the body itself, 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 immersed 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 pressed 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, than a tried thing;) but by an Experiment which may be easily made, and has divers times been so, in our Pneumatical Engine. For, though the air be a heavy fluid, and though, whilst it uniformly 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, applied to the Engine instead of a Receiver, without any hurt; Yet when, by pumping, the air 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 air; the external air will lean so heavy upon the back of your hand, that you will imagine some ponderous weight is laid upon it. And I remember by such an Experiment, I have not only had my hand put to much pain, but have had the back of it so bend 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 'tis evident from the nature of the thing, and by Stevinus' 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 examined) that it does; (Though this man told me, he stayed a good while at the depth of betwixt 80 and 100 foot under the Sea water, which is heavier than fresh water;) For, that which Stevinus' Explication will only showiss, 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 bodies 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 satisfy those that (secluding the Question about the sense of pain,) think it an abundantly sufficient Argument, (to prove, that bodies immersed under water, are not compressed by it;) That Divers are not oppressed, and even crushed▪ by so vast a load of water, (amounting, by Stevinus' computation, to many thousands of pounds) as is incumbent on them. We will add, that though an Experiment, proposed by Monsieur Paschal to this purpose, were such, that at first sight I said that it would not succeed, (and was not upon trial mistaken in my conjecture;) yet it gave me the occasion to make another, which will, I hope, fully make out the thing I designed it for.  
The Ingenious Monsieur Paschal would persuade his Readers, that if into a glass Vessel, with lukewarm water in it, you cast a fly; and, by a Rammer, forcibly press that water, you shall not be able to kill, or hurt the fly. Which, says he, will live as well, and walk up and down as lively, in lukewarm water, as in the air. But, upon trial with a strong fly, the Animal was (as we expected,) presently drowned, and so made moveless, by the lukewarm 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 exposed to. We took then a somewhat slender Cylindrical pipe of Glass, 
Fig. 24.  sealed 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 moved to and fro; and would suffer neither water, nor air, to get by betwixt it, and the internal surface of the Glass. We also provided some small Tadpoles (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 smallness, swim freely to & fro in so little water as our pipe contained; & partly because those Creatures, being as yet but in their Infancy, were more tender, and, consequently, far more exposed to be injured by compression, than other Animals of the same Bulk, but come to their full age and growth, would be, (as indeed such young Tadpoles are so soft and tender, that they seem, in comparison to the bigger sort of flies, to be but organised Jelly.) One of these Tadpoles being put into the water, and some Inches of air being left in the pipe, for the use anon to be mentioned; the water and air, and consequently the Tadpole, were by the intrusion of the plug or rammer, with as great a force as a man was able to employ, violently compressed; and yet, though the Tadpole seemed to be compressed into a little less Bulk than 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 injured by this compression; and most manifest it is, he was not crushed 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 oppressed by It: Since, whether or no water weighs in water, 'tis manifest that in our Experiment, the water, and consequently the Tadpole, was very forcibly by an External Agent compressed betwixt the violently condensed air, and the rammer. And, by the notice we took of the quantity of air before the compression began, and that to which it was reduced by compression; The moderatest estimate we could make, was, That it was reduced into an eighth, or tenth part of its former space; and so (according to what we have elsewhere proved) the pressure that was upon the air, (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 crushed, if it pressed 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 immersed bodies; yet a Diver may very well remain unoppressed at a great depth under water, as long as the pressure of it is uniform against all the parts exposed thereunto.  
FINIS.