Hydrostatical paradoxes made out by new experiments, for the most physical and easie / by Robert Boyle ...
         Boyle, Robert, 1627-1691.
      
       
         
           1666
        
      
       Approx. 260 KB of XML-encoded text transcribed from 147 1-bit group-IV TIFF page images.
       
         Text Creation Partnership,
         Ann Arbor, MI ; Oxford (UK) :
         2007-01 (EEBO-TCP Phase 1).
         A28989
         Wing B3985
         ESTC R17464
         13161211
         ocm 13161211
         98187
         
           
            This keyboarded and encoded edition of the work described above is co-owned by the institutions providing financial support to the Early English Books Online Text Creation Partnership. This Phase I text is available for reuse, according to the terms of
             Creative Commons 0 1.0 Universal
            . The text can be copied, modified, distributed and performed, even for commercial purposes, all without asking permission.
          
        
      
       
         Early English books online.
      
       
         (EEBO-TCP ; phase 1, no. A28989)
         Transcribed from: (Early English Books Online ; image set 98187)
         Images scanned from microfilm: (Early English books, 1641-1700 ; 446:26)
      
       
         
           
             Hydrostatical paradoxes made out by new experiments, for the most physical and easie / by Robert Boyle ...
             Boyle, Robert, 1627-1691.
          
           [36], 247 p. : 3 plates, fold.
           
             Printed by William Hall, for Richard Davis ...,
             Oxford :
             1666.
          
           
             Reproduction of original in Huntington Library.
          
        
      
    
     
       
         Created by converting TCP files to TEI P5 using tcp2tei.xsl, TEI @ Oxford.
         Re-processed by University of Nebraska-Lincoln and Northwestern, with changes to facilitate morpho-syntactic tagging. Gap elements of known extent have been transformed into placeholder characters or elements to simplify the filling in of gaps by user contributors.
      
       
         EEBO-TCP is a partnership between the Universities of Michigan and Oxford and the publisher ProQuest to create accurately transcribed and encoded texts based on the image sets published by ProQuest via their Early English Books Online (EEBO) database (http://eebo.chadwyck.com). The general aim of EEBO-TCP is to encode one copy (usually the first edition) of every monographic English-language title published between 1473 and 1700 available in EEBO.
         EEBO-TCP aimed to produce large quantities of textual data within the usual project restraints of time and funding, and therefore chose to create diplomatic transcriptions (as opposed to critical editions) with light-touch, mainly structural encoding based on the Text Encoding Initiative (http://www.tei-c.org).
         The EEBO-TCP project was divided into two phases. The 25,363 texts created during Phase 1 of the project have been released into the public domain as of 1 January 2015. Anyone can now take and use these texts for their own purposes, but we respectfully request that due credit and attribution is given to their original source.
         Users should be aware of the process of creating the TCP texts, and therefore of any assumptions that can be made about the data.
         Text selection was based on the New Cambridge Bibliography of English Literature (NCBEL). If an author (or for an anonymous work, the title) appears in NCBEL, then their works are eligible for inclusion. Selection was intended to range over a wide variety of subject areas, to reflect the true nature of the print record of the period. In general, first editions of a works in English were prioritized, although there are a number of works in other languages, notably Latin and Welsh, included and sometimes a second or later edition of a work was chosen if there was a compelling reason to do so.
         Image sets were sent to external keying companies for transcription and basic encoding. Quality assurance was then carried out by editorial teams in Oxford and Michigan. 5% (or 5 pages, whichever is the greater) of each text was proofread for accuracy and those which did not meet QA standards were returned to the keyers to be redone. After proofreading, the encoding was enhanced and/or corrected and characters marked as illegible were corrected where possible up to a limit of 100 instances per text. Any remaining illegibles were encoded as <gap>s. Understanding these processes should make clear that, while the overall quality of TCP data is very good, some errors will remain and some readable characters will be marked as illegible. Users should bear in mind that in all likelihood such instances will never have been looked at by a TCP editor.
         The texts were encoded and linked to page images in accordance with level 4 of the TEI in Libraries guidelines.
         Copies of the texts have been issued variously as SGML (TCP schema; ASCII text with mnemonic sdata character entities); displayable XML (TCP schema; characters represented either as UTF-8 Unicode or text strings within braces); or lossless XML (TEI P5, characters represented either as UTF-8 Unicode or TEI g elements).
         
          Keying and markup guidelines are available at the
           Text Creation Partnership web site
          .
        
      
       
         
         
      
    
     
       
         eng
      
       
         
           Hydrostatics -- Early works to 1800.
        
      
    
     
        2006-05 TCP
        Assigned for keying and markup
      
        2006-05 Aptara
        Keyed and coded from ProQuest page images
      
        2006-07 Derek Lee
        Sampled and proofread
      
        2006-07 Derek Lee
        Text and markup reviewed and edited
      
        2006-09 pfs
        Batch review (QC) and XML conversion
      
    
  
   
     
       
         
         
         
           HYDROSTATICAL
           PARADOXES
           ,
           Made
           out
           by
           New
           EXPERIMENTS
           ,
           (
           For
           the
           most
           part
           PHYSICAL
           and
           Easie
           .
           )
        
         
           By
           the
           Honourable
           
             ROBERT
             BOYLE
          
           ,
           Fellow
           of
           the
           Royall
           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
           
           Physico-Mechanical
           Treatise
           about
           the
           Aire
           :
           But
           part
           of
           the
           Appendix
           consisting
           of
           Experiments
           ,
           which
           the
           Authour
           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
           pass'd
           since
           divers
           of
           them
           were
           try'd
           ,
           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
           design'd
           Appendix
           .
           And
           therefore
           he
           resolv'd
           to
           repeat
           divers
           Experiments
           and
           Observations
           ,
           that
           he
           might
           set
           down
           their
           Phaenomena
           whil'st
           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
           
           Tryals
           ,
           yet
           his
           Expectation
           was
           sadly
           disappointed
           by
           that
           heavy
           ,
           as
           well
           as
           just
           ,
           Visitation
           of
           the
           Plague
           which
           happened
           at
           London
           whil'st
           the
           Author
           was
           in
           the
           Country
           :
           and
           which
           much
           earlier
           then
           was
           apprehended
           ,
           began
           to
           make
           havock
           of
           the
           People
           ,
           at
           so
           sad
           a
           rate
           that
           not
           only
           the
           Glass-men
           there
           were
           scatter'd
           ,
           and
           had
           ,
           as
           they
           themselves
           advertis'd
           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
           shap'd
           Glasses
           ,
           and
           other
           Mechanical
           Implements
           requisite
           to
           his
           purposes
           ;
           And
           the
           same
           Calamity
           continuing
           still
           ,
           without
           yet
           affording
           us
           any
           certaine
           ground
           of
           determining
           when
           it
           will
           end
           :
           The
           Author
           chuses
           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
           impos'd
           on
           me
           by
           the
           Royal
           Society
           ,
           the
           Reader
           will
           ,
           I
           hope
           ,
           need
           no
           more
           then
           this
           intimation
           ,
           to
           keep
           him
           from
           wandering
           to
           find
           some
           passages
           Worded
           as
           parts
           of
           a
           Discourse
           pronounce'd
           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
           't
           is
           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
           Physico-Mechanical
           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
           desir'd
           to
           bring
           in
           an
           Accompt
           in
           Writing
           ,
           that
           might
           be
           Registred
           (
           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
           induc'd
           to
           add
           the
           Explications
           of
           the
           Phaenomena
           I
           describ'd
           ,
           whilst
           I
           perceiv'd
           that
           by
           a
           small
           addition
           of
           pains
           I
           might
           much
           gratifie
           divers
           Ingenious
           Friends
           that
           were
           not
           so
           well
           vers'd
           in
           Hydrostaticks
           as
           in
           the
           other
           parts
           of
           real
           Learning
           .
        
         
         
           Having
           thus
           been
           induc'd
           to
           enlarge
           the
           Account
           of
           my
           Experiments
           till
           it
           had
           attain'd
           the
           bulk
           't
           is
           now
           arriv'd
           at
           ,
           I
           confess
           I
           was
           without
           much
           difficulty
           perswaded
           ,
           that
           to
           suffer
           it
           to
           pass
           abroad
           *
           in
           the
           Company
           of
           the
           Appendix
           wherewith
           't
           is
           publish'd
           ,
           would
           not
           prove
           unacceptable
           to
           the
           Curious
           ,
           no
           more
           then
           an
           improper
           introduction
           to
           the
           rest
           of
           my
           Appendix
           ,
           and
           that
           for
           several
           Reasons
           .
        
         
           For
           (
           first
           )
           the
           Hydrostaticks
           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
           exercis'd
           on
           attentively
           consider'd
           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
           knowledg
           of
           such
           unobvious
           
           Truths
           .
           Nor
           are
           the
           delightfulness
           ,
           and
           the
           subtilty
           of
           the
           Hydrostaticks
           ,
           the
           only
           things
           for
           vvhich
           vve
           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
           Hydrostaticks
           ;
           upon
           whose
           Principles
           depend
           ,
           besides
           many
           other
           things
           ,
           the
           Explications
           of
           most
           of
           the
           Physico
           .
           Mechanical
           Experiments
           ,
           we
           have
           ventur'd
           to
           present
           the
           Publick
           ,
           and
           the
           Decision
           of
           those
           many
           Coutroversies
           ,
           which
           they
           ,
           and
           the
           Phaenomena
           of
           the
           Torrecellian
           Experiment
           have
           occasion'd
           among
           the
           Modern
           Inquirers
           into
           Nature
           .
        
         
           But
           the
           use
           of
           this
           Art
           is
           not
           alone
           Speculative
           ,
           but
           Practical
           ,
           since
           not
           onely
           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
           
           workes
           :
           But
           that
           the
           Hydrostaticks
           may
           be
           made
           divers
           ways
           serviceable
           to
           the
           Chymists
           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
           *
           elsewhere
           deliver'd
           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
           litle
           ,
           and
           not
           very
           happily
           cultivated
           .
           For
           being
           not
           look'd
           upon
           as
           a
           Discipline
           purely
           Mathematical
           ,
           the
           generality
           of
           Mathematicians
           have
           not
           in
           their
           Writings
           so
           much
           as
           taken
           notice
           of
           it
           ,
           much
           less
           improv'd
           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
           easie
           Demonstrations
           )
           
           among
           divers
           others
           that
           have
           more
           of
           Geometrical
           Subtility
           ,
           then
           usefulness
           ,
           Those
           Mathematicians
           ,
           that
           ,
           (
           like
           
             Marinus
             Ghetaldus
             ,
             Stevinus
          
           ,
           and
           Galileo
           )
           have
           added
           anything
           considerable
           to
           the
           Hydrostaticks
           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
           Peripateticks
           ,
           and
           other
           School-Philosophers
           ,
           though
           on
           some
           Occasions
           ,
           as
           when
           they
           tell
           us
           ,
           That
           water
           weighs
           not
           in
           water
           ,
           nor
           aire
           in
           aire
           ,
           they
           deliver
           assertions
           about
           matters
           belonging
           to
           the
           Hydrostaticks
           ,
           (
           which
           term
           ,
           in
           this
           Treatise
           ,
           I
           often
           take
           in
           a
           large
           sense
           because
           most
           of
           the
           things
           delivered
           about
           the
           weight
           of
           Bodys
           may
           by
           easy
           variations
           ,
           be
           made
           applicable
           to
           other
           Fluids
           )
           yet
           they
           are
           so
           far
           from
           having
           illustrated
           ,
           or
           improv'd
           them
           ,
           that
           they
           have
           but
           broach'd
           or
           
           credited
           ,
           divers
           of
           the
           most
           erroneous
           conceits
           ,
           that
           are
           entertain'd
           about
           them
           .
           So
           that
           ,
           there
           being
           but
           few
           Treatises
           written
           about
           the
           Hydrostaticks
           ,
           and
           those
           commonly
           bound
           up
           among
           other
           Mathematical
           works
           ,
           and
           so
           written
           ,
           as
           to
           require
           Mathematical
           Readers
           ,
           this
           usefull
           part
           of
           Philosophy
           ,
           has
           been
           scarce
           known
           any
           farther
           then
           by
           name
           ,
           to
           the
           genèrality
           ev'n
           of
           those
           Learned
           men
           ,
           that
           have
           been
           inquisitive
           into
           the
           other
           parts
           of
           it
           ,
           and
           are
           deservedly
           reckoned
           among
           the
           ingenious
           Cultivators
           of
           the
           modern
           Philosophy
           .
           But
           this
           is
           not
           all
           ,
           For
           some
           eminent
           men
           ,
           that
           have
           of
           late
           years
           ,
           treated
           of
           matters
           Hydrostatical
           ;
           having
           been
           prepossess'd
           with
           some
           errenous
           Opinions
           of
           the
           peripatetick
           School
           ,
           and
           finding
           it
           difficult
           ,
           to
           consult
           experience
           ,
           about
           the
           truth
           of
           their
           Conclusions
           ,
           have
           interwoven
           divers
           erroneous
           Doctrines
           among
           the
           sounder
           propositions
           ,
           which
           they
           either
           borrow'd
           from
           Archimedes
           ,
           and
           either
           circumspect
           Mathematicians
           ,
           or
           devis'd
           
           themselves
           ,
           and
           these
           mistakes
           being
           deliver'd
           in
           a
           Mathematical
           dress
           ,
           and
           mingled
           with
           Propositions
           demonstrably
           true
           ,
           the
           Reputation
           of
           such
           Learned
           Men
           ,
           (
           from
           which
           I
           am
           far
           from
           desiring
           to
           detract
           ,
           )
           and
           the
           unqualifiedness
           of
           most
           Readers
           ,
           to
           examine
           Mathematical
           things
           ,
           has
           procur'd
           so
           general
           an
           entertainment
           for
           those
           Errors
           ,
           that
           now
           the
           Hydrostaticks
           is
           grown
           a
           part
           of
           Learning
           ,
           which
           't
           is
           not
           only
           difficult
           to
           attain
           ,
           but
           dangerous
           to
           Study
           .
        
         
           Wherefore
           ,
           though
           neither
           the
           Occasion
           and
           designe
           of
           this
           Treatise
           exacted
           ,
           nor
           my
           want
           of
           skill
           and
           leasure
           qualified
           me
           to
           Write
           either
           a
           Body
           or
           Elements
           of
           Hydrostaticks
           :
           yet
           I
           hop'd
           I
           might
           doe
           something
           ,
           both
           towards
           the
           illustrating
           ,
           and
           towards
           the
           rescue
           of
           so
           valuable
           a
           Discipline
           ,
           by
           Publishing
           the
           ensuing
           Tract
           ;
           where
           I
           endeavour
           to
           disprove
           the
           receiv'd
           errors
           ,
           by
           establishing
           Paradoxes
           còntrary
           to
           them
           ,
           and
           to
           make
           the
           Truths
           
           the
           better
           understood
           and
           receiv'd
           ,
           partly
           by
           away
           of
           Explicating
           them
           unimploy'd
           in
           Hydrostatical
           Books
           ,
           and
           partly
           by
           confirming
           the
           things
           I
           deliver
           by
           Physical
           and
           sensible
           Experiments
           .
           And
           over
           and
           above
           this
           ,
           the
           more
           to
           recommend
           Hydrostaticks
           Themselves
           to
           the
           Reader
           ,
           I
           have
           ,
           besides
           the
           Paradoxes
           ,
           oppos'd
           to
           the
           Errors
           I
           would
           disprove
           ,
           taken
           occasion
           by
           the
           same
           way
           ,
           to
           make
           out
           some
           of
           the
           usefullest
           of
           those
           Hydrostatical
           Truths
           ,
           that
           are
           wont
           to
           seem
           strange
           to
           Beginners
           .
        
         
           If
           it
           be
           here
           demanded
           ,
           why
           I
           have
           made
           some
           of
           my
           Explications
           so
           prolix
           ,
           and
           have
           on
           several
           occasions
           inculcated
           some
           things
           .
           I
           answer
           ,
           That
           those
           who
           are
           not
           us'd
           to
           read
           Mathematical
           Books
           ,
           are
           wont
           to
           be
           so
           indispos'd
           to
           apprehend
           things
           ,
           that
           must
           be
           explicated
           by
           Schemes
           ,
           and
           I
           have
           found
           the
           generality
           of
           Learned
           men
           ,
           and
           ev'n
           of
           those
           new
           Philosophers
           that
           are
           not
           skill'd
           in
           Mathematicks
           ,
           so
           
           much
           more
           unacquainted
           ,
           then
           I
           before
           imagin'd
           both
           with
           the
           principles
           and
           Theorems
           of
           Hydrostaticks
           ,
           and
           with
           the
           ways
           of
           explicating
           and
           proving
           them
           ,
           that
           I
           fear'd
           ,
           that
           neither
           the
           Paradoxes
           themselves
           ,
           that
           I
           maintain
           ,
           nor
           the
           Hypotheses
           about
           the
           weight
           and
           pressure
           of
           the
           aire
           ,
           upon
           which
           ,
           little
           less
           then
           my
           whole
           Pneumatical
           Book
           depends
           ,
           would
           be
           throughly
           understood
           without
           such
           a
           clear
           Explication
           of
           some
           Hydrostatical
           Theorems
           ,
           as
           to
           a
           person
           not
           vers'd
           in
           Mathematical
           writings
           ,
           could
           scarce
           be
           satisfactorily
           deliver'd
           in
           few
           words
           .
           And
           therefore
           ,
           though
           I
           do
           not
           doubt
           ,
           that
           those
           who
           are
           good
           at
           the
           most
           compendious
           ways
           of
           demonstrating
           ,
           will
           think
           ,
           I
           might
           in
           divers
           places
           ,
           have
           spar'd
           many
           words
           without
           injury
           to
           my
           proofs
           ,
           and
           though
           I
           am
           my self
           ,
           of
           the
           same
           mind
           I
           exspect
           to
           find
           them
           of
           ;
           yet
           ,
           I
           confess
           that
           't
           was
           out
           of
           choice
           that
           I
           declind
           that
           close
           and
           concise
           way
           of
           writing
           ,
           that
           in
           other
           cases
           I
           am
           wont
           most
           
           to
           esteem
           .
           For
           Writing
           now
           not
           to
           credit
           my self
           ,
           but
           to
           instruct
           others
           ,
           I
           had
           rather
           Geometricians
           should
           not
           commend
           the
           shortness
           of
           my
           Proofs
           ,
           then
           that
           those
           other
           Readers
           ,
           whom
           I
           chiefly
           design'd
           to
           gratifie
           ,
           should
           not
           throughly
           apprehend
           the
           meaning
           of
           them
           .
        
         
           But
           this
           is
           not
           all
           for
           which
           I
           am
           to
           excuse
           my selfe
           to
           Mathematicall
           Readers
           .
           For
           some
           of
           them
           ,
           I
           fear
           ,
           will
           not
           like
           that
           I
           should
           offer
           for
           Proofs
           such
           Physical
           Experiments
           ,
           as
           do
           not
           alwayes
           demonstrate
           the
           things
           ,
           they
           would
           evince
           ,
           with
           a
           Mathematical
           certainty
           and
           accuratenesse
           ;
           and
           much
           less
           will
           they
           approve
           ,
           that
           I
           should
           annex
           such
           Experiments
           to
           confirm
           the
           Explications
           ,
           as
           if
           Suppositions
           and
           Schemes
           ,
           well
           reason'd
           on
           ,
           were
           not
           sufficient
           to
           convince
           any
           rational
           man
           about
           matters
           Hydrostaticall
           .
        
         
         
           In
           Answer
           to
           this
           I
           must
           represent
           ,
           that
           in
           Physical
           Enquiries
           it
           is
           often
           sufficient
           that
           our
           determinations
           come
           very
           near
           the
           matter
           ,
           though
           they
           fall
           short
           of
           a
           Mathematical
           Exactness
           .
           And
           I
           choose
           rather
           to
           presume
           upon
           the
           equity
           of
           the
           Reader
           ,
           then
           to
           trouble
           him
           and
           my self
           with
           tedious
           Circumlocutions
           ,
           to
           avoid
           the
           possibility
           of
           being
           misunderstood
           ,
           or
           of
           needing
           his
           Candor
           .
           And
           we
           see
           ,
           that
           even
           Mathematicians
           are
           wont
           ,
           without
           finding
           any
           inconvenience
           thereby
           ,
           to
           suppose
           all
           perpendicular
           Lines
           ,
           made
           by
           pendulous
           Bodies
           ,
           to
           be
           parallel
           to
           one
           another
           :
           Though
           indeed
           they
           are
           not
           ;
           since
           ,
           being
           produc'd
           ,
           they
           would
           meet
           at
           the
           Centre
           of
           the
           Earth
           :
           And
           to
           presume
           ,
           that
           the
           Surface
           of
           every
           calme
           water
           ,
           in
           a
           Vessel
           ,
           is
           parallel
           to
           the
           Horizon
           ;
           and
           consequently
           ,
           a
           Plain
           :
           Though
           ,
           in
           strictness
           ,
           themselves
           think
           it
           the
           portion
           of
           a
           Sphere
           :
           And
           though
           also
           I
           have
           usually
           
           observ'd
           it
           to
           be
           higher
           ,
           where
           't
           is
           almost
           contiguous
           to
           the
           sides
           of
           the
           Vessel
           ,
           then
           't
           is
           in
           other
           places
           .
        
         
           Moreover
           ,
           since
           we
           find
           that
           though
           water
           will
           be
           uniformly
           rais'd
           in
           Pumps
           to
           several
           heights
           ,
           but
           not
           to
           thirty
           five
           foot
           ,
           and
           will
           in
           ordinary
           open
           pipes
           ,
           be
           almost
           of
           the
           same
           level
           within
           and
           without
           ,
           but
           not
           if
           the
           pipe
           be
           extraordinary
           slender
           ;
           Upon
           these
           ,
           and
           divers
           other
           such
           considerations
           ,
           I
           may
           have
           sometimes
           made
           use
           of
           expressions
           ,
           that
           seemed
           not
           positive
           and
           determinate
           enough
           to
           be
           employed
           about
           matters
           to
           which
           Mathematical
           Demonstrations
           are
           thought
           applicable
           .
           But
           I
           elsewhere
           give
           an
           account
           of
           the
           scruples
           I
           have
           about
           such
           Demonstrations
           ,
           as
           they
           are
           wont
           to
           be
           apply'd
           to
           Physical
           matters
           .
           And
           ,
           in
           the
           present
           Paradoxes
           ,
           I
           think
           I
           have
           not
           done
           nothing
           ,
           if
           in
           my
           Hydrostatical
           Explications
           I
           have
           made
           it
           appear
           ,
           That
           in
           
           Experiments
           made
           with
           such
           Liquors
           and
           Glasses
           ,
           as
           I
           employed
           ,
           the
           Rules
           will
           hold
           without
           any
           sensible
           ,
           or
           at
           least
           any
           considerable
           Error
           ;
           for
           thereby
           we
           may
           learn
           the
           Truth
           of
           many
           things
           ,
           for
           the
           main
           ,
           though
           in
           some
           we
           should
           not
           have
           attained
           to
           the
           exactness
           of
           measures
           and
           proportions
           ,
           which
           yet
           our
           endeavors
           may
           assist
           others
           to
           arrive
           at
           .
        
         
           And
           as
           for
           my
           confirmation
           of
           Hydrostatical
           propositions
           by
           Physical
           Experiments
           ,
           if
           some
           Readers
           dislike
           that
           way
           ,
           I
           make
           no
           doubt
           but
           that
           the
           most
           will
           not
           only
           approve
           it
           ,
           but
           thank
           me
           for
           it
           .
           For
           though
           ,
           in
           pure
           Mathematicks
           ,
           he
           that
           can
           demonstrate
           well
           ,
           may
           be
           sure
           of
           the
           Truth
           of
           a
           Conclusion
           ,
           without
           consulting
           Experience
           about
           it
           :
           Yet
           because
           demonstrations
           are
           wont
           to
           be
           built
           upon
           Suppositions
           or
           Postulates
           ;
           and
           some
           things
           ,
           though
           not
           in
           Arithmetick
           or
           Geometry
           ,
           yet
           in
           Physical
           matters
           ,
           are
           
           wont
           to
           be
           taken
           for
           granted
           ,
           about
           which
           men
           are
           lyable
           to
           slip
           into
           mistakes
           ;
           even
           when
           we
           doubt
           not
           of
           the
           Ratiocination
           ,
           we
           may
           doubt
           of
           the
           conclusion
           ,
           because
           we
           may
           ,
           of
           the
           Truth
           of
           some
           of
           the
           things
           it
           supposes
           .
           And
           this
           Consideration
           ,
           if
           there
           were
           no
           other
           ,
           will
           ,
           I
           hope
           ,
           excuse
           me
           to
           Mathematicians
           ,
           for
           ventring
           to
           confute
           some
           reasonings
           that
           are
           given
           out
           for
           Mathematical
           demonstrations
           .
           For
           I
           suppose
           it
           will
           be
           consider'd
           ,
           that
           those
           whose
           presum'd
           Demonstrations
           I
           examine
           ,
           though
           they
           were
           some
           of
           them
           Professours
           of
           Mathematicks
           ,
           yet
           did
           not
           Write
           meerly
           as
           Mathematicians
           ,
           but
           partly
           as
           Naturalists
           :
           so
           that
           to
           question
           their
           Tenets
           ,
           ought
           not
           to
           disparage
           those
           ,
           as
           well
           certain
           ,
           as
           excellent
           and
           most
           useful
           Sciences
           ,
           pure
           Mathematicks
           ,
           any
           more
           then
           that
           the
           Mathematicians
           that
           follow
           the
           Ptolemaick
           ,
           the
           Copernican
           ,
           the
           Tichonian
           ,
           or
           other
           Systemes
           
           of
           the
           world
           ,
           Write
           Books
           to
           manifest
           one
           anothers
           Paralogismes
           in
           Astronomical
           matters
           :
           And
           therefore
           (
           to
           proceed
           to
           what
           I
           was
           about
           to
           say
           )
           it
           cannot
           but
           be
           a
           satisfaction
           to
           a
           wary
           man
           to
           consult
           sense
           about
           those
           things
           that
           fall
           under
           the
           Cognisance
           of
           it
           ,
           and
           to
           examine
           by
           Experiences
           ,
           whether
           men
           have
           not
           been
           mistaken
           in
           their
           Hypotheses
           and
           Reasonings
           ,
           and
           therefore
           the
           Learned
           Stevinus
           himself
           (
           the
           chief
           of
           the
           Moderne
           Writers
           of
           Hydrostaticks
           )
           thought
           fit
           ,
           after
           the
           end
           of
           his
           Hydrostatical
           Elements
           ,
           to
           add
           in
           an
           Appendix
           some
           Pragmatical
           Examples
           (
           as
           he
           calls
           them
           )
           that
           is
           ,
           Mechanical
           Experiments
           (
           how
           cogent
           I
           now
           inquire
           not
           )
           to
           confirm
           the
           Truth
           of
           his
           Tenth
           Proposition
           ,
           to
           which
           he
           had
           ,
           not
           far
           from
           the
           beginning
           of
           his
           Book
           ,
           annexed
           what
           he
           thinks
           a
           Mathematical
           Demonstration
           .
           And
           ,
           about
           the
           very
           Subjects
           we
           are
           now
           upon
           ,
           the
           following
           
           Paradoxes
           will
           discover
           so
           many
           mistakes
           of
           eminent
           Writers
           ,
           that
           pretend
           to
           have
           Mathematically
           demonstrated
           what
           they
           teach
           ,
           that
           it
           cannot
           but
           make
           wary
           Naturalists
           (
           and
           't
           is
           chiefly
           to
           gratifie
           such
           that
           I
           publish
           this
           )
           be
           somewhat
           diffident
           of
           Conclusions
           ,
           whose
           proofs
           they
           do
           not
           well
           understand
           .
           And
           it
           cannot
           but
           ,
           to
           such
           ,
           be
           of
           great
           satisfaction
           to
           find
           the
           things
           ,
           that
           are
           taught
           them
           ,
           verified
           by
           the
           visible
           testimony
           of
           Nature
           her self
           .
           The
           importance
           of
           this
           Subject
           ,
           and
           the
           frequent
           Occasion
           I
           have
           to
           make
           use
           of
           this
           kind
           of
           Apology
           ,
           will
           I
           hope
           ,
           procure
           me
           the
           Readers
           pardon
           if
           I
           have
           insisted
           somewhat
           long
           upon
           it
           .
        
         
           After
           what
           has
           been
           hitherto
           discours'd
           ,
           't
           wil
           be
           easie
           for
           me
           to
           give
           an
           Account
           ,
           why
           I
           premised
           these
           Hydrostatical
           Paradoxes
           to
           the
           rest
           of
           the
           Appendix
           ,
           wherewith
           they
           are
           *
           now
           publish'd
           :
           For
           since
           a
           great
           part
           of
           my
           work
           in
           that
           Appendix
           ,
           was
           to
           be
           a
           further
           Explication
           
           of
           some
           things
           delivered
           in
           the
           Book
           it
           is
           subjoyn'd
           to
           ,
           and
           the
           vindication
           of
           then
           from
           invalid
           objections
           :
           And
           since
           I
           have
           generally
           observ'd
           ,
           that
           the
           objections
           that
           have
           bin
           ,
           either
           publickly
           or
           privately
           ▪
           made
           against
           the
           explications
           &
           reasonings
           contain'd
           in
           that
           Book
           ,
           were
           wont
           to
           proceed
           from
           unacquaintedness
           ,
           either
           with
           the
           true
           notion
           of
           the
           weight
           and
           spring
           of
           the
           aire
           ,
           as
           I
           maintain
           them
           ,
           or
           with
           the
           Principles
           and
           Theorems
           of
           Hydrostaticks
           ,
           or
           else
           from
           erroneous
           Conceits
           about
           them
           ;
           I
           thought
           it
           would
           much
           conduce
           to
           both
           the
           forementioned
           ends
           of
           my
           Appendix
           ,
           If
           I
           clear'd
           up
           that
           Doctrine
           to
           which
           my
           Experiments
           and
           reasonings
           have
           been
           all
           along
           Consonant
           ,
           &
           whos
           's
           being
           either
           not
           known
           ,
           or
           misunderstood
           ,
           seems
           to
           have
           occasion'd
           the
           objections
           that
           have
           been
           hitherto
           made
           against
           the
           Hypotheses
           I
           have
           propos'd
           ,
           or
           the
           Explications
           I
           have
           thence
           given
           .
           And
           however
           ,
           since
           the
           Proofs
           I
           offer
           for
           my
           opinions
           are
           for
           the
           most
           part
           drawn
           from
           
           Experiments
           new
           &
           easie
           ,
           and
           that
           my
           aim
           is
           but
           to
           discover
           Truths
           ,
           or
           make
           them
           out
           by
           clearer
           explications
           ,
           without
           supposing
           ,
           like
           those
           I
           dissent
           from
           ,
           any
           thing
           that
           is
           either
           precarious
           or
           scarce
           ,
           if
           at
           all
           ,
           intelligible
           ;
           I
           hope
           ,
           that
           if
           I
           should
           not
           prove
           happy
           enough
           to
           reach
           my
           ends
           ,
           yet
           the
           Ingenious
           and
           Equitable
           Reader
           will
           approve
           my
           Designe
           ,
           and
           be
           advantaged
           by
           my
           Experiments
           .
           Of
           which
           some
           of
           the
           chiefest
           ,
           and
           some
           of
           the
           most
           difficult
           ,
           having
           been
           seen
           (
           divers
           of
           them
           more
           then
           once
           )
           by
           the
           
             Royal
             Society
          
           it self
           ,
           or
           by
           inquisitive
           Members
           of
           it
           ;
           it
           will
           ,
           I
           presume
           ,
           be
           but
           a
           reasonable
           request
           ,
           if
           the
           Reader
           ,
           that
           shall
           have
           the
           curiosity
           to
           try
           them
           over
           again
           ,
           be
           desired
           not
           to
           be
           hasty
           in
           distrusting
           the
           matters
           of
           fact
           ,
           in
           case
           he
           should
           not
           be
           able
           at
           first
           to
           make
           every
           thing
           succeed
           according
           to
           expectation
           .
           For
           as
           easie
           as
           I
           have
           endeavour'd
           to
           make
           these
           Experiments
           ,
           yet
           I
           dare
           not
           promise
           my self
           that
           they
           will
           all
           of
           them
           be
           priviledg'd
           from
           the
           fate
           
           whereto
           I
           have
           observ'd
           other
           Physico-Mathematical
           ones
           to
           be
           not
           seldome
           obnoxious
           from
           some
           unheeded
           Physical
           Circumstance
           ,
           by
           which
           those
           that
           are
           not
           acquainted
           with
           the
           subtleties
           of
           Nature
           ,
           or
           ,
           at
           least
           for
           the
           time
           ,
           do
           not
           sufficiently
           consider
           them
           ,
           are
           apt
           to
           be
           imposed
           upon
           .
        
         
           This
           Advertisement
           will
           perhaps
           be
           best
           illustrated
           ,
           &
           recommended
           by
           an
           instance
           .
           And
           therefore
           I
           shall
           subjoyne
           one
           that
           will
           possibly
           seem
           somewhat
           odd
           .
        
         
           It
           has
           been
           taken
           notice
           of
           by
           two
           or
           three
           Ingenious
           modern
           Mathematicians
           ,
           and
           I
           have
           had
           occasion
           to
           make
           it
           out
           by
           particular
           Experiments
           ,
           that
           warm
           water
           is
           lighter
           
             in
             specie
          
           then
           cold
           :
           whence
           it
           has
           been
           deduc'd
           ,
           that
           wax
           ,
           and
           other
           Bodies
           ,
           very
           near
           aequiponderant
           with
           common
           water
           ,
           will
           swim
           in
           that
           which
           is
           cold
           ,
           and
           sinck
           in
           that
           which
           is
           hot
           ,
           or
           luke-warm
           .
           Which
           Experiment
           ,
           though
           as
           it
           may
           be
           (
           and
           perhaps
           it
           has
           been
           )
           tryed
           ,
           I
           readily
           allow
           to
           be
           agreeable
           to
           the
           known
           Laws
           of
           the
           Hydrostaticks
           ;
           
           Yet
           I
           have
           sometimes
           undertaken
           that
           the
           Tryal
           should
           have
           a
           quite
           contrary
           event
           .
           To
           this
           purpose
           having
           taken
           some
           yellow
           Bees-wax
           ,
           which
           was
           formed
           into
           a
           Pellet
           of
           the
           bigness
           of
           a
           Cherry
           ,
           and
           ,
           by
           the
           help
           of
           a
           little
           Lead
           ,
           was
           made
           so
           near
           aequiponderant
           to
           cold
           water
           ,
           that
           ;
           being
           but
           a
           very
           little
           heavier
           ,
           a
           very
           small
           diminution
           of
           its
           weight
           would
           make
           it
           emerge
           ,
           I
           remov'd
           it
           out
           of
           the
           very
           cold
           water
           ,
           into
           some
           that
           had
           bin
           purposely
           made
           lukewarm
           ,
           (
           or
           a
           little
           more
           then
           so
           )
           where
           it
           quickly
           ,
           somewhat
           to
           the
           wonder
           of
           the
           lookers
           on
           ,
           appeard
           to
           swim
           on
           the
           top
           of
           the
           water
           .
           And
           that
           it
           might
           not
           be
           suspected
           that
           it
           was
           supported
           by
           any
           visible
           bubbles
           ,
           which
           I
           have
           observed
           ,
           in
           some
           cases
           ,
           to
           buoy
           up
           even
           heavy
           Bodies
           ,
           and
           deceive
           the
           unskilful
           ,
           or
           unattentive
           ;
           I
           briskly
           enough
           duck'd
           the
           bullet
           2
           or
           3
           times
           under
           water
           to
           throw
           them
           off
           ,
           notwithstanding
           which
           it
           constantly
           return'd
           to
           float
           ,
           and
           yet
           being
           remov'd
           again
           into
           the
           same
           cold
           water
           it
           had
           been
           taken
           
           out
           of
           ,
           and
           duck'd
           as
           before
           to
           free
           it
           from
           adherent
           bubbles
           ,
           it
           lay
           quietly
           at
           the
           bottom
           ,
           and
           ,
           though
           rais'd
           several
           times
           to
           the
           upper
           part
           of
           the
           water
           ,
           would
           immediately
           subside
           again
           ,
           and
           fall
           to
           the
           very
           lowest
           .
           Now
           that
           which
           invited
           me
           to
           promise
           an
           Experiment
           which
           seems
           to
           contradict
           the
           principles
           of
           the
           Hydrostaticks
           ,
           was
           not
           any
           distrust
           of
           those
           principles
           themselves
           ,
           but
           a
           conjecture
           ,
           that
           as
           by
           warmth
           the
           water
           would
           be
           made
           a
           little
           lighter
           in
           specie
           then
           't
           was
           before
           ;
           so
           by
           the
           same
           warmth
           the
           spirituous
           and
           more
           agitable
           parts
           of
           the
           wax
           ,
           whose
           texture
           is
           loose
           enough
           ,
           would
           be
           somwhat
           (
           though
           not
           visibly
           )
           expanded
           ,
           and
           would
           by
           that
           expansion
           gain
           a
           greater
           advantage
           towards
           floating
           ,
           then
           the
           increas'd
           lightness
           of
           the
           water
           would
           give
           it
           disposition
           to
           sinck
           .
           And
           I
           confirm'd
           this
           conjecture
           by
           a
           farther
           experiment
           ,
           which
           at
           first
           was
           it self
           somewhat
           surprising
           to
           the
           Beholders
           .
           For
           when
           the
           wax
           was
           first
           taken
           out
           of
           the
           cold
           water
           ,
           &
           immediately
           immers'd
           in
           the
           
           warm
           ,
           it
           would
           readily
           enough
           sinck
           ,
           &
           being
           (
           with
           a
           quill
           or
           a
           knife
           )
           rais'd
           to
           the
           top
           of
           the
           water
           ,
           it
           would
           again
           fall
           down
           ,
           but
           more
           slowly
           then
           at
           the
           begining
           ,
           &
           aftersome
           few
           minutes
           ,
           if
           it
           were
           rais'd
           to
           the
           upper
           parts
           of
           the
           water
           ,
           it
           would
           remain
           a
           float
           .
           (
           And
           I
           have
           known
           it
           ,
           when
           it
           had
           remain'd
           a
           while
           longer
           at
           the
           bottom
           ,
           so
           to
           emerge
           ,
           that
           if
           I
           were
           sure
           no
           unheeded
           bubbles
           had
           been
           newly
           generated
           ,
           and
           held
           it
           up
           ,
           it
           might
           be
           said
           to
           emerge
           of
           its
           own
           accord
           )
           as
           on
           the
           other
           side
           ,
           being
           put
           into
           the
           cold
           water
           as
           soon
           as
           ever
           it
           was
           taken
           out
           of
           the
           warm
           ,
           it
           would
           at
           the
           very
           first
           float
           ,
           and
           being
           then
           knock'd
           downwards
           ,
           it
           would
           ,
           readily
           enough
           ,
           regain
           the
           upper
           part
           of
           the
           water
           ,
           but
           if
           I
           continu'd
           to
           send
           it
           downwards
           about
           6
           or
           7
           times
           (
           more
           or
           fewer
           )
           successively
           ,
           it
           would
           emerge
           every
           time
           more
           slowly
           then
           other
           ,
           and
           at
           length
           not
           emerge
           at
           all
           ,
           even
           when
           I
           try'd
           it
           in
           water
           made
           heavy
           ,
           by
           being
           highly
           infrigidated
           with
           salt
           aud
           snow
           plac'd
           about
           the
           Glass
           .
           Which
           Phaenomena
           I
           had
           
           thought
           it
           reasonable
           to
           expect
           ,
           because
           I
           presum'd
           ,
           that
           the
           Wax
           being
           remov'd
           immediately
           out
           of
           the
           warm
           water
           ,
           into
           the
           cold
           ,
           must
           require
           some
           time
           ,
           to
           loose
           the
           adventitious
           expansion
           ,
           which
           the
           warmth
           had
           given
           it
           ,
           and
           must
           be
           depriv'd
           of
           it
           by
           degrees
           ,
           by
           the
           coldness
           of
           the
           water
           into
           which
           the
           wax
           was
           transferr'd
           .
           As
           on
           the
           other
           side
           ,
           there
           must
           be
           some
           time
           necessary
           for
           so
           little
           a
           warmth
           ,
           as
           that
           of
           the
           tepid
           (
           or
           little
           more
           then
           tepid
           )
           water
           ,
           to
           give
           the
           wax
           that
           addition
           of
           dimensions
           (
           which
           also
           it
           must
           receive
           by
           degrees
           )
           that
           was
           necessary
           ,
           in
           spite
           of
           the
           rarefaction
           of
           the
           water
           ,
           to
           make
           it
           float
           .
           I
           might
           add
           ,
           that
           these
           Tryals
           were
           repeated
           ,
           for
           the
           main
           ,
           with
           more
           Bullets
           of
           wax
           then
           one
           ,
           and
           that
           they
           succeeded
           far
           otherwise
           ,
           when
           ,
           instead
           of
           a
           piece
           of
           wax
           ,
           we
           imploy'd
           a
           pois'd
           glass
           bubble
           ,
           in
           which
           the
           temperature
           could
           make
           either
           no
           change
           at
           all
           ,
           or
           no
           considerable
           change
           of
           dimensions
           .
           And
           to
           these
           I
           might
           add
           other
           circumstances
           ,
           if
           I
           did
           not
           remember
           ,
           
           that
           I
           mention
           these
           Tryals
           but
           occasionally
           ,
           and
           to
           make
           the
           caution
           ,
           formerly
           recommended
           to
           the
           Reader
           ,
           appear
           not
           to
           be
           impertinent
           ,
           since
           a
           Hydrostatical
           Experiment
           ,
           true
           in
           its
           self
           ,
           may
           easily
           miscarry
           by
           over-looking
           such
           Circumstances
           as
           't
           is
           not
           easie
           to
           be
           aware
           of
           .
        
         
           But
           by
           this
           Advertisement
           I
           would
           by
           no
           means
           divert
           Men
           from
           being
           diffident
           of
           Hydrostatical
           Traditions
           and
           Experiments
           .
           For
           ,
           besides
           the
           many
           Erroneous
           Opinions
           ,
           there
           are
           matters
           of
           fact
           ,
           whose
           Truth
           ,
           thò
           not
           question'd
           ,
           but
           built
           upon
           ,
           I
           think
           ought
           to
           be
           brought
           to
           tryal
           .
           For
           ,
           even
           whilst
           I
           was
           concluding
           this
           Preface
           ,
           I
           found
           that
           divers
           even
           of
           the
           Moderns
           ,
           &
           particularly
           a
           very
           learned
           Man
           that
           has
           lately
           Writen
           of
           Hydrostaticks
           ,
           have
           much
           troubled
           themselves
           to
           render
           a
           reason
           why
           ,
           since
           ,
           according
           to
           their
           Doctrine
           ,
           water
           weighs
           not
           in
           water
           ,
           Wooden
           vessels
           ,
           though
           of
           a
           substance
           lighter
           then
           water
           ,
           being
           by
           leaks
           ,
           or
           otherwise
           ,
           fil'd
           with
           water
           ,
           should
           sinck
           and
           remain
           at
           
           the
           bottom
           of
           the
           water
           :
           whereas
           judging
           this
           Phaenomenon
           disagreable
           to
           what
           I
           look
           upon
           as
           the
           Laws
           of
           the
           Hydrostaticks
           ,
           I
           was
           confirm'd
           in
           that
           opinion
           ,
           by
           having
           had
           the
           curiosity
           to
           make
           some
           tryals
           of
           it
           ,
           wtth
           4
           or
           5
           vessels
           of
           differing
           shapes
           and
           sizes
           ,
           whereof
           two
           were
           of
           wax
           ,
           which
           ,
           though
           a
           matter
           but
           very
           little
           lighter
           then
           water
           ,
           I
           could
           not
           sinck
           ,
           or
           keep
           sunck
           by
           pouring
           water
           into
           them
           ,
           or
           suffering
           them
           to
           fill
           themselves
           at
           leaks
           made
           near
           the
           bottom
           ,
           and
           if
           they
           were
           depressed
           by
           force
           or
           weights
           ,
           they
           ,
           as
           also
           the
           wooden
           Vessels
           ,
           would
           upon
           the
           removal
           of
           the
           impediment
           (
           and
           sometimes
           with
           the
           cavity
           upwards
           )
           emerge
           .
           And
           I
           am
           the
           more
           solicitous
           to
           have
           things
           in
           the
           Hydrostaticks
           duly
           ascertain'd
           ,
           because
           
             the
             weighing
             of
             bodies
             in
             Liquors
          
           may
           hereafter
           appear
           to
           be
           one
           of
           the
           general
           ways
           I
           have
           employ'd
           ,
           and
           would
           recommend
           ,
           for
           the
           examining
           of
           almost
           all
           sorts
           of
           tangible
           Bodies
           .
        
      
       
         
         
           THE
           CONTENTS
           .
        
         
           
             PAradox
             .
             1.
             
             That
             in
             Water
             and
             other
             Fluids
             ,
             the
             lower
             parts
             are
             press'd
             by
             the
             upper
             .
             24
          
           
             Par.
             2.
             
             That
             a
             lighter
             Fluid
             may
             gravitate
             or
             weigh
             upon
             a
             heavier
             .
             43
          
           
             Par.
             3.
             
             That
             if
             a
             Body
             contignous
             to
             the
             water
             be
             altogether
             ,
             or
             in
             part
             ,
             lower
             than
             the
             highest
             level
             of
             the
             said
             water
             ,
             the
             lower
             part
             of
             the
             Body
             will
             be
             press'd
             upward
             by
             the
             water
             that
             touches
             it
             beneath
             .
             67
          
           
             Par.
             4.
             
             That
             in
             the
             ascension
             of
             water
             in
             Pumps
             ,
             &c.
             there
             needs
             nothing
             to
             raise
             the
             Water
             ,
             but
             a
             competent
             weight
             of
             an
             External
             Fluid
             .
             94
          
           
             Par.
             5.
             
             That
             the
             pressure
             of
             an
             Externall
             Fluid
             is
             able
             to
             keep
             an
             Heterogeneous
             Liquor
             suspended
             at
             the
             same
             height
             in
             several
             Pipes
             ,
             though
             those
             Pipes
             be
             of
             very
             different
             Diameters
             .
             106
          
           
             Par.
             6.
             
             If
             a
             Body
             be
             plac'd
             under
             water
             ,
             with
             its
             uppermost
             Surface
             parallel
             to
             the
             Horizon
             ;
             how
             much
             water
             soever
             there
             may
             be
             on
             this
             or
             that
             side
             aboyd
             the
             Body
             ,
             the
             direct
             pressure
             sustain'd
             by
             the
             Body
             (
             for
             we
             now
             consider
             not
             the
             Lateral
             nor
             the
             recoyling
             pressure
             ,
             to
             which
             the
             Body
             may
             be
             expos'd&
             if
             quite
             environ'd
             with
             water
             )
             is
             no
             more
             then
             that
             of
             a
             Colomne
             of
             water
             ,
             having
             the
             Horizontal
             superficies
             of
             the
             Body
             for
             its
             Basis
             ,
             and
             the
             perpendicular
             depth
             of
             the
             water
             for
             it's
             height
             .
          
           
             And
             so
             likewise
             ,
             If
             the
             water
             that
             leans
             upon
             the
             Body
             be
             contain'd
             in
             pipes
             open
             at
             both
             ends
             ;
             the
             pressure
             of
             the
             water
             is
             to
             be
             estimated
             by
             the
             weight
             of
             a
             pillar
             of
             water
             ,
             whose
             Basis
             is
             equal
             to
             the
             lower
             Orifice
             of
             the
             pipe
             ,
             (
             which
             we
             suppose
             to
             be
             parallel
             to
             the
             Horizon
             )
             and
             its
             height
             equal
             
             to
             a
             perpendicular
             reaching
             thence
             to
             the
             top
             of
             the
             water
             ;
             though
             the
             pipe
             be
             much
             inclin'd
             towards
             the
             Horizon
             ,
             or
             thought
             it
             be
             irregularly
             shap'd
             ,
             and
             much
             broader
             in
             some
             parts
             ,
             then
             the
             said
             Orifice
             .
             117
          
           
             Par.
             7.
             
             That
             a
             Body
             immers'd
             in
             a
             Fluid
             ,
             sustains
             a
             lateral
             pressure
             from
             the
             Fluid
             ▪
             and
             that
             increas'd
             ,
             as
             the
             depth
             of
             the
             immers'd
             Body
             ,
             beneath
             the
             Surface
             of
             the
             Fluid
             ,
             increaseth
             .
             142
          
           
             Par.
             8.
             
             That
             water
             may
             be
             made
             as
             well
             to
             depress
             a
             Body
             lighter
             then
             it self
             ,
             as
             to
             buoy
             it
             up
             .
             160
          
           
             Par.
             9.
             
             That
             ,
             what
             ever
             is
             said
             of
             positive
             Levity
             ,
             a
             parcel
             of
             oyle
             lighter
             then
             water
             ,
             may
             be
             kept
             in
             water
             without
             ascending
             in
             it
             .
             165
          
           
             Par.
             10.
             
             That
             the
             cause
             of
             the
             Ascension
             of
             water
             in
             Syphom
             ,
             and
             of
             its
             flowing
             through
             them
             ,
             may
             be
             explicated
             without
             having
             a
             recourse
             to
             nature's
             abhorrency
             of
             a
             Vacuum
             .
             170
          
           
             Par.
             11.
             
             That
             a
             solid
             Body
             ,
             as
             ponderous
             as
             any
             yet
             known
             ,
             though
             near
             the
             Top
             of
             the
             water
             ,
             it
             will
             sinck
             by
             in
             own
             weight
             ;
             yet
             if
             it
             be
             plac'd
             at
             a
             greater
             depth
             then
             that
             of
             twenty
             times
             its
             own
             thickness
             ▪
             it
             will
             not
             sinck
             ,
             if
             its
             descern
             be
             not
             assisted
             by
             the
             weight
             of
             the
             Incumbent
             water
             .
             184
          
           
             Appendix
             .
             1.
             
             Containing
             an
             Answer
             to
             seven
             Objections
             ,
             propos'd
             by
             a
             late
             Learned
             Writer
             ,
             to
             evince
             ,
             that
             the
             upper
             parts
             of
             water
             press
             not
             upon
             the
             lower
             .
             193
          
           
             Ap.
             2.
             
             Concerning
             the
             Reason
             why
             Divers
             ,
             &
             others
             who
             descend
             to
             the
             bottom
             of
             the
             sea
             ,
             are
             not
             oppress'd
             by
             the
             weight
             of
             the
             incumbent
             water
             .
             221
          
        
      
       
         
         
         
           Imprimatur
           ,
        
         
           
             ROBERTUS
             SAY
             ,
          
           VICE-CANCELLARIUS
           OXON
           .
        
      
    
     
       
         
         
           HYDROSTATICAL
           PARADOXES
           ,
           Made
           out
           by
           NEW
           EXPERIMENTS
           :
           Presented
           to
           the
           ROYAL
           SOCIETY
           ,
           (
           The
           Lord
           Viscount
           Brouncker
           being
           then
           President
           .
           )
           
             May
             1664.
             
          
        
         
           
             My
             LORD
             ,
          
        
         
           TO
           obey
           the
           orders
           of
           the
           Society
           ,
           that
           forbid
           the
           making
           of
           Prefaces
           and
           Apologies
           in
           Accounts
           of
           the
           Nature
           of
           that
           which
           you
           expect
           from
           me
           ;
           I
           shall
           without
           any
           further
           preamble
           begin
           with
           taking
           notice
           ,
           that
           
           upon
           perusal
           of
           Paschall's
           small
           French
           Book
           ,
           which
           was
           put
           into
           my
           hands
           ,
           I
           find
           it
           to
           consist
           of
           two
           distinct
           Treatises
           :
           The
           one
           
             of
             the
             AEquilibrium
          
           of
           Liquors
           ,
           as
           he
           calls
           it
           ;
           and
           the
           other
           
             of
             the
             weight
             of
             the
             Mass
             of
             the
             Air.
             
          
        
         
           As
           for
           this
           latter
           ,
           (
           which
           I
           shall
           mention
           first
           ,
           because
           I
           can
           in
           very
           few
           words
           dispatch
           the
           little
           I
           have
           to
           say
           of
           it
           )
           Though
           it
           be
           an
           ingenious
           discourse
           ,
           and
           containes
           things
           ,
           which
           if
           they
           had
           been
           published
           at
           the
           time
           ,
           when
           it
           is
           said
           to
           have
           been
           written
           ,
           would
           probably
           have
           been
           very
           wellcome
           to
           the
           Curious
           :
           yet
           I
           have
           very
           little
           else
           to
           say
           of
           it
           in
           this
           place
           ,
           in
           regard
           that
           since
           that
           time
           ,
           such
           kind
           of
           Experiments
           have
           been
           so
           prosecuted
           ,
           that
           I
           presume
           it
           is
           needless
           ,
           and
           would
           not
           be
           acceptable
           to
           repeat
           what
           
             Monsieur
             Paschall
          
           has
           written
           ,
           in
           this
           Society
           ,
           which
           has
           seen
           the
           same
           
           Truths
           ,
           and
           divers
           others
           of
           the
           like
           Nature
           ,
           more
           clearly
           made
           out
           by
           Experiments
           ,
           which
           could
           not
           be
           made
           by
           
             Monsieur
             Paschall
          
           ,
           and
           those
           other
           Learned
           Men
           ,
           that
           wanted
           the
           advantage
           of
           such
           Engines
           and
           Instruments
           ,
           as
           have
           in
           this
           place
           been
           frequently
           made
           use
           of
           .
        
         
           Wherefore
           having
           already
           at
           a
           former
           meeting
           given
           you
           ,
           by
           word
           of
           Mouth
           ,
           an
           account
           of
           Paschall's
           Ingenious
           Invention
           ,
           of
           a
           pair
           of
           Bellows
           without
           vent
           ,
           to
           measure
           the
           various
           Pressure
           of
           the
           Atmosphaere
           ;
           I
           remember
           nothing
           else
           that
           needs
           hinder
           me
           from
           proceeding
           to
           the
           other
           part
           of
           his
           Book
           ,
           
             The
             Treatise
             of
             the
             AEquilibrium
             of
             Liquors
             .
          
        
         
           This
           I
           find
           so
           short
           ,
           and
           so
           worthy
           of
           the
           Author
           ,
           that
           to
           give
           you
           all
           that
           I
           judge
           worth
           taking
           notice
           of
           in
           it
           ,
           would
           obliege
           me
           to
           transcribe
           almost
           the
           whole
           Tract
           ;
           and
           therefore
           I
           shall
           
           rather
           invite
           you
           to
           read
           the
           whole
           ,
           then
           divert
           you
           from
           the
           designe
           by
           culling
           out
           any
           part
           of
           it
           ;
           yet
           if
           you
           will
           not
           be
           satisfied
           without
           something
           of
           more
           particular
           ,
           I
           shall
           be
           oblig'd
           to
           tell
           you
           ,
           That
           the
           Discourse
           consisting
           partly
           of
           Conclusions
           and
           partly
           of
           Experiments
           ;
           the
           former
           seemed
           to
           me
           to
           be
           almost
           all
           of
           them
           (
           there
           being
           but
           few
           that
           I
           doubt
           of
           )
           consonant
           to
           the
           Principles
           and
           Lawes
           of
           the
           Hydrostaticks
           .
           But
           as
           for
           the
           latter
           ,
           the
           Experimental
           proofs
           he
           offers
           of
           his
           opinions
           are
           such
           ,
           that
           I
           confess
           I
           have
           no
           mind
           to
           make
           use
           of
           them
           .
        
         
           And
           the
           Reasons
           why
           ,
           notwithstanding
           that
           I
           like
           most
           of
           Paschall's
           Assertions
           ,
           I
           decline
           imploying
           his
           way
           of
           proving
           them
           ,
           are
           principally
           these
           .
        
         
           First
           ,
           Because
           though
           the
           Experiments
           he
           mentions
           be
           delivered
           in
           such
           a
           manner
           ,
           as
           is
           usual
           in
           mentioning
           
           matters
           of
           fact
           ;
           yet
           I
           remember
           not
           that
           he
           expresly
           says
           that
           he
           actually
           try'd
           them
           ,
           and
           therefore
           he
           might
           possibly
           have
           set
           them
           down
           as
           things
           that
           must
           happen
           ,
           upon
           a
           just
           confidence
           that
           he
           was
           not
           mistaken
           in
           his
           Ratiocinations
           .
           And
           of
           the
           reasonableness
           of
           this
           Doubt
           of
           mine
           ,
           I
           shall
           ere
           long
           have
           occasion
           to
           give
           an
           instance
           .
        
         
           Secondly
           ,
           Whether
           or
           no
           
             Monsieur
             Paschall
          
           ever
           made
           these
           Experiments
           himself
           ;
           he
           does
           not
           seem
           to
           have
           been
           very
           desirous
           ,
           that
           others
           should
           make
           them
           after
           him
           .
           For
           he
           supposes
           the
           Phaenomena
           he
           builds
           upon
           to
           be
           produc'd
           fifteen
           or
           twenty
           foot
           under
           water
           .
           And
           one
           of
           them
           requires
           ,
           that
           a
           Man
           should
           sit
           there
           with
           the
           End
           of
           a
           Tube
           leaning
           upon
           his
           Thigh
           .
           But
           he
           neither
           teaches
           us
           how
           a
           Man
           shall
           be
           enabled
           to
           continue
           under
           water
           ,
           nor
           how
           in
           a
           great
           Cistern
           full
           of
           
           water
           ,
           twenty
           foot
           deep
           ,
           the
           Experimenter
           shall
           be
           able
           to
           discern
           the
           alterations
           ,
           that
           happen
           to
           Mercury
           and
           other
           Bodies
           at
           the
           Bottome
           .
        
         
           And
           Thirdly
           ,
           These
           Experiments
           require
           not
           only
           Tubes
           twenty
           foot
           long
           ,
           and
           a
           great
           Vessel
           of
           at
           least
           as
           many
           feet
           in
           depth
           ,
           which
           will
           not
           in
           this
           Countrey
           be
           easily
           procured
           ,
           but
           they
           require
           Brass
           Cylinders
           ,
           or
           Pluggs
           ,
           made
           with
           an
           exactness
           ,
           that
           ,
           though
           easily
           supposed
           by
           a
           Mathematician
           ,
           will
           scarce
           be
           found
           obtainable
           from
           a
           Tradesman
           .
        
         
           These
           difficulties
           making
           the
           Experiments
           propos'd
           by
           
             Monsieur
             Paschall
          
           more
           ingenious
           then
           practicable
           ,
           I
           was
           induc'd
           on
           this
           occasion
           to
           bethink
           my self
           ▪
           of
           a
           far
           more
           Expeditious
           Way
           ,
           to
           make
           out
           ,
           not
           only
           most
           of
           the
           Conclusions
           wherein
           we
           agree
           ,
           but
           others
           that
           he
           mentions
           not
           ;
           and
           this
           with
           so
           much
           more
           ease
           and
           clearnesse
           ,
           
           That
           not
           only
           This
           Illustrious
           Assembly
           ,
           but
           persons
           no
           more
           than
           moderately
           vers'd
           in
           the
           Vulgar
           principles
           of
           the
           Hydrostaticks
           ,
           may
           easily
           enough
           apprehend
           what
           is
           design'd
           to
           be
           deliver'd
           ,
           if
           they
           will
           but
           bring
           with
           them
           a
           due
           Attention
           ,
           and
           minds
           dispos'd
           to
           preferre
           Reason
           and
           Experience
           to
           vulgar
           Opinions
           and
           Authors
           ;
           which
           last
           clause
           I
           annex
           ,
           because
           the
           following
           Discourse
           ,
           pretending
           to
           confute
           several
           of
           those
           ,
           challenges
           a
           right
           to
           except
           against
           their
           Authority
           .
        
         
           It
           not
           being
           my
           present
           Task
           to
           deliver
           the
           Elements
           ,
           or
           a
           Body
           of
           Hydrostaticks
           ,
           but
           only
           ten
           or
           twelve
           Paradoxes
           ,
           which
           I
           conceive
           to
           be
           proveable
           by
           this
           new
           way
           of
           making
           them
           out
           ,
           I
           shall
           ,
           to
           avoid
           Confusion
           ,
           Deliver
           Them
           in
           as
           many
           distinct
           propositions
           ;
           After
           each
           of
           which
           ,
           I
           shall
           indeavour
           in
           a
           proof
           ,
           or
           an
           Explication
           ,
           
           to
           show
           ,
           both
           that
           it
           is
           true
           ,
           and
           why
           it
           ought
           to
           be
           so
           .
           To
           all
           these
           I
           shall
           to
           avoid
           needless
           Repetitions
           ,
           premise
           a
           word
           or
           two
           by
           way
           either
           of
           postulatum
           or
           Lemma
           .
        
         
           And
           because
           I
           remember
           to
           what
           Assembly
           I
           address
           This
           Discourse
           ,
           I
           shall
           make
           use
           of
           no
           other
           then
           an
           easie
           supposition
           I
           met
           with
           in
           a
           short
           Paper
           (
           about
           a
           Mercuriall
           Phaenomenon
           )
           brought
           in
           a
           year
           or
           two
           since
           to
           this
           Learned
           Society
           ,
           by
           a
           deservedly
           Famous
           Member
           of
           it
           *
           ,
           For
           though
           his
           supposal
           be
           made
           upon
           occasion
           of
           an
           Experiment
           of
           another
           Nature
           ,
           then
           any
           of
           the
           ensuing
           ,
           it
           may
           be
           easily
           accomodated
           to
           my
           present
           purpose
           .
        
         
           This
           postulatum
           or
           Lemma
           ,
           consists
           of
           three
           parts
           ;
           the
           first
           of
           them
           more
           ,
           and
           the
           two
           last
           ,
           less
           principal
           .
        
         
         
           Suppose
           we
           then
           ,
           
             (
             First
          
           )
           That
           if
           a
           Pipe
           open
           at
           both
           Ends
           ,
           and
           held
           perpendicular
           to
           the
           Horizon
           ,
           have
           the
           lower
           of
           them
           under
           Water
           ,
           there
           passes
           an
           Imaginary
           plain
           or
           Surface
           ,
           which
           touching
           that
           Orifice
           is
           parallel
           to
           the
           Horizon
           ;
           and
           consequently
           parallel
           as
           to
           sense
           to
           the
           upper
           Surface
           of
           the
           water
           ,
           and
           this
           being
           but
           a
           help
           to
           the
           Imagination
           will
           readily
           be
           granted
           .
        
         
           Secondly
           ,
           To
           this
           it
           will
           be
           consonant
           ,
           that
           each
           part
           of
           this
           designable
           surface
           ,
           will
           be
           as
           much
           ,
           and
           no
           more
           press'd
           ,
           as
           any
           other
           equal
           part
           of
           it
           ,
           by
           the
           water
           that
           is
           perpendicularly
           incumbent
           on
           it
           .
           For
           the
           water
           or
           other
           Fluid
           being
           supposed
           to
           be
           of
           an
           homogeneous
           substance
           ,
           as
           to
           gravity
           ,
           and
           being
           of
           an
           equal
           height
           upon
           all
           the
           parts
           of
           the
           imaginary
           Surface
           ;
           there
           is
           no
           reason
           why
           one
           part
           should
           be
           more
           press'd
           by
           a
           perpendicular
           pillar
           of
           that
           incumbent
           fluid
           ,
           then
           any
           
           other
           equal
           part
           of
           the
           same
           Surface
           by
           another
           perpendicularly
           incumbent
           pillar
           of
           the
           same
           or
           equal
           Basis
           and
           height
           ,
           as
           well
           as
           of
           the
           same
           Liquor
           .
        
         
           But
           Thirdly
           ,
           Though
           whilst
           our
           imaginary
           Surface
           is
           equally
           press'd
           upon
           in
           all
           parts
           of
           it
           ,
           the
           Liquor
           must
           retain
           its
           former
           position
           ;
           yet
           if
           any
           one
           part
           comes
           to
           have
           a
           greater
           weight
           incumbent
           on
           it
           ,
           then
           there
           is
           upon
           the
           rest
           ,
           that
           part
           must
           be
           displac'd
           ,
           or
           depress'd
           ,
           as
           it
           happens
           ,
           when
           a
           stone
           or
           other
           Body
           heavier
           then
           water
           sincks
           in
           water
           .
           For
           wherever
           such
           a
           a
           Body
           happens
           to
           be
           underneath
           the
           water
           ,
           that
           part
           of
           the
           imaginary
           plain
           that
           is
           contiguous
           to
           the
           lower
           part
           of
           the
           stone
           ,
           having
           on
           it
           a
           greater
           weight
           then
           other
           parts
           of
           the
           same
           Surface
           ,
           must
           needs
           give
           way
           ,
           and
           this
           will
           be
           done
           successively
           till
           the
           stone
           arrive
           at
           the
           Bottom
           ;
           and
           if
           ,
           on
           the
           other
           side
           ,
           any
           part
           of
           the
           Imaginary
           Surface
           be
           
           less
           press'd
           upon
           then
           all
           the
           rest
           ;
           it
           will
           by
           the
           greater
           pressure
           on
           the
           other
           parts
           of
           the
           Surface
           be
           impell'd
           upwards
           ,
           till
           it
           have
           attain'd
           a
           height
           ,
           at
           which
           the
           pressure
           (
           of
           the
           rais'd
           water
           ,
           and
           the
           lighter
           or
           floating
           Body
           (
           if
           any
           there
           be
           )
           that
           leans
           upon
           it
           ,
           and
           gravitates
           together
           with
           it
           ,
           upon
           the
           subjacent
           part
           of
           the
           Imaginary
           Surface
           )
           will
           be
           equal
           to
           that
           which
           bears
           upon
           the
           other
           parts
           of
           the
           same
           Surface
           .
        
         
           And
           because
           this
           seems
           to
           be
           the
           likeliest
           thing
           to
           be
           Question'd
           in
           our
           Assumption
           ,
           
           though
           he
           that
           considers
           it
           attentively
           ,
           will
           easily
           enough
           be
           induc'd
           to
           grant
           it
           :
           Yet
           I
           shall
           here
           endeavour
           to
           evince
           it
           Experimentally
           ,
           and
           that
           by
           no
           other
           way
           of
           proof
           ,
           then
           the
           same
           I
           imploy
           all
           along
           this
           present
           discourse
           .
        
         
         
           Take
           then
           a
           Cylindrical
           glass
           pipe
           ▪
           of
           a
           convenient
           Bore
           open
           at
           both
           Ends
           ,
           let
           the
           Tube
           be
           steadily
           held
           perpendicular
           to
           the
           Horizon
           ,
           the
           lower
           end
           of
           it
           being
           two
           or
           three
           inches
           beneath
           the
           Surface
           of
           a
           convenient
           quantity
           of
           water
           ,
           which
           ought
           not
           to
           fill
           the
           Glass
           Vessel
           that
           contains
           it
           .
           The
           pipe
           being
           held
           in
           this
           posture
           ,
           't
           is
           manifest
           ,
           that
           the
           water
           within
           the
           pipe
           ,
           will
           be
           almost
           in
           a
           level
           with
           the
           Surface
           of
           the
           water
           without
           the
           pipe
           ,
           because
           the
           external
           and
           internal
           water
           (
           as
           I
           am
           wont
           for
           Brevities
           sake
           to
           call
           them
           )
           have
           free
           intercourse
           with
           one
           another
           by
           the
           open
           Orifice
           of
           the
           immers'd
           End
           of
           the
           pipe
           :
           yet
           I
           thought
           fit
           to
           insert
           the
           word
           almost
           ,
           because
           if
           the
           pipe
           be
           any
           thing
           slender
           ,
           the
           Surface
           of
           the
           water
           in
           it
           ,
           will
           always
           be
           somewhat
           higher
           then
           that
           of
           the
           water
           without
           it
           ,
           for
           reasons
           that
           't
           is
           not
           so
           necessary
           we
           should
           now
           inquire
           
           after
           ,
           as
           't
           is
           ,
           that
           we
           should
           here
           desire
           to
           have
           this
           taken
           notice
           of
           once
           for
           all
           ;
           That
           mistakes
           may
           be
           avoided
           without
           a
           troublesome
           repetition
           of
           the
           difference
           in
           heights
           of
           the
           Surface
           of
           Liquors
           within
           pipes
           and
           without
           them
           ,
           in
           case
           they
           be
           any
           thing
           slender
           .
        
         
           The
           pipe
           being
           held
           in
           the
           newly
           mention'd
           posture
           ,
           if
           you
           gently
           poure
           a
           convenient
           Quantity
           of
           Oyle
           upon
           the
           external
           water
           ,
           you
           shall
           see
           ,
           That
           as
           the
           Oyle
           grows
           higher
           and
           higher
           above
           the
           Surface
           of
           That
           water
           ,
           the
           water
           within
           it
           ,
           will
           rise
           higher
           and
           higher
           ,
           and
           continue
           to
           do
           so
           ,
           as
           long
           as
           you
           continue
           to
           poure
           on
           oyle
           ;
           Of
           which
           the
           Reason
           seems
           manifestly
           to
           be
           this
           ;
           That
           in
           the
           Imaginary
           plaine
           that
           passes
           by
           the
           Orifice
           of
           the
           immers'd
           end
           of
           the
           pipe
           ,
           all
           that
           is
           not
           within
           the
           Compass
           of
           the
           Orifice
           ,
           is
           expos'd
           to
           an
           additional
           pressure
           from
           
           the
           weight
           of
           the
           oyle
           which
           swims
           upon
           the
           water
           ,
           and
           that
           pressure
           must
           still
           be
           increas'd
           ,
           as
           there
           is
           more
           and
           more
           oyle
           poured
           on
           ;
           whereas
           a
           Circular
           part
           of
           the
           Imaginary
           plain
           ,
           equal
           to
           the
           Orifice
           of
           the
           Glasse
           ,
           is
           by
           the
           sides
           of
           the
           pipe
           fenc'd
           from
           the
           immediate
           pressure
           of
           the
           oyle
           ;
           so
           that
           all
           those
           other
           parts
           of
           the
           water
           ,
           being
           far
           more
           press'd
           ,
           then
           that
           part
           which
           is
           comprehended
           within
           the
           Cavity
           of
           the
           Tube
           :
           and
           consequently
           the
           press'd
           parts
           of
           the
           external
           water
           ,
           are
           by
           the
           equal
           gravitation
           of
           the
           oyle
           ,
           upon
           the
           parts
           of
           the
           external
           water
           ,
           impell'd
           up
           into
           the
           Cavity
           of
           the
           pipe
           ,
           where
           they
           find
           less
           resistance
           ,
           then
           any
           where
           else
           ,
           till
           they
           arrive
           at
           such
           a
           height
           ,
           that
           the
           Cylinder
           of
           water
           ,
           within
           the
           pipe
           ,
           do's
           as
           much
           gravitate
           upon
           the
           subjacent
           part
           of
           the
           Imaginary
           Surface
           ,
           as
           the
           water
           and
           oyle
           together
           ,
           do
           upon
           every
           other
           
           equal
           part
           of
           the
           same
           Surface
           or
           plain
           .
        
         
           But
           as
           well
           the
           former
           Lemma
           ,
           as
           this
           Experiment
           ,
           will
           be
           sufficiently
           both
           clear'd
           and
           confirm'd
           by
           the
           following
           Explications
           ;
           to
           which
           I
           should
           for
           that
           Reason
           forthwith
           proceed
           ;
           Were
           it
           not
           that
           ,
           since
           divers
           passages
           of
           the
           following
           Treatise
           suppose
           the
           Aire
           to
           be
           a
           Body
           not
           devoid
           of
           weight
           ,
           which
           yet
           divers
           Learned
           adherents
           to
           the
           Peripatetick
           Philosophy
           do
           resolutely
           deny
           ,
           it
           seems
           requisite
           to
           premise
           something
           for
           the
           proof
           of
           this
           Truth
           .
        
         
           And
           though
           I
           think
           the
           Arguments
           we
           have
           imploy'd
           to
           that
           purpose
           already
           ,
           do
           strongly
           evince
           it
           :
           yet
           if
           I
           may
           be
           allow'd
           to
           anticipate
           one
           of
           my
           own
           Experiments
           of
           the
           Appendix
           ,
           I
           shall
           give
           an
           instance
           of
           the
           weight
           of
           the
           Aire
           ,
           not
           lyable
           so
           much
           as
           to
           those
           invalid
           objections
           ,
           which
           
             some
             of
          
           the
           Aristotelians
           have
           made
           against
           those
           
           Proofs
           ,
           wherewith
           we
           have
           been
           so
           happy
           ,
           as
           to
           satisfie
           the
           learned'st
           even
           of
           our
           professed
           Adversaries
           .
        
         
           We
           caus'd
           then
           to
           be
           blown
           at
           the
           flame
           of
           a
           Lamp
           ,
           a
           Bubble
           of
           glass
           ,
           (
           of
           about
           the
           bigness
           of
           a
           small
           Hen-egge
           )
           which
           ,
           that
           it
           might
           be
           light
           enough
           to
           be
           weigh'd
           in
           exact
           Scales
           ,
           ought
           to
           be
           of
           no
           greater
           thickness
           ,
           then
           is
           judged
           necessary
           to
           keep
           it
           from
           being
           (
           when
           seal'd
           up
           with
           none
           but
           very
           much
           expanded
           aire
           in
           it
           )
           broken
           by
           the
           pressure
           of
           the
           ambient
           Atmosphaere
           .
           This
           bubble
           was
           (
           like
           a
           Peare
           with
           its
           stemme
           )
           furnish'd
           with
           a
           very
           slender
           pipe
           of
           Glass
           ,
           at
           which
           it
           was
           blown
           ,
           that
           it
           might
           be
           readily
           seald
           up
           ;
           and
           then
           (
           the
           Aire
           within
           it
           being
           by
           the
           flame
           of
           the
           Lamp
           gradually
           rarified
           ,
           as
           much
           as
           conveniently
           could
           be
           )
           whilst
           the
           Body
           of
           the
           Bubble
           was
           exceeding
           hot
           ,
           the
           newly
           mentioned
           stemme
           was
           nimbly
           put
           into
           
           the
           middle
           of
           the
           flame
           ;
           where
           ,
           by
           reason
           of
           its
           slenderness
           ,
           the
           Glass
           ,
           which
           was
           exceeding
           thin
           ,
           was
           immediately
           melted
           ;
           whereby
           the
           Bubble
           was
           Hermetically
           seal'd
           up
           .
           This
           Glass
           being
           permitted
           leasurely
           to
           coole
           ,
           I
           could
           afterwards
           keep
           it
           by
           me
           an
           hour
           ,
           or
           a
           day
           ,
           or
           a
           week
           ,
           or
           longer
           ,
           if
           I
           thought
           fit
           ;
           and
           when
           I
           had
           a
           mind
           to
           shew
           the
           Experiment
           ,
           I
           put
           it
           in
           one
           of
           the
           scales
           of
           an
           exact
           ballance
           ,
           that
           would
           turn
           ,
           perhaps
           with
           the
           30th
           ,
           or
           50th
           ,
           or
           a
           lesse
           part
           of
           a
           grain
           ;
           and
           having
           carefully
           counterpois'd
           it
           ,
           I
           then
           warily
           broke
           off
           the
           seal'd
           end
           ,
           placing
           a
           sheet
           of
           paper
           just
           under
           the
           scale
           to
           receive
           the
           fragments
           of
           the
           Glass
           :
           and
           putting
           in
           again
           those
           fragments
           ,
           that
           scale
           wherein
           the
           Glass
           was
           would
           considerably
           preponderate
           ;
           which
           it
           must
           do
           upon
           the
           account
           of
           the
           Weight
           of
           Aire
           ,
           there
           being
           no
           other
           cause
           ,
           either
           
           needful
           ,
           or
           justly
           assignable
           ,
           but
           the
           weight
           of
           the
           Aire
           that
           rush'd
           into
           the
           Cavity
           of
           the
           Glass
           ,
           as
           finding
           less
           resistance
           there
           then
           elsewhere
           ,
           by
           reason
           that
           the
           included
           Aire
           had
           it's
           spring
           much
           weakn'd
           by
           it's
           great
           expansion
           .
        
         
           This
           Experiment
           I
           many
           times
           tryed
           ,
           sometimes
           before
           some
           Virtuosi
           ,
           and
           sometimes
           before
           others
           ;
           who
           all
           allowed
           it
           to
           be
           conclusive
           .
           For
           here
           it
           could
           not
           be
           objected
           as
           against
           the
           weighing
           of
           Aire
           in
           a
           Bladder
           ,
           (
           which
           objections
           yet
           I
           could
           easily
           answer
           ,
           if
           it
           were
           now
           proper
           )
           that
           the
           aire
           which
           ponderates
           ,
           it
           stuff'd
           with
           the
           Effluvia
           of
           him
           that
           blows
           the
           Bladder
           ,
           and
           (
           besides
           that
           )
           is
           not
           aire
           in
           its
           Natural
           state
           ,
           but
           violently
           compress'd
           .
           For
           here
           't
           is
           the
           free
           aire
           ,
           and
           in
           it's
           wonted
           laxity
           ,
           that
           makes
           the
           Glass
           preponderate
           .
        
         
           And
           that
           there
           is
           a
           great
           Ingress
           of
           
           the
           external
           aire
           ,
           is
           evident
           by
           these
           three
           Phaenomena
           .
           The
           one
           ,
           that
           if
           you
           lend
           an
           attentive
           Ear
           ,
           you
           shall
           plainly
           heare
           a
           kind
           of
           whistling
           noise
           to
           be
           made
           by
           the
           external
           aire
           ,
           as
           it
           rushes
           violently
           in
           upon
           the
           breaking
           of
           the
           Glass
           ;
           The
           other
           ,
           that
           the
           Rarefaction
           of
           the
           aire
           ,
           seal'd
           up
           in
           the
           bubble
           ,
           being
           very
           great
           ,
           there
           is
           a
           great
           deal
           of
           space
           left
           for
           the
           ambient
           aire
           to
           fill
           upon
           its
           admission
           ;
           and
           the
           greatness
           of
           this
           Rarefaction
           may
           be
           guess'd
           at
           ,
           both
           by
           the
           breaking
           of
           such
           bubbles
           now
           and
           then
           by
           the
           pressure
           of
           the
           External
           aire
           ,
           which
           is
           not
           competently
           assisted
           by
           the
           Internal
           to
           resist
           ;
           and
           also
           by
           the
           third
           Phaenomenon
           I
           intended
           to
           take
           notice
           of
           ,
           namely
           ,
           That
           if
           ,
           instead
           of
           breaking
           off
           the
           seal'd
           end
           of
           the
           Glass
           in
           the
           aire
           ,
           you
           break
           it
           under
           water
           ,
           that
           Liquor
           will
           ,
           by
           the
           Pressure
           of
           the
           Atmosphaere
           ,
           be
           forc'd
           to
           spring
           up
           like
           an
           artificial
           Fountaine
           
           into
           the
           Cavity
           of
           the
           Bubble
           ,
           and
           fill
           about
           three
           quarters
           of
           it
           .
           By
           which
           last
           circumstance
           I
           gather
           ,
           that
           the
           weight
           of
           the
           aire
           is
           more
           considerable
           then
           ev'n
           many
           ,
           who
           admit
           the
           aire
           to
           have
           weight
           ,
           seem
           to
           imagine
           .
           For
           we
           must
           not
           suppose
           ,
           that
           all
           the
           aire
           contain'd
           in
           the
           Bubble
           ,
           when
           broken
           ,
           weighs
           no
           more
           then
           the
           weight
           requisite
           in
           the
           opposite
           Scale
           ,
           to
           reduce
           the
           Ballance
           to
           an
           Aequilibrium
           ;
           since
           this
           additional
           weight
           is
           onely
           that
           of
           the
           aire
           ,
           that
           intrudes
           on
           the
           breaking
           of
           the
           glass
           ;
           which
           aire
           ,
           by
           the
           Observations
           newly
           mention'd
           to
           have
           been
           made
           with
           water
           ,
           appears
           to
           be
           but
           about
           three
           quarters
           of
           the
           whole
           aire
           contain'd
           in
           the
           broken
           Bubble
           ;
           and
           yet
           ,
           according
           both
           to
           our
           Estimate
           ,
           and
           that
           of
           divers
           Virtuosi
           ,
           and
           some
           of
           them
           eminent
           Mathematicians
           ,
           when
           the
           capacity
           of
           the
           Bubble
           was
           short
           of
           two
           cubical
           Inches
           ,
           (
           and
           so
           proportionably
           
           in
           other
           glasses
           ,
           )
           the
           nice
           Ballance
           we
           us'd
           ,
           manifested
           the
           newly
           admitted
           Aire
           to
           amount
           to
           some
           times
           near
           halfe
           a
           grain
           ,
           and
           sometimes
           beyond
           it
           .
        
         
           And
           because
           one
           of
           the
           last
           Experiments
           that
           I
           made
           to
           this
           purpose
           ,
           with
           seal'd
           Bubbles
           was
           none
           of
           the
           least
           accurate
           ,
           I
           shall
           conclude
           this
           Subject
           with
           the
           following
           account
           of
           it
           .
        
         
           A
           thin
           glass
           Bubble
           ,
           blown
           at
           the
           flame
           of
           a
           Lamp
           ,
           and
           Hermetically
           seal'd
           when
           the
           contained
           aire
           was
           exceedingly
           rarified
           ,
           was
           Counterpoiz'd
           in
           a
           nice
           paire
           of
           Scales
           ,
           and
           then
           the
           seal'd
           apex
           being
           broken
           off
           ,
           and
           put
           again
           into
           the
           same
           Scale
           ,
           the
           weight
           appear'd
           to
           be
           increas'd
           by
           the
           re-admitted
           aire
           ,
           a
           pretty
           deal
           above
           11
           /
           16
           ;
           ths
           ,
           and
           consequently
           very
           near
           ,
           if
           not
           full
           ¾
           of
           a
           graine
           :
           Lastly
           ,
           having
           by
           some
           slight
           (
           for
           't
           is
           no
           very
           easie
           matter
           )
           fill'd
           it
           
           with
           common
           water
           ,
           we
           weigh'd
           the
           glass
           and
           water
           together
           ,
           and
           found
           the
           latter
           ,
           besides
           the
           former
           ,
           to
           amount
           to
           906
           grains
           :
           so
           that
           supposing
           ,
           according
           to
           our
           former
           Estimate
           ,
           countenanced
           by
           some
           Tryals
           ,
           that
           the
           re-admitted
           aire
           ,
           which
           amounted
           to
           ¾
           of
           a
           grain
           ,
           fill'd
           but
           ¾
           of
           the
           whole
           Cavity
           of
           the
           Bubble
           ,
           the
           aire
           that
           was
           in
           it
           ,
           when
           seal'd
           ,
           possessing
           one
           quarter
           of
           that
           Cavity
           ,
           the
           whole
           aire
           contain'd
           in
           the
           Bubble
           ,
           may
           be
           reasonably
           presum'd
           to
           weigh
           a
           whole
           grain
           ;
           in
           which
           case
           we
           might
           conclude
           (
           abstracting
           from
           some
           little
           Niceties
           not
           fit
           to
           be
           taken
           notice
           of
           here
           ;
           as
           elsewhere
           )
           that
           the
           water
           in
           our
           Experiment
           ,
           weighed
           very
           little
           more
           then
           nine
           hundred
           times
           as
           much
           as
           an
           equal
           quantity
           of
           Aire
           .
           And
           therefore
           ,
           though
           we
           allow
           ,
           that
           in
           an
           Experiment
           so
           diligently
           made
           ,
           as
           this
           was
           ,
           the
           aire
           praexistent
           in
           the
           bubble
           did
           not
           adaequately
           possess
           so
           much
           
           as
           a
           fourth
           part
           ,
           but
           about
           a
           fifth
           or
           a
           sixth
           of
           its
           Cavity
           ,
           the
           aire
           will
           yet
           appear
           so
           heavy
           ,
           that
           this
           Experiment
           will
           agree
           well
           with
           those
           others
           ,
           recorded
           in
           another
           Treatise
           ,
           wherein
           we
           assign'd
           
             (
             numero
             rotundo
          
           )
           a
           thousand
           to
           one
           ,
           for
           the
           proportion
           wherein
           the
           specifick
           Gravity
           of
           water
           exceeds
           that
           of
           aire
           .
        
         
           
           
             PARADOX
             I.
             
          
           
             That
             in
             Water
             ,
             and
             other
             Fluids
             ,
             the
             lower
             parts
             are
             press'd
             by
             the
             upper
             .
          
           
             PRovide
             a
             Glass
             vessel
             of
             a
             convenient
             height
             and
             breadth
             A.
             B.
             C.
             D.
             fill'd
             with
             water
             almost
             to
             the
             Top
             ;
             Then
             take
             a
             glass
             Pipe
             ,
             open
             at
             both
             Ends
             ,
             Cylindrical
             ,
             and
             of
             a
             small
             Bore
             ,
             (
             as
             about
             the
             eighth
             or
             sixth
             part
             of
             an
             Inch
             in
             Diameter
             .
             )
             Put
             the
             lower
             End
             of
             this
             Pipe
             into
             clear
             Oyle
             or
             Spirit
             of
             Turpentine
             ;
             and
             having
             by
             Suction
             rais'd
             the
             Liquor
             to
             what
             part
             of
             the
             Pipe
             you
             think
             fit
             ,
             as
             soon
             as
             it
             is
             there
             ,
             you
             must
             ,
             very
             nimbly
             removing
             your
             Lips
             ,
             stop
             the
             upper
             Orifice
             with
             the
             pulp
             of
             your
             finger
             ,
             that
             the
             rais'd
             Liquor
             may
             not
             fall
             back
             again
             :
             Then
             
             taking
             the
             Pipe
             and
             that
             Liquor
             out
             of
             the
             Oyle
             of
             Turpentine
             ,
             place
             it
             perpendicularly
             in
             the
             Glass
             of
             water
             ,
             so
             as
             that
             the
             Surface
             of
             the
             Oyle
             in
             the
             Pipe
             be
             somewhat
             higher
             then
             that
             of
             the
             water
             without
             the
             Pipe
             ;
             and
             having
             so
             done
             ,
             though
             you
             take
             off
             your
             finger
             from
             the
             upper
             Orifice
             of
             the
             Pipe
             ,
             the
             Oyle
             will
             not
             fall
             down
             at
             the
             lower
             Orifice
             ,
             though
             that
             be
             open
             ,
             but
             will
             remain
             suspended
             at
             the
             same
             height
             ,
             or
             near
             there
             abouts
             ,
             that
             it
             rested
             at
             before
             .
          
           
             Now
             Oyle
             of
             Turpentine
             ,
             being
             a
             heavy
             Fluid
             ,
             does
             ,
             as
             such
             ,
             tend
             downwards
             ,
             and
             not
             being
             stopp'd
             by
             the
             Glass
             it self
             ,
             whose
             lower
             Orifice
             is
             left
             open
             ,
             it
             would
             certainly
             fall
             down
             through
             the
             Pipe
             ,
             if
             it
             were
             not
             kept
             suspended
             by
             the
             pressure
             (
             upwards
             )
             of
             the
             water
             beneath
             it
             .
             There
             appearing
             no
             other
             Cause
             to
             which
             the
             Effect
             can
             reasonably
             be
             ascrib'd
             ,
             and
             this
             being
             
             sufficient
             to
             give
             an
             Account
             of
             it
             ,
             as
             we
             shall
             presently
             see
             .
             For
             that
             it
             is
             not
             any
             contrariety
             in
             Nature
             ,
             betwixt
             the
             oyle
             and
             the
             water
             ,
             as
             Liquors
             that
             will
             not
             mingle
             ,
             is
             evident
             from
             hence
             ,
             That
             if
             you
             had
             remov'd
             your
             finger
             when
             the
             Pipe
             was
             not
             so
             deeply
             immers'd
             in
             the
             Glass
             ,
             but
             that
             the
             Surface
             of
             the
             oyl
             in
             the
             Pipe
             was
             an
             Inch
             or
             two
             more
             elevated
             above
             that
             of
             the
             water
             in
             the
             Glass
             ,
             then
             in
             our
             present
             case
             we
             suppose
             it
             to
             be
             ;
             The
             Oyle
             ,
             notwithstanding
             its
             presum'd
             contrariety
             to
             water
             ,
             would
             have
             freely
             subsided
             in
             the
             Pipe
             ,
             till
             it
             had
             attain'd
             an
             aequipollency
             of
             pressure
             with
             the
             External
             Water
             .
          
           
             The
             Reason
             therefore
             of
             the
             Phaenomenon
             seems
             to
             be
             plainly
             this
             .
             Supposing
             the
             imaginary
             surface
             ,
             on
             which
             the
             Extremity
             Q
             of
             the
             pipe
             
               P
               Q
            
             leans
             ,
             to
             be
             
               G
               H.
            
             If
             that
             part
             of
             the
             Surface
             ,
             on
             which
             the
             Oyl
             leans
             at
             Q
             ,
             be
             as
             much
             ,
             and
             no
             more
             charged
             ,
             or
             press'd
             upon
             
             by
             the
             weight
             of
             the
             incumbent
             Cylinder
             of
             Oyle
             
               Q
               X
            
             ,
             then
             the
             other
             parts
             of
             the
             same
             imaginary
             Surface
             
               G
               H
            
             are
             by
             the
             water
             incumbent
             on
             Them
             ,
             there
             is
             no
             Reason
             why
             that
             part
             at
             Q
             should
             be
             displac'd
             ,
             either
             by
             being
             depress'd
             by
             the
             weight
             of
             the
             Cylinder
             of
             Oyle
             
               X
               Q
            
             ,
             or
             rais'd
             by
             the
             equal
             pressure
             of
             water
             upon
             the
             other
             parts
             of
             the
             Superficies
             
               G
               H.
            
             
          
           
             And
             that
             this
             Aequilibrium
             ,
             betwixt
             the
             Oyle
             and
             the
             Water
             ,
             is
             the
             true
             cause
             of
             the
             Phaenomenon
             ,
             may
             be
             confirm'd
             by
             observing
             what
             happens
             ,
             if
             the
             altitude
             of
             either
             of
             the
             two
             Liquors
             be
             alter'd
             in
             Relation
             to
             the
             other
             .
          
           
             And
             
               (
               First
               ,
            
             )
             we
             have
             already
             taken
             notice
             ,
             That
             if
             the
             Cylinder
             of
             Oyle
             reach
             in
             the
             Pipe
             ,
             much
             higher
             then
             that
             of
             the
             Surface
             of
             the
             water
             ,
             the
             oyle
             will
             descend
             :
             Of
             which
             the
             Reason
             is
             ,
             Because
             the
             designable
             Surface
             
               G
               H
            
             ,
             being
             more
             charg'd
             at
             Q
             then
             
             any
             where
             else
             ,
             the
             part
             Q
             ,
             being
             unable
             to
             resist
             so
             great
             a
             pressure
             ,
             must
             necessarily
             be
             thrust
             out
             of
             place
             by
             the
             descending
             oyle
             .
          
           
             Secondly
             ,
             This
             subsiding
             will
             continue
             but
             till
             the
             Surface
             of
             the
             Oyle
             in
             the
             Pipe
             be
             fallen
             almost
             as
             low
             as
             that
             of
             the
             water
             without
             the
             Pipe
             ;
             because
             then
             ,
             and
             not
             before
             ,
             the
             parts
             at
             Q
             are
             but
             as
             much
             press'd
             by
             the
             oyle
             ,
             as
             the
             other
             parts
             of
             the
             Surface
             
               G
               H
            
             are
             by
             the
             water
             that
             leans
             upon
             them
             .
          
           
             Thirdly
             ,
             'T
             is
             a
             concluding
             Circumstance
             to
             our
             present
             purpose
             ,
             That
             if
             the
             Oyle
             and
             Water
             being
             in
             an
             Aequilibrium
             ,
             you
             gently
             lift
             up
             the
             Pipe
             ,
             as
             from
             Q
             to
             S
             ,
             the
             depth
             of
             the
             water
             being
             lessend
             ,
             the
             oyle
             in
             the
             Pipe
             will
             grow
             praeponderant
             ,
             and
             therefore
             will
             fall
             out
             in
             Drops
             or
             Globuls
             ,
             which
             by
             the
             greater
             Specifick
             Gravity
             of
             the
             water
             ,
             will
             be
             buoy'd
             up
             to
             the
             Top
             of
             the
             Liquor
             ,
             and
             there
             flote
             :
             And
             
             still
             as
             you
             lift
             up
             the
             Pipe
             higher
             and
             higher
             ,
             towards
             the
             Surface
             
               L
               M
            
             ,
             more
             and
             more
             of
             the
             Oyle
             will
             run
             out
             .
             But
             if
             you
             stop
             the
             Pipe
             any
             where
             in
             its
             Ascent
             ,
             as
             at
             S
             ,
             the
             Effluxion
             of
             the
             oyle
             will
             likewise
             be
             stopp'd
             .
             And
             at
             the
             imaginary
             Superficies
             ▪
             
               J
               K
            
             ,
             as
             by
             Reason
             of
             the
             shallowness
             of
             the
             water
             from
             L
             to
             J
             ,
             or
             M
             to
             K
             ,
             the
             pressure
             of
             the
             water
             upon
             the
             other
             parts
             of
             the
             Surface
             is
             not
             near
             so
             great
             ,
             as
             it
             was
             upon
             the
             Surface
             
               G
               H
            
             ,
             where
             the
             water
             had
             a
             greater
             depth
             :
             So
             by
             reason
             of
             the
             proportionate
             Effluxion
             of
             the
             oyle
             ,
             whil'st
             the
             Pipe
             was
             lifted
             up
             from
             Q
             to
             S
             ,
             the
             remaining
             Cylinder
             of
             oyle
             incumbent
             on
             S
             ,
             is
             not
             able
             to
             press
             that
             part
             of
             the
             Superficies
             
               J
               K
            
             more
             strongly
             then
             the
             other
             parts
             of
             the
             same
             Superficies
             ,
             are
             prest
             by
             the
             water
             Incumbent
             on
             them
             .
             And
             if
             the
             Pipe
             be
             lifted
             up
             till
             the
             lower
             Orifice
             be
             almost
             rais'd
             to
             V
             ;
             that
             is
             ,
             almost
             
             as
             high
             as
             the
             uppermost
             Surface
             of
             the
             water
             
               L
               M
            
             ,
             so
             much
             of
             the
             oyle
             will
             ,
             for
             the
             Reason
             already
             given
             ,
             run
             out
             ,
             that
             there
             will
             scarce
             be
             any
             left
             in
             the
             Pipe
             
               T
               V.
            
             
          
           
             Fourthly
             ,
             But
             if
             when
             the
             Pipe
             rests
             at
             the
             Surface
             
               G
               H
            
             ,
             where
             the
             oyle
             is
             in
             an
             Aequilibrium
             with
             the
             water
             ;
             you
             should
             instead
             of
             lifting
             it
             from
             Q
             to
             S
             ,
             thrust
             it
             down
             from
             Q
             to
             O
             ;
             then
             the
             External
             water
             would
             not
             only
             sustaine
             the
             oyle
             ,
             but
             make
             it
             ascend
             in
             the
             Pipe
             to
             a
             height
             equal
             to
             the
             distance
             
               E
               G
            
             ;
             and
             so
             the
             Pipe
             will
             containe
             besides
             a
             longer
             Cylinder
             of
             oyle
             
               AE
               W
            
             ,
             a
             shorter
             one
             of
             water
             
               AE
               O.
            
             For
             the
             pipe
             being
             transferr'd
             from
             the
             position
             
               P
               Q
            
             ,
             to
             the
             position
             
               O
               N
            
             ,
             there
             is
             a
             new
             Imaginary
             Surface
             
               E
               F
            
             ,
             that
             passes
             by
             the
             lower
             Orifice
             of
             the
             Pipe.
             Now
             the
             part
             of
             this
             Surface
             at
             O
             will
             not
             ,
             by
             the
             Incumbent
             oyle
             alone
             ,
             be
             press'd
             as
             much
             as
             the
             other
             parts
             of
             the
             same
             
             Surface
             are
             by
             the
             Incumbent
             water
             .
             For
             the
             oyl
             alone
             was
             but
             in
             Aequilibrium
             with
             the
             water
             ,
             when
             it
             was
             no
             deeper
             then
             
               L
               G
            
             ,
             or
             
               H
               M
            
             ;
             so
             that
             the
             other
             parts
             of
             the
             Superficies
             
               E
               F
            
             ,
             being
             more
             press'd
             upon
             by
             the
             water
             ,
             then
             the
             part
             at
             O
             by
             the
             oyle
             ,
             the
             oyle
             must
             give
             place
             ,
             and
             be
             buoy'd
             up
             by
             the
             water
             ,
             (
             which
             ,
             if
             it
             were
             not
             for
             the
             weight
             of
             the
             oyle
             ,
             would
             be
             impell'd
             up
             into
             the
             pipe
             full
             as
             high
             as
             the
             Surface
             of
             the
             External
             water
             )
             till
             the
             pressure
             of
             the
             admitted
             water
             
               O
               AE
            
             ,
             and
             the
             Cylinder
             of
             oyle
             
               AE
               W
            
             ,
             do
             both
             together
             gravitate
             as
             much
             upon
             the
             part
             O
             ,
             as
             the
             rest
             of
             the
             Incumbent
             water
             does
             upon
             the
             other
             parts
             of
             the
             same
             Superficies
             
               E
               F.
            
             
          
           
             Fifthly
             and
             lastly
             ,
             'T
             is
             very
             agreeable
             to
             what
             has
             been
             delivered
             ,
             touching
             the
             Aequilibrium
             of
             the
             oyle
             and
             water
             in
             the
             pipe
             
               P
               Q
            
             ,
             that
             the
             Surface
             X
             of
             the
             oyle
             in
             the
             pipe
             ,
             will
             not
             
             be
             of
             the
             same
             level
             with
             
               L
               M
            
             ,
             that
             of
             the
             External
             water
             ,
             but
             a
             little
             higher
             than
             it
             .
             For
             though
             the
             slenderness
             of
             the
             Pipe
             do
             somewhat
             contribute
             to
             this
             Effect
             ,
             yet
             there
             would
             be
             an
             inequality
             ,
             though
             not
             so
             great
             ,
             betwixt
             these
             Surfaces
             upon
             this
             Account
             ,
             That
             oyle
             of
             Turpentine
             being
             in
             Specie
             ,
             (
             as
             they
             speak
             in
             the
             Schools
             )
             that
             is
             bulk
             for
             bulk
             ,
             a
             lighter
             Liquor
             than
             Water
             ,
             it
             is
             requisite
             that
             the
             height
             of
             it
             ,
             incumbent
             on
             the
             part
             Q
             ,
             be
             greater
             than
             that
             of
             the
             water
             on
             the
             other
             parts
             of
             the
             same
             Surface
             
               G
               H
            
             ,
             to
             make
             the
             pressure
             of
             the
             oyle
             on
             the
             part
             it
             leans
             upon
             ,
             equal
             to
             the
             pressure
             of
             the
             water
             on
             the
             other
             parts
             of
             the
             Surface
             .
             And
             if
             the
             inequality
             were
             greater
             betwixt
             the
             Specifick
             Gravities
             of
             these
             two
             Liquors
             ,
             the
             inequalities
             betwixt
             the
             Surface
             X
             ,
             and
             the
             Surface
             
               L
               M
            
             would
             be
             also
             greater
             ,
             as
             may
             be
             try'd
             by
             substituting
             for
             common
             
             water
             ,
             oyle
             of
             Tartar
             
               per
               deliquium
            
             ,
             which
             is
             a
             saline
             Liquor
             much
             heavier
             than
             it
             .
             And
             that
             ,
             in
             case
             the
             Pipe
             containe
             not
             a
             lighter
             Liquor
             then
             the
             External
             fluid
             ,
             the
             Surface
             of
             the
             Liquor
             in
             the
             Pipe
             will
             not
             be
             higher
             than
             that
             of
             the
             Liquor
             without
             it
             ,
             we
             shall
             by
             and
             by
             have
             opportunity
             to
             manifest
             by
             Experience
             .
          
           
             From
             what
             has
             been
             hitherto
             shewen
             ,
             we
             may
             safely
             infer
             the
             Proposition
             ,
             upon
             whose
             occasion
             all
             this
             has
             been
             delivered
             .
             For
             since
             the
             oyle
             in
             a
             Pipe
             ,
             open
             at
             both
             Ends
             ,
             may
             be
             kept
             suspended
             in
             any
             part
             under
             water
             ,
             as
             at
             Q
             ,
             because
             it
             is
             there
             in
             an
             Aequilibrium
             with
             the
             External
             water
             ;
             and
             since
             being
             lifted
             up
             in
             the
             water
             ,
             as
             from
             Q
             to
             S
             ,
             the
             oyle
             can
             no
             longer
             be
             kept
             suspended
             ,
             but
             by
             its
             own
             gravity
             will
             runne
             out
             .
             And
             since
             ,
             in
             a
             word
             ,
             the
             deeper
             the
             water
             is
             ,
             the
             greater
             weight
             and
             pressure
             is
             requir'd
             in
             the
             Cylinder
             of
             
             oyle
             ,
             to
             be
             able
             to
             countervail
             the
             pressure
             of
             the
             water
             ,
             and
             keep
             it self
             from
             being
             lifted
             up
             thereby
             ;
             there
             seems
             no
             cause
             to
             doubt
             but
             that
             the
             parts
             of
             the
             water
             incumbent
             on
             the
             Superficies
             
               G
               H
            
             ,
             do
             more
             press
             that
             Superficies
             ,
             than
             the
             parts
             of
             the
             water
             contiguous
             to
             the
             Superficies
             
               J
               K
            
             do
             press
             that
             ;
             and
             consequently
             ,
             that
             the
             parts
             of
             the
             water
             that
             are
             under
             the
             uppermost
             Surface
             of
             it
             ,
             are
             press'd
             by
             those
             of
             the
             same
             Fluid
             that
             are
             directly
             over
             them
             :
             As
             we
             saw
             also
             that
             the
             upper
             parts
             of
             the
             oyle
             ,
             whil'st
             the
             pipe
             was
             in
             raising
             from
             Q
             to
             S
             ,
             depress'd
             the
             lower
             so
             much
             ,
             as
             to
             force
             them
             quite
             out
             of
             the
             Pipe
             ;
             there
             being
             in
             these
             cases
             no
             reason
             why
             the
             lowermost
             parts
             of
             a
             Liquor
             should
             press
             more
             ,
             or
             have
             a
             stronger
             Endeavour
             against
             any
             other
             Liquor
             (
             or
             any
             other
             Body
             )
             the
             higher
             the
             Liquor
             incumbent
             reaches
             ,
             if
             these
             inferiour
             parts
             deriv'd
             their
             pessure
             only
             
             from
             their
             own
             particular
             Gravity
             ,
             (
             which
             is
             no
             greater
             then
             that
             of
             the
             other
             Homogeneous
             parts
             of
             the
             Liquor
             )
             and
             therefore
             they
             must
             derive
             the
             great
             force
             wherewith
             they
             press
             from
             the
             weight
             of
             the
             Incumbent
             parts
             ,
             which
             consequently
             must
             be
             allow'd
             to
             press
             upon
             them
             .
          
           
             But
             before
             I
             proceed
             to
             the
             following
             propositions
             ,
             it
             will
             not
             be
             amiss
             to
             mention
             here
             ,
             once
             for
             all
             ,
             a
             few
             advertisements
             ,
             to
             avoid
             the
             necessity
             of
             repeating
             the
             same
             things
             in
             the
             sequel
             of
             the
             Discourse
             .
          
           
             And
             First
             ,
             What
             is
             here
             said
             of
             the
             pressure
             of
             the
             parts
             of
             water
             upon
             one
             another
             ,
             and
             the
             other
             Affections
             that
             we
             shall
             attribute
             to
             it
             ,
             in
             the
             following
             paper
             ,
             are
             to
             be
             apply'd
             to
             heavy
             Fluids
             in
             general
             ,
             unless
             there
             shall
             appear
             some
             particular
             Cause
             of
             excepting
             some
             of
             them
             in
             particular
             Cases
             .
          
           
             Secondly
             ,
             Whereas
             I
             lately
             intimated
             ,
             
             That
             the
             inequality
             betwixt
             the
             Surfaces
             of
             the
             oyle
             in
             the
             Pipe
             ,
             and
             of
             the
             External
             water
             ,
             was
             in
             part
             to
             be
             ascrib'd
             to
             the
             slenderness
             of
             the
             Pipe
             ,
             to
             be
             imploy'd
             in
             these
             Experiments
             ,
             I
             did
             it
             for
             this
             cause
             ,
             that
             ,
             whatever
             the
             Reason
             of
             it
             be
             ,
             (
             which
             we
             need
             not
             here
             inquire
             after
             ,
             )
             we
             are
             assur'd
             by
             Experience
             ,
             as
             we
             have
             elsewhere
             shewn
             ,
             That
             when
             Glass
             pipes
             come
             to
             be
             slender
             ,
             water
             and
             many
             other
             Liquors
             (
             though
             not
             Quicksilver
             )
             will
             have
             within
             them
             a
             higher
             Surface
             then
             that
             of
             the
             same
             Liquor
             without
             them
             ,
             and
             this
             inequality
             of
             Surfaces
             (
             as
             far
             as
             we
             have
             yet
             try'd
             )
             increases
             with
             the
             slenderness
             of
             the
             pipe
             .
             But
             this
             ,
             as
             to
             our
             present
             Experiment
             ,
             is
             a
             matter
             of
             so
             little
             moment
             ,
             That
             it
             may
             suffice
             to
             have
             intimated
             that
             we
             did
             not
             oversee
             it
             .
          
           
             Thirdly
             ,
             Wherefore
             ,
             notwithstanding
             this
             little
             inconvenience
             of
             slender
             
             Glasses
             ,
             we
             think
             it
             Expedient
             to
             imploy
             such
             in
             the
             following
             Experiments
             ,
             because
             we
             found
             ,
             that
             in
             those
             of
             a
             wide
             Bore
             ,
             upon
             such
             little
             inequalities
             of
             pressure
             as
             are
             not
             easily
             to
             be
             avoided
             ,
             the
             oyle
             and
             water
             will
             pass
             by
             one
             another
             in
             the
             Cavity
             of
             the
             pipe
             ,
             and
             so
             spoile
             the
             Experiment
             ,
             which
             requires
             that
             the
             oyle
             within
             the
             pipe
             be
             kept
             in
             an
             intire
             and
             distinct
             Body
             .
          
           
             Fourthly
             ,
             Common
             oyle
             and
             water
             ,
             or
             any
             other
             two
             Liquors
             that
             will
             not
             mingle
             ,
             may
             serve
             the
             turn
             in
             most
             of
             these
             Experiments
             ;
             but
             we
             rather
             chuse
             oyle
             of
             Turpentine
             ,
             because
             it
             is
             light
             and
             thin
             ,
             clear
             and
             colourless
             ,
             and
             may
             be
             easily
             had
             in
             quantities
             ,
             and
             is
             not
             so
             apt
             to
             spot
             ones
             Cloaths
             ,
             or
             obstinately
             to
             adhere
             to
             the
             porous
             Bodies
             it
             chances
             to
             fall
             on
             ,
             as
             Common
             ,
             and
             other
             express'd
             oyles
             .
             And
             for
             their
             sakes
             to
             whom
             the
             odour
             is
             offensive
             ,
             
             we
             presently
             correct
             it
             ,
             by
             mingling
             with
             it
             a
             convenient
             quantity
             of
             oyle
             of
             Rhodium
             ,
             or
             some
             other
             Chymical
             oyle
             that
             is
             odoriferous
             .
          
           
             Fifthly
             ,
             Oyle
             of
             Turpentine
             ,
             though
             it
             be
             not
             reckon'd
             among
             the
             saline
             Menstruums
             ,
             will
             yet
             (
             as
             we
             elsewhere
             note
             )
             work
             upon
             Copper
             ,
             and
             so
             by
             digesting
             it
             upon
             crude
             filings
             of
             that
             Metal
             ,
             we
             obtaine
             a
             deep
             green
             Liquor
             ,
             which
             may
             be
             made
             use
             of
             instead
             of
             the
             Limpid
             oyle
             ,
             to
             make
             the
             Distinction
             of
             the
             Liquors
             more
             conspicuous
             .
          
           
             Sixthly
             ,
             And
             for
             the
             same
             purpose
             we
             often
             use
             instead
             of
             clear
             water
             ,
             a
             strong
             Decoction
             of
             Brazill
             ,
             or
             Logg-wood
             ,
             or
             else
             Red
             Inck
             it self
             ,
             I
             say
             ,
             a
             
               strong
               Decoction
            
             ,
             because
             unless
             the
             Liquor
             be
             so
             deeply
             ting'd
             ,
             as
             to
             appear
             Opacous
             in
             the
             Glass
             ,
             when
             it
             comes
             into
             the
             slender
             pipe
             ,
             its
             Colour
             will
             be
             so
             diluted
             ,
             as
             to
             be
             scarce
             discernable
             .
          
           
           
             Seventhly
             ,
             In
             the
             shape
             of
             the
             Glass
             Vessel
             ,
             we
             need
             not
             be
             Curious
             ;
             though
             that
             of
             a
             wide
             Mouth'd
             Jarr
             ,
             express'd
             in
             the
             Scheme
             ,
             be
             for
             some
             uses
             more
             convenient
             than
             other
             shapes
             .
             The
             depth
             of
             these
             Glasses
             ,
             and
             the
             length
             of
             the
             Pipes
             must
             be
             determin'd
             by
             the
             Experiments
             ,
             about
             which
             one
             means
             to
             imploy
             them
             .
             To
             make
             out
             the
             first
             Paradox
             already
             prov'd
             ,
             a
             Glass
             of
             about
             five
             or
             six
             Inches
             deep
             ,
             and
             a
             Pipe
             about
             as
             many
             Inches
             long
             ,
             will
             serve
             the
             turn
             :
             but
             for
             some
             others
             of
             the
             following
             Experiments
             ,
             tall
             Cylindrical
             Glasses
             will
             be
             requisite
             ;
             and
             for
             some
             ,
             Broad
             ones
             likewise
             will
             be
             Expedient
             .
          
           
             Eighthly
             ,
             One
             must
             not
             be
             discourag'd
             by
             not
             being
             able
             at
             the
             first
             or
             second
             time
             ,
             to
             suck
             up
             oyle
             of
             Turpentine
             to
             the
             due
             height
             ,
             and
             stop
             it
             with
             ones
             finger
             from
             relapsing
             ;
             but
             one
             must
             try
             again
             ,
             and
             again
             ;
             especially
             
             since
             many
             Tryals
             of
             this
             kind
             may
             be
             made
             in
             a
             few
             Minutes
             :
             and
             for
             Beginners
             't
             is
             a
             safe
             and
             good
             ,
             though
             not
             the
             shortest
             way
             ,
             to
             suck
             up
             rather
             more
             Liquor
             then
             one
             judges
             will
             be
             needful
             ;
             because
             having
             fill'd
             the
             Pipe
             to
             that
             height
             ,
             you
             may
             by
             letting
             in
             the
             Aire
             warily
             and
             slowly
             ,
             between
             the
             Orifice
             of
             the
             Glass
             and
             the
             pulp
             of
             your
             finger
             ,
             suffer
             so
             much
             Liquor
             to
             run
             out
             of
             the
             Pipe
             ,
             as
             will
             reduce
             it
             to
             the
             height
             you
             desire
             ;
             and
             there
             ,
             by
             close
             stopping
             the
             Orifice
             with
             your
             finger
             ,
             you
             may
             keep
             it
             suspended
             as
             long
             as
             you
             please
             ,
             and
             immerse
             it
             into
             any
             Heterogeneous
             Liquor
             ,
             and
             take
             it
             out
             again
             at
             pleasure
             without
             spilling
             any
             of
             it
             .
             By
             which
             slight
             Expedient
             alone
             ,
             I
             can
             decline
             several
             Difficulties
             ,
             and
             do
             many
             things
             ,
             which
             ,
             according
             to
             Paschal's
             way
             ,
             require
             a
             great
             deal
             of
             Trouble
             and
             Apparatus
             to
             be
             perform'd
             .
          
           
           
             Lastly
             ,
             In
             such
             Experiments
             where
             it
             may
             be
             of
             use
             ,
             That
             there
             be
             a
             considerable
             disparity
             betwixt
             the
             two
             unmingled
             Liquors
             ,
             we
             may
             (
             as
             is
             above
             intimated
             )
             instead
             of
             fair
             water
             ,
             imploy
             
               Oleum
               Tartari
               per
               deliquium
            
             ,
             and
             tinge
             it
             with
             Brazill
             or
             Chochineele
             ;
             from
             either
             of
             which
             ,
             but
             especially
             from
             the
             latter
             ,
             it
             will
             obtaine
             an
             exceeding
             deep
             Redness
             :
             and
             where
             one
             would
             avoid
             strong
             sents
             and
             oyliness
             ,
             he
             may
             ,
             if
             he
             will
             be
             at
             the
             Charge
             ,
             imploy
             oyle
             of
             Tartar
             
               per
               deliquium
            
             ,
             instead
             of
             fair
             water
             ,
             and
             highly
             Rectified
             Spirit
             of
             Wine
             ,
             instead
             of
             oyle
             of
             Turpentine
             .
             For
             these
             two
             Liquors
             ,
             though
             they
             will
             both
             readily
             mingle
             with
             water
             ,
             will
             not
             with
             one
             another
             ;
             and
             if
             a
             great
             quantity
             of
             some
             other
             Liquor
             be
             to
             be
             substituted
             for
             simple
             water
             ,
             when
             these
             Chymical
             Liquors
             are
             not
             to
             be
             had
             in
             plenty
             ,
             one
             may
             imploy
             (
             as
             we
             have
             done
             )
             a
             very
             strong
             Solution
             made
             
             of
             Sea-salt
             ,
             and
             filtred
             through
             Cap-paper
             :
             this
             Brine
             being
             near
             about
             as
             Limpid
             as
             common
             water
             ,
             and
             farre
             heavier
             than
             it
             .
             And
             for
             a
             Curiosity
             ,
             we
             have
             added
             to
             the
             two
             lately
             mentioned
             Liquors
             (
             oyle
             of
             Tartar
             ,
             and
             Spirit
             of
             Wine
             )
             some
             oyl
             of
             Turpentine
             ,
             and
             thereby
             had
             three
             Liquors
             of
             different
             Gravities
             ,
             which
             will
             not
             by
             shaking
             ,
             be
             brought
             so
             to
             mingle
             ,
             as
             not
             quickly
             to
             part
             again
             ,
             &
             retire
             each
             within
             its
             own
             Surface
             ;
             and
             by
             thrusting
             a
             Pipe
             with
             water
             in
             the
             bottom
             of
             it
             (
             placing
             also
             ones
             finger
             upon
             the
             upper
             Orifice
             )
             beneath
             the
             Surface
             of
             the
             lowermost
             of
             these
             Liquors
             ,
             and
             by
             opportunely
             raising
             or
             depressing
             it
             ,
             one
             may
             somewhat
             vary
             the
             Experiment
             in
             a
             way
             not
             unpleasant
             ;
             but
             explicable
             upon
             the
             same
             grounds
             with
             the
             rest
             of
             the
             Phaenomena
             mentioned
             in
             this
             Discourse
             .
          
        
         
           
           
             PARADOX
             .
             II.
             
          
           
             That
             a
             lighter
             Fluid
             may
             gavitate
             or
             weigh
             upon
             a
             heavier
             .
          
           
             I
             Know
             that
             this
             is
             contrary
             to
             the
             common
             opinion
             ,
             not
             only
             of
             the
             Schools
             ▪
             but
             ev'n
             of
             divers
             hodiern
             Mathematicians
             ,
             and
             Writers
             of
             Hydrostaticks
             ;
             some
             of
             whom
             have
             absolutely
             rejected
             this
             Paradox
             ,
             though
             they
             do
             but
             doubt
             of
             the
             truth
             of
             the
             former
             .
          
           
             But
             when
             I
             consider
             ,
             that
             whether
             the
             cause
             of
             Gravity
             be
             the
             pulsion
             of
             any
             superior
             substance
             ,
             or
             the
             Magnetical
             attraction
             of
             the
             Earth
             ,
             or
             whatever
             else
             it
             be
             ,
             there
             is
             in
             all
             heavy
             Bodies
             ,
             as
             such
             ,
             a
             constant
             tendency
             towards
             the
             Centre
             ,
             or
             lowermost
             parts
             of
             the
             Earth
             ;
             I
             do
             not
             see
             why
             that
             
             tendency
             or
             endeavour
             should
             be
             destroy'd
             by
             the
             interposition
             of
             any
             other
             heavy
             Body
             ;
             Though
             what
             would
             otherwise
             be
             the
             effect
             of
             that
             endeavour
             ,
             namely
             an
             approach
             towards
             the
             Centre
             ,
             may
             be
             hindred
             by
             another
             Body
             ,
             which
             being
             heavier
             then
             it
             ,
             obtains
             by
             its
             greater
             gravity
             a
             lower
             place
             ;
             but
             then
             the
             lighter
             Body
             tending
             downwards
             ,
             must
             needs
             press
             upon
             the
             heavier
             that
             stands
             in
             its
             way
             ,
             and
             must
             together
             with
             that
             heavier
             press
             upon
             whatever
             Body
             it
             is
             that
             supports
             them
             both
             ,
             with
             a
             weight
             consisting
             of
             the
             united
             gravities
             of
             the
             more
             ,
             and
             the
             less
             heavy
             Body
             .
          
           
             But
             that
             which
             keeps
             Learned
             Men
             from
             acknowledging
             this
             Truth
             ,
             seems
             to
             be
             this
             ,
             That
             a
             lighter
             Liquor
             (
             or
             other
             Body
             )
             being
             environ'd
             with
             a
             heavyer
             ,
             will
             not
             fall
             down
             but
             emerge
             to
             the
             Top
             ;
             whence
             they
             conclude
             ,
             that
             ,
             in
             such
             Cases
             ,
             it
             is
             not
             to
             be
             considered
             
             as
             a
             heavy
             ,
             but
             as
             a
             Light
             Body
             .
          
           
             But
             to
             this
             I
             answer
             ,
             That
             though
             in
             Respect
             of
             the
             heavier
             Liquor
             ,
             the
             less
             heavy
             may
             in
             some
             sence
             be
             said
             to
             be
             light
             ;
             yet
             ,
             notwithstanding
             that
             relative
             or
             Comparative
             Levity
             ,
             it
             retains
             all
             its
             absolute
             Gravity
             ,
             tending
             downwards
             as
             strongly
             as
             before
             ;
             though
             by
             a
             contrary
             and
             more
             potent
             Endeavour
             upwards
             of
             the
             contiguous
             liquor
             (
             whose
             lower
             parts
             ,
             if
             less
             resisted
             ,
             are
             pressed
             upwards
             by
             the
             higher
             elsewhere
             incumbent
             ;
             according
             to
             the
             Doctrine
             partly
             delivered
             already
             ,
             and
             partly
             to
             be
             cleared
             by
             the
             proof
             of
             the
             next
             proposition
             ,
             )
             its
             endeavor
             downward
             is
             so
             surmounted
             that
             it
             is
             forcibly
             carry'd
             up
             .
             Thus
             when
             a
             piece
             of
             some
             light
             wood
             being
             held
             under
             water
             ,
             is
             let
             go
             and
             suffer'd
             to
             emerge
             ,
             though
             it
             he
             buoy'd
             up
             by
             the
             water
             ,
             whose
             specifick
             Gravity
             is
             greater
             ,
             yet
             ev'n
             whilst
             it
             alcends
             it
             remains
             a
             heavy
             
             Body
             ;
             so
             that
             the
             aggregate
             of
             the
             water
             &
             the
             ascending
             wood
             weighs
             more
             then
             the
             water
             alone
             would
             doe
             ;
             And
             when
             it
             floats
             upon
             the
             upper
             part
             of
             the
             water
             ,
             as
             part
             of
             it
             is
             extant
             above
             the
             surface
             ,
             so
             part
             of
             it
             is
             immerst
             beneath
             it
             ,
             which
             confirms
             what
             we
             were
             saying
             ,
             That
             a
             lighter
             Body
             may
             gravitate
             upon
             a
             heavier
             .
          
           
             And
             thus
             there
             is
             little
             doubt
             to
             be
             made
             but
             that
             if
             a
             man
             stand
             in
             one
             of
             the
             scales
             of
             a
             Ballance
             with
             a
             heavy
             stone
             ty'd
             to
             his
             hand
             ,
             and
             hanging
             freely
             by
             his
             side
             ,
             if
             then
             he
             lift
             that
             weight
             as
             high
             above
             his
             head
             as
             he
             can
             ,
             notwithstanding
             that
             the
             stones
             motion
             upwards
             makes
             it
             seem
             a
             light
             Body
             in
             respect
             of
             the
             Man
             whose
             Body
             it
             leaves
             beneath
             it
             ,
             yet
             it
             dos
             not
             ,
             either
             during
             its
             ascent
             or
             after
             ,
             loose
             any
             thing
             of
             its
             connatural
             weight
             .
             For
             the
             Man
             that
             lifts
             it
             up
             shall
             feel
             its
             tendency
             downwards
             to
             continue
             ,
             
             though
             his
             force
             ,
             being
             greater
             than
             that
             tendency
             ,
             be
             able
             ,
             notwithstanding
             that
             tendency
             ,
             to
             carry
             it
             up
             :
             and
             when
             it
             is
             aloft
             ,
             it
             will
             so
             press
             against
             his
             hand
             ,
             as
             to
             offend
             ,
             if
             not
             also
             to
             bruise
             it
             ;
             and
             the
             Stone
             ,
             and
             the
             Man
             that
             supports
             it
             ,
             will
             weigh
             no
             less
             in
             the
             Scale
             he
             stands
             in
             ,
             then
             if
             he
             did
             not
             at
             all
             support
             it
             ,
             and
             they
             were
             both
             of
             them
             weigh'd
             apart
             .
          
           
             Likewise
             ,
             if
             you
             put
             into
             one
             Scale
             a
             wide
             mouth'd
             Glass
             full
             of
             water
             ,
             and
             a
             good
             quantity
             of
             pouder'd
             common
             Salt
             ;
             and
             into
             the
             other
             Scale
             ,
             a
             Counterpoise
             to
             them
             both
             ;
             you
             may
             observe
             ,
             that
             ,
             though
             at
             the
             beginning
             the
             Salt
             will
             manifestly
             lie
             at
             the
             bottome
             ,
             and
             afterwards
             by
             degrees
             be
             so
             taken
             up
             into
             the
             Body
             of
             the
             Liquor
             ,
             that
             not
             a
             grain
             will
             appear
             there
             ;
             yet
             nevertheless
             (
             as
             far
             as
             I
             can
             judge
             by
             my
             Experiments
             )
             the
             weight
             in
             that
             Scale
             will
             not
             be
             diminished
             by
             the
             
             weight
             of
             as
             much
             Sale
             as
             is
             incessantly
             either
             carried
             up
             ,
             or
             supported
             by
             the
             restless
             motion
             of
             the
             dissolving
             Corpuscles
             of
             the
             water
             ;
             but
             both
             the
             one
             and
             the
             other
             ,
             (
             allowing
             for
             what
             may
             evaporate
             )
             will
             concurrently
             gravitate
             upon
             the
             Scale
             that
             the
             glass
             containing
             them
             leans
             on
             .
          
           
             But
             of
             this
             more
             elsewhere
             .
             Now
             to
             prove
             the
             proposiion
             by
             the
             New
             Method
             ,
             we
             have
             propos'd
             to
             our self
             in
             this
             Discourse
             .
          
           
             Take
             a
             slender
             Glass
             pipe
             ,
             and
             having
             suck'd
             up
             into
             it
             fair
             water
             ,
             to
             the
             height
             of
             3
             or
             4
             Inches
             ,
             stop
             nimbly
             the
             upper
             Orifice
             with
             your
             finger
             ,
             and
             inmerse
             the
             lower
             into
             a
             Glass
             full
             of
             oyle
             of
             Turpenrine
             ,
             till
             the
             Surface
             of
             the
             oyle
             in
             the
             Vessel
             be
             somwhat
             higher
             than
             that
             of
             the
             water
             in
             the
             Pipe
             ;
             then
             removing
             your
             finger
             ,
             though
             the
             Pipe
             do
             thereby
             become
             open
             at
             both
             Ends
             ,
             the
             water
             will
             not
             
             fall
             down
             ,
             being
             hinder'd
             by
             the
             pressure
             of
             the
             oyle
             of
             Turpentine
             .
             As
             will
             be
             obvious
             to
             them
             that
             have
             attentively
             consider'd
             the
             Explication
             of
             the
             former
             Paradox
             ;
             there
             being
             but
             this
             difference
             between
             this
             Experiment
             and
             that
             there
             Explain'd
             ,
             that
             here
             the
             water
             is
             in
             the
             Pipe
             ,
             and
             the
             oyle
             in
             the
             Vessel
             ,
             whereas
             there
             the
             oyle
             was
             in
             the
             Pipe
             ,
             and
             the
             water
             in
             the
             Vessel
             .
             And
             if
             you
             either
             poure
             more
             oyle
             into
             the
             Glass
             ,
             or
             thrust
             the
             Pipe
             deeper
             into
             the
             oyle
             ,
             you
             shall
             see
             that
             the
             water
             will
             be
             buoyed
             up
             towards
             the
             top
             of
             the
             Pipe
             ;
             that
             is
             ,
             a
             heavier
             Liquor
             will
             be
             lifted
             up
             by
             a
             lighter
             .
             And
             since
             ,
             by
             the
             Explication
             of
             the
             first
             Proposition
             ,
             it
             appears
             ,
             that
             the
             Reason
             why
             the
             Liquor
             is
             in
             this
             case
             rais'd
             in
             the
             Pipe
             ,
             is
             the
             Gravity
             of
             the
             Liquor
             that
             raises
             it
             ,
             we
             must
             allow
             that
             a
             lighter
             Liquor
             in
             specie
             ,
             may
             by
             its
             gravity
             press
             against
             a
             heavier
             .
          
           
           
             And
             it
             agrees
             very
             well
             with
             our
             Explication
             ,
             both
             of
             this
             ,
             and
             of
             the
             first
             Experiment
             ,
             that
             as
             there
             ,
             the
             Surface
             of
             the
             oyle
             in
             the
             pipe
             was
             always
             higher
             than
             that
             of
             the
             water
             without
             it
             ,
             because
             the
             oyle
             being
             the
             lighter
             Liquor
             ,
             a
             greater
             height
             of
             it
             was
             requir'd
             to
             make
             an
             Aequilibrium
             ;
             so
             in
             our
             present
             Experiment
             ,
             the
             Surface
             of
             the
             Liquor
             in
             the
             Pipe
             will
             alwayes
             be
             lower
             than
             that
             of
             the
             oyle
             without
             it
             .
          
           
             For
             in
             the
             imaginary
             plain
             
               E
               F
            
             ,
             
             the
             Cylinder
             of
             water
             
               J
               G
            
             ,
             contain'd
             in
             the
             Pipe
             
               J
               H
            
             ,
             will
             ,
             by
             reason
             of
             its
             greater
             gravity
             ,
             press
             as
             much
             upon
             the
             part
             J
             ,
             as
             the
             distill'd
             oyle
             
               (
               K
               E
               ,
               J
               L
               ,
               )
            
             being
             a
             lighter
             Liquor
             ,
             can
             do
             upon
             the
             other
             parts
             of
             the
             same
             suppos'd
             plain
             
               E
               F
            
             ,
             though
             the
             oyle
             reach'd
             to
             a
             greater
             height
             above
             it
             .
          
           
             This
             second
             Paradox
             ,
             we
             have
             hitherto
             been
             discoursing
             of
             ,
             may
             be
             also
             
             prov'd
             by
             what
             we
             formerly
             deliver'd
             ,
             to
             make
             out
             the
             Truth
             of
             the
             third
             part
             of
             the
             Lemma
             premised
             to
             these
             Propositions
             .
          
           
             But
             because
             this
             and
             the
             former
             Paradox
             are
             of
             importance
             ,
             not
             only
             in
             themselves
             but
             to
             the
             rest
             of
             this
             Treatise
             ,
             and
             are
             likely
             (
             in
             most
             Readers
             )
             to
             meet
             with
             indisposition
             enough
             to
             be
             receiv'd
             ,
             I
             will
             subjoyn
             in
             this
             place
             a
             couple
             of
             such
             Experiments
             ,
             as
             will
             not
             ,
             I
             hope
             ,
             be
             unacceptable
             ;
             that
             I
             devis'd
             ,
             the
             one
             to
             confirm
             this
             second
             Paradox
             ,
             and
             the
             other
             to
             prove
             the
             first
             .
          
           
             Some
             of
             the
             Gentlemen
             now
             present
             may
             possibly
             remeber
             ,
             that
             about
             the
             end
             of
             the
             Year
             that
             preceded
             the
             two
             last
             ,
             I
             brought
             into
             this
             place
             a
             centain
             new
             Instrument
             of
             Glass
             ,
             whereby
             I
             made
             it
             appear
             ,
             that
             the
             upper
             parts
             of
             water
             gravitate
             upon
             the
             lower
             ;
             which
             I
             did
             by
             sincking
             a
             Body
             ,
             
             that
             was
             already
             under
             water
             ,
             by
             pouring
             more
             water
             upon
             it
             .
          
           
             But
             that
             Experiment
             belonging
             to
             other
             papers
             ,
             I
             shall
             here
             substitute
             another
             perform'd
             by
             an
             Instrument
             ,
             which
             though
             it
             makes
             not
             so
             fine
             a
             shew
             ,
             may
             be
             more
             easily
             provided
             ,
             and
             will
             as
             well
             as
             that
             other
             (
             though
             you
             were
             pleas'd
             to
             command
             that
             from
             me
             )
             serve
             to
             make
             out
             the
             same
             Truth
             ;
             which
             I
             shall
             apply
             my self
             to
             do
             ,
             as
             soon
             as
             I
             have
             ,
             by
             an
             Improvement
             of
             the
             Expedient
             I
             am
             to
             propose
             ,
             made
             good
             my
             late
             promise
             of
             confirming
             the
             second
             Paradox
             .
          
           
             And
             before
             I
             can
             well
             draw
             an
             Argument
             from
             these
             Experiments
             ,
             for
             either
             of
             the
             propositions
             to
             be
             prov'd
             by
             them
             ,
             
             I
             must
             briefly
             repeat
             what
             I
             have
             elsewhere
             deliver'd
             already
             (
             on
             another
             occasion
             )
             touching
             the
             cause
             of
             the
             sincking
             
             of
             such
             Bubbles
             .
             Namely
             that
             the
             Bubble
             X.
             consisting
             ▪
             of
             Glass
             ,
             
             which
             is
             heavier
             in
             specie
             then
             Water
             ;
             and
             Aire
             ,
             which
             is
             lighter
             in
             specie
             then
             Water
             ;
             and
             ,
             if
             you
             please
             ,
             also
             of
             Water
             itself
             ,
             which
             is
             of
             the
             same
             specifick
             Gravity
             with
             Water
             ;
             as
             long
             as
             this
             whole
             aggregate
             of
             several
             Bodys
             is
             lighter
             then
             an
             equal
             bulk
             of
             Water
             ,
             it
             will
             float
             ;
             but
             in
             case
             it
             grows
             heavier
             then
             so
             much
             water
             ,
             it
             must
             ,
             according
             to
             the
             known
             Laws
             of
             the
             Hydrostaticks
             ,
             necessarily
             sinck
             ,
             (
             being
             not
             otherwise
             supported
             .
             )
             Now
             when
             there
             is
             any
             competent
             pressure
             (
             whether
             produc'd
             by
             weight
             or
             otherwise
             ,
             )
             upon
             the
             water
             ,
             in
             which
             this
             Bubble
             is
             for
             the
             most
             part
             immers'd
             ,
             because
             the
             glass
             is
             a
             firm
             Body
             &
             the
             water
             ,
             though
             a
             Liquor
             ,
             either
             suffers
             no
             compression
             ,
             or
             but
             an
             inconsiderable
             one
             ;
             the
             Aire
             included
             in
             the
             Bubble
             ,
             being
             a
             springy
             
             and
             very
             compressible
             Body
             ,
             will
             be
             compell'd
             to
             shrink
             ,
             and
             thereby
             possessing
             less
             Room
             ,
             then
             it
             did
             before
             ,
             the
             contiguous
             water
             will
             succeed
             in
             its
             place
             ;
             which
             being
             a
             body
             above
             a
             thousand
             times
             heavier
             then
             aire
             ,
             the
             Bubble
             will
             thereby
             become
             heavier
             then
             an
             equall
             Bulk
             of
             water
             ,
             and
             consequently
             will
             sink
             :
             but
             if
             that
             force
             or
             pressure
             be
             remov'd
             ,
             the
             Imprison'd
             Aire
             will
             by
             its
             own
             Spring
             free
             it self
             from
             the
             intruding
             water
             ;
             and
             the
             Aggregate
             of
             Bodys
             ,
             that
             makes
             up
             the
             Bubble
             ,
             being
             thereby
             grown
             lighter
             then
             an
             equal
             bulk
             of
             water
             ,
             the
             subsided
             bubble
             will
             presently
             emerge
             to
             the
             Top.
             
          
           
             This
             Explication
             of
             the
             Causes
             of
             the
             sinking
             of
             Bubbles
             agrees
             ,
             in
             some
             things
             ,
             with
             the
             Doctrine
             of
             the
             Learned
             Jesuites
             
               Kercher
               &
               Shottus
            
             ,
             and
             some
             other
             writers
             ,
             in
             the
             Acount
             they
             give
             
             of
             those
             two
             Experiments
             that
             are
             commonly
             known
             by
             the
             name
             ,
             the
             one
             of
             the
             Romane
             ,
             the
             other
             of
             the
             Florentine
             Experiments
             .
             But
             there
             are
             also
             particulars
             wherein
             I
             (
             who
             have
             never
             a
             recourse
             to
             a
             
               fuoa
               Vacui
               ,
            
             )
             dissent
             from
             their
             Doctrine
             ;
             the
             principles
             I
             go
             upon
             ,
             having
             invited
             and
             assisted
             me
             to
             make
             that
             Experiment
             ,
             afford
             me
             some
             new
             Phaenomena
             ,
             which
             agree
             not
             with
             their
             Opinions
             ,
             but
             do
             with
             mine
             :
             but
             I
             forbear
             to
             mention
             them
             here
             ,
             because
             they
             belong
             to
             other
             Papers
             ;
             and
             for
             the
             same
             reason
             I
             omit
             some
             accession
             of
             Ludicrous
             Phaenomena
             (
             as
             they
             call
             them
             ,
             )
             which
             I
             remember
             I
             have
             sometimes
             added
             to
             those
             ,
             which
             our
             Industrious
             Authors
             have
             already
             deduc'd
             from
             those
             Experiments
             .
          
           
             These
             things
             being
             premis'd
             ,
             I
             proceed
             to
             the
             confirmation
             of
             the
             second
             Paradox
             ,
             by
             the
             following
             Experiment
             .
          
           
           
             Take
             a
             long
             glass
             pipe
             ,
             seal'd
             or
             otherwise
             exactly
             stop'd
             at
             one
             end
             and
             open
             at
             the
             other
             (
             whose
             Orifice
             if
             it
             be
             no
             wider
             ,
             then
             that
             it
             may
             be
             conveniently
             stop'd
             with
             mans
             .
             Thumb
             ,
             the
             Tube
             will
             be
             the
             fitter
             to
             exhibit
             some
             other
             Phanomena
             .
             Into
             this
             pipe
             pour
             such
             a
             quantity
             of
             common
             water
             ,
             as
             that
             there
             may
             be
             a
             foot
             ,
             or
             half
             a
             yard
             ,
             or
             some
             other
             competent
             part
             left
             unfill'd
             ,
             for
             the
             use
             to
             be
             by
             and
             by
             mention'd
             .
             Then
             having
             poiz'd
             a
             glass
             Bubble
             with
             a
             slender
             neck
             ,
             in
             such
             a
             manner
             as
             that
             though
             it
             will
             keep
             at
             the
             Top
             of
             the
             water
             ,
             yet
             a
             very
             little
             addition
             of
             weight
             ,
             will
             suffice
             to
             sinck
             it
             ,
             put
             this
             Bubble
             thus
             poiz'd
             into
             the
             Tube
             ;
             where
             it
             will
             swim
             in
             the
             upper
             part
             of
             the
             water
             ,
             as
             long
             as
             it
             is
             let
             alone
             ,
             but
             if
             you
             gently
             pour
             oyle
             of
             Turpentine
             upon
             it
             ,
             (
             I
             say
             gently
             to
             avoid
             confounding
             the
             Liquors
             )
             you
             will
             perceive
             that
             ,
             for
             a
             while
             ,
             the
             
             Bubble
             will
             continue
             where
             it
             was
             :
             but
             if
             you
             continue
             pouring
             on
             oyl
             ,
             till
             it
             have
             attain'd
             a
             sufficient
             height
             above
             the
             water
             ,
             (
             which
             ,
             't
             will
             be
             easie
             to
             peceive
             ,
             because
             those
             two
             liquors
             will
             keep
             themselves
             distinct
             )
             you
             shall
             see
             the
             Bubble
             subside
             till
             it
             fall
             to
             the
             Bottom
             ,
             and
             continue
             there
             as
             long
             as
             the
             oyl
             remains
             at
             the
             height
             above
             the
             water
             .
          
           
             The
             Reason
             of
             this
             Phanomenon
             ,
             according
             to
             our
             Doctrine
             ,
             is
             this
             ,
             That
             the
             oyl
             of
             Turpentine
             ,
             though
             a
             lighter
             Liquor
             then
             water
             ,
             yet
             gravitates
             upon
             the
             subjacent
             water
             ,
             and
             by
             its
             pressuce
             forces
             some
             of
             it
             into
             the
             cavity
             of
             the
             bubble
             at
             the
             open
             Orifice
             of
             its
             neck
             ,
             whereby
             the
             Buble
             ,
             which
             was
             before
             but
             very
             little
             less
             heavy
             then
             an
             equal
             Bulk
             of
             water
             ,
             being
             by
             this
             accession
             made
             a
             little
             more
             heavy
             must
             necessarily
             sinck
             ;
             and
             the
             cause
             of
             its
             submersion
             ,
             namely
             the
             pressure
             of
             the
             
             oyle
             ,
             continuing
             ,
             it
             must
             remain
             at
             the
             bottom
             .
          
           
             And
             to
             confirm
             this
             explication
             I
             shall
             add
             ,
             that
             in
             case
             ,
             by
             inclining
             the
             Tube
             or
             otherwise
             ,
             you
             remove
             the
             Cylinder
             of
             oyl
             ,
             or
             a
             competent
             part
             of
             it
             ,
             (
             in
             case
             it
             were
             longer
             then
             was
             necessary
             ,
             )
             the
             Bubble
             will
             again
             emerge
             to
             the
             Top
             of
             the
             water
             (
             for
             ,
             as
             for
             the
             oyle
             ,
             that
             is
             too
             light
             a
             Liquor
             to
             buoy
             it
             up
             ;
             )
             which
             happens
             only
             because
             the
             pressure
             of
             the
             oyle
             upon
             the
             water
             being
             taken
             of
             the
             Aire
             ,
             by
             vertue
             of
             its
             own
             spring
             ,
             is
             able
             to
             recover
             its
             former
             Expansion
             ,
             and
             reduce
             the
             bubble
             to
             be
             as
             light
             as
             't
             was
             before
             .
          
           
             And
             now
             we
             may
             proceed
             to
             that
             other
             Experiment
             ,
             by
             which
             we
             lately
             promis'd
             to
             confirm
             the
             first
             Paradox
             .
             And
             in
             some
             regard
             this
             following
             Experiment
             has
             been
             preferr'd
             ,
             as
             more
             strange
             ,
             to
             that
             I
             have
             been
             reciting
             .
             
             For
             it
             seem'd
             much
             less
             improbable
             ,
             that
             of
             two
             Heterogeneous
             Liquors
             ,
             the
             inferior
             should
             be
             press'd
             upon
             by
             the
             incumbent
             ,
             which
             ,
             though
             lighter
             ,
             kept
             in
             an
             intire
             body
             above
             it
             ;
             then
             that
             in
             water
             ,
             which
             is
             a
             Homogeneous
             Liquor
             ;
             and
             whose
             parts
             mingle
             most
             freely
             and
             exquisitely
             with
             one
             another
             ,
             the
             upper
             part
             should
             press
             upon
             the
             lower
             ;
             and
             that
             they
             will
             do
             so
             ,
             may
             appear
             by
             the
             Experiment
             it
             is
             now
             time
             to
             sub
             joyn
             .
          
           
             Provide
             a
             long
             Tube
             and
             a
             poiz'd
             Bubble
             ,
             as
             in
             the
             former
             Experiment
             ,
             then
             having
             pour'd
             water
             into
             the
             Tube
             ,
             till
             it
             reach
             above
             5
             or
             6
             Inches
             (
             for
             a
             determinate
             height
             is
             no
             way
             necessary
             )
             above
             the
             Bottome
             ,
             cast
             in
             the
             Bubble
             ,
             which
             will
             not
             only
             swim
             ,
             but
             if
             you
             thrust
             it
             down
             into
             the
             water
             it
             will
             of
             it self
             emerge
             to
             the
             upper
             part
             of
             it
             .
             Wherefore
             take
             a
             slender
             Wand
             ,
             or
             a
             Wire
             ,
             or
             a
             slender
             
             glass
             pipe
             ,
             or
             any
             such
             Body
             that
             is
             long
             enough
             for
             your
             purpose
             ,
             and
             with
             it
             having
             thrust
             the
             bubble
             beneath
             the
             Surface
             of
             the
             water
             ,
             pour
             water
             slowly
             into
             the
             Tube
             (
             whose
             Cavity
             will
             not
             be
             near
             fill'd
             by
             the
             rod
             or
             wire
             )
             till
             it
             have
             attain'd
             a
             competent
             height
             ,
             (
             which
             ,
             in
             my
             last
             Tryals
             ,
             was
             about
             a
             Foot
             ,
             or
             half
             a
             Yard
             above
             the
             bubble
             :
             )
             and
             you
             shall
             see
             ,
             that
             the
             bubble
             ,
             which
             before
             endeavour'd
             to
             emerge
             ,
             will
             by
             the
             additional
             weight
             of
             the
             incumbent
             water
             ,
             be
             depress'd
             to
             the
             bottom
             of
             the
             Tube
             .
             After
             which
             you
             may
             safely
             remove
             the
             wire
             ,
             or
             other
             body
             that
             kept
             it
             from
             rising
             .
             For
             as
             the
             weight
             of
             the
             Incumbent
             water
             was
             that
             which
             made
             it
             sinck
             ,
             so
             that
             weight
             continuing
             on
             it
             ,
             the
             bubble
             will
             continue
             at
             the
             bottom
             .
          
           
             But
             yet
             it
             is
             not
             without
             cause
             ,
             that
             we
             imploy
             a
             wire
             ,
             or
             some
             such
             thing
             ,
             in
             this
             Experiment
             ,
             though
             we
             affirm
             
             it
             to
             be
             onely
             the
             weight
             of
             the
             Incumbent
             water
             ,
             that
             makes
             the
             Bubble
             sinck
             .
             For
             if
             you
             should
             pour
             water
             into
             the
             Tube
             ,
             to
             the
             height
             lately
             mention'd
             ,
             or
             ev'n
             to
             a
             greater
             ,
             if
             you
             did
             not
             make
             use
             of
             the
             Wire
             ,
             it
             would
             not
             serve
             the
             turn
             ;
             because
             that
             as
             fast
             as
             you
             pour
             in
             the
             water
             ,
             the
             Bubble
             being
             left
             to
             it self
             ,
             will
             rise
             together
             with
             it
             ;
             and
             so
             ,
             keeping
             always
             near
             the
             upper
             part
             of
             the
             water
             ,
             it
             will
             never
             suffer
             the
             Liquor
             to
             be
             so
             high
             above
             it
             ,
             as
             it
             must
             be
             ,
             before
             it
             can
             depress
             it
             .
             But
             to
             confirm
             ,
             that
             't
             is
             the
             weight
             of
             the
             Superior
             water
             that
             sincks
             the
             Bubble
             ,
             and
             keeps
             it
             at
             the
             Bottom
             ;
             if
             you
             take
             out
             of
             the
             Tube
             a
             competent
             quantity
             of
             that
             Liquor
             ,
             and
             so
             take
             of
             the
             pressure
             of
             it
             from
             the
             Bubble
             ,
             this
             will
             presently
             ,
             without
             any
             other
             help
             ,
             begin
             to
             swim
             ,
             and
             regain
             the
             upper
             part
             of
             the
             water
             ;
             whence
             it
             may
             at
             pleasure
             be
             praecipitated
             ,
             by
             pouring
             back
             
             into
             the
             Tube
             the
             water
             that
             was
             taken
             out
             of
             it
             .
             And
             these
             Confirmations
             ,
             added
             to
             the
             former
             Proofs
             of
             the
             first
             and
             second
             Paradoxes
             ,
             being
             we
             conceive
             sufficient
             to
             satisfie
             Impartial
             Readers
             of
             the
             Truth
             of
             them
             ,
             we
             should
             presently
             advance
             to
             the
             next
             Proposition
             ,
             if
             we
             did
             not
             think
             fit
             to
             interpose
             here
             a
             Scholium
             .
          
           
             
               SCHOLIUM
               .
            
             
               IT
               may
               perchance
               be
               wondred
               at
               ,
               why
               ,
               since
               we
               lately
               mention'd
               our
               having
               made
               some
               Tryals
               with
               oyle
               of
               Tartar
               
                 per
                 deliquium
              
               ,
               we
               did
               not
               in
               the
               present
               Experiment
               ,
               in
               stead
               of
               fair
               water
               ,
               make
               use
               of
               that
               ,
               it
               being
               a
               very
               much
               heavier
               Liquor
               ,
               and
               (
               though
               it
               may
               be
               incorporated
               with
               express'd
               oyles
               )
               unmingleable
               in
               such
               Tryals
               with
               oyle
               of
               Turpentine
               .
               But
               to
               this
               I
               answer
               ,
               
               That
               ev'n
               in
               such
               slender
               pipes
               ,
               as
               those
               made
               use
               of
               about
               the
               first
               Experiment
               ,
               I
               found
               that
               oyle
               of
               Tartar
               was
               ponderous
               enough
               to
               flow
               down
               ,
               though
               slowly
               ,
               into
               the
               oyle
               of
               Turpentine
               at
               one
               side
               of
               the
               immers'd
               Orifice
               ,
               whilst
               the
               oyle
               pass'd
               upwards
               by
               it
               along
               the
               other
               side
               of
               the
               pipe
               .
               And
               my
               knowledge
               of
               this
               could
               not
               but
               make
               me
               a
               little
               wonder
               ,
               That
               so
               Curious
               a
               person
               ,
               as
               
                 Monsieur
                 Paschall
              
               ,
               should
               somewhere
               teach
               ,
               That
               if
               a
               Tube
               of
               above
               14
               foot
               long
               ,
               and
               having
               its
               Orifice
               placed
               14
               foot
               under
               water
               ,
               be
               full
               of
               Quicksilver
               ,
               the
               fluid
               Metal
               will
               not
               all
               run
               out
               at
               the
               Bottom
               of
               the
               pipe
               ,
               though
               the
               Top
               of
               it
               be
               left
               open
               to
               the
               Aire
               ,
               but
               will
               be
               stop'd
               at
               a
               foot
               high
               in
               the
               pipe
               ,
               For
               the
               Impetus
               ,
               that
               its
               fall
               will
               give
               it
               ,
               must
               probably
               make
               it
               flow
               quite
               out
               of
               the
               pipe
               :
               And
               ,
               not
               here
               to
               mention
               those
               Tryals
               of
               ours
               with
               Quicksilver
               and
               slender
               
               Tubes
               ,
               that
               made
               me
               think
               this
               very
               improbable
               ;
               if
               we
               consider
               that
               the
               Experiment
               will
               not
               succeed
               with
               much
               more
               favourable
               circumstances
               ,
               betwixt
               oyle
               of
               Turpentine
               and
               oyle
               of
               Tartar
               ,
               though
               the
               heavier
               of
               these
               two
               Liquors
               be
               many
               times
               lighter
               that
               quick
               .
               silver
               :
               It
               tempts
               me
               much
               to
               suspect
               ,
               that
               
                 Monsieur
                 Paschall
              
               never
               actually
               made
               the
               Experiment
               ,
               at
               least
               with
               a
               Tube
               as
               big
               as
               his
               Scheam
               would
               make
               one
               guess
               ,
               but
               yet
               thought
               he
               might
               safely
               set
               it
               down
               ,
               it
               being
               very
               consequent
               to
               those
               Principles
               ,
               of
               whose
               Truth
               he
               was
               fully
               perswaded
               .
               And
               indeed
               ,
               were
               it
               not
               for
               the
               impetus
               ,
               the
               Quicksilver
               would
               acquire
               in
               falling
               from
               such
               a
               height
               ,
               the
               Ratiocanation
               were
               no
               way
               unworthy
               of
               him
               .
            
             
               But
               Experiments
               that
               are
               but
               speculatively
               true
               ,
               should
               be
               propos'd
               as
               such
               ,
               and
               may
               oftentimes
               fail
               in
               practise
               ;
               because
               there
               may
               intervene
               divers
               
               other
               things
               capable
               of
               making
               there
               miscarry
               ,
               which
               are
               overlook'd
               by
               the
               peculator
               ▪
               that
               is
               wont
               to
               compute
               only
               the
               consequences
               of
               that
               particullar
               thing
               which
               he
               principally
               considers
               ;
               As
               in
               this
               case
               our
               Author
               seems
               not
               to
               haue
               consider'd
               ,
               that
               in
               such
               Tubes
               ,
               as
               the
               Torricelliah
               Experiment
               is
               wont
               to
               be
               made
               in
               the
               largness
               of
               them
               would
               make
               them
               unfit
               for
               this
               Tryal
               .
            
             
               And
               I
               have
               known
               Ingenious
               men
               ,
               that
               are
               very
               well
               exercis'd
               in
               making
               such
               Experiments
               ,
               complaine
               ,
               that
               they
               could
               never
               make
               this
               of
               Paschall's
               to
               succeed
               .
               In
               which
               attempts
               ,
               that
               the
               size
               of
               the
               Tubes
               much
               contributed
               to
               the
               unsuccesfulness
               of
               the
               Tryals
               ,
               I
               shall
               (
               without
               repeating
               what
               has
               been
               already
               intimated
               to
               that
               purpose
               )
               in
               the
               following
               part
               of
               this
               Discourse
               have
               
               opportunity
               to
               manifest
               ;
               and
               withal
               to
               adde
               as
               Illustrious
               a
               proof
               of
               this
               our
               second
               Paradox
               ,
               as
               almost
               any
               we
               have
               yet
               given
               .
            
          
        
         
           
           
             PARADOX
             III.
             
          
           
             That
             if
             a
             Body
             contiguous
             to
             the
             water
             be
             altogether
             ,
             or
             in
             part
             ,
             lower
             than
             the
             highest
             level
             of
             the
             said
             water
             ,
             the
             lower
             part
             of
             the
             Body
             will
             be
             press'd
             upward
             by
             the
             water
             that
             touches
             it
             beneath
             ,
          
           
             THis
             may
             be
             prov'd
             by
             what
             has
             been
             already
             delivered
             in
             the
             Explication
             of
             the
             first
             Experiment
             :
             For
             where
             ever
             we
             conceive
             the
             lowest
             part
             of
             the
             Body
             ,
             which
             is
             either
             totally
             ,
             or
             in
             part
             ,
             immers'd
             in
             water
             ,
             to
             be
             there
             the
             imaginary
             Superficies
             being
             beneath
             the
             true
             Superficies
             ,
             every
             part
             of
             that
             imaginary
             Superficies
             must
             be
             press'd
             upwards
             ,
             by
             vertue
             of
             the
             weight
             of
             the
             water
             incumbent
             on
             
             all
             the
             other
             parts
             of
             the
             same
             Superficies
             ,
             and
             so
             that
             part
             of
             it
             ,
             on
             which
             the
             immers'd
             Body
             chances
             to
             leane
             ,
             must
             for
             the
             same
             Reason
             have
             an
             endeavour
             upwards
             .
             And
             if
             that
             Endeavour
             be
             stronger
             then
             that
             wherewith
             the
             weight
             of
             the
             Body
             tends
             downwards
             ,
             then
             (
             supposing
             there
             be
             no
             Accidental
             Impediment
             )
             the
             Body
             will
             be
             buoy'd
             or
             lifted
             up
             .
             And
             though
             the
             Body
             be
             heavier
             then
             so
             much
             water
             ,
             and
             consequently
             will
             subside
             ,
             yet
             that
             Endeavour
             upwards
             of
             the
             water
             ,
             that
             touches
             its
             lower
             part
             ,
             is
             onely
             rendred
             ineffectual
             to
             the
             raising
             or
             supporting
             the
             body
             ,
             but
             not
             destroyed
             ;
             the
             force
             of
             the
             heavy
             Body
             being
             from
             time
             to
             time
             resisted
             ,
             and
             retarded
             by
             the
             water
             ,
             as
             much
             as
             it
             would
             be
             if
             that
             Body
             were
             put
             into
             One
             Scale
             ,
             and
             the
             weight
             of
             as
             much
             water
             ,
             as
             is
             equal
             to
             it
             in
             bulk
             ,
             were
             put
             into
             the
             other
             .
          
           
           
             To
             confirm
             this
             ,
             we
             may
             have
             recourse
             to
             what
             we
             said
             in
             the
             Explication
             of
             the
             second
             Experiment
             .
             
             For
             in
             case
             the
             slender
             pipe
             ,
             wherein
             the
             water
             is
             kept
             suspended
             ,
             be
             thrust
             deeper
             into
             the
             oyl
             or
             in
             case
             these
             be
             more
             oyle
             pour'd
             into
             the
             Vessel
             ,
             the
             water
             will
             be
             impell'd
             up
             higher
             into
             the
             pipe
             ;
             which
             it
             would
             not
             be
             ,
             if
             the
             oyle
             ,
             though
             bulk
             for
             bulk
             a
             lighter
             Body
             ,
             did
             not
             press
             against
             the
             lower
             Surface
             of
             the
             vvater
             ,
             (
             where
             ,
             alone
             ,
             the
             two
             Liquors
             are
             contiguous
             ,
             )
             more
             forcibly
             then
             the
             water
             by
             its
             gravity
             tends
             dovvnvvards
             .
             And
             even
             vvhen
             the
             Liquors
             rest
             in
             an
             Aequilibrium
             ,
             the
             oyle
             continually
             presses
             upvvards
             ,
             against
             the
             lower
             Surface
             of
             the
             water
             ;
             since
             in
             that
             continual
             endeavour
             upvvards
             consists
             its
             constant
             resistance
             to
             the
             continual
             endeavour
             that
             the
             gravity
             of
             the
             water
             gives
             it
             to
             descend
             .
             And
             since
             the
             same
             Phaenomenon
             happens
             ,
             
             whether
             we
             suspend
             water
             in
             oyle
             ,
             as
             in
             the
             second
             Experiment
             ,
             on
             oyle
             in
             water
             ,
             as
             in
             the
             first
             :
             it
             appears
             ,
             that
             the
             proposition
             is
             as
             well
             applicable
             to
             those
             cases
             ,
             where
             the
             sustein'd
             Body
             is
             specifically
             heavier
             ,
             as
             to
             those
             where
             't
             is
             specifically
             lighter
             then
             the
             subjacent
             fluid
             .
          
           
             But
             a
             further
             and
             clearer
             proof
             of
             this
             Doctrine
             will
             appear
             in
             the
             Explication
             of
             the
             next
             proposition
             .
             In
             the
             mean
             time
             ,
             to
             confirm
             that
             part
             of
             out
             Discourse
             ,
             where
             we
             mention'd
             the
             Resistance
             made
             by
             the
             water
             to
             Bodies
             that
             sinck
             in
             it
             ,
             Let
             us
             suppose
             ,
             in
             the
             annexed
             Figure
             ,
             That
             the
             pipe
             E
             F
             contains
             an
             oyle
             specifically
             heavier
             then
             water
             ,
             
             (
             as
             are
             the
             oyls
             of
             Guaisteum
             ,
             of
             Cinnamon
             ,
             or
             Cloves
             ,
             and
             some
             others
             ,
             )
             and
             then
             ,
             That
             the
             oyle
             in
             the
             pipe
             ,
             and
             the
             water
             without
             ,
             being
             at
             rest
             in
             an
             Aequilibrium
             ,
             the
             pipe
             be
             slowly
             
             rais'd
             towards
             the
             Top
             of
             the
             Vessel
             .
             'T
             is
             evident
             ,
             from
             our
             former
             Doctrine
             ,
             and
             from
             Experience
             too
             ,
             that
             there
             will
             run
             out
             drops
             of
             oyle
             ,
             which
             will
             fall
             from
             the
             bottom
             of
             the
             pipe
             ,
             to
             that
             of
             the
             Vessel
             ;
             but
             far
             more
             slowly
             then
             if
             they
             fell
             out
             of
             the
             same
             pipe
             in
             the
             Aire
             .
          
           
             Now
             to
             compute
             how
             much
             the
             pressure
             of
             the
             water
             against
             the
             lower
             parts
             of
             the
             drop
             amounts
             too
             ,
             let
             us
             suppose
             the
             drop
             to
             be
             G
             ,
             to
             whose
             lowermost
             part
             there
             is
             contigueus
             ,
             in
             any
             assignable
             place
             where
             it
             falls
             ,
             the
             imaginary
             Superficies
             
               H
               J.
            
             'T
             is
             evident
             ,
             That
             if
             the
             drop
             of
             oyle
             were
             not
             there
             ,
             its
             place
             would
             be
             supplied
             by
             an
             equal
             bulk
             of
             water
             ;
             which
             being
             of
             the
             same
             specifick
             Gravity
             with
             the
             rest
             of
             the
             water
             in
             the
             Vessel
             ,
             the
             Surface
             
               H
               J
            
             would
             be
             laden
             every
             where
             alike
             ;
             and
             consequently
             to
             part
             of
             it
             would
             be
             displac'd
             ▪
             But
             now
             ,
             
             the
             drop
             of
             oyle
             being
             heavier
             then
             so
             much
             water
             ,
             that
             part
             of
             the
             imaginary
             superficies
             ,
             on
             which
             that
             drop
             leans
             ,
             has
             more
             weight
             upon
             it
             ,
             then
             any
             other
             equal
             part
             of
             the
             same
             Superficies
             ;
             and
             consequently
             ,
             will
             give
             place
             to
             the
             descending
             drop
             .
             And
             since
             the
             case
             of
             every
             other
             suppos'd
             Surface
             ,
             at
             which
             the
             drop
             can
             be
             conceiv'd
             to
             arrive
             in
             its
             descent
             ,
             will
             be
             the
             same
             with
             that
             of
             the
             Superficies
             
               H
               J
            
             ;
             it
             will
             for
             the
             Reason
             newly
             given
             ,
             continue
             falling
             till
             it
             comes
             to
             the
             bottom
             of
             the
             Vessel
             which
             will
             suffer
             it
             to
             fall
             no
             further
             .
             And
             in
             case
             the
             drop
             G
             were
             not
             ,
             as
             we
             suppose
             it
             ,
             of
             a
             substance
             heavier
             in
             specie
             then
             water
             ,
             but
             just
             equal
             to
             it
             ,
             the
             contiguous
             part
             of
             the
             Superficies
             
               H
               J
            
             would
             be
             neither
             more
             nor
             less
             charged
             then
             the
             other
             parts
             of
             the
             same
             Supeficies
             ;
             and
             the
             part
             lean'd
             on
             would
             be
             neither
             depress'd
             nor
             rais'd
             ,
             but
             the
             drop
             G
             
             would
             continue
             in
             the
             same
             place
             .
             And
             so
             we
             may
             prove
             ,
             (
             what
             is
             affirm'd
             by
             Archimedes
             ,
             and
             other
             Hydrostatical
             Writers
             )
             That
             a
             Body
             acquiponderant
             
               in
               specie
            
             to
             water
             ,
             will
             rest
             in
             any
             assignable
             place
             of
             the
             water
             where
             't
             is
             put
             .
          
           
             And
             (
             to
             proceed
             further
             )
             since
             ,
             if
             the
             drop
             G
             were
             of
             a
             matter
             but
             acquiponderant
             to
             water
             it
             would
             not
             sinck
             lower
             at
             all
             ,
             no
             more
             then
             emerge
             ;
             it
             follows
             ,
             that
             though
             being
             heavier
             in
             specie
             then
             water
             ,
             it
             will
             fall
             ,
             yet
             the
             gravity
             upon
             whose
             account
             it
             falls
             ,
             is
             no
             more
             then
             that
             by
             which
             it
             surmounts
             an
             equal
             bulk
             of
             water
             ;
             (
             since
             ,
             if
             it
             were
             not
             for
             that
             over
             plus
             ,
             the
             resistance
             of
             the
             water
             would
             hinder
             it
             from
             falling
             at
             all
             :
             )
             and
             consequently
             ,
             it
             looses
             in
             the
             water
             just
             as
             much
             of
             the
             weight
             it
             would
             have
             in
             the
             aire
             ,
             as
             so
             much
             water
             ,
             weigh'd
             likewise
             in
             the
             same
             aire
             ,
             would
             amount
             to
             .
          
           
             Which
             is
             a
             Physicall
             Account
             of
             
             that
             grand
             Theorem
             of
             the
             Hydrostaticks
             ,
             which
             I
             do
             not
             remember
             that
             I
             have
             seen
             made
             out
             in
             any
             Printed
             Book
             ,
             both
             solidly
             and
             clearly
             ;
             The
             Learned
             Stevinus
             himself
             ,
             to
             whom
             the
             later
             Writers
             are
             wont
             to
             refer
             ,
             having
             but
             an
             obscure
             (
             and
             not
             Physical
             )
             demonstration
             of
             it
             .
          
           
             And
             ,
             because
             this
             Theorem
             is
             not
             only
             very
             noble
             ,
             but
             (
             as
             we
             else
             where
             manifest
             )
             very
             useful
             ,
             't
             will
             not
             be
             amiss
             to
             add
             ,
             That
             it
             may
             easily
             be
             confirm'd
             by
             Experiment
             .
          
           
             For
             if
             you
             take
             (
             for
             instance
             )
             a
             piece
             of
             Lead
             ,
             and
             hang
             it
             by
             a
             Horse
             haire
             (
             that
             being
             suppos'd
             very
             near
             acquiponderant
             to
             water
             )
             from
             one
             of
             the
             Scales
             of
             an
             exact
             Ballance
             ;
             and
             ,
             when
             you
             have
             put
             a
             just
             Connterpoize
             in
             the
             other
             Scale
             ,
             suffer
             the
             Lead
             to
             sinck
             in
             a
             ressel
             of
             water
             ,
             till
             it
             be
             perfectly
             covered
             with
             it
             ,
             but
             hangs
             freely
             in
             it
             ,
             the
             counterpoize
             will
             very
             
             much
             preponderance
             ,
             And
             ,
             part
             of
             the
             Counterpoize
             being
             taken
             out
             till
             the
             Ballatice
             be
             again
             reduc'd
             to
             an
             Aequilibrium
             ,
             you
             may
             easily
             (
             by
             subducting
             what
             you
             have
             taken
             out
             ,
             and
             comparing
             it
             with
             the
             whole
             weight
             of
             the
             Lead
             in
             the
             aire
             )
             find
             what
             part
             of
             its
             weight
             it
             looses
             in
             the
             water
             And
             then
             if
             you
             weigh
             any
             other
             piece
             of
             the
             same
             Lead
             ,
             suppose
             a
             Lump
             of
             12
             ounces
             ,
             and
             hang
             it
             by
             a
             Horse
             haire
             at
             one
             scale
             ,
             you
             may
             be
             sure
             that
             by
             puting
             into
             the
             other
             scale
             a
             weight
             less
             by
             a
             twelfth
             part
             ,
             (
             supposing
             Lead
             to
             water
             to
             be
             as
             twelve
             to
             one
             )
             that
             is
             eleven
             ounces
             ,
             though
             the
             weights
             be
             farr
             from
             an
             Aequilibrium
             in
             the
             Aire
             ,
             they
             will
             be
             reduc'd
             to
             it
             when
             the
             Lead
             it
             cover'd
             with
             water
             .
          
           
             The
             pressure
             of
             water
             against
             the
             lower
             part
             of
             the
             Body
             immers'd
             in
             it
             may
             be
             confirmed
             by
             adding
             ;
             That
             we
             may
             thence
             deduce
             the
             cause
             of
             
             the
             emergency
             of
             wood
             and
             other
             Bodyes
             lighter
             then
             water
             ;
             which
             though
             a
             familiar
             Effect
             ,
             I
             have
             not
             found
             its
             cause
             to
             have
             been
             so
             much
             as
             enquired
             into
             by
             many
             ,
             nor
             perhaps
             to
             have
             been
             well
             rendred
             by
             any
             .
             If
             we
             suppose
             then
             that
             the
             pipe
             be
             almost
             fill'd
             ,
             not
             with
             a
             sincking
             but
             a
             swimming
             oyle
             ,
             as
             oyle
             of
             Turpentine
             ,
             if
             ,
             as
             in
             the
             first
             Experiment
             ,
             the
             lower
             orifice
             be
             thrust
             under
             water
             ,
             (
             to
             a
             far
             less
             depth
             then
             that
             of
             the
             oyle
             in
             the
             pipe
             )
             and
             the
             upper
             be
             slovvly
             unstop'd
             ,
             the
             oyl
             vvill
             (
             as
             vve
             formerly
             declar'd
             )
             get
             out
             in
             drops
             at
             the
             bottom
             of
             the
             pipe
             .
             But
             to
             determine
             vvhy
             these
             drops
             ,
             being
             quite
             cover'd
             and
             surrounded
             vvith
             vvater
             ,
             and
             press'd
             by
             it
             as
             vvell
             dovvnvvards
             as
             upvvards
             ,
             should
             rather
             emerge
             then
             descend
             ,
             I
             shall
             not
             content
             my self
             to
             say
             ,
             that
             vvater
             
               in
               specie
            
             heavier
             then
             this
             kind
             of
             oyle
             ;
             For
             ,
             besides
             that
             in
             some
             cases
             (
             e're
             long
             to
             be
             mention'd
             )
             I
             have
             
             made
             the
             water
             to
             depress
             ev'n
             this
             kind
             off
             oyle
             ,
             and
             besides
             that
             't
             is
             not
             every
             piece
             of
             wood
             lighter
             in
             specie
             then
             water
             that
             will
             float
             upon
             water
             ,
             how
             shallow
             soever
             it
             be
             :
             The
             Question
             is
             how
             this
             praepollent
             Gravity
             of
             the
             water
             comes
             to
             raise
             up
             the
             oyle
             ,
             though
             there
             be
             perchance
             much
             more
             water
             ,
             for
             it
             to
             break
             its
             way
             thorough
             ,
             above
             it
             ,
             then
             beneath
             it
             .
          
           
             The
             Reason
             then
             of
             the
             emersion
             of
             Lighter
             Bodies
             in
             heavier
             fluids
             ,
             seems
             to
             be
             this
             ,
             That
             the
             endeavour
             upwards
             of
             the
             water
             ,
             contiguous
             to
             the
             lower
             part
             of
             the
             Body
             ,
             is
             stronger
             then
             the
             endeavour
             downwards
             of
             the
             same
             Body
             ,
             and
             the
             water
             incumbent
             on
             it
             .
             As
             ,
             in
             the
             former
             Scheme
             ,
             supposing
             the
             Drop
             G
             to
             be
             the
             oyle
             of
             Turpentine
             ,
             and
             to
             touch
             the
             two
             imaginary
             and
             parallel
             plains
             
               H
               J
               ,
               K
               L
            
             ;
             't
             is
             evident
             ,
             that
             upon
             the
             lower
             part
             of
             the
             Drop
             ,
             N
             ,
             there
             is
             a
             greater
             pressure
             of
             
             water
             ,
             then
             upon
             the
             upper
             part
             of
             the
             same
             Drop
             ,
             M
             :
             because
             that
             upon
             all
             the
             surface
             
               K
               L
               ▪
            
             there
             is
             but
             an
             uniform
             pressure
             of
             water
             
               A
               K
               B
               L
            
             ,
             and
             upon
             all
             the
             parts
             of
             the
             surface
             
               H
               I
            
             ,
             there
             is
             a
             greater
             weight
             of
             water
             
               A
               H
               B
               I
            
             ,
             except
             at
             the
             part
             N
             ;
             for
             there
             the
             oyle
             G
             ,
             being
             not
             so
             heavy
             as
             so
             much
             water
             ,
             the
             oyle
             being
             expos'd
             to
             a
             greater
             pressure
             from
             beneath
             ,
             then
             its
             own
             gravity
             (
             and
             that
             of
             the
             water
             incumbent
             on
             it
             )
             will
             enable
             it
             to
             resist
             ,
             must
             necessarily
             give
             way
             and
             be
             impell'd
             upwards
             .
             And
             the
             case
             being
             the
             same
             between
             that
             and
             any
             other
             parallel
             plain
             ,
             wheresoever
             we
             suppose
             it
             to
             be
             in
             its
             ascent
             ,
             it
             must
             consequently
             be
             impell'd
             further
             and
             further
             upwards
             till
             it
             arrive
             at
             the
             Top
             ;
             and
             there
             it
             will
             float
             upon
             the
             water
             :
             Or
             ,
             (
             to
             Explicate
             the
             matter
             without
             Figures
             )
             when
             a
             specifically
             lighter
             Body
             is
             immers'd
             under
             water
             ,
             it
             is
             press'd
             
             against
             by
             two
             pillars
             of
             water
             ;
             the
             one
             bearing
             against
             the
             upper
             ,
             and
             the
             other
             against
             the
             lower
             part
             ;
             and
             because
             the
             lengths
             of
             both
             these
             Pillars
             must
             be
             computed
             from
             the
             Top
             of
             the
             water
             ,
             the
             lower
             part
             of
             the
             immers'd
             body
             must
             be
             press'd
             upon
             by
             a
             Pillar
             longer
             then
             the
             upper
             part
             by
             the
             thickness
             of
             the
             immers'd
             Body
             ;
             and
             consequently
             must
             be
             press'd
             more
             upwards
             then
             downwards
             .
             And
             by
             how
             much
             the
             greater
             disparity
             of
             specifick
             Gravity
             there
             is
             betwixt
             the
             water
             and
             the
             emerging
             Body
             ,
             by
             so
             much
             the
             swifter
             
               (
               caeteris
               paribus
            
             )
             it
             will
             ascend
             :
             because
             so
             much
             the
             more
             will
             there
             be
             of
             pressure
             upon
             all
             the
             other
             parts
             of
             the
             imaginary
             surface
             ,
             then
             upon
             that
             part
             that
             happens
             to
             be
             contiguous
             to
             the
             Bottom
             of
             the
             ascending
             Body
             .
          
           
             And
             upon
             the
             same
             Grounds
             we
             may
             give
             (
             what
             we
             have
             not
             yet
             met
             with
             )
             
             a
             good
             solution
             of
             that
             Probleme
             ,
             propos'd
             by
             Hydrostatical
             Writers
             ,
             why
             ,
             if
             a
             Cylindrical
             stick
             be
             cut
             in
             two
             parts
             ,
             the
             one
             as
             long
             again
             as
             the
             other
             ,
             and
             both
             of
             them
             ,
             having
             been
             detain'd
             under
             water
             at
             the
             same
             depth
             ,
             be
             let
             go
             at
             the
             same
             time
             and
             permitted
             to
             emerge
             ,
             the
             greater
             will
             rise
             faster
             then
             the
             lesser
             .
             For
             suppose
             one
             of
             these
             Bodies
             ,
             as
             
               O
               P
            
             ,
             to
             be
             two
             foot
             high
             ,
             and
             the
             other
             ,
             
               Q
               R
            
             ,
             to
             be
             half
             so
             much
             ,
             and
             that
             the
             lowermost
             Surfaces
             of
             both
             be
             in
             the
             same
             imaginary
             plaine
             ,
             parallel
             to
             the
             uppermost
             surface
             of
             the
             water
             and
             three
             foot
             distant
             from
             it
             ;
             in
             this
             case
             there
             will
             be
             against
             the
             lower
             part
             of
             each
             of
             the
             wooden
             Bodies
             a
             pressure
             ,
             (
             from
             the
             laterally
             superior
             water
             )
             equal
             to
             that
             upon
             all
             the
             other
             parts
             of
             the
             Imaginary
             plain
             ,
             whereto
             those
             Bodies
             are
             contiguous
             ;
             But
             whereas
             upon
             the
             upper
             surface
             of
             the
             shorter
             Body
             ,
             
               Q
               R
            
             ,
             there
             will
             lean
             
             a
             pillar
             of
             water
             two
             foot
             high
             ,
             the
             pillar
             of
             the
             same
             Liquor
             that
             will
             lean
             upon
             the
             Top
             of
             the
             taller
             Body
             ,
             
               P
               O
            
             ,
             will
             be
             but
             one
             foot
             high
             ;
             as
             the
             attentive
             considerer
             will
             easily
             perceive
             .
             So
             that
             the
             wooden
             Bodys
             being
             lighter
             
               in
               specie
            
             then
             water
             ,
             both
             of
             them
             will
             be
             impell'd
             upwards
             ;
             but
             that
             compounded
             pillar
             ,
             (
             if
             I
             may
             so
             call
             it
             )
             which
             consists
             of
             one
             foot
             of
             wood
             and
             two
             foot
             of
             water
             ,
             will
             by
             its
             gravity
             more
             resist
             the
             being
             rais'd
             ,
             then
             that
             which
             consists
             of
             two
             foot
             of
             wood
             and
             but
             one
             foot
             of
             water
             :
             so
             that
             the
             cause
             of
             the
             unequal
             celerity
             in
             the
             Ascension
             of
             these
             Bodys
             consists
             chieflly
             ,
             (
             for
             I
             would
             neither
             overvalue
             nor
             exclude
             Concomitant
             Causes
             )
             that
             the
             difference
             of
             the
             pressure
             against
             the
             upper
             and
             lower
             part
             of
             each
             body
             respectively
             is
             greater
             in
             one
             then
             in
             the
             other
             .
          
           
             And
             hence
             we
             may
             probably
             deduce
             a
             reason
             of
             what
             we
             often
             observe
             in
             the
             
             Distillation
             of
             the
             oyles
             of
             Annisseeds
             ,
             Cloves
             ,
             and
             diverse
             ▪
             Aromatick
             vegetables
             ,
             in
             Lembecks
             by
             the
             intervention
             of
             water
             ;
             for
             oftentimes
             ,
             when
             the
             fire
             has
             not
             been
             well
             regulated
             ,
             there
             will
             come
             over
             ,
             besides
             the
             floating
             Oyle
             ,
             a
             whitish
             water
             ,
             which
             will
             not
             in
             a
             long
             time
             become
             cleare
             .
             And
             as
             we
             have
             elswhere
             taught
             ,
             That
             whiteness
             to
             proceed
             from
             the
             numerous
             reflections
             from
             the
             oyly
             substance
             of
             the
             Concrete
             '
             by
             the
             heat
             of
             the
             fire
             broken
             into
             innumerable
             little
             Globuls
             ,
             and
             dispers'd
             through
             the
             Body
             of
             the
             water
             ;
             so
             the
             reason
             why
             this
             whiteness
             continues
             so
             long
             ,
             seems
             to
             be
             chiefly
             (
             for
             I
             mention
             not
             such
             things
             ,
             as
             ,
             the
             great
             surfaces
             that
             these
             little
             Globuls
             have
             in
             respect
             of
             their
             Bulk
             )
             that
             ,
             because
             of
             the
             exceeding
             minuteness
             of
             these
             Drops
             ,
             the
             height
             of
             the
             water
             that
             presses
             upon
             the
             upper
             part
             ,
             is
             almost
             equal
             to
             that
             of
             the
             water
             that
             
             presses
             against
             the
             lower
             part
             ;
             so
             that
             the
             difference
             between
             these
             two
             pressures
             being
             inconsiderable
             ,
             it
             has
             power
             to
             raise
             the
             Drops
             but
             very
             slowly
             ,
             (
             insomuch
             that
             upon
             this
             ground
             I
             devis'd
             a
             Menstruum
             ,
             wherewith
             I
             could
             mingle
             oyle
             in
             drops
             so
             exceedingly
             minute
             ,
             that
             ,
             ev'n
             when
             there
             was
             but
             a
             few
             spoonfuls
             of
             the
             mixture
             ,
             it
             would
             continue
             whitish
             for
             divers
             whole
             days
             together
             )
             though
             at
             length
             they
             will
             emerge
             ;
             and
             the
             sooner
             ,
             because
             whilst
             they
             swim
             up
             and
             down
             ,
             as
             they
             frequently
             chance
             to
             meet
             and
             run
             into
             one
             another
             ,
             they
             compose
             greater
             Drops
             ;
             which
             are
             (
             for
             the
             Reason
             already
             given
             )
             less
             slowly
             impell'd
             up
             by
             the
             water
             :
             at
             the
             Top
             of
             which
             ,
             the
             Chymist
             ;
             after
             a
             due
             time
             ,
             is
             wont
             to
             find
             new
             oyl
             floating
             .
             But
             whether
             this
             be
             any
             way
             applicable
             to
             the
             swimming
             of
             the
             insensible
             particles
             of
             corroded
             metals
             in
             Aquaflortis
             ,
             and
             other
             saline
             .
             
             Menstruums
             ,
             I
             must
             not
             now
             stay
             to
             enquire
             .
          
           
             One
             thing
             more
             there
             is
             ,
             that
             I
             would
             point
             at
             before
             I
             dismiss
             this
             Paradox
             ;
             Namely
             ,
             that
             ,
             for
             the
             same
             Reason
             we
             have
             all
             this
             while
             deduc'd
             ,
             when
             the
             emergent
             drop
             ,
             or
             any
             other
             Body
             ,
             floats
             upon
             the
             Top
             of
             the
             water
             ,
             it
             will
             sinck
             just
             so
             far
             ,
             (
             &
             no
             farther
             )
             till
             the
             immers'd
             part
             of
             the
             floating
             Body
             be
             equal
             in
             Bulke
             to
             as
             much
             water
             as
             is
             equal
             in
             weight
             to
             the
             whole
             Body
             .
             
             For
             suppose
             ,
             in
             the
             annexed
             figure
             ,
             Y
             to
             be
             a
             Cube
             of
             wood
             three
             foot
             high
             and
             six
             pound
             in
             weight
             ;
             this
             wood
             ,
             being
             much
             heavier
             then
             Aire
             ,
             will
             sinck
             into
             the
             water
             ,
             till
             it
             come
             to
             an
             imaginary
             superficies
             ,
             
               X
               W
            
             ,
             where
             ,
             having
             the
             position
             newly
             describ'd
             ,
             it
             will
             necessarily
             acquiesce
             .
             For
             all
             the
             other
             equal
             parts
             of
             the
             Superficies
             ,
             
               X
               ,
               W
               ,
               Q
            
             ,
             being
             lean'd
             upon
             by
             pillars
             of
             water
             equal
             
             in
             height
             to
             the
             part
             
               X
               A
            
             ,
             or
             
               W
               B
            
             ,
             if
             the
             whole
             weight
             of
             the
             wooden
             Cube
             be
             greater
             then
             that
             of
             as
             much
             water
             as
             is
             equal
             to
             the
             immers'd
             part
             ,
             it
             must
             necessarily
             sinck
             lower
             ,
             because
             the
             subjacent
             part
             of
             the
             Surface
             (
             at
             
               V
               ,
            
             )
             will
             be
             more
             charg'd
             then
             any
             of
             the
             Rest
             .
             And
             ,
             on
             the
             other
             side
             ,
             if
             the
             Cube
             were
             lighter
             then
             as
             much
             water
             as
             that
             whose
             place
             the
             immers'd
             part
             takes
             up
             ;
             it
             must
             by
             the
             greater
             pressure
             of
             the
             water
             upon
             the
             other
             parts
             of
             the
             imaginary
             superficies
             
               X
               W
            
             ,
             then
             upon
             that
             contiguous
             to
             the
             wood
             ,
             (
             as
             at
             V
             )
             be
             impell'd
             upward
             ,
             til
             the
             pressure
             of
             the
             whole
             wood
             upon
             the
             part
             it
             leans
             on
             ,
             be
             of
             the
             same
             degree
             with
             that
             of
             the
             rest
             of
             the
             water
             ,
             upon
             the
             rest
             of
             the
             superficies
             :
             and
             consequently
             be
             the
             same
             with
             the
             water
             ,
             whose
             place
             the
             immers'd
             part
             of
             it
             takes
             up
             .
             The
             lightness
             of
             that
             immers'd
             part
             ,
             in
             respect
             of
             so
             much
             water
             ,
             being
             recompenc'd
             
             by
             the
             weight
             of
             the
             unimmers'd
             part
             ,
             which
             is
             extant
             above
             the
             Superficies
             of
             the
             water
             .
             And
             we
             see
             ,
             that
             when
             a
             piece
             of
             wood
             fals
             into
             water
             ,
             though
             ,
             by
             the
             impetus
             it
             acquires
             in
             falling
             ,
             it
             passes
             through
             divers
             imaginary
             plains
             that
             lye
             beneath
             its
             due
             station
             ;
             yet
             the
             greater
             pressure
             ,
             to
             which
             each
             of
             those
             plains
             is
             expos'd
             in
             all
             its
             other
             parts
             ,
             then
             in
             that
             which
             is
             contiguous
             to
             the
             Bottom
             of
             the
             wood
             ,
             dos
             quickly
             impel
             it
             up
             again
             ,
             till
             ,
             after
             some
             emersions
             and
             subsidings
             ,
             it
             rests
             at
             length
             in
             such
             a
             position
             ,
             as
             the
             newly
             explicated
             Hydrostatical
             Theorem
             assignes
             it
             .
          
           
             
             
               SCHOLIUM
               .
            
             
               THis
               Ingenious
               Proposition
               (
               about
               floating
               Bodys
               )
               is
               taught
               and
               prov'd
               after
               the
               manner
               of
               Mathematicians
               ,
               by
               the
               most
               subtle
               Archimedes
               and
               his
               Commentators
               :
               and
               we
               have
               newly
               been
               endeavouring
               to
               manifest
               the
               Physical
               reason
               why
               it
               must
               be
               true
               .
               But
               partly
               because
               the
               Proposition
               ought
               to
               hold
               ,
               not
               only
               in
               such
               intire
               and
               homogeneous
               Bodyes
               as
               men
               exemplifie
               it
               in
               ,
               (
               such
               as
               a
               piece
               of
               wood
               ,
               or
               a
               Lump
               of
               wax
               )
               but
               in
               all
               Bodyes
               ,
               though
               of
               a
               concave
               figure
               ,
               and
               made
               up
               of
               many
               Bodys
               of
               never
               so
               differing
               natures
               ;
               (
               and
               perhaps
               some
               of
               them
               joyn'd
               together
               only
               by
               their
               superincumbency
               upon
               one
               another
               )
               and
               partly
               because
               that
               a
               Truth
               ,
               which
               is
               one
               of
               the
               main
               and
               usefullest
               of
               the
               Hydrostaticks
               ,
               and
               may
               be
               of
               so
               much
               
               importance
               to
               Navigation
               ,
               has
               noyet
               (
               that
               I
               know
               of
               )
               been
               attemtpted
               to
               be
               demonstrated
               otherwise
               then
               upon
               Paper
               :
               it
               will
               not
               be
               amiss
               ,
               for
               the
               satisfaction
               of
               such
               of
               those
               whom
               it
               may
               concern
               ,
               as
               are
               not
               vers'd
               in
               Mathematical
               Demonstrations
               ,
               to
               add
               an
               Experiment
               which
               I
               made
               to
               prove
               it
               Mechanically
               ;
               as
               exactly
               as
               is
               necessary
               for
               the
               satisfaction
               of
               such
               persons
               .
            
             
               After
               (
               then
               )
               having
               imploy'd
               several
               Vessels
               ,
               some
               of
               wood
               ,
               some
               of
               Laton
               ,
               and
               some
               of
               other
               materials
               ,
               to
               compass
               what
               I
               desir'd
               ;
               we
               found
               glasses
               to
               be
               the
               most
               commodious
               we
               could
               procure
               .
               And
               therefore
               filling
               a
               large
               and
               deep
               glass
               to
               a
               convenient
               height
               with
               fair
               water
               ,
               we
               plac'd
               in
               it
               another
               deeper
               glass
               ,
               shap'd
               like
               a
               Goblet
               or
               Tumbler
               ,
               that
               it
               might
               be
               the
               fitter
               for
               swimming
               ;
               and
               having
               furnish'd
               it
               first
               with
               Ballast
               ,
               and
               then
               ,
               for
               merryment
               
               sake
               ,
               with
               a
               wooden
               Deck
               ,
               by
               which
               a
               tall
               Mass
               ,
               with
               a
               Sayle
               fusten'd
               to
               it
               ,
               was
               kept
               upright
               ;
               we
               fraughted
               with
               wood
               ,
               and
               by
               degrees
               pour'd
               Sand
               into
               it
               ,
               till
               we
               had
               made
               it
               s●●●k
               just
               to
               the
               Tops
               of
               certaine
               conspicuous
               marks
               ,
               that
               we
               had
               fasten'd
               on
               the
               outside
               of
               the
               Glass
               to
               opposite
               parts
               thereof
               .
               Then
               observing
               how
               high
               the
               water
               reach'd
               in
               the
               larger
               Glass
               ,
               (
               which
               by
               reason
               of
               the
               Vessels
               Transparency
               was
               easie
               to
               be
               seen
               )
               we
               carefully
               plac'd
               two
               or
               three
               markes
               in
               the
               same
               level
               with
               the
               Horizontal
               Surface
               of
               the
               water
               ;
               and
               taking
               out
               the
               floating
               Vessel
               ,
               as
               it
               was
               ,
               with
               all
               that
               belong'd
               to
               it
               ,
               and
               wiping
               the
               outside
               dry
               ,
               we
               put
               it
               into
               a
               good
               paire
               of
               scales
               ,
               and
               having
               found
               what
               it
               amounted
               to
               ,
               we
               weigh'd
               in
               a
               competently
               large
               Viol
               (
               first
               counterpoiz'd
               apart
               )
               so
               much
               water
               ,
               (
               to
               a
               graine
               ,
               or
               thereabouts
               ,
               )
               and
               pouring
               this
               water
               
               into
               the
               large
               Glass
               above
               mentioned
               ,
               we
               found
               it
               to
               reach
               to
               the
               marks
               that
               we
               had
               fastened
               to
               the
               outside
               of
               the
               Glass
               ,
               and
               consequently
               to
               reach
               to
               the
               same
               height
               to
               which
               the
               weight
               of
               the
               floating
               glass
               ,
               and
               all
               that
               was
               added
               to
               make
               it
               resemble
               a
               Ship
               ,
               had
               made
               it
               arise
               to
               .
               By
               which
               Experiment
               (
               which
               we
               tried
               ,
               as
               to
               the
               essential
               parts
               of
               it
               ,
               with
               Vessels
               of
               differing
               sizes
               ,
               shapes
               ;
               and
               ladings
               too
               ,
               as
               Wood
               ,
               Stone
               ,
               Quick-silver
               ,
               &c.
               )
               it
               appears
               ,
               that
               the
               floating
               Vessel
               it self
               ,
               with
               all
               that
               was
               in
               it
               ,
               or
               supported
               by
               it
               ,
               was
               equal
               in
               weight
               to
               as
               much
               water
               as
               was
               equal
               in
               bulk
               to
               that
               part
               of
               the
               Vessel
               which
               was
               under
               water
               ,
               suppos'd
               to
               be
               cut
               off
               from
               the
               extant
               part
               of
               the
               same
               vessel
               by
               a
               plain
               continuing
               the
               Horizontal
               Surface
               of
               the
               water
               :
               since
               the
               weight
               of
               the
               floating
               Vessel
               ,
               which
               rais'd
               up
               the
               water
               in
               the
               larger
               Vessel
               to
               the
               greatest
               height
               it
               attain'd
               ,
               was
               the
               same
               
               with
               the
               weight
               of
               the
               water
               ,
               which
               being
               pour'd
               into
               the
               larger
               vessel
               (
               when
               the
               other
               was
               taken
               out
               )
               rais'd
               the
               water
               therein
               to
               the
               same
               height
               .
               We
               may
               also
               obtaine
               the
               same
               end
               ,
               by
               a
               somewhat
               differing
               way
               ,
               (
               which
               is
               the
               best
               way
               in
               case
               the
               Vessels
               be
               too
               great
               viz.
               to
               observe
               ,
               first
               ,
               by
               pouring
               in
               water
               out
               of
               a
               Bowle
               or
               Paile
               ,
               or
               other
               Vessel
               of
               known
               capacity
               ,
               as
               often
               as
               is
               necessary
               to
               fill
               the
               great
               Vessel
               ,
               or
               Cistern
               ,
               or
               Pond
               ,
               to
               the
               Top
               ,
               (
               or
               to
               any
               determinate
               height
               requir'd
               )
               and
               ,
               next
               ,
               letting
               out
               ,
               or
               otherwise
               removing
               all
               that
               water
               ,
               to
               put
               in
               its
               place
               the
               Vessel
               ,
               whose
               weight
               is
               to
               be
               found
               out
               .
               Thirdly
               ,
               to
               let
               ,
               or
               poure
               in
               ,
               water
               till
               the
               Vessel
               be
               afloat
               ,
               and
               by
               its
               weight
               raise
               the
               External
               water
               to
               the
               height
               it
               had
               before
               :
               And
               lastly
               ,
               to
               examine
               how
               much
               this
               water
               ,
               that
               was
               last
               pour'd
               in
               ,
               falls
               short
               in
               weight
               
               of
               the
               water
               that
               was
               in
               it
               at
               first
               ,
               and
               afterwards
               remov'd
               .
               For
               this
               difference
               will
               give
               us
               the
               weight
               of
               as
               much
               water
               ,
               as
               is
               aequiponderate
               to
               the
               whole
               floating
               Vessel
               ,
               whither
               small
               or
               great
               ,
               with
               all
               that
               it
               either
               carries
               or
               susteins
               .
               The
               Hydrostatical
               Theorem
               we
               have
               been
               considering
               ,
               and
               the
               Experiments
               whereby
               we
               have
               endeavour'd
               to
               confirm
               ,
               or
               illustrate
               it
               ,
               may
               
                 (
                 Mutatis
                 mutandis
              
               )
               be
               apply'd
               to
               a
               Ship
               with
               all
               her
               Ballast
               ,
               Lading
               ,
               Guns
               ,
               and
               Company
               ;
               it
               holding
               generally
               true
               ,
               That
               (
               to
               express
               the
               sence
               of
               the
               Proposition
               more
               briefly
               )
               
                 the
                 weight
                 of
                 a
                 floating
                 Body
                 ,
                 is
                 equal
                 to
                 as
                 much
                 water
                 ,
                 as
                 its
                 immers'd
                 part
                 takes
                 up
                 the
                 room
                 of
                 .
              
               Whence
               we
               might
               draw
               some
               Arguments
               in
               favour
               of
               the
               Learned
               Stevinus
               ,
               (
               for
               whose
               sake
               it
               partly
               was
               that
               I
               annexed
               this
               Scholium
               )
               who
               ,
               if
               I
               mis-remember
               not
               ,
               does
               somewhere
               deduce
               as
               a
               Corollary
               
               from
               certain
               Hydrostatical
               Propositions
               ,
               
               That
               a
               whole
               Ship
               ,
               and
               all
               that
               belongs
               to
               it
               ,
               and
               leans
               upon
               it
               ,
               presses
               no
               more
               nor
               less
               upon
               the
               Bottome
               it
               swims
               over
               ,
               then
               as
               much
               water
               ,
               as
               is
               equal
               in
               bulk
               to
               that
               part
               of
               the
               Ship
               which
               is
               beneath
               the
               Surface
               of
               the
               water
               .
            
          
        
         
           
           
             PARADOX
             IV.
             
          
           
             That
             in
             the
             Ascension
             of
             water
             in
             Pumps
             ,
             &c.
             there
             needs
             nothing
             to
             raise
             the
             Water
             ,
             but
             a
             competent
             weight
             of
             an
             External
             Fluid
             .
          
           
             THis
             Proposition
             may
             be
             easily
             enough
             deduc'd
             from
             the
             already
             mention'd
             Experiments
             .
             But
             yet
             ,
             for
             further
             illustration
             and
             proof
             ,
             vve
             vvill
             add
             that
             vvhich
             follovvs
             .
          
           
             Take
             a
             slender
             Glass-pipe
             ,
             (
             such
             as
             vvas
             us'd
             about
             the
             first
             Experiment
             )
             and
             suck
             into
             it
             about
             the
             height
             of
             an
             Inch
             of
             deeply
             tincted
             vvater
             ;
             and
             ,
             nimbly
             stopping
             the
             upper
             Orifice
             ,
             immerse
             the
             lovver
             part
             of
             the
             pipe
             into
             a
             Glass
             half
             fill'd
             vvith
             such
             tincted
             vvater
             ,
             till
             the
             Surface
             of
             the
             Liquor
             
             in
             the
             pipe
             be
             an
             inch
             (
             or
             as
             low
             as
             you
             would
             have
             it
             )
             beneath
             that
             of
             the
             External
             water
             .
             Then
             pouring
             on
             oyle
             of
             Turpentine
             till
             it
             swim
             3
             or
             4
             Inches
             ,
             or
             as
             high
             as
             you
             please
             above
             the
             vvater
             ;
             loosen
             gently
             your
             finger
             from
             the
             upper
             Orifice
             of
             the
             pipe
             ,
             to
             give
             the
             inclosed
             Aire
             a
             little
             intercourse
             vvith
             the
             External
             ,
             and
             you
             shall
             see
             the
             tincted
             vvater
             in
             the
             pipe
             ,
             to
             be
             impell'd
             up
             ,
             not
             only
             higher
             then
             the
             Surface
             of
             the
             External
             vvater
             ,
             but
             almost
             as
             high
             as
             that
             of
             the
             External
             oyl
             ,
             through
             vvhich
             (
             it
             being
             transparent
             and
             colourless
             )
             the
             Red
             Liquor
             may
             be
             easily
             discern'd
             .
          
           
             Novv
             in
             this
             case
             it
             cau't
             be
             pretended
             ,
             That
             the
             ascent
             of
             the
             water
             in
             the
             pipe
             proceeds
             from
             Natures
             abhorrency
             of
             a
             Vacuum
             ;
             since
             the
             pipe
             being
             full
             of
             aire
             ,
             and
             its
             Orifice
             unstopp'd
             ,
             though
             the
             vvater
             should
             not
             ascend
             ,
             no
             danger
             of
             a
             Vacuum
             vvould
             ensue
             ;
             the
             aire
             and
             the
             vvater
             remaining
             contiguous
             as
             before
             .
          
           
           
             The
             true
             Reason
             then
             of
             the
             ascent
             of
             the
             water
             ,
             in
             our
             case
             ,
             is
             but
             this
             ,
             That
             upon
             all
             the
             other
             parts
             of
             the
             Imaginary
             Superficies
             ,
             that
             passes
             by
             the
             immers'd
             Orifice
             of
             the
             pipe
             ,
             there
             is
             a
             pressure
             partly
             of
             water
             ,
             and
             partly
             of
             the
             oyle
             swimming
             upon
             that
             water
             ,
             amounting
             to
             the
             pressure
             of
             4
             or
             5
             inches
             of
             water
             ;
             whereas
             upon
             that
             part
             of
             the
             same
             superficies
             whereon
             the
             Liquor
             contain'd
             in
             the
             pipe
             leans
             ,
             there
             is
             but
             the
             pressure
             of
             one
             inch
             of
             water
             ,
             so
             that
             the
             parts
             near
             the
             immers'd
             Orifice
             must
             necessarily
             be
             thrust
             out
             of
             place
             by
             the
             other
             parts
             of
             water
             that
             are
             more
             press'd
             ;
             till
             so
             much
             Liquor
             be
             impell'd
             up
             into
             the
             pipe
             as
             makes
             the
             pressure
             on
             that
             part
             of
             the
             Imaginary
             Superficies
             ,
             as
             great
             as
             that
             of
             the
             oyle
             and
             water
             on
             any
             other
             equal
             part
             of
             it
             :
             and
             then
             ,
             by
             Vertue
             of
             the
             Aequilibrium
             ,
             (
             often
             mention'd
             )
             the
             water
             will
             rise
             no
             further
             ;
             and
             ,
             by
             vertue
             of
             the
             
             same
             Aequilibrium
             ,
             it
             will
             rest
             a
             little
             beneath
             ,
             the
             Surface
             of
             the
             External
             oyle
             ,
             because
             this
             last
             nam'd
             Liquor
             is
             lesse
             heavy
             ,
             bulk
             for
             bulk
             ,
             then
             water
             .
          
           
             And
             by
             this
             we
             may
             be
             assisted
             to
             give
             a
             reason
             of
             the
             Ascension
             of
             water
             in
             ordinary
             sucking
             Pumps
             .
             For
             as
             the
             oyle
             of
             Turpentine
             ,
             though
             a
             lighter
             Liquor
             then
             water
             ,
             and
             not
             mingleable
             with
             it
             ,
             does
             ,
             by
             leaning
             upon
             the
             Surface
             of
             the
             External
             water
             ,
             press
             up
             the
             water
             within
             the
             pipe
             ,
             to
             a
             far
             greater
             height
             then
             that
             of
             the
             External
             water
             it self
             :
             so
             the
             Aire
             ,
             which
             ,
             though
             a
             far
             lighter
             Liquor
             then
             oyle
             of
             Turpentine
             ,
             reaches
             I
             know
             not
             how
             many
             Miles
             high
             ,
             leaning
             upon
             the
             Surface
             of
             the
             water
             in
             a
             Well
             ,
             would
             press
             it
             up
             into
             the
             Cylindrical
             Cavity
             of
             the
             Pump
             ▪
             much
             higher
             then
             the
             External
             water
             it self
             reaches
             in
             the
             Well
             ,
             if
             it
             were
             not
             hinder'd
             .
          
           
             Now
             that
             which
             hinders
             it
             in
             the
             
             Pump
             ,
             is
             either
             the
             Sucker
             ,
             which
             fences
             the
             water
             in
             the
             Pump
             from
             the
             pressure
             of
             the
             External
             aire
             ,
             or
             that
             pressure
             it self
             .
             And
             therefore
             ,
             all
             that
             the
             drawing
             up
             of
             the
             Sucker
             needs
             to
             do
             ,
             is
             ,
             to
             free
             the
             water
             in
             the
             Pipe
             from
             the
             impediment
             to
             its
             Ascent
             ,
             which
             was
             given
             it
             by
             the
             Suckers
             leaning
             on
             it
             ,
             or
             the
             pillar
             of
             the
             Atmosphaeres
             being
             incumbent
             on
             it
             ;
             as
             in
             our
             Experiment
             ,
             the
             sides
             of
             the
             pipe
             do
             sufficiently
             protect
             the
             water
             in
             the
             pipe
             from
             any
             pressure
             of
             the
             External
             oyle
             ,
             that
             may
             oppose
             its
             ascent
             .
          
           
             And
             lastly
             ,
             as
             the
             water
             in
             our
             pipe
             was
             impell'd
             up
             so
             high
             ,
             and
             no
             higher
             ,
             that
             the
             Cylinder
             of
             water
             in
             the
             pipe
             was
             just
             able
             to
             ballance
             the
             pressure
             of
             the
             water
             and
             oyle
             without
             the
             pipe
             ;
             so
             in
             Pumps
             ,
             the
             water
             does
             rise
             but
             to
             a
             certain
             height
             ,
             as
             about
             33
             or
             34
             foot
             :
             and
             though
             you
             pump
             never
             so
             long
             ,
             it
             will
             be
             rais'd
             no
             
             higher
             ;
             because
             at
             that
             height
             the
             pressure
             of
             the
             water
             in
             the
             Pump
             ,
             upon
             that
             part
             of
             the
             imaginary
             Superficies
             that
             passes
             by
             the
             lower
             Orifice
             of
             it
             ,
             is
             the
             same
             with
             the
             pressure
             which
             other
             parts
             of
             that
             imaginary
             superficies
             ▪
             sustaine
             from
             as
             much
             of
             the
             External
             water
             ,
             and
             of
             the
             Atmosphaere
             ,
             as
             come
             to
             lean
             upon
             it
             .
          
           
             That
             there
             may
             be
             cases
             wherein
             water
             may
             be
             rais'd
             by
             suction
             ,
             not
             upon
             the
             Account
             of
             the
             weight
             of
             the
             aire
             ,
             but
             of
             its
             spring
             ,
             I
             have
             elsewhere
             shovvn
             ;
             and
             having
             likevvise
             in
             other
             places
             ;
             endeavour'd
             to
             explicate
             more
             particularly
             the
             ascension
             of
             vvater
             in
             Pumps
             ;
             vvhat
             has
             been
             said
             already
             may
             suffice
             to
             be
             said
             in
             this
             place
             ,
             where
             't
             is
             sufficient
             for
             me
             to
             have
             shovvn
             ,
             That
             vvhither
             or
             no
             the
             Ascension
             of
             water
             
               may
               have
            
             other
             causes
             ,
             yet
             in
             the
             cases
             propos'd
             ,
             
               it
               needs
            
             no
             more
             then
             the
             competent
             vveight
             of
             
             an
             External
             Fluid
             ,
             as
             is
             the
             Aire
             ;
             vvhose
             not
             being
             devoid
             of
             gravity
             ,
             the
             Cogency
             of
             our
             Experiments
             has
             brought
             even
             our
             Adversaries
             to
             grant
             us
             .
          
           
             For
             confirmation
             of
             this
             ,
             I
             will
             here
             add
             ,
             because
             it
             now
             comes
             into
             my
             mind
             ,
             (
             what
             might
             perhaps
             be
             elsewhere
             somewhat
             more
             properly
             mention'd
             )
             an
             Experiment
             that
             I
             did
             but
             lightly
             glance
             at
             in
             the
             Explication
             of
             the
             first
             ,
             and
             the
             Scholium
             of
             the
             second
             Paradox
             .
          
           
             In
             order
             to
             this
             I
             must
             advertise
             ,
             That
             ,
             whereas
             I
             there
             took
             notice
             ,
             that
             some
             Ingenious
             men
             had
             complain'd
             ,
             that
             ,
             contrary
             to
             the
             Experiment
             propos'd
             by
             
               Monsieur
               Paschall
            
             ,
             they
             were
             not
             at
             all
             able
             to
             keep
             Mercury
             suspended
             in
             Tubes
             ,
             however
             very
             slender
             ,
             though
             the
             lower
             end
             were
             deeply
             immers'd
             in
             water
             ,
             if
             both
             their
             ends
             were
             open
             :
             The
             Reasons
             of
             my
             doubting
             ,
             whether
             our
             Ingenious
             Author
             
             had
             ever
             made
             or
             seen
             the
             Experiment
             ,
             were
             ,
             not
             only
             that
             it
             had
             been
             unsuccesfully
             tryed
             ,
             and
             seem'd
             to
             me
             unlikely
             to
             succeed
             in
             Tubes
             more
             slender
             then
             his
             appear'd
             ;
             but
             because
             the
             Impetus
             ,
             which
             falling
             quick
             silver
             gains
             by
             the
             acceleration
             of
             motion
             it
             acquires
             in
             its
             descent
             ,
             must
             in
             all
             probability
             be
             great
             enough
             to
             make
             it
             all
             run
             out
             at
             the
             bottom
             of
             a
             Tube
             ,
             open
             at
             both
             ends
             ,
             and
             fill'd
             with
             so
             ponderous
             a
             Liquor
             ,
             though
             the
             Tube
             were
             very
             much
             shorter
             then
             that
             propos'd
             by
             
               Monsieur
               Paschall
            
             .
          
           
             This
             advertisement
             I
             premise
             to
             intimate
             ,
             that
             ,
             notwithstanding
             the
             hopelessness
             of
             the
             Experiment
             ,
             as
             it
             had
             been
             propos'd
             and
             tried
             ,
             I
             might
             have
             reason
             not
             to
             think
             it
             impossible
             to
             perform
             ,
             by
             another
             way
             ,
             the
             main
             thing
             desir'd
             ;
             which
             was
             to
             keep
             Quicksilver
             suspended
             in
             a
             Tube
             ,
             open
             at
             both
             ends
             ,
             by
             the
             resistance
             of
             the
             subjacent
             
             water
             .
             For
             by
             the
             Expedient
             I
             am
             going
             to
             propose
             ,
             I
             have
             been
             able
             to
             do
             it
             ,
             even
             with
             a
             Liquor
             much
             lighter
             then
             water
             .
          
           
             Finding
             then
             ,
             that
             even
             a
             very
             short
             Cylinder
             of
             so
             ponderous
             a
             fluid
             ,
             as
             Mercury
             ,
             would
             ,
             if
             it
             were
             once
             in
             falling
             ,
             descend
             with
             an
             impetus
             not
             easy
             to
             be
             resisted
             by
             the
             subjacent
             Liquor
             ,
             I
             thought
             upon
             the
             following
             Expedient
             to
             prevent
             this
             inconvenience
             .
             I
             took
             a
             slender
             pipe
             ,
             the
             Diameter
             of
             whose
             Cavity
             was
             little
             above
             the
             sixth
             part
             of
             an
             Inch
             ,
             and
             having
             suck'd
             in
             at
             the
             lower
             end
             of
             it
             somewhat
             lesse
             then
             half
             an
             inch
             of
             Quicksilver
             ,
             and
             nimbly
             stopp'd
             the
             upper
             Orifice
             with
             my
             finger
             ;
             I
             thrust
             the
             Quicksilver
             into
             ,
             a
             deep
             glass
             of
             oyle
             of
             Turpentine
             ,
             with
             a
             care
             not
             to
             unstop
             the
             upper
             Orifice
             ,
             till
             the
             small
             Cylinder
             of
             quicksilver
             was
             18
             or
             20
             times
             its
             depth
             beneath
             the
             Surface
             of
             the
             oyle
             .
             For
             
             by
             this
             means
             ,
             when
             I
             unstopp'd
             the
             pipe
             ,
             the
             Quicksilver
             needed
             not
             (
             as
             otherwise
             it
             would
             )
             begin
             to
             fall
             ,
             as
             having
             a
             longer
             Cylinder
             then
             was
             requisite
             to
             make
             an
             Aequilibrium
             with
             the
             other
             fluid
             .
             For
             by
             our
             Expedient
             the
             pressure
             of
             the
             oyle
             was
             already
             full
             as
             great
             ,
             if
             not
             greater
             ,
             against
             the
             lower
             part
             of
             the
             Mercurial
             Cylinder
             ,
             as
             that
             which
             the
             weight
             of
             so
             short
             a
             Cylinder
             could
             exercise
             upon
             the
             contiguous
             and
             subjacent
             oyle
             .
             And
             accordingly
             ,
             upon
             the
             removal
             of
             my
             finger
             ,
             the
             Quicksilver
             did
             not
             run
             out
             ,
             but
             remain
             suspended
             in
             the
             lower
             part
             of
             the
             pipe
             .
             And
             as
             ;
             if
             I
             rais'd
             it
             towards
             the
             Superficies
             of
             the
             oyle
             ,
             the
             Mercury
             would
             drop
             out
             for
             want
             of
             its
             wonted
             Counterpoize
             ;
             so
             ,
             if
             I
             thrust
             the
             pipe
             deeper
             into
             the
             oyle
             ,
             the
             increas'd
             pressure
             of
             the
             oyle
             would
             proportionably
             impell
             up
             the
             Mercury
             towards
             the
             higher
             parts
             of
             the
             pipe
             ,
             
             which
             being
             again
             a
             little
             ,
             and
             but
             a
             little
             ,
             rais'd
             ,
             the
             Quicksilver
             would
             fall
             down
             a
             little
             nearer
             the
             bottom
             of
             the
             pipe
             :
             and
             so
             ,
             with
             a
             not
             unpleasant
             spectacle
             ,
             the
             ponderous
             Body
             of
             quick
             silver
             was
             made
             sometimes
             to
             rise
             ,
             and
             sometimes
             to
             fall
             ;
             but
             still
             to
             float
             up
             on
             the
             Surface
             of
             a
             Liquor
             ,
             lighter
             ther
             common
             Spirit
             of
             Wine
             it self
             .
          
           
             But
             ,
             besides
             that
             the
             Experiment
             ,
             if
             the
             maker
             of
             it
             be
             not
             very
             careful
             ;
             may
             easily
             enough
             miscarry
             ,
             the
             divertisement
             it
             gives
             seldome
             proves
             lasting
             ;
             the
             oyle
             of
             Turpentine
             after
             a
             while
             insinuating
             it self
             betwixt
             the
             sides
             of
             the
             pipe
             ,
             and
             those
             of
             so
             short
             a
             Cylinder
             of
             Mercury
             ,
             and
             thereby
             disordering
             all
             .
             And
             therefore
             ,
             though
             I
             here
             mention
             this
             Experiment
             ,
             as
             I
             tryed
             it
             in
             oyle
             of
             Turpentine
             ;
             because
             that
             is
             the
             Liquor
             I
             make
             use
             of
             all
             along
             these
             Paradoxes
             ;
             and
             because
             also
             I
             would
             shew
             that
             a
             lighter
             fluid
             then
             
             water
             ,
             (
             and
             therefore
             why
             not
             aire
             ,
             if
             its
             height
             be
             greatly
             enough
             increas'd
             :
             )
             may
             by
             its
             weight
             and
             pressure
             ,
             either
             keep
             the
             Mercury
             suspended
             in
             pipes
             ,
             or
             even
             raise
             it
             in
             them
             :
             Yet
             I
             found
             water
             (
             wherewith
             I
             fill'd
             tall
             glasses
             )
             a
             fitter
             Liquor
             then
             oyle
             for
             the
             Experiment
             ;
             in
             which
             though
             I
             sought
             ,
             and
             found
             some
             other
             Phaenomena
             ,
             yet
             because
             they
             more
             properly
             belong
             to
             another
             place
             ,
             I
             shall
             leave
             them
             unmention'd
             in
             this
             .
          
           
             And
             since
             Experience
             shews
             us
             ,
             that
             a
             Cylinder
             of
             ,
             Mercury
             ,
             of
             about
             30
             Inches
             high
             ,
             is
             aequiponderant
             to
             a
             Cylinder
             of
             water
             of
             about
             33
             or
             34
             foot
             high
             ;
             it
             s
             very
             easie
             to
             conclude
             ,
             That
             the
             weight
             of
             the
             External
             aire
             ,
             which
             is
             able
             to
             raise
             and
             keep
             suspended
             33
             or
             34
             foot
             of
             water
             in
             a
             Pump
             ,
             may
             do
             the
             like
             to
             29
             or
             30
             Inches
             of
             Quicksilver
             in
             the
             Torricellian
             Experiment
             .
          
        
         
           
           
             PARADOX
             V.
             
          
           
             That
             the
             pressure
             of
             an
             External
             Fluid
             is
             able
             to
             keep
             an
             Heterogeneous
             Liquor
             suspended
             at
             the
             same
             height
             in
             several
             Pipes
             ,
             though
             those
             Pipes
             be
             of
             very
             different
             Diameters
             .
          
           
             THE
             contrary
             of
             this
             Proposition
             is
             so
             confidently
             asserted
             and
             believed
             ,
             by
             those
             Mathematicians
             ,
             and
             others
             ,
             that
             favour
             the
             Doctrine
             of
             the
             Schools
             ;
             That
             this
             perswasion
             of
             theirs
             seems
             to
             be
             the
             chief
             thing
             ,
             that
             has
             hinderd
             men
             from
             acknowledging
             ,
             that
             the
             Quicksilver
             in
             the
             Torricellian
             Experiment
             may
             be
             kept
             suspended
             by
             the
             Counterpoize
             of
             the
             external
             aire
             .
             And
             a
             famous
             writer
             ,
             that
             has
             lately
             
             treated
             ,
             as
             well
             of
             the
             Hydrostaticks
             ,
             as
             of
             the
             〈◊〉
             of
             the
             Torricellian
             experiment
             〈…〉
             the
             falsehood
             of
             our
             Paradox
             ,
             That
             ,
             laying
             aside
             all
             other
             Arguments
             ,
             he
             contents
             himself
             to
             confute
             his
             Adversaries
             with
             one
             Demonstration
             (
             as
             he
             calls
             it
             )
             grounded
             on
             the
             quite
             contrary
             of
             what
             we
             here
             assert
             .
             For
             his
             Objection
             runs
             to
             this
             sence
             .
             That
             if
             it
             were
             the
             pressure
             of
             the
             External
             Aire
             ,
             that
             kept
             the
             Quicksilver
             suspended
             in
             the
             newly
             mention'd
             experiment
             ,
             the
             height
             would
             not
             (
             as
             Experience
             shews
             it
             is
             )
             be
             the
             same
             in
             all
             Cylindrical
             pipes
             ,
             though
             of
             very
             differing
             B●●es
             .
             For
             ,
             supposing
             the
             height
             of
             the
             Mercurial
             Cylinder
             ,
             in
             a
             Tube
             of
             half
             an
             Inch
             Diameter
             ,
             to
             be
             29
             Inches
             ;
             't
             is
             plain
             ,
             that
             a
             Mercurial
             Cylinder
             of
             the
             same
             height
             ,
             and
             three
             Inches
             in
             Diameter
             ,
             must
             weigh
             divers
             times
             as
             much
             as
             the
             former
             ;
             and
             therefore
             the
             pressure
             
             of
             the
             External
             aire
             ,
             being
             but
             one
             and
             the
             same
             ,
             if
             it
             be
             a
             just
             Counterpoize
             to
             the
             greater
             Cylinder
             ,
             it
             cannot
             be
             so
             to
             the
             less
             ;
             and
             if
             it
             be
             able
             to
             keep
             the
             one
             suspended
             at
             29
             Inches
             it
             must
             be
             able
             to
             keep
             the
             other
             suspended
             at
             a
             far
             greater
             height
             ,
             which
             yet
             is
             contrary
             to
             experience
             .
             And
             indeed
             this
             Objection
             is
             so
             specious
             ,
             That
             ,
             though
             I
             elsewhere
             have
             already
             answer'd
             it
             ,
             both
             by
             reason
             and
             Experience
             ,
             as
             far
             forth
             as
             it
             concerns
             the
             Torricellian
             Experiment
             ;
             Yet
             ,
             to
             shew
             the
             mistake
             on
             which
             it
             is
             grounded
             ,
             it
             may
             be
             very
             well
             worth
             while
             to
             make
             out
             ,
             our
             proposed
             Paradox
             ,
             (
             as
             that
             whose
             truth
             will
             sufficiently
             disprove
             that
             errour
             )
             by
             shewing
             both
             that
             the
             Assertion
             is
             true
             ,
             and
             why
             it
             must
             be
             so
             .
          
           
             Provide
             then
             a
             more
             then
             ordinarily
             wide
             mouth'd
             Glass
             ,
             
             cleer
             ,
             and
             of
             a
             Convenient
             depth
             ;
             into
             which
             having
             put
             a
             convenient
             
             quantity
             of
             water
             ,
             deeply
             ting'd
             with
             Brazil
             or
             some
             other
             Pigment
             ,
             fit
             to
             the
             Orifice
             a
             broad
             but
             thin
             Cork
             ,
             in
             which
             ,
             by
             burning
             or
             cutting
             ,
             make
             divers
             round
             holes
             of
             very
             differing
             widenesses
             ;
             into
             each
             of
             which
             you
             may
             thrust
             a
             glass
             Cylinder
             ,
             open
             at
             both
             ends
             ,
             and
             of
             a
             size
             fit
             for
             the
             hole
             that
             is
             to
             receive
             it
             ;
             that
             so
             the
             several
             pipes
             may
             be
             imbrac'd
             by
             these
             several
             holes
             ;
             And
             ,
             as
             neare
             as
             you
             can
             ,
             make
             them
             parallel
             to
             one
             another
             ,
             and
             perpendicular
             to
             the
             superficies
             of
             the
             water
             ,
             into
             which
             they
             are
             to
             be
             immers'd
             .
             But
             we
             must
             not
             forget
             ,
             that
             ,
             besides
             these
             holes
             ,
             there
             is
             an
             aperture
             to
             be
             made
             in
             the
             same
             Corke
             (
             it
             matters
             not
             much
             of
             what
             figure
             or
             whereabouts
             )
             to
             receive
             the
             slender
             end
             of
             a
             glass
             Funnel
             ;
             by
             which
             oyl
             may
             be
             convey'd
             into
             the
             vessel
             ,
             when
             it
             is
             stopp'd
             with
             the
             Cork
             .
             And
             in
             the
             slender
             part
             of
             this
             Funnel
             
             we
             use
             to
             put
             some
             Cotton-week
             ,
             to
             break
             the
             violence
             of
             the
             oyl
             that
             is
             to
             be
             pour'd
             in
             ,
             which
             might
             else
             disorder
             the
             Experiment
             .
             All
             this
             being
             thus
             provided
             ,
             and
             the
             Cork
             (
             furnish'd
             with
             its
             pipes
             )
             being
             fitted
             to
             the
             Orifice
             of
             the
             Vessel
             ;
             if
             at
             the
             Funnel
             you
             pour
             in
             oyl
             of
             Turpentine
             ,
             and
             place
             the
             Glass
             betwixt
             your
             eye
             and
             the
             Light
             ;
             you
             may
             ,
             through
             that
             transparent
             Liquor
             ;
             perceive
             the
             Tincted
             water
             ,
             to
             be
             impell'd
             up
             into
             all
             the
             pipes
             ,
             and
             to
             rise
             uniformly
             in
             them
             .
             And
             ,
             when
             this
             tincted
             Liquor
             has
             attain'd
             to
             the
             height
             of
             two
             or
             three
             ,
             or
             more
             Inches
             ,
             above
             the
             lowermost
             Surface
             of
             the
             External
             oyl
             ;
             if
             you
             remove
             the
             Funnel
             ,
             (
             which
             yet
             you
             need
             not
             do
             ,
             unless
             there
             be
             yet
             oyl
             in
             it
             ,
             )
             you
             may
             plainly
             perceive
             the
             water
             to
             reach
             as
             high
             ,
             in
             one
             of
             the
             smaller
             pipes
             ,
             as
             in
             another
             three
             or
             four
             times
             as
             great
             ;
             and
             yet
             the
             
             water
             in
             the
             several
             pipes
             (
             as
             't
             is
             evident
             )
             is
             sustain'd
             ,
             at
             that
             height
             above
             the
             level
             of
             the
             other
             water
             ,
             by
             the
             pressure
             or
             counterprize
             of
             the
             external
             oyle
             ;
             which
             then
             if
             one
             being
             lighter
             in
             specie
             then
             water
             ,
             will
             have
             its
             Surface
             somewhat
             higher
             without
             the
             pipes
             ,
             then
             that
             of
             the
             Tincted
             water
             within
             them
             .
             And
             if
             by
             the
             Aperture
             ,
             that
             receives
             the
             Funnel
             ,
             you
             immerse
             ,
             almost
             to
             the
             Bottom
             of
             the
             oyle
             ,
             the
             shorter
             leg
             of
             a
             slender
             glass
             Syphon
             ,
             at
             whose
             longer
             Leg
             you
             procure
             by
             Suction
             the
             oyle
             to
             run
             out
             ;
             you
             shall
             perceive
             ,
             That
             ,
             according
             as
             the
             depth
             and
             pressure
             of
             the
             External
             third
             decreases
             ,
             so
             the
             water
             in
             the
             pipe
             will
             subside
             ;
             and
             that
             uniformely
             ,
             as
             well
             in
             the
             lesser
             as
             in
             the
             greater
             pipes
             .
          
           
             The
             Reason
             of
             this
             is
             not
             difficult
             to
             be
             render'd
             ,
             by
             the
             Doctrine
             already
             deliver'd
             .
             For
             suppose
             ,
             E
             F
             to
             be
             the
             Surface
             of
             the
             water
             ,
             both
             within
             
             and
             without
             the
             pipes
             ,
             before
             any
             oyle
             was
             poured
             on
             it
             :
             if
             we
             then
             suppose
             the
             oyle
             to
             be
             poured
             in
             through
             the
             Funnel
             ,
             its
             lightness
             in
             respect
             of
             water
             ,
             wherewith
             it
             will
             not
             mingle
             ,
             will
             keep
             it
             from
             getting
             into
             the
             cavity
             of
             the
             pipes
             
               L
               ,
               M
               ,
               N
            
             ;
             and
             therefore
             spreading
             it self
             on
             the
             outside
             of
             them
             above
             ,
             it
             must
             necessarily
             ,
             by
             its
             gravity
             ,
             press
             down
             the
             Superficies
             of
             the
             external
             water
             ,
             and
             impell
             up
             that
             liquor
             into
             the
             cavities
             of
             the
             pipes
             .
             And
             if
             we
             suppose
             the
             pouring
             on
             of
             the
             oyl
             to
             be
             continued
             till
             the
             uppermost
             surface
             of
             the
             oyl
             be
             raised
             to
             
               G
               H
            
             ,
             and
             that
             of
             the
             external
             water
             depress'd
             to
             
               I
               K
            
             ,
             (
             or
             thereabouts
             ,
             )
             an
             imaginary
             plain
             passing
             along
             the
             lower
             Orifices
             of
             the
             pipes
             ;
             I
             say
             ,
             the
             tincted
             waters
             in
             the
             pipes
             ought
             to
             have
             their
             uppermost
             Surfaces
             in
             the
             same
             level
             ,
             notwithstanding
             the
             great
             inequality
             of
             their
             Bores
             .
             For
             that
             part
             of
             the
             Surface
             
             IK
             ,
             which
             is
             comprehended
             within
             the
             Circular
             Orifice
             of
             the
             greatest
             pipe
             L
             ,
             is
             no
             more
             charged
             by
             the
             incumbent
             water
             ,
             then
             any
             other
             part
             ,
             equal
             to
             that
             Circle
             of
             the
             same
             Imaginary
             Superficies
             ,
             is
             by
             the
             water
             or
             oyle
             incumbent
             on
             it
             ;
             (
             and
             consequently
             ,
             no
             more
             then
             the
             part
             comprehended
             within
             the
             circle
             of
             the
             finall
             pipe
             N
             ,
             is
             by
             the
             water
             contain'd
             in
             that
             small
             pipe
             ;
             )
             the
             external
             oyle
             having
             as
             much
             a
             greater
             height
             upon
             the
             Superfices
             
               I
               K
            
             ,
             then
             the
             water
             within
             the
             pipe
             ,
             as
             is
             requisite
             to
             make
             the
             two
             Liquors
             Counter-ballance
             each
             other
             ,
             notwithstanding
             the
             difference
             of
             their
             specifick
             Gravities
             .
             And
             though
             the
             pipe
             L
             were
             twice
             as
             bigg
             ,
             it
             would
             Charge
             the
             subjacent
             plain
             
               I
               K
            
             no
             more
             then
             the
             pressure
             of
             the
             oyle
             on
             the
             other
             parts
             of
             the
             same
             imaginary
             Surface
             is
             able
             to
             resist
             .
             And
             yet
             this
             pressure
             of
             the
             External
             oyle
             ought
             not
             
             to
             be
             able
             to
             raise
             the
             water
             in
             the
             slender
             pipe
             N
             ,
             higher
             then
             the
             Surface
             Q
             in
             the
             same
             Level
             with
             the
             Surface
             O.
             For
             ,
             if
             the
             water
             were
             higher
             in
             the
             small
             pipe
             ;
             being
             a
             heavier
             Liquor
             then
             oyle
             ,
             it
             must
             press
             upon
             that
             part
             of
             the
             Surface
             
               I
               K
            
             ,
             it
             leans
             on
             ,
             with
             greater
             force
             then
             the
             external
             oyle
             upon
             the
             other
             parts
             of
             the
             same
             plain
             
               I
               K
            
             ;
             and
             therefore
             with
             greater
             force
             then
             the
             weight
             of
             the
             External
             oyle
             could
             resist
             .
             And
             consequently
             ,
             the
             water
             in
             the
             slender
             pipe
             must
             subside
             ,
             till
             its
             Surface
             be
             inferiour
             to
             that
             of
             the
             External
             oyle
             ;
             since
             ,
             till
             then
             ,
             the
             difference
             of
             their
             specifick
             gravities
             cannot
             permit
             them
             to
             rest
             in
             an
             Aequilibrium
             .
             To
             be
             short
             ;
             It
             is
             all
             one
             ,
             to
             the
             resistance
             of
             the
             external
             oyl
             ,
             how
             wide
             the
             Cylinder
             is
             that
             it
             supports
             in
             the
             pipe
             ;
             provided
             the
             height
             of
             it
             be
             not
             greater
             in
             respect
             of
             the
             height
             of
             the
             oyl
             ,
             then
             
             the
             difference
             of
             the
             respective
             Gravities
             of
             those
             two
             Liquors
             requires
             .
             For
             ,
             so
             long
             the
             pressure
             of
             the
             Cylinder
             of
             water-will
             be
             no
             greater
             ,
             on
             that
             part
             of
             the
             Imaginary
             Superficies
             which
             it
             leans
             upon
             ,
             then
             the
             pressure
             of
             the
             external
             oyle
             will
             be
             on
             all
             the
             other
             parts
             of
             the
             same
             Superficies
             ;
             and
             consequently
             ,
             neither
             the
             one
             ,
             nor
             the
             other
             of
             those
             Liquors
             will
             subside
             ,
             but
             they
             will
             both
             rest
             in
             an
             Aequilibrium
             ,
          
           
             But
             here
             it
             will
             not
             he
             amiss
             to
             note
             ;
             First
             ,
             that
             it
             is
             not
             necessary
             that
             the
             Glass
             Cylinders
             
               L
               ,
               M
               ,
               N
            
             ,
             should
             be
             all
             of
             the
             same
             length
             ;
             since
             ,
             the
             lower
             Orifice
             being
             open
             ,
             the
             water
             will
             rise
             to
             the
             same
             height
             within
             them
             ,
             whether
             the
             parts
             immers'd
             under
             the
             water
             be
             exactly
             of
             the
             same
             length
             or
             no.
             
          
           
             And
             Secondly
             ,
             That
             throughout
             all
             this
             Discourse
             ,
             and
             particularly
             in
             the
             
             Explication
             of
             this
             Paradox
             ,
             we
             suppose
             ,
             either
             that
             the
             slenderest
             pipes
             ,
             that
             are
             imploy'd
             about
             these
             Experiments
             ,
             are
             of
             a
             moderate
             size
             ,
             and
             not
             exceeding
             small
             ;
             Or
             that
             ,
             in
             case
             they
             be
             very
             small
             ,
             allowance
             be
             made
             in
             such
             pipes
             for
             this
             property
             ,
             That
             water
             will
             rise
             in
             them
             to
             a
             greater
             height
             ,
             then
             can
             be
             attributed
             to
             the
             bare
             Counterpoize
             of
             either
             the
             water
             or
             the
             oyle
             ,
             that
             impels
             it
             upwards
             and
             keeps
             it
             suspended
             .
             But
             this
             difference
             is
             of
             so
             little
             moment
             in
             our
             present
             Inquiries
             ,
             That
             we
             may
             safely
             neglect
             it
             ,
             (
             as
             hereafter
             we
             mean
             to
             do
             )
             now
             we
             have
             taken
             this
             notice
             of
             it
             for
             prevention
             of
             mistakes
             .
          
        
         
           
           
             PARADOX
             VI.
             
          
           
             If
             a
             Body
             be
             plac'd
             under
             water
             ,
             with
             its
             uppermost
             Surface
             parallel
             to
             the
             Horizon
             ;
             how
             much
             water
             soever
             there
             may
             be
             on
             this
             or
             that
             side
             above
             the
             Body
             ,
             the
             direct
             pressure
             sustain'd
             by
             the
             Body
             (
             for
             we
             now
             consider
             not
             the
             Lateral
             nor
             the
             recoyling
             pressure-to
             which
             the
             Body
             may
             be
             expos'd
             if
             quite
             environ'd
             with
             water
             ,
             )
             is
             no
             more
             then
             that
             of
             a
             Columne
             of
             water
             ▪
             having
             the
             Horizontal
             superficies
             of
             the
             Body
             for
             its
             Basis
             ,
             and
             the
             perpendicular
             depth
             of
             the
             water
             for
             its
             height
             .
          
           
             And
             so
             likewise
             ,
             If
             the
             water
             that
             leans
             upon
             the
             Body
             be
             contain'd
             in
             pipes
             open
             at
             both
             ends
             ;
             the
             pressure
             of
             the
             water
             is
             to
             be
             estimated
             
             by
             the
             weight
             of
             a
             pillar
             of
             water
             ,
             whose
             Basis
             is
             equal
             to
             the
             lower
             Orifice
             of
             the
             pipe
             ,
             (
             which
             we
             suppose
             to
             be
             parallel
             to
             the
             Horizon
             )
             and
             its
             height
             equal
             to
             a
             perpendicular
             reaching
             thence
             to
             the
             top
             of
             the
             water
             ;
             though
             the
             pipe
             be
             much
             inclin'd
             towards
             the
             Horizon
             ,
             or
             though
             it
             be
             irregularly
             shap'd
             ,
             and
             much
             broader
             in
             some
             parts
             ,
             then
             the
             said
             Orifice
             .
          
           
             STevinus
             ,
             in
             the
             tenth
             Proposition
             of
             his
             Hydrostatical
             Elements
             ,
             having
             propos'd
             in
             more
             general
             termes
             the
             former
             part
             of
             our
             Paradox
             ;
             annexes
             to
             se
             a
             Demonstration
             to
             this
             purpose
             .
          
           
           
             If
             the
             Bottom
             
               E
               F
            
             be
             charged
             with
             a
             greater
             weight
             then
             that
             of
             the
             water
             
               G
               H
               F
               E
            
             ,
             that
             surplusage
             must
             come
             from
             the
             adjoyning
             water
             ;
             therefore
             ,
             if
             it
             be
             possible
             ,
             let
             it
             be
             from
             the
             water
             
               A
               G
               E
               D
            
             ,
             &
             
               H
               B
               C
               F
            
             ;
             which
             granted
             ,
             the
             Bottom
             
               D
               E
            
             will
             likewise
             have
             a
             greater
             weight
             incumbent
             on
             it
             ,
             upon
             the
             score
             of
             the
             neigbouring
             water
             
               G
               H
               F
               E
            
             ,
             then
             that
             of
             the
             water
             
               A
               G
               E
               D.
            
             And
             ,
             the
             reason
             being
             the
             same
             in
             all
             the
             three
             cases
             ,
             the
             Basis
             
               F
               C
            
             must
             susteine
             a
             greater
             weight
             ,
             then
             that
             of
             the
             water
             
             
               H
               B
               C
               F.
            
             And
             therefore
             the
             whole
             bottom
             
               D
               C
            
             ,
             will
             have
             a
             greater
             weight
             incumbent
             on
             it
             ,
             then
             that
             of
             the
             whole
             water
             
               A
               B
               C
               D
            
             ;
             which
             yet
             
               (
               A
               B
               C
               D
            
             being
             a
             rectangular
             Body
             )
             would
             be
             absurd
             .
             And
             by
             the
             same
             way
             of
             reasoning
             you
             may
             evince
             ,
             That
             the
             Bottom
             
               E
               F
            
             sustains
             no
             less
             a
             weight
             ,
             then
             that
             of
             the
             water
             
               G
               H
               F
               E.
            
             And
             so
             ,
             since
             it
             sustains
             neither
             a
             greater
             weight
             ,
             nor
             a
             less
             ,
             it
             must
             sustein
             just
             as
             much
             weight
             as
             the
             Columne
             of
             water
             
               G
               H
               F
               E.
            
             
          
           
             This
             Demonstration
             of
             the
             Learned
             Stevinus
             may
             well
             enough
             be
             admitted
             by
             a
             Naturalist
             (
             though
             ,
             according
             to
             some
             Hypotheses
             touching
             the
             Cause
             and
             Nature
             of
             Gravity
             ,
             it
             may
             faile
             of
             Mathematical
             exactness
             ;
             )
             and
             by
             it
             may
             be
             confirm'd
             the
             first
             part
             of
             our
             propos'd
             Paradox
             .
             And
             some
             things
             annexed
             by
             Stevinus
             to
             this
             Demonstration
             ,
             may
             be
             also
             apply'd
             to
             
             countenance
             the
             second
             .
             But
             because
             this
             is
             one
             of
             the
             noblest
             and
             usefullest
             Subjects
             of
             the
             Hydrostaticks
             ,
             we
             think
             it
             worth
             while
             to
             illustrate
             ,
             after
             our
             manner
             ,
             each
             of
             the
             two
             parts
             of
             our
             Paradox
             by
             a
             sensible
             Experiment
             .
          
           
             First
             then
             ,
             Take
             a
             slender
             Glass
             pipe
             ,
             of
             an
             even
             Bore
             ,
             turn'd
             up
             at
             one
             end
             like
             the
             annexed
             Syphon
             .
             
             Into
             this
             Syphon
             suck
             oyl
             of
             Turpentine
             till
             the
             Liquor
             have
             fill'd
             the
             shorter
             leg
             ,
             and
             be
             rais'd
             2
             or
             3
             Inches
             in
             the
             longer
             .
             Then
             nimbly
             stopping
             the
             upper
             Orifice
             with
             your
             finger
             ,
             thrust
             the
             lower
             part
             of
             the
             Syphon
             so
             farre
             into
             a
             deep
             Glass
             full
             of
             water
             ,
             That
             the
             Surface
             of
             the
             oyle
             in
             the
             longer
             leg
             of
             the
             pipe
             ,
             may
             be
             but
             a
             little
             higher
             then
             that
             of
             the
             External
             water
             ;
             and
             ,
             upon
             the
             removal
             of
             your
             finger
             ,
             you
             will
             find
             the
             Surface
             of
             the
             oyle
             to
             vary
             but
             little
             ,
             or
             not
             at
             all
             ,
             its
             former
             Station
             .
             
             And
             as
             ,
             if
             you
             then
             thrust
             the
             pipe
             a
             little
             deeper
             ,
             you
             will
             soe
             the
             oyle
             in
             the
             shorter
             leg
             to
             begin
             to
             be
             depress'd
             ;
             so
             ,
             if
             afterwards
             you
             gently
             raise
             the
             pipe
             toward
             the
             top
             of
             the
             water
             ,
             you
             shall
             see
             the
             oyle
             not
             only
             regain
             its
             former
             station
             ,
             but
             flow
             out
             by
             degrees
             in
             drops
             that
             will
             emerge
             to
             the
             Top
             of
             the
             water
             .
             Now
             ,
             since
             the
             water
             was
             able
             ,
             at
             first
             ,
             to
             keep
             the
             oyl
             ,
             in
             the
             longer
             leg
             of
             the
             pipe
             ,
             suspended
             no
             higher
             ,
             then
             it
             would
             have
             been
             kept
             by
             a
             Cylinder
             of
             water
             equal
             to
             the
             Orifice
             of
             the
             shorter
             leg
             of
             the
             pipe
             ,
             and
             reaching
             directly
             thence
             to
             the
             Top
             of
             the
             water
             ;
             (
             as
             may
             be
             easily
             cried
             ,
             by
             making
             a
             Syphon
             ,
             where
             the
             shorter
             leg
             may
             be
             long
             enough
             to
             contain
             such
             a
             Cylinder
             of
             water
             to
             conterpoize
             the
             oyl
             in
             the
             longer
             ;
             )
             &
             since
             ,
             when
             once
             ,
             by
             the
             raising
             of
             the
             pipe
             ,
             the
             height
             of
             the
             incumbent
             water
             was
             lessen'd
             ,
             the
             oyle
             did
             more
             then
             Counter-ballance
             
             it
             ;
             (
             as
             appears
             by
             its
             flowing
             out
             of
             the
             Syphon
             ,
             )
             we
             may
             well
             conclude
             ;
             That
             ,
             though
             thence
             were
             in
             the
             Vessel
             a
             great
             deal
             of
             water
             ,
             higher
             then
             the
             immers'd
             Orifice
             of
             the
             Syphon
             ,
             (
             and
             it
             would
             be
             all
             one
             ,
             though
             the
             Syphon
             were
             placid
             at
             the
             same
             depth
             in
             a
             pond
             or
             lake
             ;
             )
             yet
             ,
             of
             all
             that
             water
             ,
             no
             more
             did
             gravitate
             upon
             the
             Orifice
             ,
             then
             that
             which
             was
             plac'd
             directly
             over
             its
             ,
             which
             was
             such
             a
             pillat
             of
             water
             ,
             as
             the
             Paradox
             describes
             .
          
           
             And
             ,
             by
             the
             way
             ,
             we
             may
             hence
             learn
             ;
             That
             though
             water
             be
             not
             included
             in
             pipes
             ,
             yet
             it
             may
             press
             as
             regularly
             upon
             a
             subjacent
             Body
             ,
             as
             if
             it
             were
             .
             And
             therefore
             we
             may
             well
             enough
             conceive
             a
             pillar
             of
             water
             ,
             in
             the
             free
             water
             it self
             ,
             where
             there
             is
             nothing
             on
             any
             side
             ,
             but
             the
             contiguous
             water
             ,
             to
             bound
             the
             imaginary
             pillar
             .
          
           
           
             But
             I
             had
             forgot
             to
             add
             ,
             That
             the
             first
             part
             of
             our
             Paradox
             will
             hold
             ,
             not
             only
             when
             the
             water
             ,
             superior
             to
             the
             Body
             it
             presses
             upon
             ,
             is
             free
             ;
             but
             also
             ,
             when
             it
             is
             included
             in
             Vessels
             of
             never
             so
             (
             seemingly
             )
             disadvantageous
             a
             shape
             .
             For
             ,
             if
             you
             so
             frame
             the
             shorter
             leg
             of
             a
             Syphon
             ,
             that
             it
             may
             expand
             its
             self
             into
             a
             funnel
             ,
             like
             that
             of
             Fig.
             6.
             employ'd
             about
             the
             proof
             of
             the
             foregoing
             (
             fisth
             )
             Paradox
             ;
             (
             for
             which
             purpose
             the
             legs
             must
             be
             at
             a
             pretty
             distance
             from
             each
             other
             :
             )
             though
             you
             fill
             that
             Funnel
             with
             water
             ,
             the
             oyle
             in
             the
             longer
             and
             slender
             leg
             of
             the
             Syphon
             will
             be
             able
             to
             resist
             the
             pressure
             of
             all
             the
             water
             ,
             notwithstanding
             the
             breadth
             of
             the
             upper
             part
             of
             the
             funnel
             .
             So
             that
             ,
             ev'n
             in
             this
             case
             also
             ,
             the
             Surface
             of
             the
             oyle
             in
             the
             longer
             leg
             ,
             will
             be
             but
             a
             little
             higher
             then
             that
             of
             the
             water
             in
             the
             funnel
             .
          
           
             For
             further
             Confirmation
             of
             this
             ;
             
             we
             caus'd
             to
             be
             made
             a
             Syphon
             ,
             so
             shap'd
             ,
             that
             one
             of
             the
             legs
             (
             which
             were
             parallel
             ,
             and
             of
             the
             same
             Bore
             ,
             )
             had
             in
             the
             midst
             of
             it
             a
             Sphaere
             of
             Glass
             ,
             save
             that
             it
             communicated
             with
             the
             upper
             and
             lower
             parts
             of
             the
             same
             leg
             .
          
           
             In
             the
             uniform
             leg
             of
             the
             Syphon
             ,
             we
             put
             a
             convenient
             quantity
             of
             oyle
             of
             Turpentine
             ,
             and
             into
             the
             other
             ,
             as
             much
             water
             as
             fill'd
             not
             only
             the
             lower
             part
             of
             it
             ,
             but
             the
             Globular
             part
             too
             .
             And
             yet
             we
             did
             not
             find
             ,
             that
             all
             this
             water
             was
             able
             to
             keep
             up
             the
             oyle
             in
             the
             uniform
             leg
             ,
             at
             a
             greater
             height
             then
             if
             the
             leg
             that
             contain'd
             the
             water
             had
             been
             uniform
             too
             ;
             as
             much
             of
             the
             water
             in
             the
             Globe
             ,
             as
             was
             not
             directly
             over
             the
             lower
             Orifice
             of
             it
             ,
             being
             supported
             by
             the
             lateral
             parts
             (
             if
             I
             may
             so
             call
             them
             )
             of
             the
             same
             Globe
             .
             And
             ,
             if
             that
             leg
             were
             ,
             instead
             of
             water
             ,
             fill'd
             with
             oyle
             ,
             and
             the
             uniform
             leg
             with
             
             water
             ;
             notwithstanding
             the
             far
             greater
             quantity
             of
             oyl
             ,
             that
             was
             necessary
             to
             fill
             that
             leg
             ,
             whereof
             the
             hollow
             sphaere
             was
             but
             a
             part
             ;
             the
             water
             in
             the
             uniform
             leg
             would
             not
             be
             kept
             up
             ▪
             so
             much
             as
             to
             the
             same
             height
             with
             the
             oyle
             in
             the
             mishapen
             leg
             .
          
           
             But
             to
             make
             this
             matter
             yet
             the
             more
             clear
             ,
             we
             caus'd
             a
             Syphon
             to
             be
             made
             of
             the
             Figure
             express'd
             in
             the
             adjoyning
             Scheme
             ;
             
             into
             which
             having
             poured
             a
             convenient
             quantity
             of
             Mercury
             ,
             till
             it
             reach'd
             in
             the
             shorter
             leg
             
               C
               D
            
             ,
             almost
             to
             the
             bottom
             of
             the
             Clobulou
             part
             E
             ,
             and
             in
             the
             longer
             leg
             
               A
               B
            
             ,
             to
             an
             equal
             height
             :
             We
             afterwards
             ,
             poured
             a
             sufficient
             quantity
             of
             water
             into
             the
             said
             longer
             leg
             
               A
               B
            
             ,
             which
             drove
             away
             the
             Quicksilver
             ,
             and
             impell'd
             it
             up
             in
             the
             shorter
             leg
             till
             it
             had
             half
             ,
             or
             more
             then
             half
             ,
             fill'd
             the
             Cavity
             of
             the
             Globular
             part
             E
             ,
             (
             which
             
             yet
             we
             did
             not
             wholly
             fill
             with
             Quicksilver
             ,
             because
             the
             Tube
             
               A
               B
            
             was
             not
             long
             enough
             for
             that
             purpose
             ;
             )
             and
             then
             we
             observ'd
             ,
             that
             ,
             notwithstanding
             the
             great
             weight
             of
             (
             that
             Body
             ,
             which
             is
             of
             all
             Bodies
             ,
             save
             one
             ,
             the
             most
             Ponderous
             )
             Quicksilver
             ,
             which
             was
             contain'd
             in
             the
             lower
             part
             of
             the
             same
             leg
             of
             the
             Syphon
             ,
             the
             surface
             of
             the
             Quicksilver
             
               H
               G
            
             ,
             was
             impell'd
             up
             as
             high
             by
             the
             water
             in
             the
             Leg
             
               A
               B
            
             ,
             as
             the
             disparity
             of
             the
             specifick
             weights
             of
             those
             two
             Liquors
             (
             whereof
             one
             is
             about
             14
             times
             as
             heavy
             as
             the
             other
             )
             did
             require
             :
             So
             that
             it
             appear'd
             not
             ,
             that
             ,
             for
             all
             the
             great
             weight
             of
             Quicksilver
             ,
             contain'd
             in
             the
             Globulous
             Cavity
             E
             ,
             there
             press'd
             any
             more
             upon
             the
             slender
             and
             subjacent
             part
             
               E
               C
            
             of
             that
             leg
             ,
             then
             as
             much
             as
             was
             plac'd
             directly
             over
             the
             lower
             Orifice
             of
             the
             said
             Cavity
             
               E
               ▪
            
             So
             that
             the
             other
             ,
             and
             lateral
             parts
             of
             that
             Mercury
             ,
             being
             
             supported
             by
             the
             concave
             sides
             of
             the
             Glass
             ,
             whereunto
             they
             were
             contiguous
             ,
             the
             water
             in
             the
             leg
             
               A
               B
            
             ,
             appear'd
             not
             any
             more
             press'd
             by
             the
             quicksilver
             ,
             then
             if
             the
             leg
             
               C
               D
            
             had
             been
             ,
             as
             well
             as
             the
             other
             ,
             of
             an
             uniform
             bigness
             ;
             and
             ,
             by
             this
             means
             ,
             if
             we
             had
             made
             the
             hollow
             Globe
             of
             a
             large
             Diameter
             ,
             a
             small
             quantity
             of
             water
             ,
             poured
             into
             the
             leg
             
               A
               B
            
             ,
             might
             have
             been
             able
             to
             raise
             a
             quantity
             of
             quicksilver
             exceedingly
             much
             heavier
             then
             it self
             .
             But
             then
             so
             little
             water
             can
             raise
             the
             quicksilver
             ,
             in
             so
             broad
             a
             pipe
             ,
             but
             to
             an
             inconsiderable
             height
             .
          
           
             To
             make
             out
             the
             second
             part
             of
             our
             Paradox
             by
             an
             Experiment
             ,
             we
             took
             three
             Glass-pipes
             ;
             the
             one
             made
             like
             a
             Bolt-head
             ,
             
             with
             a
             round
             Ball
             and
             two
             opposite
             Stemms
             ;
             the
             other
             was
             an
             irregular
             pipe
             ,
             blown
             with
             an
             Elbow
             ,
             wherewith
             it
             made
             an
             Angle
             ;
             and
             the
             third
             
             was
             as
             irregularly
             shap'd
             ,
             as
             I
             could
             get
             it
             blown
             ;
             being
             in
             some
             places
             much
             broader
             ,
             and
             in
             some
             much
             narrower
             then
             the
             lower
             Orifice
             of
             it
             .
             And
             these
             two
             last
             nam'd
             pipes
             had
             their
             upper
             ends
             so
             inserted
             into
             holes
             ,
             made
             fit
             for
             them
             in
             a
             broad
             piece
             of
             Cork
             ;
             that
             ,
             when
             they
             were
             immers'd
             ,
             they
             made
             not
             right
             Angles
             ,
             but
             very
             oblique
             ones
             ,
             with
             the
             Horizontal
             Surface
             of
             the
             Liquor
             .
             The
             other
             Glass
             likewise
             ,
             which
             consisted
             of
             a
             great
             Bubble
             ,
             and
             two
             opposite
             pipes
             ,
             was
             fastened
             to
             the
             same
             Cork
             ,
             which
             having
             before
             hand
             been
             made
             fit
             for
             a
             wide
             mouth'd
             glass
             of
             a
             good
             depth
             ,
             and
             half
             fill'd
             with
             water
             ,
             was
             thrust
             as
             a
             stopple
             into
             the
             mouth
             of
             the
             said
             glass
             ,
             so
             that
             the
             water
             a
             scended
             a
             pretty
             way
             into
             each
             of
             the
             three
             pipes
             by
             their
             lower
             Orifices
             ,
             which
             as
             well
             as
             the
             upper
             we
             left
             open
             ;
             Then
             a
             good
             quantity
             of
             oyle
             of
             Turpentine
             being
             
             pour'd
             into
             the
             same
             Vessel
             ,
             through
             a
             funnel
             ,
             the
             water
             was
             by
             the
             incumbent
             oyle
             impell'd
             up
             to
             the
             height
             of
             2
             or
             3
             Inches
             in
             each
             of
             the
             three
             pipes
             .
             Which
             argues
             ,
             that
             ,
             notwithstanding
             their
             being
             so
             unequal
             in
             bigness
             ,
             and
             so
             irregular
             in
             shape
             ,
             (
             insomuch
             that
             we
             guess'd
             one
             of
             them
             was
             10
             or
             12
             times
             greater
             in
             one
             part
             ,
             then
             in
             another
             ,
             or
             then
             it
             was
             even
             at
             the
             Orifice
             )
             the
             water
             ,
             contain'd
             in
             each
             of
             them
             ,
             press'd
             upon
             its
             lower
             Orifice
             
               no
               more
            
             (
             I
             do
             not
             add
             ,
             nor
             no
             less
             )
             then
             it
             would
             have
             done
             if
             it
             had
             been
             a
             Cylinder
             ,
             having
             the
             Orifice
             for
             its
             Basis
             ,
             and
             the
             perpendicular
             depth
             of
             the
             water
             and
             oyle
             above
             ,
             for
             its
             height
             .
             For
             in
             case
             each
             of
             the
             pipes
             had
             contein'd
             but
             such
             a
             Cylinder
             of
             water
             ,
             that
             water
             would
             nevertheless
             have
             had
             its
             uppermost
             Superficies
             at
             the
             same
             height
             :
             and
             on
             the
             other
             side
             ,
             it
             would
             have
             been
             impell'd
             up
             beyond
             it
             ,
             if
             its
             weight
             did
             
             not
             as
             strongly
             endeavour
             to
             depress
             the
             immediately
             subjacent
             water
             ,
             as
             the
             pressure
             of
             the
             External
             fluids
             endeavour'd
             to
             impel
             it
             up
             .
          
           
             And
             since
             the
             height
             of
             the
             water
             was
             about
             the
             same
             in
             the
             several
             pipes
             ,
             though
             two
             of
             them
             ,
             being
             very
             much
             inclin'd
             ,
             contain'd
             much
             more
             water
             then
             if
             they
             were
             erected
             :
             yet
             by
             the
             same
             way
             of
             reasoning
             we
             may
             gather
             ,
             That
             the
             imaginary
             plain
             ,
             passing
             by
             the
             immers'd
             Orifice
             of
             either
             of
             these
             inclining
             pipes
             ,
             sustain'd
             no
             more
             of
             pressure
             ,
             then
             it
             would
             have
             done
             from
             a
             shorter
             Cylinder
             of
             water
             if
             erected
             .
             And
             indeed
             ,
             in
             all
             these
             cases
             ,
             where
             a
             pipe
             either
             is
             broader
             in
             other
             places
             then
             at
             its
             lower
             Orifice
             ,
             or
             inclin'd
             any
             way
             towards
             the
             Horizon
             ,
             the
             weight
             of
             the
             contain'd
             Liquor
             is
             not
             all
             supported
             by
             the
             Liquor
             or
             the
             Body
             contiguous
             to
             the
             lower
             Orifice
             ,
             but
             partly
             by
             the
             sides
             of
             the
             pipe
             it self
             .
             And
             
             therefore
             if
             ,
             when
             in
             a
             slender
             pipe
             you
             have
             brought
             a
             parcel
             of
             oyl
             of
             Turpentine
             to
             be
             in
             an
             Equilibrium
             with
             the
             External
             water
             ,
             as
             in
             the
             Experiment
             belonging
             to
             the
             first
             Paradox
             ;
             If
             ,
             I
             say
             ,
             when
             this
             is
             done
             ,
             you
             incline
             the
             pipe
             towards
             the
             sides
             of
             the
             Glass
             ,
             You
             may
             indeed
             observe
             the
             Surface
             of
             the
             oyle
             in
             the
             pipe
             to
             be
             ,
             as
             before
             ,
             a
             little
             higher
             then
             that
             of
             the
             water
             without
             it
             :
             But
             you
             shall
             likewise
             see
             ,
             That
             ,
             though
             the
             Orifice
             of
             the
             pipe
             were
             not
             thrust
             deeper
             into
             the
             water
             ,
             yet
             therewill
             be
             a
             pretty
             deal
             of
             water
             got
             up
             into
             the
             pipe
             ;
             because
             the
             oyle
             not
             leaning
             now
             upon
             the
             water
             only
             ;
             as
             it
             did
             before
             ,
             but
             partly
             upon
             the
             water
             ,
             and
             partly
             upon
             the
             pipe
             ,
             its
             pressure
             upon
             the
             subjacent
             water
             is
             considerably
             lessen'd
             ;
             and
             there
             by
             the
             external
             water
             ,
             whose
             pressure
             is
             not
             diminish'd
             too
             ,
             is
             able
             to
             impel
             up
             the
             oyl
             ,
             and
             intrude
             for
             a
             little
             way
             into
             the
             pipe
             .
             But
             if
             you
             re-erect
             the
             pipe
             ,
             the
             pressure
             of
             the
             oyle
             being
             then
             again
             exerted
             
             upon
             the
             subjacent
             water
             ,
             it
             will
             be
             able
             to
             depress
             ,
             and
             drive
             it
             again
             out
             of
             the
             Cavity
             of
             the
             pipe
             .
          
           
             And
             to
             this
             agrees
             very
             well
             what
             we
             further
             try'd
             as
             follows
             :
             We
             caused
             3
             pipes
             to
             be
             blown
             (
             shap'd
             as
             the
             adjoyning
             Figures
             ;
             
             )
             one
             having
             in
             it
             divers
             acute
             Angles
             ;
             the
             other
             being
             of
             a
             winding
             form
             ,
             like
             a
             scrue
             or
             worm
             of
             the
             Limbeck
             ;
             and
             the
             third
             very
             irregularly
             crooked
             ;
             and
             yet
             each
             of
             these
             pipes
             having
             all
             its
             crooked
             parts
             ,
             and
             some
             of
             its
             streight
             &
             erected
             parts
             ,
             fil'd
             with
             oyl
             of
             Turpentine
             ;
             being
             thrust
             to
             a
             convenient
             depth
             under
             water
             and
             unstopp'd
             there
             ,
             (
             after
             the
             manner
             already
             often
             declar'd
             )
             we
             found
             ,
             that
             ,
             according
             to
             our
             Paradox
             ,
             the
             surface
             of
             the
             oyle
             in
             the
             pipe
             was
             higher
             than
             that
             of
             the
             water
             without
             it
             ,
             as
             much
             as
             it
             would
             have
             been
             in
             case
             the
             pipe
             had
             been
             streight
             ,
             (
             as
             we
             try'd
             by
             placing
             by
             the
             crookedest
             of
             them
             a
             streight
             pipe
             with
             oyle
             in
             it
             )
             though
             the
             quantity
             
             of
             the
             oyle
             ,
             in
             one
             of
             these
             pipes
             ,
             were
             perhaps
             three
             times
             as
             much
             as
             would
             have
             suffic'd
             ,
             if
             the
             pipe
             had
             been
             strait
             :
             So
             that
             this
             surplusage
             of
             oyle
             did
             not
             press
             upon
             the
             subjacent
             water
             ,
             (
             for
             if
             it
             had
             done
             so
             ,
             the
             oyle
             would
             have
             run
             out
             of
             the
             pipe
             .
             )
             And
             I
             remember
             ,
             that
             lifting
             up
             as
             much
             of
             one
             of
             these
             crooked
             pipes
             ,
             as
             I
             thought
             fit
             ,
             somewhat
             above
             the
             Surface
             of
             the
             water
             ;
             when
             the
             Superficies
             of
             the
             oyle
             in
             the
             pipe
             was
             not
             above
             half
             an
             inch
             higher
             then
             that
             of
             the
             water
             without
             it
             ,
             I
             estimated
             that
             the
             crooked
             pillar
             of
             oyl
             ,
             contain'd
             in
             that
             part
             of
             the
             pipe
             which
             was
             above
             the
             Surface
             of
             the
             water
             ,
             was
             about
             7
             or
             8
             Inches
             long
             .
             So
             true
             it
             is
             ,
             that
             the
             pressure
             of
             Liquors
             ,
             contain'd
             in
             pipes
             ,
             must
             be
             computed
             by
             the
             perpendicular
             that
             measures
             their
             height
             ,
             what
             ever
             be
             their
             length
             or
             bigness
             .
          
           
             
             
               SCHOLIUM
               .
            
             
               THE
               Learned
               Stevinus
               ,
               having
               demonstrated
               the
               Proposition
               we
               lately
               mention'd
               out
               of
               him
               ,
               subjoyns
               divers
               consectaries
               of
               which
               the
               truth
               hath
               been
               thought
               more
               questionable
               ,
               then
               that
               of
               the
               Theorem
               it self
               .
               And
               therefore
               he
               thought
               fit
               to
               add
               a
               kind
               of
               Appendix
               to
               make
               good
               a
               Paradox
               ,
               which
               seems
               to
               amount
               to
               this
               .
               That
               If
               ,
               in
               the
               Cover
               of
               a
               large
               Cylindrical
               Box
               ,
               exactly
               closed
               ,
               there
               be
               perpendicularly
               erected
               a
               Cylindrical
               Pipe
               open
               at
               both
               ends
               ,
               and
               reaching
               to
               the
               Cavity
               of
               the
               Box
               ;
               this
               Instrument
               being
               fill'd
               with
               water
               ,
               the
               circular
               Basis
               of
               it
               will
               susteine
               a
               pressure
               ,
               equal
               to
               that
               of
               the
               breadth
               of
               the
               Basis
               and
               height
               of
               the
               Pipe.
               
            
             
             
               I
               chose
               thus
               to
               express
               this
               Theorem
               ,
               (
               which
               might
               be
               ,
               according
               to
               Stevinus
               ,
               propos'd
               in
               more
               general
               terms
               ,
               )
               because
               this
               way
               of
               expressing
               it
               will
               best
               suit
               with
               the
               subsequent
               Experiment
               ,
               and
               may
               consequently
               facilitate
               the
               understanding
               of
               the
               Paradox
               .
               But
               though
               the
               Learned
               Stevinus's
               aims
               were
               to
               be
               commended
               ;
               who
               finding
               this
               Proposition
               doubted
               ,
               seems
               to
               have
               had
               a
               great
               mind
               to
               give
               an
               Experimental
               Demonstration
               of
               it
               ,
               and
               therefore
               proposes
               no
               less
               then
               five
               pragmatical
               Examples
               (
               as
               he
               calls
               them
               )
               to
               make
               out
               the
               truth
               of
               what
               he
               asserts
               ;
               yet
               in
               this
               he
               hath
               been
               somewhat
               unhappy
               ,
               that
               that
               Experiment
               ,
               which
               alone
               (
               for
               ought
               I
               can
               find
               )
               has
               been
               try'd
               of
               all
               the
               five
               ,
               is
               rejected
               as
               incompetent
               ,
               by
               those
               that
               profess
               to
               have
               purposely
               made
               tryal
               of
               it
               .
               And
               indeed
               ,
               by
               reason
               of
               the
               difficulty
               of
               bringing
               them
               to
               a
               practical
               examen
               ,
               
               I
               have
               somewhat
               doubted
               whether
               or
               no
               this
               useful
               writer
               did
               ever
               make
               all
               those
               Tryals
               himself
               ;
               rather
               then
               set
               down
               the
               events
               ,
               he
               suppos'd
               they
               must
               needs
               have
               ;
               as
               presuming
               his
               conjectures
               rightly
               deduc'd
               from
               a
               Demonstrative
               Truth
               .
               Wherefore
               though
               another
               of
               the
               Experiments
               ,
               he
               proposes
               ,
               be
               not
               free
               from
               difficulty
               ,
               yet
               having
               ,
               by
               the
               help
               of
               an
               Expedient
               ,
               made
               it
               practicable
               ,
               we
               are
               induc'd
               by
               its
               plainness
               and
               clearness
               to
               prefer
               it
               to
               what
               else
               he
               proposes
               to
               the
               same
               purpose
               .
            
             
               We
               provided
               then
               a
               vessel
               of
               Laton
               ,
               of
               the
               figure
               express'd
               in
               the
               Scheme
               ,
               
               and
               furnished
               it
               with
               a
               loose
               Bottom
               
                 C
                 D
              
               ,
               made
               of
               a
               flat
               piece
               of
               wood
               cover'd
               with
               a
               soft
               Bladder
               and
               greas'd
               on
               the
               lower
               side
               neer
               the
               edges
               ,
               that
               leaning
               on
               the
               rim
               of
               wood
               
                 G
                 H
              
               ,
               contiguous
               every
               where
               to
               the
               inside
               of
               the
               Laton
               
               it
               might
               be
               easily
               lifted
               from
               off
               this
               Rim
               ;
               and
               yet
               lye
               so
               close
               ,
               upon
               it
               ,
               that
               the
               water
               should
               not
               be
               able
               to
               get
               out
               between
               them
               :
               And
               to
               the
               midst
               of
               this
               loose
               bottom
               was
               fastned
               a
               long
               string
               ,
               of
               a
               good
               strength
               ,
               for
               the
               use
               hereafter
               to
               be
               declared
               .
               The
               Instrument
               thus
               fitted
               ,
               the
               water
               was
               poured
               in
               apace
               at
               the
               Top
               
                 A
                 B
              
               ,
               which
               ,
               by
               its
               weight
               pressing
               the
               false
               Bottom
               
                 C
                 D
              
               against
               the
               subjacent
               Rim
               ,
               
                 G
                 H
              
               ,
               contributed
               to
               make
               the
               Vessel
               the
               more
               tight
               ,
               and
               to
               hinder
               its
               own
               passing
               .
               The
               Vessel
               being
               fill'd
               with
               water
               we
               took
               the
               forementioned
               string
               ,
               one
               of
               whose
               ends
               was
               fastned
               to
               I
               ,
               the
               middle
               part
               of
               the
               loose
               Bottom
               ;
               and
               ,
               tying
               the
               other
               end
               K
               to
               the
               extremity
               of
               the
               Beam
               of
               a
               good
               pair
               of
               Scales
               ,
               we
               put
               weights
               one
               after
               another
               into
               the
               opposite
               scale
               ,
               till
               at
               length
               those
               weights
               lifted
               up
               the
               false
               Botom
               
                 C
                 D
              
               from
               the
               Rim
               
                 G
                 H
              
               ;
               and
               ,
               consequently
               ,
               
               lifted
               up
               the
               Incumbent
               water
               ;
               which
               presently
               after
               ran
               down
               between
               them
               .
               And
               having
               formerly
               ,
               before
               we
               poured
               in
               any
               water
               ,
               try'd
               what
               water
               would
               suffice
               to
               raise
               the
               Bottom
               
                 C
                 D
              
               ,
               when
               there
               was
               nothing
               but
               its
               own
               proper
               weight
               that
               was
               to
               be
               surmounted
               ;
               we
               found
               ,
               by
               deducting
               that
               weight
               from
               the
               weight
               in
               the
               scale
               ,
               and
               comparing
               the
               Residue
               with
               the
               weight
               of
               as
               much
               water
               ,
               as
               the
               cavity
               of
               the
               broad
               ,
               but
               very
               shallow
               Cylinder
               
                 B
                 E
                 C
                 H
                 G
                 D
                 F
              
               would
               have
               alone
               (
               if
               there
               had
               been
               no
               water
               in
               the
               pipe
               
                 A
                 I
              
               )
               amounted
               to
               ;
               we
               found
               ,
               I
               say
               ,
               by
               comparing
               these
               particulars
               ,
               that
               the
               pressure
               upon
               
                 C
                 D
              
               was
               by
               so
               very
               great
               odds
               more
               ,
               then
               could
               have
               been
               attributed
               to
               the
               weight
               of
               so
               little
               water
               ,
               as
               the
               Instrument
               pipe
               and
               all
               contain'd
               ,
               in
               case
               the
               water
               had
               been
               in
               an
               uniform
               Cylinder
               ,
               and
               consequently
               a
               very
               shallow
               one
               ,
               of
               a
               Basis
               
               as
               large
               as
               that
               of
               our
               Instrument
               ,
               That
               we
               could
               not
               but
               look
               upon
               the
               success
               ,
               as
               that
               ,
               which
               though
               it
               did
               not
               answer
               what
               the
               reading
               of
               Stevinus
               might
               make
               a
               man
               expect
               ;
               yet
               may
               deserve
               to
               be
               further
               prosecuted
               ,
               that
               whether
               or
               no
               the
               Paradox
               of
               Stevinus
               (
               which
               not
               only
               some
               others
               ,
               but
               the
               Learned
               Dr.
               Wallis
               himself
               question
               )
               wil
               hold
               ;
               the
               Inquiry
               he
               has
               started
               ,
               may
               be
               so
               persued
               ,
               as
               to
               occasion
               some
               improvement
               of
               this
               part
               of
               Hydrostaticks
               :
               where
               ,
               to
               define
               things
               with
               certainty
               ,
               will
               perhaps
               be
               found
               a
               difficulter
               Task
               then
               at
               first
               glance
               one
               would
               think
               ;
               both
               because
               divers
               speculative
               things
               must
               be
               taken
               into
               consideration
               ,
               whose
               Theory
               has
               not
               perhaps
               yet
               been
               clear'd
               ,
               and
               because
               of
               the
               difficulty
               that
               will
               be
               found
               in
               practice
               by
               them
               that
               shall
               go
               about
               to
               make
               Stevinus's
               Experiments
               ,
               or
               others
               of
               that
               sort
               with
               all
               requisite
               
               Accurateness
               :
               As
               indeed
               ,
               it
               is
               far
               easier
               to
               propose
               Experiments
               ,
               which
               would
               in
               likelyhood
               prove
               what
               we
               intend
               ,
               in
               case
               they
               could
               be
               made
               ,
               then
               to
               propose
               practicable
               Expedients
               how
               they
               may
               be
               made
               .
            
          
        
         
           
           
             PARADOX
             VII
             .
          
           
             That
             a
             Body
             immers'd
             in
             a
             Fluid
             ,
             sustains
             a
             lateral
             pressure
             from
             the
             Fluid
             ;
             and
             that
             increas'd
             ,
             as
             the
             depth
             of
             the
             immers'd
             Body
             ,
             beneath
             the
             Surface
             of
             the
             Fluid
             ,
             increaseth
             .
          
           
             THough
             I
             shall
             not
             wonder
             if
             this
             proposition
             seems
             strange
             enough
             to
             most
             Readers
             :
             yet
             I
             think
             I
             could
             make
             it
             out
             by
             several
             wayes
             ,
             and
             particularly
             by
             one
             that
             is
             plain
             and
             easie
             ,
             being
             but
             that
             which
             follows
             .
          
           
             Take
             then
             a
             slender
             Glass
             pipe
             (
             like
             that
             imployd
             about
             the
             first
             Experiment
             ;
             )
             
             and
             cause
             it
             to
             be
             bent
             within
             two
             or
             three
             Inches
             of
             one
             end
             ,
             so
             that
             the
             longer
             and
             the
             
             shorter
             legs
             ,
             
               E
               F
            
             and
             
               F
               G
            
             ,
             may
             make
             ,
             as
             near
             as
             can
             be
             ,
             a
             right
             Angle
             at
             F
             ;
             then
             dipping
             the
             Orifice
             of
             the
             shorter
             leg
             
               F
               G
            
             in
             oyle
             of
             Turpentine
             ,
             suck
             into
             the
             Syphon
             (
             if
             I
             may
             so
             call
             it
             )
             as
             much
             of
             the
             Liquor
             ,
             as
             will
             fill
             the
             shorter
             leg
             ,
             and
             reach
             two
             or
             three
             Inches
             high
             in
             the
             longer
             ;
             then
             ,
             nimbly
             stopping
             the
             upper
             Orifice
             with
             your
             finger
             ,
             immerse
             the
             lower
             part
             of
             the
             Glass
             under
             water
             ,
             in
             such
             manner
             as
             that
             the
             longer
             leg
             
               E
               F
            
             may
             make
             ,
             as
             to
             sense
             ,
             right
             Angles
             with
             
               (
               A
               B
            
             )
             the
             Horizontal
             Surface
             of
             the
             water
             ,
             and
             the
             shorter
             leg
             
               F
               G
            
             may
             be
             so
             far
             depress'd
             under
             that
             Surface
             ,
             That
             
               I
               K
            
             ,
             the
             Superficies
             of
             the
             oyle
             in
             the
             longer
             leg
             ,
             be
             but
             a
             little
             higher
             then
             
               A
               B
            
             ,
             that
             of
             the
             external
             water
             .
             Then
             ,
             removing
             your
             finger
             ,
             you
             may
             observe
             ,
             That
             the
             oyle
             in
             the
             Syphon
             will
             continue
             (
             with
             little
             or
             no
             change
             )
             in
             its
             former
             station
             .
             By
             which
             it
             appears
             that
             there
             
             is
             a
             lateral
             pressure
             of
             the
             water
             against
             the
             oyle
             contiguous
             to
             G
             ,
             the
             Orifice
             of
             the
             shorter
             leg
             of
             the
             pipe
             ,
             since
             it
             is
             only
             that
             pressure
             that
             hinders
             the
             efflux
             of
             the
             oyl
             at
             that
             Orifice
             ,
             notwithstanding
             the
             pressure
             of
             the
             perpendicular
             Cylinder
             of
             oyle
             that
             would
             drive
             it
             out
             .
          
           
             And
             that
             this
             pressure
             of
             the
             perpendicular
             Cylinder
             doth
             really
             urge
             the
             oyle
             in
             the
             shorter
             leg
             to
             flow
             out
             ;
             you
             may
             learn
             by
             slowly
             lifting
             the
             Syphon
             (
             without
             changing
             its
             ,
             former
             posture
             )
             towards
             the
             Surface
             of
             the
             water
             .
             For
             as
             the
             lower
             leg
             comes
             nearer
             and
             nearer
             to
             that
             Surface
             ,
             (
             to
             which
             ,
             as
             I
             newly
             intimated
             ,
             it
             is
             still
             to
             be
             kept
             parallel
             )
             the
             oyle
             in
             the
             Horizontal
             leg
             will
             be
             driven
             out
             in
             drops
             ,
             by
             the
             pressure
             of
             the
             other
             oyle
             in
             the
             perpendicular
             leg
             .
          
           
             That
             likewise
             before
             you
             begin
             to
             raise
             the
             Syphon
             ,
             the
             lateral
             pressure
             
             of
             the
             water
             against
             the
             lower
             Orifice
             of
             it
             is
             ,
             at
             least
             in
             such
             Experiments
             ,
             near
             about
             the
             same
             with
             what
             would
             be
             the
             perpendicular
             pressure
             of
             a
             Cylinder
             of
             water
             ,
             reaching
             from
             the
             same
             Orifice
             G
             (
             or
             some
             part
             of
             it
             )
             to
             the
             top
             of
             the
             water
             ,
             may
             be
             gather'd
             from
             hence
             ,
             That
             the
             Surface
             of
             the
             oyle
             in
             the
             longer
             leg
             will
             be
             a
             litle
             higher
             then
             that
             of
             the
             external
             water
             ,
             as
             (
             by
             reason
             of
             the
             often
             mention'd
             comparative
             levity
             of
             the
             oyl
             )
             it
             would
             be
             ,
             if
             we
             suppose
             ,
             That
             a
             pipe
             of
             Glass
             of
             the
             same
             bore
             ,
             and
             reaching
             to
             the
             top
             of
             the
             water
             ,
             being
             fitted
             to
             the
             Orifice
             of
             the
             Horizontal
             Leg
             (
             as
             in
             the
             annex'd
             figure
             the
             Cylinder
             ,
             
               G
               H
            
             )
             were
             fill'd
             with
             water
             .
          
           
             And
             ,
             to
             make
             out
             the
             latter
             part
             of
             our
             proposition
             ,
             we
             need
             add
             no
             more
             ,
             then
             that
             ,
             if
             you
             plunge
             the
             Syphon
             deeper
             into
             the
             water
             ,
             you
             shall
             find
             the
             oyle
             ,
             by
             the
             Lateral
             pressure
             of
             the
             water
             ,
             driven
             by
             degrees
             
             quite
             out
             of
             the
             shorter
             leg
             into
             the
             longer
             :
             and
             if
             you
             thrust
             it
             yet
             deeper
             ,
             you
             may
             observe
             that
             the
             longer
             leg
             will
             admit
             a
             Cylinder
             of
             water
             ,
             upon
             which
             that
             of
             oyle
             will
             swim
             ;
             the
             whole
             oyle
             alone
             being
             unable
             to
             counterballance
             the
             lateral
             pressure
             of
             the
             water
             at
             so
             great
             a
             depth
             .
          
           
             By
             which
             last
             circumstance
             ,
             it
             appears
             ,
             that
             water
             has
             also
             a
             lateral
             pressure
             against
             water
             it self
             ,
             and
             that
             increas'd
             according
             to
             its
             depth
             ;
             since
             otherwise
             the
             external
             water
             could
             not
             impel
             that
             in
             the
             Horizontal
             leg
             of
             the
             Syphon
             ,
             into
             the
             perpendicular
             leg
             ,
             though
             to
             doe
             so
             ,
             it
             must
             surmount
             the
             weight
             or
             resistance
             of
             the
             whole
             cylinder
             of
             oyl
             ,
             that
             must
             be
             hereby
             violently
             rais'd
             in
             the
             said
             perpendicular
             leg
             .
          
           
             But
             if
             you
             gently
             raise
             the
             Syphon
             again
             ,
             the
             lateral
             pressure
             of
             the
             water
             against
             the
             immers'd
             Orifice
             being
             diminish'd
             ,
             (
             according
             as
             the
             distance
             
             of
             that
             Orifice
             G
             from
             the
             Horizontal
             Surface
             ,
             
               A
               B
            
             ,
             comes
             to
             be
             lessen'd
             ,
             )
             the
             prevalent
             oyle
             will
             drive
             out
             the
             water
             ,
             first
             out
             of
             the
             Longer
             leg
             ,
             and
             then
             out
             of
             the
             shorter
             ,
             and
             will
             at
             length
             flow
             out
             in
             drops
             at
             the
             immers'd
             Orifice
             ,
             and
             thence
             emerge
             to
             the
             Top
             of
             the
             water
             .
          
           
             Besides
             ,
             when
             the
             oyle
             in
             the
             Syphon
             does
             just
             counterballance
             the
             external
             water
             ,
             if
             you
             keep
             the
             shorter
             leg
             parallel
             to
             the
             Surface
             of
             the
             water
             ,
             and
             move
             the
             Orifice
             of
             it
             this
             way
             or
             that
             way
             ,
             and
             place
             it
             nearer
             or
             further
             off
             from
             the
             middle
             or
             from
             the
             sides
             of
             the
             Glass
             ,
             (
             provided
             you
             keep
             it
             always
             at
             the
             same
             depth
             under
             the
             water
             ,
             )
             you
             'l
             find
             the
             oyl
             in
             the
             longer
             Leg
             to
             continue
             (
             as
             to
             sense
             )
             at
             the
             same
             height
             :
             Whence
             we
             may
             learn
             (
             what
             I
             have
             not
             yet
             found
             mention'd
             by
             any
             Writer
             ,
             )
             That
             ,
             ev'n
             in
             the
             mid'st
             of
             the
             water
             ,
             we
             may
             suppose
             a
             
             pillar
             of
             water
             ,
             of
             a
             Basis
             equal
             to
             the
             side
             of
             an
             immers'd
             Body
             ,
             (
             and
             reaching
             to
             the
             lowest
             part
             of
             it
             ;
             )
             And
             that
             ,
             though
             this
             Imaginary
             aqueous
             pillar
             ,
             such
             as
             in
             our
             figure
             
               G
               H
            
             ,
             be
             not
             included
             in
             any
             solid
             Body
             or
             stable
             superficies
             ;
             nevertheless
             it
             s
             lower
             parts
             will
             have
             a
             lateral
             pressure
             tending
             outwards
             ,
             against
             the
             imaginary
             sides
             ,
             from
             the
             weight
             of
             the
             water
             that
             is
             above
             these
             subjacent
             and
             lateral
             parts
             ;
             and
             will
             have
             that
             pressure
             increas'd
             proportionably
             to
             the
             height
             to
             which
             the
             imaginary
             pillar
             reaches
             above
             them
             .
             Which
             observation
             ,
             being
             duely
             noted
             and
             apply'd
             ,
             may
             be
             of
             no
             mean
             use
             in
             the
             explication
             of
             divers
             Hydrostatical
             phaenomena
             .
          
           
             And
             lastly
             if
             ,
             in
             stead
             of
             holding
             
               E
               F
            
             ,
             the
             longer
             leg
             of
             our
             Syphon
             ,
             perpendicular
             ,
             (
             and
             ,
             consequently
             ,
             the
             shorter
             parallel
             to
             the
             Horizon
             ,
             )
             you
             variously
             incline
             the
             former
             ,
             so
             as
             to
             
             bring
             it
             to
             make
             an
             obtuse
             or
             an
             Acute
             Angle
             with
             the
             superficies
             of
             the
             water
             
               A
               B
            
             ;
             though
             by
             this
             means
             the
             shorter
             and
             immers'd
             leg
             ,
             
               F
               G
            
             ,
             will
             in
             Situation
             sometimes
             respect
             the
             Bottom
             ,
             and
             sometimes
             the
             top
             of
             the
             Glass
             :
             yet
             in
             all
             these
             oblique
             situations
             of
             this
             leg
             ,
             and
             the
             immers'd
             Orifice
             of
             it
             G
             ,
             the
             oblique
             pressure
             of
             the
             water
             will
             so
             much
             depend
             upon
             the
             height
             of
             the
             Surface
             of
             the
             Liquor
             above
             the
             Orifice
             ,
             and
             so
             much
             conform
             to
             the
             observations
             already
             deliver'd
             ,
             That
             you
             shall
             still
             see
             the
             surface
             of
             the
             oyle
             
               I
               K
            
             ,
             in
             the
             longer
             pipe
             ,
             to
             be
             a
             little
             ,
             and
             but
             a
             little
             superiour
             to
             that
             of
             the
             external
             water
             ,
             
               A
               B
            
             ,
             and
             so
             the
             AEquilibrium
             betwixt
             the
             Liquor
             ,
             or
             Liquors
             ,
             within
             the
             Syphon
             ,
             and
             the
             water
             without
             it
             ,
             will
             ev'n
             in
             this
             case
             also
             be
             maintain'd
             .
          
           
             
             
               SCHOLIUM
               .
            
             
               REmembring
               on
               this
               Occasion
               an
               Experiment
               ,
               which
               though
               it
               do
               not
               shew
               what
               the
               precise
               quantity
               of
               Lateral
               pressure
               is
               ,
               that
               the
               lower
               parts
               of
               the
               fluid
               may
               sustain
               from
               the
               more
               elevated
               ;
               yet
               it
               may
               confirm
               the
               foregoing
               Paradox
               ,
               and
               by
               its
               Phaenomena
               afford
               some
               hints
               that
               may
               render
               it
               not
               unacceptable
               ;
               I
               shall
               subjoyn
               it
               ,
               as
               I
               set
               it
               down
               not
               long
               after
               I
               devis'd
               it
               .
            
             
               In
               the
               first
               place
               then
               ,
               there
               was
               made
               a
               glass
               Bubble
               with
               a
               slender
               neck
               ;
               and
               (
               in
               a
               word
               )
               of
               the
               figure
               express'd
               in
               the
               annex'd
               Scheme
               ;
               
               This
               Bubble
               I
               caus'd
               to
               be
               so
               poys'd
               ,
               That
               ,
               though
               it
               would
               float
               upon
               the
               water
               ,
               yet
               the
               addition
               of
               a
               weight
               small
               enough
               would
               suffice
               to
               make
               it
               sinck
               .
            
             
             
               This
               done
               ,
               I
               provided
               a
               very
               large
               wide
               mouth'd
               Glass
               ,
               and
               caus'd
               to
               be
               fitted
               to
               it
               ,
               as
               exactly
               as
               I
               could
               ,
               a
               stopple
               of
               Cork
               ,
               which
               being
               strongly
               thrust
               in
               ,
               would
               not
               easily
               be
               listed
               up
               .
               In
               the
               middle
               of
               this
               Cork
               there
               was
               burn'd
               ,
               with
               a
               heated
               instrument
               ,
               a
               round
               hole
               ;
               through
               which
               was
               thrust
               a
               long
               slender
               pipe
               of
               Glass
               ;
               so
               that
               the
               lower
               end
               of
               it
               was
               a
               pretty
               way
               beneath
               the
               Cork
               ,
               and
               the
               upper
               part
               of
               it
               was
               ,
               as
               near
               as
               could
               be
               ,
               at
               right
               Angles
               with
               the
               upper
               part
               of
               the
               said
               Cork
               .
               And
               in
               an
               other
               part
               of
               the
               stopple
               ,
               near
               the
               edge
               ,
               there
               was
               made
               another
               round
               hole
               ,
               into
               which
               was
               likewise
               thrust
               another
               small
               pipe
               ;
               whose
               lower
               part
               reach'd
               also
               a
               pretty
               way
               beneath
               the
               Cork
               ;
               but
               its
               upper
               part
               was
               but
               about
               two
               or
               three
               Inches
               high
               ;
               and
               the
               Orifice
               of
               this
               upper
               part
               was
               carefully
               clos'd
               with
               a
               stopple
               and
               Cement
               .
               Then
               the
               glass
               vessel
               being
               
               fill'd
               with
               water
               ,
               and
               the
               pois'd
               Bubble
               being
               made
               to
               float
               upon
               it
               ,
               the
               stopple
               or
               cover
               of
               the
               great
               glass
               vessel
               was
               put
               on
               ,
               and
               made
               fast
               with
               a
               close
               Cement
               ,
               that
               nothing
               might
               get
               in
               or
               out
               of
               the
               vessel
               ,
               but
               at
               the
               long
               slender
               pipe
               ;
               which
               was
               fastned
               into
               the
               Cork
               ▪
               (
               as
               was
               also
               the
               shorter
               pipe
               )
               not
               only
               by
               its
               own
               fitness
               to
               the
               hole
               ,
               it
               pass'd
               through
               ,
               but
               by
               a
               sufficient
               Quantity
               of
               the
               same
               Cement
               ,
               carefully
               apply'd
               to
               stop
               all
               crevesses
               .
            
             
               The
               Instrument
               thus
               prepar'd
               ,
               (
               and
               inclin'd
               this
               or
               that
               way
               ,
               till
               the
               floating
               Bubble
               was
               at
               a
               good
               distance
               from
               that
               end
               of
               the
               long
               pipe
               ,
               which
               reached
               a
               pretty
               way
               downwards
               beneath
               the
               Surface
               of
               the
               water
               ,
               )
               we
               began
               to
               pour
               in
               some
               of
               that
               Liquor
               at
               the
               open
               Orifice
               of
               the
               pipe
               
                 E
                 F
              
               ;
               and
               ,
               the
               mouth
               of
               the
               Vessel
               being
               exactly
               stopp'd
               ,
               the
               water
               for
               want
               of
               another
               
               place
               to
               receive
               it
               ,
               ascended
               into
               the
               pipe
               through
               which
               it
               had
               fallen
               before
               .
               And
               ,
               if
               I
               held
               my
               hand
               when
               the
               water
               I
               had
               pour'd
               in
               was
               able
               to
               reach
               but
               to
               a
               small
               height
               in
               the
               Cylinder
               ,
               as
               for
               instance
               ,
               to
               the
               Superficies
               J
               ;
               the
               Bubble
               X
               would
               yet
               continue
               floating
               .
               But
               if
               I
               continued
               pouring
               till
               the
               water
               in
               the
               pipe
               had
               attain'd
               to
               a
               considerable
               height
               above
               the
               Surface
               of
               that
               in
               the
               Vessel
               ,
               as
               if
               it
               reach'd
               to
               K
               ;
               then
               the
               Bubble
               X
               would
               presently
               sinck
               to
               the
               bottome
               of
               the
               Vessel
               ;
               and
               there
               continue
               ,
               as
               long
               as
               as
               the
               water
               continued
               at
               so
               great
               a
               height
               in
               the
               pipe
               
                 E.
                 F.
              
               
            
             
               This
               Experiment
               will
               not
               only
               teach
               us
               ,
               That
               the
               upper
               parts
               of
               the
               water
               gravitate
               upon
               those
               that
               are
               under
               them
               ,
               but
               (
               which
               is
               the
               thing
               we
               are
               now
               to
               confirm
               )
               That
               in
               a
               Vessel
               ,
               that
               is
               full
               ,
               all
               the
               lower
               parts
               are
               press'd
               by
               the
               upper
               ,
               though
               these
               lower
               be
               
               not
               directly
               beneath
               the
               upper
               ,
               but
               aside
               of
               them
               ,
               and
               perhaps
               at
               a
               good
               distance
               from
               the
               Line
               in
               which
               they
               directly
               press
               :
               These
               things
               ,
               I
               say
               ,
               may
               be
               made
               out
               by
               our
               Experiment
               .
               For
               the
               Addition
               of
               the
               Cylinder
               of
               water
               
                 K
                 J
              
               ,
               in
               the
               pipe
               
                 E
                 F
              
               ,
               makes
               the
               Bubble
               X
               subside
               ;
               as
               the
               force
               or
               pressure
               of
               any
               other
               heavy
               body
               upon
               the
               water
               in
               the
               vessel
               would
               do
               .
               And
               since
               (
               as
               may
               be
               gather'd
               from
               the
               Reason
               formerly
               given
               (
               in
               the
               Proof
               of
               the
               second
               Paradox
               )
               of
               the
               sincking
               of
               pois'd
               Bubbles
               )
               the
               included
               aire
               in
               our
               Bubble
               was
               notably
               compress'd
               ;
               it
               will
               follow
               ,
               that
               the
               Cylinder
               of
               water
               ,
               KI
               ,
               did
               press
               the
               subjacent
               water
               in
               the
               Vessel
               .
               For
               ,
               without
               so
               doing
               ,
               it
               could
               not
               be
               able
               to
               compress
               the
               aire
               in
               the
               Bubble
               .
               And
               since
               the
               said
               Bubble
               did
               not
               swimme
               directly
               under
               or
               near
               the
               pipe
               
                 E
                 F
              
               ;
               but
               at
               one
               side
               of
               it
               ,
               and
               at
               a
               pretty
               distance
               from
               it
               ,
               nay
               and
               
               floated
               above
               the
               lower
               Orifice
               ,
               F
               ,
               of
               the
               pipe
               ;
               't
               is
               evident
               that
               that
               Aqueous
               Cylinder
               ,
               JK
               ,
               does
               not
               only
               press
               upon
               the
               water
               ,
               or
               other
               Bodies
               that
               are
               directly
               under
               it
               ;
               but
               upon
               those
               also
               that
               are
               laterally
               situated
               in
               respect
               of
               it
               ,
               provided
               they
               be
               inferior
               to
               it
               .
            
             
               And
               ,
               according
               to
               this
               Doctrine
               ,
               we
               may
               conceive
               ,
               that
               every
               assignable
               part
               of
               the
               sides
               of
               the
               Vessel
               does
               sustaine
               a
               pressure
               ,
               encreas'd
               by
               the
               encrease
               of
               that
               parts
               depth
               under
               water
               ,
               and
               according
               to
               the
               largness
               of
               the
               said
               part
               .
               And
               therefore
               ,
               if
               any
               part
               were
               so
               weak
               ,
               as
               that
               it
               would
               be
               easily
               beaten
               out
               or
               broken
               by
               a
               weight
               equal
               to
               the
               Cylinder
               
                 I
                 K
              
               ,
               (
               making
               always
               a
               due
               abatement
               for
               the
               obliquity
               of
               the
               pressure
               )
               it
               would
               not
               be
               fit
               to
               be
               a
               part
               of
               our
               Vessel
               :
               Nay
               the
               Cork
               it self
               ,
               though
               it
               be
               above
               the
               Surface
               of
               the
               water
               in
               the
               Vessel
               ;
               yet
               because
               the
               water
               in
               the
               pipe
               is
               higher
               then
               it
               ,
               each
               of
               its
               
               parts
               resists
               a
               considerable
               pressure
               proportionate
               to
               its
               particular
               bigness
               ,
               and
               to
               the
               height
               of
               the
               water
               in
               the
               pipe
               .
               And
               therefore
               ,
               if
               the
               Cork
               be
               not
               well
               stopp'd
               in
               ,
               it
               may
               be
               lifted
               up
               by
               the
               pressure
               of
               the
               water
               in
               the
               pipe
               ,
               if
               that
               be
               fill'd
               to
               a
               good
               height
               .
               And
               if
               the
               Cement
               be
               not
               good
               and
               close
               ,
               the
               water
               will
               (
               not
               without
               noise
               )
               make
               it self
               a
               passage
               through
               it
               .
               And
               if
               the
               stopple
               G
               ,
               of
               the
               shorter
               pipe
               
                 G
                 H
              
               ,
               (
               which
               is
               plac'd
               there
               likewise
               to
               illustrate
               the
               present
               conjecture
               )
               do
               not
               firmly
               close
               the
               Orifice
               of
               it
               ,
               it
               may
               be
               forced
               out
               ,
               not
               without
               violence
               and
               noise
               .
               And
               ,
               for
               further
               satisfaction
               ,
               if
               ,
               in
               stead
               of
               the
               stopple
               G
               ,
               you
               close
               the
               Orifice
               with
               your
               finger
               ,
               you
               shall
               find
               it
               press'd
               upwards
               as
               strongly
               ,
               as
               it
               would
               be
               press'd
               downwards
               by
               the
               weight
               of
               a
               Cylinder
               of
               water
               of
               the
               breadth
               of
               the
               pipe
               ,
               and
               of
               a
               not
               inconsiderable
               height
               ,
               (
               for
               't
               is
               not
               easie
               to
               determine
               precisely
               ,
               
               what
               height
               :
               )
               so
               that
               (
               to
               be
               short
               )
               in
               the
               fluid
               Body
               ,
               we
               made
               our
               tryal
               with
               ,
               the
               pressure
               of
               the
               Superior
               parts
               was
               communicated
               ,
               not
               onely
               to
               those
               that
               were
               plac'd
               directly
               under
               them
               ,
               but
               ev'n
               to
               those
               that
               were
               but
               obliquely
               so
               ,
               and
               at
               a
               distance
               from
               them
               .
            
             
               I
               had
               forgot
               to
               confirm
               ,
               that
               it
               was
               the
               pressure
               of
               the
               superiour
               parts
               of
               the
               water
               ,
               that
               made
               our
               floating
               bubble
               sinck
               ,
               by
               such
               another
               circumstance
               as
               I
               took
               notice
               of
               in
               some
               of
               the
               former
               Experiments
               ;
               viz.
               that
               ,
               when
               it
               lay
               quietly
               at
               the
               bottom
               of
               the
               Vessel
               ,
               if
               by
               inclining
               the
               Instrument
               we
               pour'd
               off
               as
               much
               of
               the
               water
               in
               the
               pipe
               ,
               
                 E
                 F
              
               ,
               as
               suffic'd
               competently
               to
               diminish
               its
               height
               above
               the
               water
               in
               the
               Vessel
               
                 A
                 B
                 C
                 D
              
               ,
               the
               air
               in
               the
               bubble
               ,
               finding
               its
               former
               pressure
               alleviated
               ,
               would
               presently
               expand
               it self
               ,
               and
               make
               the
               bubble
               emerge
               .
               And
               to
               show
               ,
               That
               the
               very
               oblique
               pressure
               which
               the
               bubble
               
               sustain'd
               from
               the
               water
               in
               the
               pipe
               ,
               was
               not
               overmuch
               differing
               from
               that
               which
               it
               would
               have
               sustain'd
               from
               an
               External
               force
               ,
               or
               from
               the
               weight
               of
               water
               plac'd
               directly
               over
               it
               ;
               I
               caus'd
               two
               such
               bubbles
               to
               be
               pois'd
               ,
               and
               having
               put
               each
               of
               them
               into
               a
               long
               Cylindrical
               Glass
               ,
               open
               above
               ,
               and
               fill'd
               with
               water
               ,
               upon
               which
               it
               floated
               ,
               if
               we
               thrust
               it
               down
               a
               little
               way
               it
               would
               (
               agreeably
               to
               what
               hath
               been
               above
               related
               )
               ascend
               again
               ;
               
               so
               that
               we
               were
               forc'd
               to
               thrust
               it
               down
               to
               a
               good
               depth
               ,
               before
               the
               pressure
               of
               the
               incumbent
               water
               was
               great
               enough
               to
               make
               it
               subside
               .
            
             
               And
               perhaps
               it
               will
               not
               be
               impertinent
               to
               take
               notice
               ,
               before
               we
               conclude
               ,
               how
               the
               pressure
               of
               such
               differing
               fluids
               ,
               as
               aire
               and
               water
               ,
               may
               be
               communicated
               to
               one
               another
               .
               For
               having
               sometimes
               forborn
               to
               fill
               the
               Vessel
               
                 A
                 B
                 C
                 D
              
               quite
               full
               of
               water
               ,
               so
               
               that
               ,
               when
               the
               Cork
               was
               fitted
               to
               it
               ,
               there
               remain'd
               in
               it
               a
               pretty
               quantity
               of
               aire
               ,
               (
               as
               between
               the
               Surface
               
                 L
                 M
              
               ,
               and
               the
               Cork
               )
               nevertheless
               ,
               if
               the
               stopple
               or
               cork
               were
               very
               closely
               put
               in
               ,
               the
               pressure
               of
               the
               water
               that
               was
               afterwards
               poured
               into
               the
               pipe
               
                 E
                 F
              
               ,
               from
               J
               to
               K
               ,
               would
               make
               the
               bubble
               sinck
               ,
               little
               otherwise
               ,
               for
               ought
               I
               took
               notice
               of
               ,
               then
               if
               the
               Vessel
               had
               been
               perfectly
               fill'd
               with
               water
               ;
               the
               aire
               (
               above
               
                 L
                 M
                 ,
              
               )
               that
               was
               both
               imprisoned
               and
               compress'd
               ,
               communicating
               the
               pressure
               it
               receiv'd
               to
               the
               water
               contiguous
               to
               it
               :
            
          
        
         
           
           
             PARADOX
             VIII
             .
          
           
             That
             water
             may
             be
             made
             as
             well
             to
             depress
             a
             Body
             lighter
             then
             it self
             ,
             as
             to
             buoy
             it
             up
             .
          
           
             HOw
             strange
             soever
             this
             may
             seem
             ,
             to
             those
             that
             are
             prepossess'd
             with
             the
             vulgar
             Notions
             about
             gravity
             and
             levity
             :
             It
             need
             not
             be
             marvail'd
             at
             ,
             by
             them
             that
             have
             consider'd
             what
             has
             been
             already
             deliver'd
             .
             For
             since
             ,
             in
             Fluid
             Bodies
             ,
             the
             upper
             parts
             press
             upon
             the
             lower
             ,
             and
             upon
             other
             bodies
             that
             lie
             beneath
             them
             .
             And
             since
             ,
             when
             a
             Body
             is
             unequally
             press'd
             by
             others
             ,
             whether
             lighter
             or
             heavier
             then
             it self
             ,
             it
             must
             necessarily
             be
             thrust
             out
             of
             that
             place
             ,
             where
             it
             is
             more
             
             press'd
             ,
             to
             that
             where
             't
             is
             less
             press'd
             ;
             If
             that
             a
             parcel
             of
             oyle
             be
             by
             a
             contrivance
             so
             exposed
             to
             the
             water
             ,
             as
             that
             the
             water
             presses
             against
             its
             upper
             Superficies
             ,
             and
             not
             against
             the
             undermost
             or
             lateral
             parts
             of
             it
             ;
             If
             we
             suppose
             that
             there
             is
             nothing
             (
             whose
             pressure
             is
             not
             inferiour
             to
             that
             of
             the
             water
             )
             to
             hinder
             its
             descent
             ,
             (
             supposing
             ,
             withal
             ,
             that
             the
             oyle
             and
             water
             cannot
             pass
             by
             one
             another
             ;
             for
             which
             cause
             ,
             we
             make
             use
             of
             a
             slender
             pipe
             ;
             )
             the
             oyle
             must
             necessarily
             give
             way
             downwards
             ,
             and
             consequently
             be
             depress'd
             and
             not
             buoy'd
             up
             .
             This
             is
             easily
             exemplified
             by
             the
             following
             Experiment
             .
          
           
             Take
             a
             slender
             Glass
             Syphon
             
               E
               F
               G
               H
            
             ,
             of
             the
             bore
             we
             have
             often
             mention'd
             ,
             
             whose
             shorter
             leg
             
               G
               H
            
             may
             be
             about
             3
             or
             4
             Inches
             long
             ,
             and
             as
             parallel
             as
             the
             Artificer
             can
             make
             it
             to
             the
             longer
             
               E
               F
            
             ;
             dip
             the
             shorter
             leg
             in
             oyle
             of
             Turpentine
             ,
             till
             the
             oyle
             
             quite
             fill
             the
             shorter
             leg
             ,
             and
             reach
             to
             an
             equal
             height
             in
             the
             longer
             ,
             as
             from
             F
             to
             J.
             Then
             stopping
             the
             Orifice
             E
             of
             the
             longer
             leg
             with
             your
             finger
             ,
             and
             immersing
             the
             replenish'd
             part
             of
             the
             Syphon
             about
             an
             inch
             under
             water
             ,
             you
             shall
             perceive
             that
             as
             you
             thrust
             it
             lower
             and
             lower
             ,
             upon
             the
             removal
             of
             your
             finger
             ,
             the
             oyle
             in
             the
             shorter
             leg
             will
             be
             made
             to
             sinck
             about
             an
             inch
             or
             somewhat
             more
             ;
             and
             as
             afterwards
             you
             thrust
             the
             pipe
             deeper
             ,
             the
             oyle
             in
             the
             shorter
             leg
             will
             ,
             by
             the
             weight
             of
             the
             incumbent
             water
             ,
             
               H
               K
            
             ,
             be
             driven
             downward
             more
             and
             more
             ,
             till
             it
             come
             to
             the
             very
             bottom
             of
             the
             shorter
             leg
             ;
             whence
             ,
             by
             continuing
             the
             immersion
             ,
             you
             may
             impel
             it
             into
             the
             longer
             .
             The
             cause
             of
             which
             Phaenomenon
             ,
             I
             suppose
             to
             be
             already
             clearly
             enough
             assign'd
             ,
             to
             make
             it
             needless
             to
             add
             any
             thing
             here
             about
             it
             .
          
           
             It
             remains
             ,
             that
             ,
             before
             I
             proceed
             
             to
             the
             next
             proposition
             ,
             I
             add
             ;
             That
             ,
             to
             Exemplifie
             at
             once
             three
             Paradoxes
             ,
             (
             both
             this
             ,
             and
             the
             next
             foregoing
             ,
             
             and
             the
             second
             )
             I
             caus'd
             to
             be
             made
             a
             slender
             Glass-pipe
             ,
             of
             the
             Figure
             express'd
             in
             the
             annexed
             Scheme
             ,
             and
             having
             ,
             by
             the
             lower
             Orifice
             L
             ,
             suck'd
             into
             it
             as
             much
             oyle
             of
             Turpentine
             ,
             as
             reach'd
             in
             the
             longest
             leg
             ,
             
               N
               O
            
             ,
             as
             high
             as
             the
             Top
             of
             the
             other
             part
             of
             the
             Glass
             ;
             (
             namely
             ,
             to
             the
             part
             P
             ,
             in
             the
             same
             level
             with
             the
             Orifice
             
               L
               ,
            
             )
             I
             first
             stopp'd
             the
             upper
             Orifice
             of
             it
             ,
             O
             ,
             with
             my
             finger
             .
             And
             then
             ,
             thrusting
             it
             as
             before
             under
             water
             to
             a
             convenient
             depth
             ,
             upon
             the
             removal
             of
             my
             finger
             ,
             the
             External
             water
             did
             first
             drive
             away
             the
             oyle
             that
             was
             in
             
               L
               M
            
             ,
             that
             part
             of
             the
             crooked
             pipe
             which
             was
             parallel
             to
             the
             Horizon
             ;
             then
             it
             depress'd
             the
             same
             oyle
             to
             the
             bottom
             of
             the
             shorter
             leg
             ,
             that
             is
             from
             M
             to
             N
             :
             And
             lastly
             ,
             
             it
             impell'd
             it
             all
             up
             into
             the
             longer
             leg
             
               N
               P
               O
            
             ,
             to
             what
             height
             I
             thought
             fit
             .
             So
             that
             the
             oyle
             was
             press'd
             by
             the
             water
             both
             laterally
             ,
             downwards
             ,
             and
             upwards
             :
             the
             causes
             of
             which
             are
             easily
             deducible
             from
             the
             Doctrine
             already
             deliver'd
             .
          
        
         
           
           
             PARADOX
             IX
             .
          
           
             That
             ,
             what
             ever
             is
             said
             of
             positive
             Levity
             ,
             a
             parcel
             of
             oyle
             lighter
             then
             water
             ,
             may
             be
             kept
             in
             water
             without
             ascending
             in
             it
             .
          
           
             TO
             make
             out
             what
             I
             have
             to
             represent
             about
             this
             Paradox
             the
             more
             intelligible
             ,
             the
             best
             way
             perhaps
             will
             be
             to
             set
             down
             the
             Considerations
             that
             induc'd
             me
             to
             judge
             the
             thing
             it
             pretends
             to
             feasible
             .
             And
             in
             order
             to
             this
             ,
             it
             would
             be
             expedient
             to
             consider
             ,
             why
             it
             is
             that
             a
             Body
             lighter
             
               in
               specie
            
             then
             water
             ,
             being
             plac'd
             never
             so
             much
             beneath
             the
             Superficies
             of
             that
             Liquor
             ,
             will
             rather
             emerge
             to
             the
             
             Top
             ,
             then
             sinck
             to
             the
             bottom
             of
             it
             ;
             if
             we
             had
             not
             already
             consider'd
             that
             problem
             in
             the
             Explication
             of
             the
             third
             Paradox
             .
             But
             being
             now
             allow'd
             to
             apply
             to
             our
             present
             purpose
             what
             hath
             been
             there
             deliver'd
             ,
             I
             shall
             forthwith
             subjoyne
             ,
             That
             't
             was
             easie
             enough
             for
             me
             to
             collect
             from
             hence
             ,
             that
             ,
             the
             Reason
             why
             it
             seems
             not
             possible
             ,
             That
             a
             parcel
             of
             oyle
             lighter
             then
             water
             ,
             should
             without
             violence
             be
             kept
             from
             emerging
             to
             the
             Top
             of
             it
             ,
             being
             this
             ,
             
               That
               since
               the
               Surface
               of
               a
               Vessel
               full
               of
               standing
               water
               is
               (
               Physically
               speaking
               )
               Horizontal
               ,
               the
               water
               that
               presses
               against
               the
               lower
               part
               of
               the
               immers'd
               Body
               ,
               must
               needs
               be
               deeper
               then
               that
               which
               presses
               against
               the
               upper
               :
            
             If
             I
             could
             so
             order
             the
             matter
             that
             the
             water
             that
             leans
             upon
             the
             upper
             part
             of
             the
             Body
             should
             be
             being
             higher
             then
             the
             level
             of
             the
             rest
             of
             the
             water
             have
             a
             height
             great
             enough
             to
             ballance
             that
             which
             presses
             
             against
             the
             lower
             ,
             (
             and
             the
             Bodies
             not
             shift
             places
             by
             passing
             one
             by
             the
             other
             )
             the
             oyle
             might
             be
             kept
             suspended
             betwixt
             two
             parcels
             of
             water
             .
          
           
             To
             reduce
             this
             to
             practise
             ,
             I
             took
             the
             following
             course
             ;
             having
             suck'd
             into
             a
             slender
             pipe
             ▪
             (
             such
             as
             that
             imploy'd
             about
             the
             first
             experiment
             about
             an
             Inch
             of
             water
             ,
             and
             kept
             it
             suspended
             there
             by
             stopping
             the
             Orifice
             of
             the
             pipe
             ;
             I
             thrust
             the
             lower
             part
             of
             the
             pipe
             about
             two
             inches
             beneath
             the
             Surface
             of
             some
             oyl
             of
             Turpentitie
             (
             which
             ,
             to
             make
             the
             effect
             the
             clearer
             ,
             I
             sometimes
             tinge
             deeply
             with
             Copper
             :
             )
             then
             removing
             my
             finger
             ,
             the
             oyle
             being
             press'd
             against
             the
             immers'd
             Orifice
             with
             a
             greater
             force
             ,
             then
             the
             weight
             of
             so
             little
             suspended
             water
             could
             resist
             ,
             that
             oyle
             was
             impell'd
             into
             the
             lower
             part
             of
             the
             pipe
             to
             the
             height
             of
             near
             an
             inch
             ;
             and
             then
             again
             I
             stopp'd
             the
             upper
             Orifice
             of
             the
             pipe
             with
             my
             
             finger
             ,
             and
             thereby
             keeping
             both
             the
             Liquors
             suspended
             in
             it
             ,
             I
             thrust
             the
             pipe
             into
             a
             Glass
             full
             of
             water
             ,
             three
             or
             four
             inches
             beneath
             the
             Surface
             of
             it
             ;
             and
             then
             (
             for
             the
             Reason
             just
             now
             given
             )
             the
             water
             ,
             upon
             the
             Removal
             of
             my
             finger
             ,
             will
             press
             in
             at
             the
             lower
             Orifice
             of
             the
             pipe
             ,
             and
             impell
             up
             the
             oyle
             ,
             
             till
             they
             come
             to
             such
             a
             station
             ,
             as
             that
             express'd
             in
             the
             annex'd
             Scheme
             :
             where
             
               P
               Q
            
             is
             the
             water
             ,
             newly
             impell'd
             up
             into
             the
             pipe
             ,
             
               Q
               R
            
             is
             the
             oyl
             ,
             and
             
               R
               S
            
             the
             water
             that
             was
             at
             first
             suck'd
             into
             the
             pipe
             .
             For
             in
             this
             station
             ,
             these
             three
             liquors
             do
             altogether
             as
             much
             gravitate
             upon
             the
             part
             P
             ,
             as
             the
             incumbent
             water
             alone
             does
             upon
             the
             other
             parts
             of
             the
             imaginary
             superficies
             
               G
               H
            
             ;
             and
             yet
             the
             oyle
             ,
             
               R
               Q
            
             ,
             does
             not
             ascend
             ,
             because
             the
             diffluence
             of
             the
             water
             ,
             
               R
               S
            
             ,
             being
             hindred
             by
             the
             sides
             of
             the
             pipe
             ,
             its
             superficies
             ,
             
               T
               S
            
             ,
             is
             higher
             then
             
               A
               D
            
             ,
             the
             
             Superficies
             of
             the
             rest
             of
             the
             water
             ;
             by
             which
             means
             the
             incumbent
             water
             may
             be
             brought
             to
             have
             upon
             the
             upper
             part
             R
             of
             the
             oleous
             Cylinder
             ,
             as
             great
             a
             pressure
             as
             that
             of
             the
             water
             ,
             that
             endeavours
             to
             impel
             upwards
             the
             lower
             part
             Q
             of
             the
             same
             suspended
             Cylinder
             of
             oyle
             .
          
        
         
           
           
             PARADOX
             X.
             
          
           
             That
             the
             cause
             of
             the
             Ascension
             of
             water
             in
             Syphons
             ,
             and
             of
             its
             flowing
             through
             them
             ,
             may
             be
             explicated
             without
             having
             a
             recourse
             to
             natures
             abhorrency
             of
             a
             Vacuum
             .
          
           
             BOth
             Philosophers
             and
             Mathematicians
             ,
             having
             too
             generally
             confest
             themselves
             reduc'd
             to
             fly
             to
             a
             
               fuga
               vacui
            
             ,
             for
             an
             account
             of
             the
             cause
             of
             the
             running
             of
             water
             and
             other
             Liquors
             through
             Syphons
             .
             And
             ev'n
             those
             moderns
             ,
             that
             admit
             a
             Vacuum
             ,
             having
             (
             as
             far
             as
             I
             have
             met
             with
             )
             either
             left
             the
             Phaenomenon
             unexplicated
             ,
             or
             endeavour'd
             to
             explain
             it
             by
             disputable
             Notions
             :
             I
             think
             the
             Curious
             much
             oblig'd
             to
             
             Monsieur
             Paschal
             ,
             for
             having
             ingeniously
             endeavour'd
             to
             shew
             ▪
             That
             this
             difficult
             Probleme
             need
             not
             reduce
             us
             to
             have
             recourse
             to
             a
             
               fuga
               vacut
            
             .
             And
             indeed
             his
             Explication
             of
             the
             motion
             of
             water
             in
             Syphons
             ,
             seems
             to
             me
             so
             consonant
             to
             Hydrostatical
             principles
             ,
             that
             I
             think
             it
             not
             necessary
             to
             alter
             any
             thing
             in
             it
             .
             But
             as
             for
             the
             experiment
             he
             propounds
             to
             justifie
             his
             Ratiocination
             ,
             I
             fear
             his
             Readers
             will
             scarce
             be
             much
             invited
             to
             attempt
             it
             .
             For
             ,
             besides
             that
             it
             requires
             a
             great
             quantity
             of
             Quicksilver
             ;
             and
             a
             new
             kind
             of
             Syphon
             ,
             15
             or
             20
             foot
             long
             ;
             the
             Vessels
             of
             Quicksilver
             must
             be
             plac'd
             6
             or
             7
             yards
             under
             water
             ,
             that
             is
             ,
             at
             so
             great
             a
             depth
             ,
             that
             I
             doubt
             whether
             men
             ,
             that
             are
             not
             divers
             ,
             will
             be
             able
             conveniently
             to
             observe
             the
             progress
             of
             the
             Tryal
             .
          
           
             Wherefore
             we
             will
             substitute
             a
             way
             ,
             which
             may
             be
             try'd
             in
             a
             glass
             Tube
             ,
             not
             
             two
             foot
             deep
             ,
             by
             the
             help
             of
             another
             peculiarly
             contriv'd
             glass
             ,
             to
             be
             prepar'd
             by
             a
             skilful
             hand
             .
             Provide
             then
             a
             glass
             Tube
             
               A
               B
               C
               D
            
             ,
             of
             a
             good
             wideness
             ,
             and
             half
             a
             yard
             or
             more
             in
             depth
             ;
             provide
             also
             a
             Syphon
             of
             two
             legs
             
               F
               K
            
             ,
             and
             
               K
               G
            
             ,
             whereunto
             is
             joyn'd
             (
             at
             the
             upper
             part
             of
             the
             Syphon
             )
             a
             pipe
             
               E
               K
            
             ,
             in
             such
             manner
             ,
             as
             that
             the
             Cavity
             of
             the
             pipe
             communicates
             with
             the
             cavities
             of
             the
             syphon
             ;
             
             so
             that
             if
             you
             should
             pour
             in
             water
             at
             E
             ,
             it
             would
             run
             out
             at
             F
             and
             G.
             To
             each
             of
             the
             two
             Legs
             of
             this
             new
             Syphon
             ,
             must
             be
             ty'd
             with
             a
             string
             a
             pipe
             of
             Glass
             ,
             I
             and
             H
             ,
             seal'd
             at
             one
             end
             ,
             and
             open
             at
             the
             other
             ;
             at
             which
             it
             admits
             a
             good
             part
             of
             the
             leg
             of
             the
             Syphon
             to
             which
             it
             is
             fastned
             ,
             and
             which
             leg
             must
             reach
             a
             pretty
             way
             beneath
             the
             Surface
             of
             the
             water
             ,
             wherewith
             the
             said
             pipe
             is
             to
             be
             almost
             fill'd
             .
             But
             as
             one
             of
             these
             legs
             is
             longer
             
             then
             the
             other
             ,
             so
             the
             surface
             of
             the
             water
             in
             the
             suspended
             pipe
             I
             ,
             that
             is
             fastned
             to
             the
             shorter
             leg
             
               K
               F
            
             ,
             must
             be
             higher
             (
             that
             is
             ,
             nearer
             to
             K
             or
             
               A
               B
            
             )
             then
             the
             surface
             of
             the
             water
             in
             the
             pipe
             H
             ,
             suspended
             from
             the
             longer
             leg
             KG
             ;
             that
             (
             according
             to
             what
             is
             usual
             in
             Syphons
             )
             the
             water
             may
             run
             from
             a
             higher
             vessel
             to
             a
             lower
             .
          
           
             All
             things
             being
             thus
             provided
             ;
             and
             the
             pipe
             
               E
               K
            
             being
             held
             ,
             or
             otherwise
             made
             fast
             that
             it
             may
             not
             be
             mov'd
             ;
             you
             must
             gently
             poure
             oyle
             of
             Turpentine
             into
             the
             Tube
             
               A
               B
               C
               D
            
             ,
             (
             which
             ,
             if
             you
             have
             not
             much
             oyle
             ,
             you
             may
             before
             hand
             fill
             with
             water
             till
             the
             liquor
             reach
             near
             the
             Bottom
             of
             the
             suspended
             pipes
             ,
             as
             to
             the
             superficies
             
               X
               Y
            
             )
             till
             it
             reach
             higher
             then
             the
             top
             of
             the
             Syphon
             
               F
               K
               G
            
             ,
             (
             whose
             Orifice
             E
             you
             may
             ,
             if
             you
             please
             ,
             in
             the
             mean
             time
             close
             with
             your
             finger
             or
             otherwise
             ,
             and
             afterwards
             unstop
             )
             
             and
             then
             the
             oyle
             pressing
             upon
             the
             water
             will
             make
             it
             ascend
             into
             the
             legs
             of
             the
             Syphon
             ;
             and
             pass
             through
             it
             ,
             out
             of
             the
             uppermost
             vessel
             J
             ,
             into
             the
             lowermost
             H
             ;
             and
             if
             the
             vessel
             J
             were
             supply'd
             with
             water
             ,
             the
             course
             of
             the
             water
             through
             the
             Syphon
             would
             continue
             longer
             ,
             then
             here
             (
             by
             reason
             of
             the
             paucity
             of
             water
             )
             it
             can
             do
             .
          
           
             Now
             in
             this
             Experiment
             we
             manifestly
             see
             the
             water
             made
             to
             take
             its
             course
             through
             the
             legs
             of
             a
             Syphon
             from
             a
             higher
             vessel
             into
             a
             lower
             ,
             and
             yet
             the
             top
             of
             the
             Syphon
             being
             perforated
             at
             K
             ,
             the
             aire
             has
             free
             access
             to
             each
             of
             the
             legs
             of
             it
             ,
             through
             the
             hollow
             pipe
             
               E
               K
            
             which
             communicates
             with
             them
             both
             .
             So
             that
             ,
             in
             our
             case
             ,
             (
             where
             there
             is
             no
             danger
             of
             a
             Vacuum
             ,
             though
             the
             water
             should
             not
             run
             through
             the
             Syphon
             )
             the
             fear
             of
             a
             Vacuum
             cannot
             with
             any
             shew
             of
             Reason
             be
             pretended
             to
             be
             the
             cause
             of
             its
             running
             .
             Wherefore
             
             we
             must
             seek
             out
             some
             other
             .
          
           
             And
             it
             will
             not
             be
             very
             difficult
             to
             find
             ,
             that
             't
             is
             partly
             the
             pressure
             of
             the
             oyle
             ,
             and
             partly
             the
             contrivance
             and
             situation
             of
             the
             vessels
             ;
             if
             we
             will
             but
             consider
             the
             matter
             somewhat
             more
             atentively
             .
             For
             the
             oyle
             ,
             that
             reaches
             much
             higher
             then
             K
             ,
             and
             consequently
             then
             the
             leggs
             of
             the
             Syphon
             ,
             presses
             upon
             the
             surface
             of
             the
             External
             water
             ,
             in
             each
             of
             the
             suspended
             pipes
             I
             and
             H.
             I
             say
             the
             
               External
               water
            
             ,
             because
             the
             oyle
             floating
             upon
             the
             water
             ,
             and
             the
             Orifice
             of
             both
             the
             legs
             F
             and
             G
             being
             immers'd
             under
             the
             water
             ,
             the
             oyle
             has
             no
             access
             to
             the
             cavity
             of
             either
             of
             those
             legs
             .
             Wherefore
             ,
             since
             the
             oyle
             gravitates
             upon
             the
             water
             without
             the
             legs
             ,
             and
             not
             upon
             that
             within
             them
             ,
             and
             since
             its
             height
             above
             the
             water
             is
             great
             enough
             to
             press
             up
             the
             water
             into
             the
             Cavity
             of
             the
             legs
             of
             the
             Syphon
             ,
             and
             impel
             it
             as
             high
             as
             K
             ,
             the
             
             water
             must
             by
             that
             pressure
             be
             made
             to
             ascend
             .
          
           
             And
             this
             raising
             of
             the
             water
             happening
             at
             first
             in
             both
             legs
             ,
             (
             for
             the
             cause
             is
             in
             both
             the
             same
             )
             there
             will
             be
             a
             kind
             of
             conflict
             about
             K
             betwixt
             the
             two
             ascending
             portions
             of
             water
             ,
             and
             therefore
             we
             will
             now
             examine
             which
             must
             prevaile
             .
          
           
             And
             if
             we
             consider
             ,
             That
             the
             pressure
             ,
             sustein'd
             by
             the
             two
             parcels
             of
             water
             in
             the
             suspended
             pipes
             I
             and
             H
             ,
             depends
             upon
             the
             height
             of
             the
             oyle
             that
             presses
             upon
             them
             respectively
             ;
             it
             may
             seem
             (
             at
             the
             first
             view
             )
             That
             the
             water
             should
             be
             driven
             out
             of
             the
             lower
             vessel
             into
             the
             higher
             .
             For
             if
             we
             suppose
             that
             part
             of
             the
             shorter
             leg
             that
             is
             unimmers'd
             under
             water
             to
             be
             6
             Inches
             long
             ,
             &
             the
             unimmers'd
             part
             of
             the
             longer
             leg
             to
             be
             seaven
             Inches
             ;
             because
             the
             surface
             of
             the
             water
             in
             the
             vessel
             I
             ,
             is
             an
             Inch
             higher
             ,
             then
             that
             of
             
             the
             water
             in
             the
             vessel
             H
             ,
             it
             will
             follow
             ,
             That
             there
             is
             a
             greater
             pressure
             upon
             the
             water
             ,
             whereinto
             the
             longer
             leg
             is
             dip'd
             ,
             by
             the
             weight
             of
             an
             Inch
             of
             oyle
             :
             so
             that
             that
             liquor
             being
             an
             inch
             higher
             upon
             the
             surface
             of
             the
             water
             in
             the
             pipe
             H
             ,
             then
             upon
             that
             in
             the
             pipe
             I
             ,
             it
             seems
             that
             the
             water
             ought
             rather
             to
             be
             impell'd
             from
             H
             towards
             K
             ,
             then
             from
             I
             towards
             K.
             
          
           
             But
             then
             we
             must
             consider
             ,
             That
             ,
             though
             the
             descent
             of
             the
             water
             in
             the
             leg
             G
             ,
             be
             more
             resisted
             then
             that
             in
             the
             other
             leg
             ,
             by
             as
             much
             pressure
             as
             the
             weight
             of
             
               an
               Inch
               of
               oyle
            
             can
             amount
             to
             ;
             Yet
             being
             longer
             by
             an
             Inch
             then
             the
             water
             in
             the
             leg
             F
             ,
             it
             tends
             downwards
             more
             strongly
             by
             the
             weight
             of
             an
             
               Inch
               of
               water
            
             ,
             by
             which
             length
             it
             exceeds
             the
             water
             in
             the
             opposite
             leg
             .
             So
             that
             an
             inch
             of
             water
             being
             
               (
               ceteris
               paribus
            
             )
             heavier
             then
             an
             Inch
             of
             oyle
             ;
             the
             water
             in
             the
             longer
             leg
             ,
             notwithstanding
             
             the
             greater
             resistance
             of
             the
             external
             oyle
             ,
             has
             a
             stronger
             endeavour
             downwards
             ,
             then
             has
             the
             water
             in
             the
             shorter
             leg
             ;
             though
             the
             descent
             of
             this
             be
             resisted
             but
             by
             a
             depth
             of
             oyl
             less
             by
             an
             Inch.
             So
             that
             all
             things
             computed
             ,
             the
             motion
             must
             be
             made
             towards
             that
             way
             where
             the
             endeavour
             is
             most
             forcible
             ;
             and
             consequently
             the
             course
             of
             the
             water
             must
             be
             from
             the
             upper
             vessel
             ,
             and
             the
             shorter
             leg
             ,
             into
             the
             longer
             leg
             ,
             and
             so
             into
             the
             lower
             vessel
             .
          
           
             The
             application
             of
             this
             to
             what
             happens
             in
             Syphons
             is
             obvious
             enough
             .
             For
             ,
             when
             once
             the
             water
             is
             brought
             to
             run
             through
             a
             Syphon
             ,
             the
             aire
             (
             which
             is
             a
             fluid
             and
             has
             some
             gravity
             ,
             and
             has
             no
             access
             into
             the
             cavity
             of
             the
             Syphon
             ,
             )
             must
             necessarily
             gravitate
             upon
             the
             water
             whereinto
             the
             legs
             of
             the
             Syphon
             are
             dip'd
             ,
             and
             not
             upon
             that
             which
             is
             within
             the
             Syphon
             :
             and
             consequently
             ,
             though
             the
             incumbent
             
             aire
             have
             somewhat
             a
             greater
             height
             upon
             the
             water
             in
             the
             lower
             vessel
             ,
             then
             upon
             that
             in
             the
             upper
             ;
             yet
             the
             gravitation
             it
             thereby
             exercises
             upon
             the
             former
             more
             then
             upon
             the
             latter
             ,
             being
             very
             inconsiderable
             ,
             the
             water
             in
             the
             longer
             leg
             much
             preponderating
             (
             by
             reason
             of
             its
             length
             )
             the
             water
             in
             the
             shorter
             leg
             ,
             the
             efflux
             must
             be
             out
             of
             that
             leg
             ,
             and
             not
             out
             of
             the
             other
             .
             And
             the
             pressure
             of
             the
             External
             aire
             being
             able
             to
             raise
             water
             (
             as
             we
             find
             by
             sucking
             Pumps
             )
             to
             a
             far
             greater
             height
             ,
             then
             that
             of
             the
             shorter
             leg
             of
             the
             Syphon
             ;
             the
             efflux
             will
             continue
             ,
             for
             the
             same
             reason
             ,
             till
             the
             exhaustion
             of
             the
             water
             ,
             or
             some
             other
             circumstance
             ,
             alter
             the
             case
             .
             But
             ,
             if
             the
             legs
             of
             the
             Syphon
             should
             exceed
             34
             or
             35
             foot
             of
             perpendicular
             altitude
             ;
             the
             water
             would
             not
             flow
             through
             it
             ;
             
             the
             pressure
             of
             the
             external
             aire
             being
             unable
             ,
             (
             as
             
             has
             been
             elsewhere
             declared
             ,
             )
             to
             raise
             water
             to
             such
             a
             height
             .
             And
             if
             a
             hole
             being
             made
             at
             the
             top
             of
             a
             Syphon
             ,
             that
             hole
             should
             be
             unstopp'd
             while
             the
             water
             is
             running
             ,
             the
             course
             of
             it
             would
             presently
             cease
             .
             For
             ,
             in
             that
             case
             ,
             the
             aire
             would
             gravitate
             upon
             the
             water
             ,
             as
             well
             within
             as
             without
             the
             cavity
             of
             the
             Syphon
             ;
             and
             so
             the
             water
             in
             each
             leg
             would
             ,
             by
             its
             own
             weight
             ,
             fall
             back
             into
             the
             vessel
             belonging
             to
             it
             .
          
           
             But
             because
             this
             last
             circumstance
             ,
             though
             clearly
             deducible
             from
             Hydrostatical
             principles
             and
             Experiments
             ,
             has
             not
             ,
             that
             I
             know
             of
             ,
             been
             verified
             by
             particular
             Tryals
             ,
             I
             caus'd
             two
             Syphons
             to
             be
             made
             ,
             the
             one
             of
             Tin
             ,
             the
             other
             of
             Glass
             ;
             each
             of
             which
             had
             ,
             at
             the
             upper
             part
             of
             the
             flexure
             ,
             a
             small
             round
             hole
             or
             socket
             ,
             which
             I
             could
             stop
             and
             unstop
             ,
             at
             pleasure
             ,
             with
             the
             pulp
             of
             my
             finger
             .
             So
             that
             ,
             
             when
             the
             water
             was
             running
             through
             the
             Syphon
             ,
             in
             case
             I
             remov'd
             my
             finger
             ,
             the
             water
             would
             presently
             fall
             ,
             partly
             into
             one
             of
             the
             subjacent
             vessels
             ,
             and
             partly
             into
             the
             other
             .
             And
             if
             the
             legs
             of
             the
             Syphon
             were
             so
             unequal
             in
             length
             ,
             that
             the
             water
             in
             the
             one
             had
             a
             far
             greater
             height
             (
             or
             depth
             )
             then
             in
             the
             other
             ;
             there
             seem'd
             to
             be
             ,
             when
             the
             liquor
             began
             to
             take
             its
             course
             through
             the
             Syphon
             ,
             some
             light
             pressure
             from
             the
             external
             aire
             upon
             the
             finger
             ,
             wherewith
             I
             stopp'd
             the
             Orifice
             of
             the
             socket
             made
             at
             the
             flexure
             .
          
           
             And
             on
             this
             occasion
             I
             will
             add
             ,
             what
             I
             more
             then
             once
             try'd
             ;
             to
             shew
             ,
             at
             how
             very
             minute
             a
             passage
             the
             pressure
             of
             the
             External
             aire
             may
             be
             communicated
             ,
             to
             Bodyes
             fitted
             to
             receive
             it
             .
             For
             ,
             having
             for
             this
             purpose
             stopp'd
             the
             orifice
             of
             one
             of
             the
             above
             mentioned
             Syphons
             ,
             (
             insteed
             of
             doing
             it
             with
             my
             finger
             ,
             )
             with
             a
             piece
             of
             oyl'd
             paper
             ,
             
             carefully
             fastned
             with
             Cement
             to
             the
             sides
             of
             the
             socket
             ;
             I
             found
             ,
             as
             I
             expected
             ,
             that
             though
             hereby
             the
             Syphon
             was
             so
             well
             clos'd
             ,
             that
             the
             water
             ran
             freely
             through
             :
             yet
             ,
             if
             I
             made
             a
             hole
             with
             the
             point
             of
             a
             needle
             ,
             the
             aire
             would
             at
             so
             very
             little
             an
             orifice
             insinuate
             it self
             into
             the
             cavity
             of
             the
             Syphon
             ,
             and
             ,
             thereby
             gravitating
             as
             well
             within
             as
             without
             ,
             make
             the
             water
             in
             the
             legs
             to
             fall
             down
             into
             the
             vessels
             .
             And
             though
             ,
             if
             I
             held
             the
             point
             of
             the
             needle
             in
             the
             hole
             I
             made
             ,
             and
             then
             caus'd
             one
             to
             suck
             at
             the
             longer
             leg
             ;
             this
             small
             stopple
             ,
             without
             any
             other
             help
             from
             my
             hand
             ,
             suffic'd
             to
             make
             the
             Syphon
             fit
             for
             use
             :
             Yet
             if
             I
             remov'd
             the
             needle
             ,
             the
             aire
             would
             (
             not
             without
             some
             noise
             )
             presently
             get
             in
             at
             the
             hole
             ,
             and
             put
             a
             final
             stop
             to
             the
             course
             of
             the
             water
             .
             Nor
             was
             I
             able
             to
             take
             out
             the
             needle
             and
             put
             it
             in
             again
             so
             nimbly
             ,
             but
             that
             
             the
             aire
             found
             time
             to
             get
             into
             the
             Syphon
             ;
             and
             ,
             till
             the
             hole
             were
             again
             stopp'd
             ,
             render
             it
             useless
             ,
             notwithstanding
             that
             the
             water
             was
             by
             suction
             endeavour'd
             to
             be
             set
             a
             running
             .
          
        
         
           
           
             PARADOX
             XI
             .
          
           
             That
             a
             solid
             Body
             ,
             as
             ponderous
             as
             any
             yet
             known
             ,
             though
             near
             the
             Top
             of
             the
             water
             it
             will
             sinck
             by
             its
             own
             weight
             ;
             yet
             if
             it
             be
             plac'd
             at
             a
             greater
             depth
             then
             that
             of
             twenty
             times
             its
             own
             thickness
             ,
             it
             will
             not
             sinck
             ,
             if
             its
             descent
             be
             not
             assisted
             by
             the
             weight
             of
             the
             incumbent
             water
             .
          
           
             THis
             Paradox
             ,
             having
             never
             been
             (
             that
             I
             know
             of
             )
             propos'd
             as
             yet
             by
             any
             ,
             has
             seem'd
             so
             little
             credible
             to
             those
             to
             whom
             I
             have
             mention'd
             it
             ,
             (
             without
             excepting
             Mathematicians
             themselves
             ,
             )
             that
             I
             can
             scarce
             hope
             it
             should
             be
             readily
             and
             generally
             received
             in
             this
             Illustrious
             Company
             ,
             upon
             
             less
             clear
             Testimony
             ,
             then
             that
             of
             Experience
             .
             And
             therefore
             ,
             though
             (
             if
             I
             mistake
             not
             )
             some
             part
             of
             this
             proposition
             may
             be
             plausibly
             deduc'd
             by
             the
             help
             of
             an
             Instrument
             ingeniously
             thought
             upon
             by
             
               Monsieur
               Paschal
            
             ;
             Yet
             I
             shall
             have
             recourse
             to
             my
             own
             Method
             for
             the
             making
             of
             it
             out
             ,
             for
             these
             two
             Reasons
             .
             The
             one
             ,
             That
             a
             great
             part
             of
             the
             Paradox
             must
             be
             Explicated
             ,
             as
             well
             as
             prov'd
             ,
             by
             the
             Doctrine
             already
             setled
             in
             this
             paper
             .
             The
             other
             ,
             That
             the
             Experiment
             propos'd
             by
             
               Monsieur
               Paschal
            
             ,
             being
             to
             be
             done
             in
             a
             deep
             River
             ,
             and
             requiring
             a
             Tube
             20
             foot
             long
             ,
             whose
             Bottome
             must
             be
             fitted
             with
             a
             Brass
             Cylinder
             ,
             made
             with
             an
             exactness
             ,
             scarce
             (
             if
             at
             all
             )
             to
             be
             hoped
             for
             from
             our
             Workmen
             :
             If
             I
             should
             build
             any
             thing
             on
             this
             so
             difficult
             an
             Experiment
             ,
             (
             which
             himself
             does
             not
             affirm
             to
             have
             ever
             been
             actually
             tryed
             ,
             )
             I
             fear
             most
             men
             
             would
             rather
             reject
             the
             Experiment
             as
             a
             Chimaerical
             thing
             ,
             then
             receive
             for
             its
             sake
             a
             Doctrine
             that
             appears
             to
             them
             very
             Extravagant
             .
          
           
             Let
             us
             then
             ,
             to
             imploy
             in
             this
             case
             also
             the
             method
             we
             have
             hitherto
             made
             use
             of
             ,
             Fill
             a
             Glass
             vessel
             ,
             
               A
               B
               C
               D
            
             ,
             almost
             full
             of
             water
             ;
             
             only
             ,
             in
             regard
             that
             there
             is
             a
             great
             depth
             of
             water
             requisite
             to
             some
             Circumstances
             of
             the
             Experiment
             ,
             This
             last
             must
             not
             be
             so
             shallow
             as
             those
             hitherto
             imploy'd
             :
             but
             a
             deep
             Cylinder
             ,
             or
             Tube
             seal'd
             at
             one
             end
             ,
             whose
             depth
             must
             be
             at
             least
             two
             or
             three
             foot
             ,
             though
             its
             breadth
             need
             not
             be
             above
             2
             or
             3
             Inches
             ;
             and
             ,
             to
             keep
             it
             upright
             ,
             it
             may
             be
             plac'd
             in
             a
             socket
             of
             metal
             or
             wood
             ,
             of
             a
             size
             and
             weight
             convenient
             for
             such
             a
             purpose
             .
             This
             Glass
             being
             thus
             fitted
             in
             water
             ,
             let
             us
             suppose
             
               E
               F
            
             ,
             to
             be
             a
             round
             and
             flat
             piece
             of
             solid
             Brass
             ,
             having
             about
             an
             
             Inch
             in
             Diameter
             ,
             and
             a
             fourth
             or
             sixth
             part
             of
             an
             inch
             in
             thickness
             .
             This
             Cylinder
             ,
             being
             immers'd
             under
             water
             till
             it
             be
             just
             cover'd
             by
             the
             uppermost
             Surface
             of
             that
             Liquor
             ,
             and
             being
             let
             go
             ,
             must
             necessarily
             fall
             downwards
             in
             it
             ;
             because
             if
             we
             suppose
             the
             imaginary
             Superficies
             ,
             
               G
               H
            
             ,
             to
             pass
             along
             the
             Circle
             F
             ,
             which
             is
             the
             lower
             part
             of
             the
             Brass
             Body
             ,
             that
             metal
             being
             
               in
               specie
            
             far
             heavier
             then
             water
             ,
             the
             Brass
             that
             leans
             upon
             the
             part
             F
             ,
             must
             far
             more
             gravitate
             upon
             the
             said
             part
             F
             ,
             then
             the
             incumbent
             water
             does
             upon
             any
             other
             part
             of
             the
             Superficies
             
               G
               H
            
             ;
             and
             ,
             consequently
             ,
             the
             subjacent
             water
             at
             F
             will
             be
             thrust
             out
             of
             place
             by
             the
             descending
             Body
             .
             And
             because
             that
             ,
             in
             what
             part
             soever
             of
             the
             water
             ,
             not
             exceeding
             nine
             times
             its
             thickness
             measured
             from
             the
             Top
             of
             the
             water
             
               A
               C
            
             ,
             the
             ponderous
             Body
             ,
             
               E
               F
            
             ,
             shall
             happen
             to
             be
             ;
             there
             will
             be
             still
             ,
             by
             reason
             
             of
             the
             specifick
             gravity
             of
             the
             Metal
             ,
             a
             greater
             pressure
             upon
             that
             part
             of
             the
             imaginary
             Superficies
             that
             passes
             along
             the
             bottome
             of
             the
             Body
             on
             which
             the
             part
             F
             shall
             happen
             to
             lean
             ,
             then
             upon
             any
             other
             part
             of
             the
             same
             imaginary
             Superficies
             ;
             the
             Brass
             Body
             would
             still
             descend
             by
             vertue
             of
             its
             own
             weight
             ,
             though
             it
             were
             not
             assisted
             by
             the
             weight
             of
             the
             water
             that
             is
             over
             it
             .
             But
             let
             us
             suppose
             it
             to
             be
             plac'd
             under
             water
             on
             the
             designable
             plain
             
               J
               K
            
             ;
             and
             let
             this
             plain
             ,
             which
             (
             as
             all
             other
             imaginary
             plains
             )
             is
             ,
             as
             well
             as
             the
             real
             Surface
             of
             the
             water
             ,
             to
             be
             conceiv'd
             parallel
             to
             the
             Horizon
             ;
             and
             let
             the
             depth
             or
             distance
             of
             this
             plaine
             ,
             from
             the
             uppermost
             Surface
             of
             the
             water
             ,
             be
             (
             some
             what
             )
             above
             nine
             times
             the
             thickness
             of
             the
             Brass
             Body
             :
             I
             say
             that
             ,
             in
             this
             case
             ,
             the
             body
             would
             not
             descend
             ,
             if
             it
             were
             not
             press'd
             downwards
             by
             
             the
             weight
             of
             the
             water
             it
             has
             over
             it
             .
             For
             Brass
             being
             but
             about
             nine
             times
             *
             as
             heavy
             as
             water
             of
             an
             equal
             bulk
             to
             it
             ,
             the
             Body
             
               E
               F
            
             alone
             would
             press
             upon
             the
             part
             F
             ,
             but
             as
             much
             as
             a
             Cylinder
             of
             water
             would
             ,
             which
             having
             an
             equal
             Basis
             were
             8
             or
             9
             times
             as
             high
             as
             the
             Brass
             is
             thick
             .
             But
             now
             all
             the
             other
             parts
             of
             the
             Imaginary
             surfaces
             ,
             
               I
               K
            
             ,
             being
             press'd
             upon
             by
             the
             incumbent
             water
             ,
             which
             is
             as
             high
             above
             them
             as
             the
             newly
             mention'd
             Cylinder
             of
             water
             would
             be
             ;
             there
             is
             no
             reason
             why
             the
             part
             F
             should
             be
             depress'd
             ,
             rather
             then
             any
             other
             part
             of
             the
             Superficies
             
               J
               K
            
             :
             But
             because
             it
             is
             true
             ,
             which
             we
             formerly
             taught
             ;
             namely
             ,
             that
             water
             retains
             its
             gravity
             in
             water
             ;
             and
             that
             too
             ,
             though
             a
             body
             ,
             heavier
             
               in
               specie
            
             then
             it
             ,
             be
             plac'd
             
             immediately
             under
             it
             ;
             it
             will
             necessarily
             happen
             ,
             That
             in
             what
             part
             soever
             the
             solid
             body
             be
             plac'd
             ,
             provided
             it
             be
             every
             way
             environ'd
             with
             the
             water
             ,
             it
             must
             ,
             for
             the
             Reason
             newly
             given
             ,
             be
             made
             to
             move
             downwards
             ,
             partly
             by
             its
             own
             weight
             ,
             and
             partly
             by
             that
             of
             the
             incumbent
             water
             ;
             and
             must
             continue
             to
             sinck
             ,
             till
             it
             come
             to
             the
             bottom
             ,
             or
             some
             other
             body
             that
             hinders
             its
             farther
             descent
             .
          
           
             But
             in
             case
             the
             water
             above
             the
             solid
             body
             did
             not
             gravitate
             upon
             it
             ,
             and
             thereby
             assist
             its
             descent
             ;
             or
             ,
             in
             case
             that
             the
             incumbent
             water
             were
             by
             some
             Artifice
             or
             other
             ,
             so
             remov'd
             ,
             That
             none
             of
             the
             lateral
             water
             (
             if
             I
             may
             so
             call
             it
             )
             could
             succeed
             in
             its
             place
             to
             lean
             upon
             the
             solid
             ;
             then
             it
             will
             follow
             ,
             from
             what
             we
             have
             newly
             shown
             ,
             that
             the
             solid
             would
             be
             kept
             suspended
             .
             And
             in
             case
             it
             were
             plac'd
             much
             deeper
             in
             the
             water
             ,
             as
             over
             against
             the
             
             point
             L
             or
             M
             ;
             Then
             ,
             if
             we
             conceive
             the
             incumbent
             water
             to
             be
             remov'd
             or
             fenc'd
             off
             from
             it
             ,
             the
             pressure
             of
             the
             solid
             alone
             upon
             the
             part
             F
             ,
             of
             the
             imaginary
             Superficies
             
               L
               M
            
             ,
             being
             very
             much
             inferior
             to
             that
             of
             the
             water
             upon
             the
             other
             parts
             of
             the
             same
             Surface
             ,
             the
             part
             F
             would
             be
             strongly
             impell'd
             upwards
             ,
             by
             a
             force
             proportionate
             to
             the
             difference
             of
             those
             two
             pressures
             .
             And
             therefore
             ,
             since
             I
             have
             found
             by
             tryals
             ,
             purposely
             made
             in
             scales
             marvellously
             exact
             ,
             and
             with
             refined
             Gold
             ,
             (
             purer
             then
             perhaps
             any
             that
             was
             ever
             weighed
             in
             water
             )
             That
             Gold
             ,
             though
             much
             the
             ponderoufest
             of
             bodies
             yet
             known
             in
             the
             world
             ,
             is
             not
             full
             20
             times
             as
             heavy
             as
             water
             of
             the
             same
             Bulk
             ;
             I
             kept
             within
             compass
             (
             as
             well
             as
             imploy'd
             a
             round
             number
             ,
             as
             they
             call
             it
             )
             when
             I
             said
             ,
             That
             no
             body
             (
             yet
             known
             ,
             )
             how
             ponderous
             soever
             ,
             will
             subside
             in
             water
             by
             its
             own
             weight
             alone
             ,
             if
             it
             
             were
             so
             plac'd
             under
             water
             ,
             that
             the
             depth
             of
             the
             water
             did
             above
             twenty
             times
             exceed
             the
             height
             of
             the
             Body
             ;
             (
             not
             to
             mention
             here
             ,
             that
             though
             gold
             and
             water
             being
             weigh'd
             in
             the
             aire
             ,
             their
             proportion
             is
             above
             19
             to
             one
             ,
             yet
             in
             the
             water
             ,
             gold
             does
             ,
             as
             other
             sincking
             bodies
             ,
             loose
             as
             much
             of
             its
             weight
             ,
             as
             that
             of
             an
             equal
             bulk
             of
             water
             amounts
             too
             .
             )
          
           
             I
             was
             saying
             just
             now
             ,
             that
             in
             case
             the
             Brazen
             body
             were
             plac'd
             low
             eenough
             beneath
             the
             Surface
             of
             the
             water
             ,
             and
             kept
             from
             being
             depress'd
             by
             any
             incumbent
             water
             ,
             it
             would
             be
             supported
             by
             the
             subjacent
             water
             .
             And
             this
             is
             that
             very
             thing
             that
             I
             am
             now
             to
             shew
             by
             an
             Experiment
             .
          
           
             Let
             then
             the
             Brass
             body
             
               E
               F
            
             ,
             be
             the
             cover
             of
             a
             brass
             Valve
             ;
             
             (
             as
             in
             the
             annexed
             figure
             :
             )
             and
             let
             the
             Valve
             be
             fastned
             with
             some
             strong
             and
             close
             Cement
             
             to
             a
             Glass
             pipe
             ,
             
               O
               P
            
             ,
             (
             open
             at
             both
             ends
             )
             and
             of
             a
             competent
             length
             and
             wideness
             .
             For
             then
             the
             Body
             ,
             
               E
               F
            
             ,
             being
             the
             undermost
             part
             of
             the
             Instrument
             ,
             and
             not
             sticking
             to
             any
             other
             part
             of
             it
             ,
             will
             fall
             by
             its
             own
             weight
             if
             it
             be
             not
             supported
             .
             Now
             then
             ,
             tying
             a
             thred
             to
             a
             Button
             Q
             ,
             (
             that
             is
             wont
             to
             be
             made
             in
             the
             middle
             of
             the
             doors
             of
             Brass
             valves
             )
             you
             must
             ,
             by
             pulling
             that
             string
             streight
             and
             upwards
             ,
             make
             the
             Body
             ,
             
               E
               F
            
             ,
             shut
             the
             orifice
             of
             the
             Valve
             ,
             as
             close
             as
             you
             can
             ;
             (
             which
             is
             easily
             and
             presently
             done
             .
             )
             Then
             thrusting
             the
             Valve
             under
             water
             ,
             to
             the
             depth
             of
             a
             foot
             or
             more
             ;
             the
             Cement
             and
             the
             sides
             of
             the
             Glass
             ,
             
               O
               P
            
             ,
             (
             which
             reaches
             far
             above
             the
             top
             of
             the
             water
             
               X
               Y
            
             )
             will
             keep
             the
             water
             from
             coming
             to
             beare
             upon
             the
             upper
             part
             of
             the
             body
             
               E
               F
            
             ;
             and
             consequently
             the
             imaginary
             Surface
             ,
             
               V
               W
            
             ,
             (
             that
             passes
             by
             the
             lower
             part
             of
             the
             said
             
             body
             )
             will
             ,
             where
             it
             is
             contiguous
             thereunto
             ,
             be
             press'd
             upon
             only
             by
             the
             proper
             weight
             of
             the
             body
             
               E
               F
            
             ;
             but
             in
             its
             other
             parts
             ,
             by
             the
             much
             greater
             weight
             of
             the
             incumbent
             water
             .
             So
             that
             ,
             though
             you
             let
             go
             the
             string
             ,
             (
             that
             held
             the
             body
             ,
             
               E
               F
            
             ,
             close
             to
             the
             rest
             of
             the
             Instrument
             )
             the
             said
             body
             will
             not
             at
             all
             sinck
             ,
             though
             there
             be
             nothing
             but
             water
             beneath
             it
             to
             support
             it
             .
          
           
             And
             to
             manifest
             that
             't
             is
             onely
             the
             pressure
             of
             the
             water
             ,
             of
             a
             competent
             depth
             ,
             that
             keeps
             the
             solid
             suspended
             ;
             if
             you
             slowly
             lift
             up
             the
             instrument
             towards
             
               (
               X
               Y
            
             )
             the
             top
             of
             the
             water
             ;
             you
             shall
             find
             ,
             that
             ,
             though
             for
             a
             while
             the
             parts
             of
             the
             Valve
             will
             continue
             united
             ,
             as
             they
             were
             before
             ;
             yet
             ,
             when
             once
             it
             is
             rais'd
             so
             near
             the
             Surface
             ,
             (
             as
             between
             the
             plain
             
               J
               K
            
             ,
             and
             
               X
               Y
            
             )
             that
             the
             single
             weight
             of
             
               E
               F
            
             ,
             upon
             the
             subjacent
             part
             of
             the
             imaginary
             plain
             that
             
             passes
             by
             it
             ,
             is
             greater
             then
             the
             pressure
             of
             the
             incumbent
             water
             upon
             other
             parts
             of
             the
             same
             plain
             ;
             that
             Body
             ,
             being
             no
             more
             supported
             as
             formerly
             ,
             will
             fall
             down
             ,
             and
             the
             water
             will
             get
             into
             the
             pipe
             ,
             and
             ascend
             therein
             ,
             to
             the
             level
             of
             the
             External
             water
             .
          
           
             But
             if
             ,
             when
             the
             Valve
             is
             first
             thrust
             under
             water
             ,
             and
             before
             you
             let
             go
             the
             thred
             that
             keeps
             its
             parts
             together
             ,
             you
             thrust
             it
             down
             to
             a
             good
             depth
             ,
             as
             to
             the
             Superficies
             
               R
               S
            
             :
             then
             ,
             though
             you
             should
             hang
             a
             considerable
             weight
             ,
             as
             L
             ,
             to
             the
             Valve
             
               E
               F
            
             ,
             (
             as
             I
             am
             going
             to
             shew
             you
             a
             Tryal
             with
             a
             Massy
             Cylinder
             of
             stone
             broader
             then
             the
             Valve
             ,
             and
             of
             divers
             inches
             in
             length
             )
             the
             surplusage
             of
             pressure
             on
             the
             other
             parts
             of
             the
             plain
             ,
             
               V
               W
            
             ,
             (
             now
             in
             
               R
               S
            
             )
             over
             and
             above
             what
             the
             weight
             of
             the
             body
             
               E
               F
            
             ,
             and
             that
             of
             the
             Cylindrical
             stone
             ,
             L
             ,
             to
             boot
             ,
             can
             amount
             to
             ,
             on
             that
             part
             of
             the
             Surface
             vvhich
             is
             contiguous
             
             to
             the
             said
             body
             
               E
               F
            
             ,
             will
             be
             great
             enough
             to
             press
             so
             hard
             against
             the
             lower
             part
             of
             the
             Valve
             ,
             that
             its
             own
             weight
             ,
             though
             assisted
             with
             that
             of
             the
             stone
             ,
             will
             not
             be
             able
             to
             disjoyne
             them
             .
          
           
             By
             which
             (
             to
             note
             that
             by
             the
             way
             )
             you
             may
             see
             ,
             that
             though
             ,
             when
             two
             flat
             and
             polish'd
             marbles
             are
             joyn'd
             together
             ,
             we
             find
             it
             is
             impossible
             to
             sever
             them
             without
             force
             ;
             we
             need
             not
             have
             recourse
             to
             a
             
               fuga
               vacui
            
             ,
             to
             Explicate
             the
             cause
             of
             their
             Cohaesion
             ,
             whilst
             they
             are
             environ'd
             by
             the
             Aire
             ,
             which
             is
             a
             Fluid
             not
             devoid
             of
             Gravity
             ,
             and
             reaching
             above
             the
             Marbles
             no
             body
             knows
             how
             high
             .
          
           
             And
             to
             evince
             ,
             That
             't
             is
             only
             such
             a
             pressure
             of
             the
             water
             ,
             as
             I
             have
             been
             declaring
             ,
             that
             causes
             the
             Cohaesion
             of
             the
             parts
             of
             the
             Valve
             ;
             if
             you
             gently
             lift
             it
             up
             towards
             the
             top
             of
             the
             water
             ,
             you
             will
             quickly
             find
             the
             Brass
             body
             ,
             
             
               E
               F
            
             ,
             drawn
             down
             by
             the
             stone
             
               (
               L
            
             )
             that
             hangs
             at
             it
             ;
             as
             you
             will
             perceive
             by
             the
             waters
             getting
             in
             between
             the
             parts
             of
             the
             Valve
             ,
             and
             ascending
             into
             the
             pipe
             .
          
           
             To
             which
             I
             shall
             only
             add
             ,
             what
             you
             will
             quickly
             see
             ,
             That
             ,
             in
             perfect
             Conformity
             to
             our
             Doctrine
             ,
             the
             pressure
             of
             the
             body
             ,
             
               E
               F
            
             ,
             upon
             the
             subjacent
             water
             ,
             being
             very
             much
             increased
             by
             the
             weight
             of
             the
             stone
             that
             hangs
             at
             it
             ,
             the
             Valve
             needs
             not
             ,
             as
             before
             ,
             be
             lifted
             up
             above
             the
             plain
             
               J
               K
            
             ,
             to
             overcome
             the
             resistance
             of
             the
             water
             ,
             being
             now
             enabled
             to
             do
             it
             before
             it
             is
             rais'd
             near
             so
             high
             .
          
        
         
           
           
             APPENDIX
             I.
             
          
           
             Containing
             an
             Answer
             to
             seven
             Objections
             ,
             propos'd
             by
             a
             late
             Learned
             Writer
             ,
             to
             evince
             ,
             that
             the
             upper
             parts
             of
             water
             press
             not
             upon
             the
             lower
             .
          
           
             AFter
             I
             had
             ,
             this
             Morning
             ,
             made
             an
             end
             of
             reviewing
             the
             foregoing
             papers
             ,
             there
             came
             into
             my
             hands
             some
             questions
             lately
             publish'd
             ,
             among
             other
             things
             ,
             by
             a
             very
             recent
             Writer
             of
             Hydrostaticks
             .
             In
             one
             of
             which
             Questions
             .
             the
             Learned
             Author
             strongly
             defends
             the
             contrary
             to
             what
             has
             there
             been
             in
             some
             places
             prov'd
             ,
             and
             divers
             places
             suppos'd
             .
          
           
             The
             Author
             of
             these
             Erotemata
             
             asserts
             ,
             That
             ,
             
               in
               consistent
               water
               ,
               the
               upper
               parts
               do
               not
               gravitate
               or
               press
               upon
               the
               lower
               .
            
          
           
             And
             therefore
             ,
             I
             think
             it
             will
             be
             neither
             useless
             ,
             nor
             improper
             ,
             briefly
             to
             examine
             here
             the
             Arguments
             he
             produces
             .
             Not
             useless
             ;
             because
             the
             Opinion
             he
             asserts
             ,
             both
             is
             ,
             and
             has
             long
             been
             ,
             very
             generally
             receiv'd
             ;
             and
             because
             too
             ,
             it
             is
             of
             so
             great
             importance
             ,
             that
             many
             of
             the
             Erroneous
             Tenets
             and
             Conclusions
             ,
             of
             those
             that
             (
             whether
             professedly
             or
             incidentally
             )
             treat
             of
             Hydrostatical
             matters
             ,
             are
             built
             upon
             it
             .
             And
             not
             improper
             ;
             because
             our
             Learned
             Author
             seems
             to
             have
             done
             his
             Reader
             the
             favour
             to
             summe
             up
             into
             one
             page
             all
             the
             Arguments
             for
             his
             Opinions
             that
             are
             dispersedly
             to
             be
             found
             in
             his
             own
             or
             others
             mens
             Books
             .
             So
             that
             in
             answering
             these
             ,
             we
             may
             hope
             to
             do
             much
             towards
             a
             satisfactory
             Decision
             of
             so
             important
             
             a
             Controversie
             .
             And
             ,
             after
             what
             we
             have
             already
             deliver'd
             ,
             our
             Answers
             will
             be
             so
             seasonable
             ,
             that
             they
             will
             not
             need
             to
             be
             long
             :
             The
             things
             they
             are
             built
             on
             having
             been
             already
             made
             out
             ,
             in
             the
             respective
             places
             whereto
             the
             Reader
             is
             referr'd
             .
          
           
             Our
             Author
             then
             maintains
             ,
             that
             ,
             in
             Consistent
             water
             ,
             the
             Superiour
             do
             not
             actually
             press
             the
             Inferiour
             parts
             ,
             by
             the
             seven
             following
             Arguments
             .
          
           
             Object
             .
             1.
             
             
               Sayes
               he
            
             ,
             Because
             else
             the
             inferiour
             parts
             of
             the
             water
             would
             be
             more
             dense
             then
             the
             Superior
             ,
             since
             they
             would
             be
             compress'd
             and
             condens'd
             by
             the
             weight
             of
             them
             .
          
           
             Ans
             .
             But
             if
             the
             Corpuscles
             ,
             whereof
             water
             consists
             ,
             be
             suppos'd
             to
             be
             perfectly
             solid
             &
             hard
             ;
             the
             inferior
             Corpuscles
             may
             be
             press'd
             upon
             by
             the
             weight
             of
             the
             superior
             ,
             without
             being
             compress'd
             or
             condens'd
             by
             them
             .
             As
             it
             would
             
             happen
             ,
             if
             Diamond
             dust
             were
             lay'd
             together
             in
             a
             tall
             heap
             :
             For
             though
             the
             upper
             parts
             ,
             being
             heavy
             and
             solid
             Corpuscles
             ,
             cannot
             be
             deny'd
             to
             lean
             and
             press
             upon
             the
             lower
             ;
             yet
             these
             ,
             by
             reason
             of
             their
             Adamantine
             hardness
             ,
             would
             not
             be
             thereby
             compress'd
             .
             And
             't
             is
             possible
             too
             ,
             that
             the
             Corpuscles
             of
             water
             ,
             though
             not
             so
             perfectly
             hard
             ,
             but
             that
             they
             may
             a
             little
             yield
             to
             an
             extream
             force
             ,
             be
             solid
             enough
             not
             to
             admit
             from
             such
             a
             weight
             ,
             as
             that
             of
             the
             incumbent
             water
             ,
             (
             at
             least
             in
             such
             small
             heights
             as
             observations
             are
             wont
             to
             be
             made
             in
             ,
             )
             any
             compression
             ,
             great
             enough
             to
             be
             sensible
             ;
             As
             ,
             besides
             some
             Tryals
             I
             have
             formerly
             mention'd
             in
             another
             place
             ,
             those
             made
             in
             the
             presence
             of
             this
             Illustrious
             Company
             seem
             sufficiently
             to
             argue
             ;
             viz.
             That
             water
             is
             not
             sensibly
             compressible
             by
             an
             ordinary
             force
             .
             And
             I
             find
             not
             ,
             by
             those
             that
             
             make
             the
             Objection
             ,
             that
             they
             ever
             took
             pains
             to
             try
             ,
             whether
             in
             deep
             places
             of
             the
             Sea
             ,
             the
             lower
             parts
             are
             not
             more
             condens'd
             then
             the
             upper
             :
             nor
             do
             I
             see
             any
             absurdity
             ,
             that
             would
             follow
             from
             admitting
             them
             to
             be
             so
             .
          
           
             Object
             .
             2.
             
             
               Our
               Authors
               second
               Argument
               is
            
             ,
             Because
             Divers
             feel
             not
             ,
             under
             water
             ,
             the
             weight
             of
             the
             water
             that
             lyes
             upon
             them
             .
          
           
             Ans
             .
             But
             for
             Answer
             to
             this
             Argument
             ,
             I
             shall
             content
             my self
             to
             make
             a
             reference
             to
             the
             ensuing
             Appendix
             ,
             where
             this
             matter
             will
             be
             considered
             at
             large
             ;
             and
             where
             ;
             I
             hope
             ,
             it
             will
             be
             made
             to
             appear
             ,
             that
             the
             phaenomenon
             may
             proceed
             ,
             partly
             from
             the
             firm
             Texture
             of
             the
             Divers
             body
             ,
             and
             partly
             from
             the
             nature
             of
             that
             pressure
             which
             is
             exercis'd
             against
             bodyes
             immers'd
             in
             fluids
             ;
             which
             ,
             in
             that
             case
             ,
             (
             as
             to
             sense
             )
             presses
             every
             where
             equally
             ,
             against
             all
             
             the
             parts
             of
             the
             body
             ,
             expos'd
             to
             their
             Action
             .
          
           
             Object
             .
             3.
             
             
               The
               third
               Argument
               is
            
             ,
             That
             ev'n
             the
             slightest
             Herbs
             growing
             at
             the
             bottom
             of
             the
             water
             ,
             and
             shooting
             up
             in
             it
             to
             a
             good
             height
             ,
             are
             not
             oppress'd
             or
             lay'd
             by
             the
             incumbent
             water
             .
          
           
             Ans
             .
             But
             the
             Answer
             to
             that
             is
             easie
             ,
             out
             of
             the
             foregoing
             Doctrine
             .
             For
             the
             Plants
             ,
             we
             speak
             of
             ,
             sustain
             not
             the
             pressure
             of
             the
             water
             above
             them
             by
             their
             own
             strength
             ;
             but
             by
             the
             help
             of
             the
             pressure
             of
             water
             that
             is
             beneath
             :
             which
             being
             it self
             press'd
             by
             the
             water
             that
             is
             (
             though
             not
             perpendicularly
             over
             it
             )
             superior
             to
             it
             ,
             presses
             them
             upwards
             so
             forcibly
             ,
             that
             if
             they
             were
             not
             by
             their
             Roots
             ,
             or
             otherwise
             fastned
             to
             the
             ground
             ,
             they
             ,
             being
             
               in
               specie
            
             lighter
             then
             water
             ,
             would
             be
             buoy'd
             up
             to
             the
             top
             of
             the
             water
             ,
             and
             made
             to
             float
             ;
             as
             we
             often
             see
             that
             weeds
             do
             ,
             which
             storms
             ,
             or
             
             other
             accidents
             have
             torn
             from
             their
             native
             soyle
             .
          
           
             Object
             .
             4.
             
             
               A
               fourth
               Objection
               is
               this
            
             ,
             That
             a
             heavy
             Body
             ty'd
             to
             a
             string
             ,
             and
             let
             down
             under
             water
             ,
             is
             supported
             ,
             and
             drawn
             out
             with
             as
             much
             ease
             ,
             as
             it
             would
             be
             if
             it
             had
             no
             water
             incumbent
             on
             it
             ;
             nay
             ,
             with
             greater
             ease
             ,
             because
             heavy
             bodyes
             weigh
             less
             in
             water
             then
             out
             of
             it
             .
          
           
             Ans
             .
             But
             an
             Account
             of
             this
             is
             easie
             to
             be
             rendred
             out
             of
             our
             Doctrine
             ;
             For
             ,
             though
             the
             water
             incumbent
             on
             the
             heavy
             body
             do
             really
             endeavour
             to
             make
             it
             sinck
             lower
             ,
             yet
             that
             endeavour
             is
             rendred
             ineffectual
             ,
             to
             that
             purpose
             ,
             by
             the
             equal
             pressure
             of
             the
             water
             upon
             all
             the
             other
             parts
             of
             the
             Imaginary
             surface
             ,
             that
             is
             contiguous
             to
             the
             bottom
             of
             the
             immers'd
             body
             .
             And
             that
             pressure
             upon
             the
             other
             parts
             of
             that
             suppos'd
             plain
             ,
             being
             equal
             not
             only
             to
             the
             pressure
             of
             the
             pillar
             of
             water
             ,
             
             but
             to
             that
             pillar
             ,
             and
             to
             the
             weight
             of
             as
             much
             water
             as
             the
             immers'd
             body
             fills
             the
             place
             of
             ;
             it
             must
             needs
             follow
             ,
             That
             not
             only
             the
             hand
             that
             susteins
             the
             body
             ,
             should
             not
             feel
             the
             weight
             of
             the
             incumbent
             water
             ,
             but
             should
             be
             able
             to
             lift
             up
             the
             Body
             more
             easily
             in
             the
             water
             ,
             then
             in
             the
             aire
             .
             But
             though
             the
             pressure
             of
             the
             water
             incumbent
             on
             the
             stone
             can
             not
             ,
             for
             the
             reason
             assign'd
             ,
             be
             felt
             in
             the
             case
             propos'd
             ;
             yet
             if
             you
             remove
             that
             water
             ,
             (
             as
             in
             the
             Experiment
             brought
             for
             the
             proof
             of
             the
             last
             Paradox
             ,
             )
             it
             will
             quickly
             appear
             by
             the
             pressure
             against
             the
             lower
             part
             of
             the
             heavy
             body
             ,
             and
             its
             inability
             to
             descend
             by
             its
             own
             weight
             ,
             when
             it
             is
             any
             thing
             deep
             under
             water
             ;
             it
             will
             (
             I
             say
             )
             quickly
             appear
             ,
             by
             what
             will
             follow
             upon
             the
             absence
             of
             the
             Incumbent
             water
             ,
             how
             great
             a
             pressure
             it
             exercis'd
             upon
             the
             stone
             whilst
             it
             lean'd
             on
             it
             .
          
           
           
             Object
             .
             5.
             
             
               The
               fifth
               Argument
               is
               propos'd
               in
               these
               words
               ,
            
             Because
             a
             Bucket
             full
             of
             water
             ,
             is
             lighter
             in
             the
             water
             ,
             then
             out
             of
             it
             ;
             nor
             does
             weigh
             more
             when
             full
             within
             the
             water
             ,
             then
             when
             empty
             out
             of
             it
             ;
             nay
             it
             weighs
             less
             ,
             for
             the
             reason
             newly
             assign'd
             
               (
               in
               the
               fourth
               Objection
               ;
               )
            
             therefore
             the
             water
             of
             the
             Bucket
             ,
             because
             it
             is
             within
             water
             ,
             does
             not
             gravitate
             ,
             nor
             consequently
             press
             downwards
             ,
             either
             the
             Bucket
             ,
             or
             the
             water
             under
             the
             Bucket
             .
             
               This
               is
               the
               grand
               and
               obvious
               Experiment
               ,
               upon
               which
               the
               Schools
               ,
               and
               the
               generality
               of
               Writers
               ,
               have
               very
               confidently
               built
               this
               Axiom
               :
            
             That
             the
             Elements
             do
             not
             gravitate
             in
             their
             proper
             place
             ;
             
               and
               particularly
               ,
               that
               water
               weighs
               not
               (
               as
               they
               speak
               )
               in
               its
               own
               Element
               .
            
          
           
             Ans
             .
             What
             they
             mean
             by
             proper
             or
             
               natural
               place
            
             ,
             I
             shall
             not
             stand
             to
             examine
             ,
             nor
             to
             enquire
             whether
             they
             can
             prove
             ,
             that
             water
             or
             any
             other
             sublunary
             
             body
             possesses
             any
             place
             ,
             but
             upon
             this
             account
             ,
             that
             the
             cause
             of
             gravity
             ,
             or
             some
             other
             movent
             ,
             enables
             it
             to
             expel
             other
             contiguous
             Bodies
             (
             that
             are
             less
             heavie
             or
             less
             moved
             ,
             )
             out
             of
             the
             place
             they
             possess'd
             before
             ;
             and
             gives
             it
             an
             incessant
             tendencie
             ,
             or
             endeavour
             towards
             the
             lowermost
             parts
             of
             the
             Earth
             .
          
           
             But
             as
             to
             the
             Example
             propos'd
             ,
             it
             s
             very
             easie
             to
             give
             an
             account
             of
             it
             .
             For
             suppose
             ABCD
             ,
             to
             be
             a
             Well
             ;
             wherein
             ,
             by
             the
             string
             
               E
               F
            
             ,
             the
             Bucket
             is
             suspended
             under
             water
             ,
             and
             has
             its
             Bottom
             contiguous
             to
             the
             imaginary
             plain
             
               I
               K.
            
             If
             now
             we
             suppose
             the
             Bucket
             to
             consist
             only
             of
             wood
             ,
             lighter
             then
             water
             ,
             it
             will
             not
             only
             not
             press
             upon
             the
             hand
             that
             holds
             the
             Rope
             at
             E
             ,
             but
             will
             be
             buoyd
             up
             ,
             till
             the
             upper
             parts
             of
             the
             Bucket
             be
             above
             the
             top
             of
             the
             water
             ;
             because
             the
             wood
             ,
             whereof
             the
             Bucket
             is
             made
             ,
             being
             lighter
             
               in
               specie
            
             
             then
             water
             ,
             the
             pressure
             of
             the
             water
             in
             the
             Bucket
             G
             ,
             and
             the
             rest
             of
             the
             water
             incumbent
             on
             that
             ,
             together
             with
             the
             weight
             of
             the
             Bucket
             it self
             ,
             must
             necessarily
             be
             unable
             to
             press
             the
             part
             H
             so
             strongly
             ,
             as
             the
             other
             parts
             of
             the
             imaginary
             plaine
             
               I
               K
            
             are
             press'd
             by
             the
             weight
             of
             the
             meer
             water
             incumbent
             on
             them
             .
             But
             if
             ,
             as
             t
             is
             usual
             ,
             the
             Bucket
             consists
             partly
             of
             wood
             ,
             partly
             of
             iron
             ;
             the
             Aggregate
             may
             often
             indeed
             be
             heavier
             then
             an
             equal
             bulk
             of
             water
             :
             But
             then
             the
             hand
             ,
             that
             draws
             up
             the
             Bucket
             by
             the
             Rope
             
               F
               E
            
             ,
             ought
             not
             ,
             according
             to
             our
             Doctrine
             ,
             to
             feel
             the
             weight
             of
             all
             the
             Bucket
             ,
             much
             less
             that
             of
             the
             water
             contein'd
             in
             it
             .
             For
             though
             that
             aggregate
             of
             wood
             and
             iron
             ,
             which
             we
             here
             call
             the
             Bucket
             ,
             be
             heavier
             then
             so
             much
             water
             ;
             yet
             it
             tends
             not
             downwards
             with
             its
             whole
             weight
             ,
             but
             only
             with
             that
             surplusage
             of
             weight
             ,
             whereby
             
             it
             exceeds
             as
             much
             water
             as
             is
             equal
             to
             it
             in
             Bulk
             ;
             which
             surplusage
             is
             not
             wont
             to
             be
             very
             considerable
             .
             And
             as
             for
             the
             water
             in
             the
             Cavity
             ,
             G
             ,
             of
             the
             Bucket
             ,
             there
             is
             no
             reason
             why
             it
             should
             at
             all
             load
             the
             hand
             at
             E
             ,
             though
             really
             the
             water
             both
             in
             the
             Bucket
             and
             over
             it
             do
             tend
             downwards
             with
             their
             full
             weight
             ;
             because
             that
             the
             rest
             of
             the
             water
             ,
             
               L
               I
            
             ,
             and
             
               M
               K
            
             ,
             do
             full
             as
             strongly
             press
             upon
             the
             rest
             of
             the
             imaginary
             Superficies
             
               I
               K
            
             ,
             as
             the
             Bucket
             aud
             the
             incumbent
             water
             do
             upon
             the
             part
             H
             :
             and
             consequently
             the
             bottom
             of
             the
             Bucket
             is
             every
             whit
             as
             strongly
             press'd
             upwards
             by
             the
             weight
             of
             the
             water
             ,
             upon
             all
             the
             other
             parts
             of
             the
             plain
             
               I
               K
            
             ;
             as
             it
             tends
             downwards
             ,
             by
             virtue
             of
             the
             weight
             of
             the
             Incumbent
             water
             ,
             that
             is
             partly
             in
             the
             Bucket
             ,
             and
             partly
             above
             it
             ;
             and
             so
             these
             pressures
             ballancing
             one
             another
             ,
             the
             hand
             that
             draws
             the
             
             Rope
             at
             E
             ,
             has
             no
             more
             to
             lift
             up
             then
             the
             surplusage
             of
             weight
             ,
             whereby
             the
             empty
             Bucket
             exceeds
             the
             weight
             of
             as
             much
             water
             as
             is
             equall
             in
             bulk
             (
             I
             say
             ,
             not
             to
             the
             Bucket
             as
             't
             is
             a
             hollow
             Instrument
             ,
             but
             )
             to
             the
             wood
             and
             iron
             whereof
             the
             Bucket
             consists
             .
          
           
             And
             because
             this
             Example
             of
             the
             lightness
             of
             fil'd
             Buckets
             within
             the
             water
             has
             for
             so
             many
             Ages
             gain'd
             credit
             to
             ,
             if
             it
             have
             not
             been
             the
             only
             ground
             of
             ,
             the
             assertion
             ,
             That
             water
             weighs
             not
             in
             its
             own
             Element
             ,
             or
             in
             its
             proper
             place
             ;
             I
             shall
             add
             (
             though
             I
             can
             scarse
             present
             it
             to
             such
             a
             company
             as
             this
             without
             smiles
             )
             an
             Experiment
             that
             I
             made
             to
             convince
             those
             ,
             that
             were
             ,
             through
             unskilfulness
             or
             prejudice
             ,
             indispos'd
             to
             admit
             the
             Hydrostatical
             account
             I
             have
             been
             giving
             of
             the
             phaenomenon
             .
             I
             took
             then
             a
             round
             wooden
             Box
             ,
             which
             I
             substituted
             in
             the
             room
             of
             a
             Bucket
             ;
             and
             (
             having
             fill'd
             it
             with
             melted
             
             Butter
             ,
             into
             which
             ,
             when
             it
             was
             congeal'd
             ,
             some
             small
             bitts
             of
             lead
             were
             put
             ,
             to
             make
             it
             a
             little
             heavier
             then
             so
             much
             water
             ,
             )
             I
             caus'd
             a
             small
             string
             of
             twin'd
             silk
             to
             pass
             through
             two
             small
             holes
             ,
             made
             in
             the
             opposite
             parts
             of
             the
             upper
             edge
             of
             the
             box
             ,
             and
             to
             be
             suspended
             at
             one
             end
             of
             the
             beam
             of
             a
             pair
             of
             Gold-smiths
             Scales
             ;
             and
             then
             putting
             it
             into
             a
             vessel
             full
             of
             water
             ,
             till
             it
             was
             let
             down
             there
             ,
             to
             what
             depth
             I
             pleas'd
             ,
             it
             appear'd
             that
             not
             only
             the
             least
             endeavour
             of
             my
             hand
             would
             either
             support
             it
             ,
             or
             transport
             to
             and
             fro
             in
             the
             water
             ,
             or
             draw
             it
             up
             to
             the
             top
             of
             it
             ;
             and
             this
             ,
             whether
             the
             box
             were
             made
             use
             of
             ,
             or
             whether
             the
             butter
             and
             lead
             alone
             ,
             without
             the
             box
             ,
             were
             suspended
             by
             the
             silken
             string
             :
             but
             (
             to
             evince
             ,
             that
             it
             was
             not
             the
             strength
             of
             my
             hand
             ,
             or
             the
             smallness
             of
             the
             immers'd
             body
             ,
             that
             kept
             me
             from
             feeling
             any
             considerable
             resistance
             ,
             )
             
             I
             cast
             some
             grains
             into
             the
             scale
             that
             hung
             at
             the
             other
             end
             of
             the
             above
             mention'd
             Beame
             ,
             and
             presently
             rais'd
             the
             Lead
             and
             Butter
             to
             the
             surface
             of
             the
             water
             .
             So
             that
             unless
             the
             Schoolmen
             will
             say
             that
             the
             butter
             &
             lead
             were
             in
             their
             own
             Element
             ;
             we
             must
             be
             allow'd
             to
             think
             ,
             that
             the
             easie
             sustentation
             ,
             and
             elevation
             of
             the
             box
             ,
             did
             not
             proceed
             from
             hence
             ,
             That
             those
             bodyes
             weigh'd
             not
             because
             they
             were
             in
             their
             natural
             place
             .
             And
             yet
             in
             this
             case
             ,
             the
             effect
             is
             the
             same
             with
             that
             which
             happens
             when
             a
             bucket
             is
             drawing
             out
             of
             a
             well
             .
          
           
             And
             ,
             to
             manifest
             that
             't
             was
             the
             pressure
             of
             the
             water
             against
             the
             lower
             part
             of
             the
             surface
             of
             our
             suspended
             body
             ,
             that
             made
             it
             so
             easie
             to
             be
             supported
             in
             the
             water
             ,
             or
             rais'd
             to
             the
             top
             of
             it
             ;
             I
             shall
             add
             ,
             that
             though
             a
             few
             grains
             suffic'd
             to
             bring
             the
             upper
             surface
             of
             the
             butter
             to
             the
             top
             of
             the
             water
             :
             
             yet
             afterwards
             there
             was
             a
             considerable
             weight
             requisite
             ,
             to
             raise
             more
             &
             more
             of
             its
             parts
             above
             the
             waters
             surface
             ;
             &
             a
             considerabler
             yet
             ,
             to
             lift
             the
             whole
             body
             quite
             out
             of
             the
             water
             .
             Which
             is
             very
             consonant
             to
             our
             Doctrine
             .
             For
             ,
             suppose
             the
             bucket
             to
             be
             at
             the
             part
             N
             ,
             half
             in
             and
             half
             out
             of
             the
             water
             :
             the
             hand
             or
             counterpoise
             ,
             that
             supports
             it
             in
             that
             posture
             ,
             must
             have
             a
             far
             greater
             strength
             then
             needed
             to
             sustein
             it
             ,
             when
             it
             was
             quite
             under
             water
             ;
             because
             that
             now
             the
             imaginary
             plain
             
               P
               Q
            
             ,
             passing
             by
             the
             bottom
             of
             the
             bucket
             ,
             has
             on
             its
             other
             parts
             but
             a
             little
             depth
             of
             water
             ,
             as
             from
             L
             to
             P
             ,
             or
             M
             to
             Q
             ,
             and
             consequently
             the
             bottom
             of
             the
             bucket
             ,
             H
             ,
             will
             searce
             be
             press'd
             upwards
             above
             half
             as
             strongly
             as
             when
             the
             bucket
             was
             quite
             under
             water
             .
             And
             if
             it
             be
             raised
             to
             O
             ,
             &
             consequently
             quite
             out
             of
             the
             water
             ;
             that
             liquor
             reaching
             no
             longer
             to
             the
             bottom
             
             of
             the
             bucket
             ,
             can
             no
             longer
             contribute
             to
             its
             supportation
             ;
             and
             therefore
             a
             weight
             not
             only
             equal
             ,
             but
             somewhat
             superiour
             to
             the
             full
             weight
             of
             the
             bucket
             ,
             and
             all
             that
             it
             contains
             ,
             (
             being
             all
             suppos'd
             to
             be
             weighd
             in
             the
             aire
             ,
             )
             will
             be
             necessary
             to
             lift
             it
             clear
             out
             of
             the
             water
             .
          
           
             But
             to
             dwell
             longer
             on
             this
             subject
             cannot
             but
             be
             tedious
             to
             those
             that
             have
             been
             any
             thing
             attentive
             to
             the
             former
             Discourses
             .
             I
             proceed
             therefore
             to
             our
             Authors
             sixth
             Argument
             ,
             which
             is
             ,
          
           
             Object
             .
             6.
             
             That
             Horse-hairs
             ,
             which
             are
             held
             to
             be
             of
             the
             same
             gravity
             with
             water
             ,
             keep
             whatever
             place
             is
             given
             them
             in
             that
             Liquor
             ;
             nor
             are
             depress'd
             by
             the
             weight
             of
             the
             super-incumbent
             water
             .
          
           
             Answ
             .
             Whether
             the
             matter
             of
             fact
             bestrictly
             and
             universally
             true
             ,
             is
             scarce
             worth
             the
             examining
             ,
             especially
             since
             we
             find
             the
             difference
             in
             point
             of
             specifick
             
             gravity
             ,
             betwixt
             most
             Horse-haires
             ,
             and
             most
             waters
             ,
             to
             be
             inconsiderable
             enough
             .
             But
             the
             phaenomenon
             ,
             supposing
             the
             truth
             of
             it
             ,
             is
             very
             easily
             explicable
             ,
             according
             to
             the
             Doctrine
             above
             deliver'd
             .
             For
             supposing
             in
             the
             last
             Scheme
             the
             body
             ,
             R
             ,
             to
             be
             bulk
             for
             bulk
             exactly
             equiponderant
             to
             water
             ;
             't
             is
             plain
             there
             is
             no
             reason
             why
             that
             body
             should
             press
             the
             part
             S
             ,
             of
             the
             imaginary
             Superficies
             
               I
               ▪
               K
            
             ,
             either
             more
             or
             less
             then
             that
             part
             S
             would
             be
             press'd
             ,
             if
             ,
             the
             body
             R
             being
             annihilated
             or
             remov'd
             ,
             it
             were
             succeeded
             by
             parcel
             of
             water
             of
             just
             the
             same
             bulk
             and
             weight
             .
             And
             consequently
             ,
             though
             all
             the
             water
             directly
             above
             the
             solid
             R
             do
             really
             lean
             upon
             that
             body
             ,
             and
             endeavour
             to
             depress
             it
             ;
             yet
             that
             endeavour
             being
             resisted
             by
             an
             equal
             and
             contrary
             endeavour
             ,
             that
             proceeds
             (
             as
             we
             have
             been
             but
             too
             often
             faine
             to
             declare
             )
             from
             the
             pressure
             
             exercis'd
             upon
             the
             other
             parts
             of
             the
             Superficies
             ,
             
               I
               K
            
             ,
             by
             the
             water
             incumbent
             on
             them
             ;
             the
             body
             ,
             R
             ,
             will
             be
             neither
             depress'd
             nor
             rais'd
             .
             And
             its
             case
             being
             the
             same
             in
             what
             part
             of
             the
             water
             soever
             it
             be
             plac'd
             ,
             provided
             it
             be
             perfectly
             environ'd
             with
             that
             Liquor
             ;
             it
             must
             keep
             in
             the
             water
             (
             which
             in
             this
             whole
             Discourse
             we
             suppose
             to
             be
             Homogeneous
             as
             to
             gravity
             )
             the
             place
             you
             please
             to
             give
             it
             .
          
           
             And
             ,
             (
             to
             add
             That
             on
             this
             occasion
             )
             though
             Mathematicians
             have
             hitherto
             contented
             themselves
             to
             prove
             ,
             that
             in
             case
             a
             Body
             could
             be
             found
             or
             provided
             ,
             that
             were
             exactly
             equiponderant
             to
             water
             ,
             it
             would
             retaine
             any
             assignable
             place
             in
             it
             ;
             yet
             the
             Curiosity
             we
             had
             ,
             to
             give
             an
             Experimental
             proof
             of
             this
             Truth
             ,
             at
             length
             produc'd
             some
             glass
             Bubbles
             ,
             which
             some
             Gentlemen
             here
             present
             have
             not
             perhaps
             forgot
             ,
             that
             were
             (
             by
             a
             dexterous
             hand
             we
             
             employ'd
             about
             it
             )
             so
             exquisitely
             pois'd
             ,
             as
             ,
             to
             the
             wonder
             of
             the
             Beholders
             ,
             to
             retain
             the
             places
             given
             them
             ,
             sometimes
             in
             the
             middle
             ,
             sometimes
             near
             the
             top
             ,
             &
             sometimes
             near
             the
             bottom
             of
             the
             water
             (
             though
             that
             were
             Homogeneous
             )
             for
             a
             great
             while
             ,
             till
             some
             change
             of
             consistence
             or
             gravity
             in
             the
             water
             ,
             or
             some
             of
             its
             parts
             ,
             made
             the
             bubble
             rise
             or
             fall
             .
          
           
             The
             Application
             of
             this
             ,
             to
             what
             has
             been
             objected
             concerning
             Horse-hairs
             ,
             being
             too
             easie
             to
             need
             to
             be
             insisted
             on
             ,
             there
             remains
             to
             be
             dispatched
             our
             Authors
             seventh
             and
             last
             Argument
             ,
             which
             is
             this
             .
          
           
             Object
             .
             7.
             
             That
             ,
             otherwise
             ,
             all
             the
             inferiour
             parts
             of
             the
             water
             would
             be
             in
             perpetual
             motion
             ,
             and
             perpetually
             expell'd
             by
             the
             Superior
             .
          
           
             Answ
             .
             But
             if
             ,
             by
             the
             inferior
             parts
             ,
             he
             means
             ,
             such
             portions
             as
             are
             of
             any
             considerable
             bulk
             ;
             the
             Answer
             newly
             made
             to
             the
             last
             objection
             (
             where
             we
             
             shew'd
             that
             the
             body
             ,
             R
             ,
             would
             retain
             its
             place
             any
             where
             in
             the
             water
             ,
             and
             consequently
             near
             the
             bottome
             )
             will
             shew
             the
             invalidity
             of
             this
             Objection
             .
             And
             unless
             we
             knew
             of
             what
             bignesse
             and
             shape
             the
             Corpuscles
             of
             water
             are
             ,
             it
             would
             perhaps
             be
             to
             little
             purpose
             to
             dispute
             how
             far
             it
             may
             be
             granted
             ,
             or
             may
             be
             true
             in
             the
             particles
             that
             water
             is
             made
             up
             of
             .
             Onely
             this
             I
             shall
             add
             ▪
             That
             ,
             whereas
             this
             Learned
             Authour
             mentions
             it
             as
             an
             absurdity
             ,
             that
             the
             lower
             parts
             of
             water
             should
             be
             in
             perpetual
             motion
             :
             And
             Stevinus
             himself
             ,
             in
             the
             beginning
             of
             his
             Hydrostatical
             Elements
             ,
             seems
             to
             me
             to
             speak
             somewhat
             inconsiderately
             of
             this
             matter
             ;
             and
             though
             ,
             as
             I
             lately
             said
             ,
             I
             allow
             such
             sensible
             bodies
             ,
             as
             those
             whose
             gravity
             in
             water
             Writers
             are
             wont
             to
             dispute
             of
             ,
             to
             be
             capable
             of
             retaining
             their
             places
             in
             water
             ,
             if
             they
             be
             
               in
               specie
            
             equiponderant
             to
             it
             :
             Yet
             I
             
             am
             so
             far
             from
             thinking
             it
             absurd
             ,
             that
             the
             inferiour
             Corpuseles
             of
             water
             should
             be
             perpetually
             in
             motion
             ;
             that
             I
             see
             not
             how
             otherwise
             they
             could
             constitute
             a
             Fluid
             body
             ,
             That
             restless
             Motion
             of
             their
             parts
             ,
             being
             one
             of
             the
             generalest
             Attributes
             of
             Liquors
             ;
             and
             being
             ,
             in
             water
             ,
             though
             not
             immediately
             to
             be
             seen
             ,
             yet
             to
             be
             easily
             discover'd
             by
             its
             Effects
             :
             As
             ,
             when
             Salt
             ,
             being
             cast
             into
             water
             ,
             the
             aqueous
             parts
             that
             are
             contiguous
             to
             it
             ,
             and
             consequently
             near
             to
             the
             bottom
             ,
             do
             soon
             carry
             up
             many
             of
             the
             faline
             ones
             ,
             to
             the
             very
             top
             of
             the
             water
             ;
             where
             ,
             after
             a
             while
             ,
             they
             are
             wont
             to
             disclose
             themselves
             in
             little
             floating
             grains
             of
             a
             Cubical
             shape
             .
          
           
             But
             ,
             of
             this
             restless
             motion
             of
             the
             parts
             of
             Liquors
             having
             professedly
             treated
             elsewhere
             already
             ;
             
             I
             shall
             add
             nothing
             at
             present
             :
             But
             rather
             take
             
             notice
             of
             what
             our
             Authour
             subjoyns
             to
             the
             last
             of
             his
             Arguments
             ,
             (
             as
             the
             Grand
             thing
             which
             they
             suppose
             )
             in
             these
             words
             ,
             
               Ratio
               porro
               ,
               a
               priori
               ,
               hujus
               sententiae
               videtur
               esse
               ,
               quia
               res
               non
               dicitur
               gravitare
               nisi
               quatenus
               habet
               infra
               se
               Corpus
               levius
               se
               in
               specie
               .
            
             The
             erroniousness
             of
             which
             conceit
             ,
             if
             I
             should
             now
             go
             about
             solemnly
             to
             evince
             ;
             I
             as
             well
             fear
             it
             would
             be
             tedious
             ,
             as
             I
             hope
             it
             will
             be
             needless
             to
             those
             ,
             that
             have
             not
             forgot
             what
             may
             concern
             this
             subject
             in
             the
             former
             part
             of
             the
             now
             at
             length
             finish'd
             discourse
             ;
             and
             especially
             where
             I
             mention
             those
             Experiments
             ,
             which
             show
             ,
             That
             neither
             a
             stone
             ,
             nor
             Gold
             it self
             ,
             when
             plac'd
             deep
             under
             water
             ,
             would
             sinck
             in
             it
             ,
             if
             the
             Superiour
             water
             ,
             that
             gravitates
             on
             it
             ,
             did
             not
             contribute
             to
             its
             depression
             .
          
        
         
           
           
             APPENDIX
             II.
             
          
           
             Concerning
             the
             Reason
             why
             Divers
             ,
             and
             others
             who
             descend
             to
             the
             Bottome
             of
             the
             Sea
             ,
             are
             not
             oppress'd
             by
             the
             weight
             of
             the
             incumbent
             water
             .
          
           
             AMongst
             the
             difficulties
             that
             belong
             to
             the
             Hydrostaticks
             ,
             there
             is
             one
             which
             is
             so
             noble
             ,
             and
             which
             does
             still
             so
             much
             both
             exercise
             and
             pose
             the
             wits
             of
             the
             Curious
             ,
             That
             perchance
             it
             will
             not
             be
             unacceptable
             ,
             if
             to
             the
             former
             Experiments
             we
             add
             ,
             by
             way
             of
             Appendix
             ,
             one
             that
             may
             conduce
             to
             the
             solving
             of
             this
             difficult
             problem
             ;
             viz.
             Why
             men
             ,
             deep
             under
             water
             ,
             feel
             no
             inconvenience
             by
             the
             pressure
             of
             so
             great
             
             a
             weight
             of
             water
             as
             they
             are
             plac'd
             under
             ?
          
           
             The
             common
             Answer
             of
             Philosophers
             and
             other
             Writers
             to
             this
             puzling
             Question
             ,
             is
             ,
             That
             the
             Elements
             do
             not
             gravitate
             in
             their
             own
             proper
             places
             ;
             and
             so
             ,
             water
             in
             particular
             has
             no
             gravitation
             upon
             water
             ,
             nor
             consequently
             upon
             bodies
             every
             way
             surrounded
             with
             water
             .
             But
             that
             this
             Solution
             is
             not
             to
             be
             admitted
             ,
             may
             be
             easily
             gather'd
             from
             our
             proofs
             of
             the
             first
             Paradox
             ,
             and
             from
             divers
             other
             particulars
             ,
             applicable
             to
             the
             same
             purpose
             ,
             that
             may
             be
             met
             with
             in
             the
             foregoing
             papers
             .
          
           
             A
             famous
             VVriter
             ,
             and
             ,
             for
             ought
             I
             know
             ,
             the
             Recentest
             (
             except
             
               Monsieur
               Paschal
            
             )
             that
             has
             treated
             of
             Hydrostaticks
             ,
             having
             rendred
             this
             Reason
             of
             the
             Phaenomenon
             .
          
           
             [
             The
             Superior
             parts
             of
             consistent
             water
             
               (
               as
               he
               speaks
            
             )
             press
             not
             the
             inferior
             ,
             unless
             
             beneath
             the
             inferior
             there
             be
             a
             Body
             lighter
             in
             specie
             then
             water
             ;
             and
             therefore
             ,
             since
             a
             humane
             Body
             is
             heavier
             in
             specie
             then
             water
             ,
             it
             is
             not
             press'd
             by
             the
             incumbent
             water
             ,
             because
             this
             does
             not
             endeavor
             to
             be
             beneath
             a
             humane
             Body
             .
             ]
             
               He
               subjoyns
               ,
               contrary
               to
               his
               Custome
               ,
               this
               confident
               Epiphonema
               ,
            
             Qui
             aliam
             causam
             hujus
             rei
             assignant
             ,
             errant
             &
             alios
             decipiunt
             .
          
           
             But
             ,
             by
             his
             favour
             ,
             notwithstanding
             this
             confidence
             ,
             I
             shall
             not
             scruple
             to
             seek
             another
             Reason
             of
             the
             Phaenomenon
             .
             For
             I
             have
             abundantly
             prov'd
             ,
             that
             (
             contrary
             to
             the
             Assertion
             on
             which
             his
             Explication
             is
             built
             )
             the
             upper
             parts
             of
             water
             press
             against
             the
             lower
             ,
             whether
             a
             body
             heavier
             or
             lighter
             
               in
               specie
            
             then
             water
             be
             underneath
             the
             lower
             .
             And
             ,
             the
             contrary
             of
             which
             being
             the
             
               〈◊〉
               〈◊〉
               〈◊〉
               〈◊〉
               〈◊〉
            
             in
             this
             Controversie
             ,
             perhaps
             the
             matter
             may
             be
             somewhat
             cleard
             ,
             by
             mentioning
             here
             a
             distinction
             ,
             
             which
             I
             sometimes
             make
             use
             of
             .
             I
             consider
             then
             a
             body
             may
             be
             said
             to
             gravitate
             upon
             another
             body
             in
             two
             senses
             .
             For
             sometimes
             it
             actually
             sincks
             into
             ,
             or
             gets
             beneath
             the
             body
             that
             was
             under
             it
             ,
             as
             a
             sincking
             stone
             gravitates
             upon
             water
             ,
             and
             which
             I
             call
             Praevalent
             ,
             or
             successful
             Gravitation
             ;
             &
             sometimes
             it
             does
             not
             actually
             ,
             at
             least
             not
             visibly
             descend
             ,
             but
             only
             exercises
             its
             gravitation
             by
             pressing
             against
             the
             subjacent
             body
             that
             hinders
             its
             descent
             ;
             as
             when
             a
             VVoman
             carries
             a
             Paile
             of
             water
             on
             her
             head
             ,
             though
             the
             weight
             do
             not
             actually
             get
             nearer
             the
             Center
             of
             the
             Earth
             ;
             yet
             actually
             presses
             with
             its
             whole
             gravity
             upon
             the
             Womans
             head
             ,
             and
             back
             ,
             and
             other
             subjacent
             parts
             that
             hinder
             its
             actual
             descent
             ;
             and
             according
             to
             this
             Doctrine
             I
             cannot
             admit
             our
             Authors
             reasoning
             ,
             that
             because
             a
             mans
             body
             is
             bulk
             for
             bulk
             heavier
             then
             water
             ,
             therefore
             the
             water
             
             does
             not
             endeavour
             to
             place
             its
             self
             beneath
             it
             .
             For
             water
             ,
             being
             a
             heavy
             body
             ,
             derives
             from
             the
             cause
             of
             its
             gravity
             ,
             (
             what
             ever
             that
             be
             )
             an
             incessant
             endeavour
             towards
             the
             Center
             of
             the
             Earth
             ;
             nor
             is
             there
             any
             Reason
             ,
             why
             it
             s
             happening
             to
             be
             incumbent
             on
             a
             body
             heavier
             
               in
               specie
            
             then
             it self
             ,
             should
             destroy
             that
             endeavour
             .
             And
             therefore
             ,
             though
             it
             may
             be
             said
             that
             the
             water
             does
             not
             endeavour
             to
             place
             it self
             beneath
             a
             humane
             body
             ,
             because
             indeed
             an
             inanimate
             Liquor
             cannot
             properly
             be
             said
             to
             act
             for
             this
             or
             any
             other
             end
             ;
             yet
             the
             water
             being
             a
             heavy
             body
             ,
             tends
             continually
             towards
             the
             lower
             part
             of
             the
             Earth
             ;
             and
             therefore
             will
             get
             beneath
             any
             body
             that
             is
             plac'd
             betwixt
             it
             and
             that
             ,
             (
             without
             regard
             whether
             the
             inferior
             body
             be
             heavier
             or
             lighter
             
               in
               specie
            
             then
             it self
             )
             as
             far
             as
             the
             degree
             of
             its
             gravity
             will
             enable
             it
             ;
             nor
             would
             it
             ever
             rest
             ,
             till
             
             it
             have
             reach'd
             the
             lowermost
             parts
             of
             the
             Earth
             ,
             if
             the
             greater
             ponderousness
             of
             the
             earth
             and
             other
             heavy
             bodies
             did
             not
             hinder
             ,
             (
             not
             its
             endeavour
             downwards
             ,
             nor
             its
             pressure
             upon
             subjacent
             bodies
             ,
             but
             only
             )
             its
             actual
             descent
             .
          
           
             This
             Learned
             Author
             himself
             tells
             us
             ,
             (
             as
             well
             as
             Stevinus
             ,
             and
             others
             ,
             that
             have
             written
             of
             the
             Hydrostaticks
             ,
             unanimously
             teach
             ,
             )
             that
             if
             the
             bottom
             of
             a
             vessel
             be
             parallel
             to
             the
             Horizon
             ,
             the
             weight
             of
             water
             ,
             that
             rests
             upon
             it
             ,
             is
             equal
             to
             a
             pillar
             of
             water
             ,
             having
             that
             bottome
             for
             its
             Basis
             ,
             and
             for
             its
             height
             a
             perpendicular
             reaching
             thence
             to
             the
             uppermost
             Surface
             of
             the
             water
             .
             Nor
             is
             it
             reasonable
             to
             conceive
             that
             there
             will
             be
             any
             difference
             in
             this
             pressure
             of
             the
             incumbent
             water
             ,
             whether
             the
             bottom
             be
             of
             Deale
             that
             will
             swimme
             ,
             or
             of
             Box
             that
             will
             sinck
             in
             water
             ;
             or
             to
             speak
             more
             generally
             ,
             whether
             it
             be
             of
             Wood
             ,
             
               in
               specie
            
             lighter
             then
             water
             ,
             
             or
             of
             Copper
             ,
             or
             some
             other
             Metal
             ,
             that
             is
             
               in
               specie
            
             heavier
             then
             it
             .
             And
             since
             water
             ,
             being
             not
             a
             solid
             Body
             ,
             but
             a
             fluid
             ,
             consists
             (
             as
             other
             fluids
             )
             of
             innumerable
             Corpuscles
             ,
             that
             ,
             though
             extreamly
             minute
             ,
             have
             their
             own
             sizes
             and
             figures
             ;
             And
             since
             the
             pressure
             of
             water
             upon
             the
             bottom
             of
             a
             vessel
             is
             proportionate
             to
             its
             perpendicular
             height
             over
             the
             bottom
             ;
             'T
             is
             manifest
             ,
             that
             the
             upper
             Corpuscles
             press
             the
             bottom
             as
             well
             as
             the
             lower
             ;
             which
             ,
             since
             they
             cannot
             do
             immediately
             ,
             they
             must
             do
             by
             pressing
             the
             intermediate
             ones
             .
             And
             I
             have
             already
             shown
             (
             discoursing
             one
             of
             the
             former
             Paradoxes
             ,
             )
             that
             the
             Superior
             parts
             of
             water
             do
             not
             onely
             presse
             those
             that
             are
             directly
             under
             them
             ,
             but
             communicate
             a
             pressure
             to
             those
             that
             are
             aside
             of
             them
             ,
             and
             at
             a
             distance
             from
             them
             .
          
           
             And
             if
             it
             be
             objected
             ,
             That
             water
             
             endeavours
             to
             get
             beneath
             a
             Bottome
             of
             Glass
             Vessels
             ,
             or
             other
             bodies
             heavier
             
               in
               specie
            
             then
             its
             self
             ,
             because
             under
             that
             bottome
             there
             is
             aire
             ,
             which
             is
             a
             body
             lighter
             
               in
               specie
            
             then
             water
             :
             I
             say
             ,
             that
             this
             is
             precarious
             ;
             for
             the
             indisputable
             gravity
             of
             the
             water
             is
             alone
             sufficient
             to
             make
             it
             always
             tend
             downwards
             ,
             (
             though
             it
             cannot
             always
             move
             downwards
             )
             what
             ever
             body
             be
             beneath
             it
             .
             And
             who
             can
             assure
             the
             makers
             of
             this
             Objection
             ,
             That
             there
             are
             not
             beneath
             even
             the
             bottome
             of
             Rivers
             ,
             or
             of
             the
             Sea
             ,
             (
             where
             yet
             they
             say
             water
             is
             consistent
             ,
             and
             rests
             as
             in
             its
             own
             place
             ,
             )
             vast
             spaces
             replenished
             but
             with
             aire
             ,
             fumes
             ,
             or
             fire
             ,
             or
             some
             other
             body
             lighter
             then
             water
             ?
             For
             ,
             (
             not
             to
             mention
             that
             the
             Cartesians
             take
             the
             Earth
             we
             tread
             on
             ,
             to
             be
             but
             a
             thin
             Crust
             of
             the
             Terrestrial
             Globe
             ,
             whose
             inside
             ,
             as
             farre
             as
             the
             Center
             ,
             is
             replenish'd
             with
             a
             subtle
             fluid
             
             matter
             ,
             like
             that
             whereof
             the
             Sunne
             consists
             .
             )
             We
             know
             that
             in
             some
             places
             ,
             as
             particularly
             at
             a
             Famous
             Coal-mine
             in
             Scotland
             ,
             there
             are
             great
             Cavities
             that
             reach
             a
             good
             way
             under
             that
             ground
             that
             serves
             there
             for
             a
             bottome
             to
             the
             Sea
             :
             So
             that
             ,
             for
             ought
             these
             Objectors
             know
             ,
             ev'n
             according
             to
             their
             own
             Doctrine
             ,
             the
             water
             ev'n
             in
             the
             Sea
             ,
             may
             endeavour
             to
             get
             beneath
             a
             body
             heavier
             
               in
               specie
            
             then
             it self
             .
          
           
             But
             ,
             for
             my
             part
             ,
             I
             cannot
             but
             think
             ,
             that
             ,
             to
             imagine
             the
             water
             knows
             ,
             whether
             or
             no
             there
             be
             aire
             or
             some
             lighter
             body
             then
             it self
             beneath
             the
             body
             it
             leans
             on
             ,
             and
             the
             superior
             parts
             do
             accordingly
             exercise
             or
             suspend
             their
             pressure
             upon
             the
             inferior
             ;
             is
             to
             forget
             that
             it
             is
             a
             heavy
             Liquor
             ,
             and
             an
             inanimate
             Body
             .
          
           
             Another
             Solution
             there
             is
             of
             this
             Hydrostatical
             problem
             ,
             we
             have
             been
             
             discoursing
             of
             ,
             which
             I
             met
             with
             in
             a
             Printed
             Letter
             of
             Monsieur
             
               Des
               Cartes
            
             ,
             in
             these
             terms
             .
          
           
             Je
             ne
             me
             ,
             &c.
             
             I
             remember
             not
             what
             reason
             't
             is
             that
             Stevinus
             gives
             ,
             
             why
             one
             feels
             not
             weight
             of
             water
             ,
             when
             one
             is
             under
             it
             :
             but
             the
             true
             one
             is
             ,
             that
             there
             can
             no
             more
             of
             water
             gravitate
             upon
             the
             body
             that
             is
             in
             it
             ,
             or
             under
             it
             ,
             then
             as
             much
             water
             as
             could
             descend
             in
             case
             that
             body
             left
             its
             place
             .
             Thus
             for
             Example
             :
             
             If
             there
             were
             a
             Man
             in
             the
             Barrel
             ,
             B
             ,
             that
             should
             with
             his
             Body
             so
             stop
             the
             hole
             ,
             A
             ,
             as
             to
             hinder
             the
             waters
             getting
             out
             ,
             he
             would
             feel
             upon
             himself
             the
             weight
             of
             the
             whole
             Cylinder
             of
             water
             ,
             
               A
               B
               C
            
             ,
             of
             which
             I
             suppose
             the
             Basis
             to
             be
             equal
             to
             the
             hole
             A
             ;
             for
             as
             much
             as
             if
             he
             sunck
             down
             through
             the
             hole
             ,
             all
             the
             Cylinder
             of
             water
             would
             descend
             too
             ,
             but
             if
             he
             be
             a
             little
             higher
             ,
             as
             about
             B
             ,
             so
             that
             he
             does
             no
             longer
             hinder
             the
             water
             from
             running
             
             out
             at
             the
             hole
             A
             ,
             he
             ought
             not
             to
             Feel
             any
             weight
             of
             the
             water
             which
             is
             over
             him
             ,
             betwixt
             B
             and
             C
             ,
             because
             if
             he
             should
             descend
             toward
             A
             ,
             that
             water
             would
             not
             descend
             with
             him
             ,
             but
             contrarywise
             a
             part
             of
             the
             water
             which
             is
             beneath
             him
             towards
             A
             ,
             of
             equal
             bulk
             to
             his
             Body
             ,
             would
             ascend
             into
             its
             place
             :
             so
             that
             in
             stead
             of
             feeling
             the
             water
             to
             press
             him
             from
             the
             Top
             downward
             ,
             he
             ought
             to
             feel
             that
             it
             buoys
             him
             upward
             from
             the
             bottome
             ;
             which
             by
             Experience
             we
             see
             .
          
           
             Thus
             far
             this
             subtil
             Philosopher
             :
             for
             whose
             Ratiocinations
             though
             I
             am
             wont
             to
             have
             much
             respect
             ,
             yet
             I
             must
             take
             the
             liberty
             to
             confess
             my self
             unsatisfy'd
             with
             this
             .
             For
             haveing
             already
             sufficiently
             prov'd
             ,
             That
             the
             upper
             parts
             of
             water
             press
             the
             lower
             ,
             and
             the
             bodies
             plac'd
             beneath
             them
             ,
             whether
             such
             bodies
             be
             lighter
             
               in
               specie
            
             then
             water
             or
             heavier
             ;
             we
             have
             subverted
             the
             Foundation
             ,
             upon
             
             which
             Monsieur
             Cartes's
             ingenious
             ,
             though
             unsatisfactory
             ,
             Explication
             is
             built
             .
             And
             yet
             I
             shall
             add
             
               ex
               abundanti
            
             ,
             That
             supposing
             what
             he
             sayes
             ,
             That
             in
             case
             the
             solid
             B
             should
             descend
             towards
             A
             ,
             the
             incumbent
             water
             would
             not
             descend
             with
             it
             ,
             but
             a
             part
             of
             the
             subjacent
             water
             ,
             equal
             in
             bulk
             to
             the
             solid
             ,
             would
             ascend
             ,
             and
             succeed
             in
             its
             room
             ;
             yet
             that
             is
             but
             accidental
             ,
             by
             reason
             of
             the
             steinchness
             and
             fulness
             of
             the
             Vessel
             .
             And
             though
             indeed
             the
             Superior
             water
             cannot
             actually
             desend
             upon
             the
             depression
             of
             the
             solid
             at
             B
             ,
             if
             ,
             at
             the
             same
             time
             while
             that
             body
             descends
             ,
             an
             equal
             bulk
             of
             water
             succeeds
             in
             its
             place
             :
             Yet
             both
             the
             solid
             about
             C
             ,
             and
             the
             water
             that
             succeeds
             it
             ,
             do
             ,
             in
             their
             turns
             ,
             hinder
             the
             descent
             of
             the
             Superior
             water
             ;
             which
             therefore
             must
             gravitate
             upon
             which
             soever
             of
             the
             two
             it
             be
             that
             actually
             comes
             to
             be
             
             plac'd
             directly
             under
             it
             ,
             if
             there
             be
             nothing
             ,
             before
             the
             displacing
             of
             the
             solid
             ,
             capable
             to
             take
             away
             the
             natural
             gravity
             ,
             upon
             whose
             account
             the
             water
             ,
             over
             B
             and
             C
             ,
             does
             incessantly
             tend
             downwards
             .
             And
             though
             Monsieur
             
               Des
               Cartes
            
             does
             not
             so
             clearly
             express
             himselfe
             ,
             whether
             he
             supposes
             the
             hole
             at
             
               A
               ▪
            
             to
             be
             stopp'd
             with
             some
             other
             body
             ,
             when
             the
             solid
             is
             plac'd
             about
             B
             :
             yet
             ,
             because
             he
             is
             wont
             to
             speak
             consistently
             ,
             I
             presume
             he
             means
             ,
             that
             when
             the
             solid
             is
             remov'd
             to
             B
             ,
             the
             hole
             at
             A
             is
             otherwise
             sufficiently
             stopp'd
             ;
             I
             say
             then
             ,
             that
             the
             reason
             why
             the
             solid
             ,
             which
             ,
             whilst
             at
             A
             ,
             sustain'd
             a
             great
             pressure
             from
             the
             incumbent
             water
             ,
             feels
             not
             the
             weight
             of
             it
             ,
             when
             plac'd
             at
             B
             ,
             is
             not
             that
             which
             
               Monsieur
               des
               Cartes
            
             gives
             ,
             but
             this
             ,
             That
             the
             solid
             being
             environ'd
             with
             water
             ,
             the
             subjacent
             water
             does
             (
             as
             we
             have
             often
             had
             occasion
             to
             manifest
             )
             
             press
             it
             upwards
             ,
             full
             as
             strongly
             (
             and
             somewhat
             more
             )
             as
             the
             weight
             of
             the
             incumbent
             water
             presses
             it
             downwards
             ;
             So
             that
             a
             mans
             body
             ,
             in
             stead
             of
             sincking
             ,
             would
             be
             buoy'd
             up
             ;
             if
             ,
             as
             it
             is
             a
             little
             heavier
             ,
             it
             were
             a
             little
             lighter
             
               in
               specie
            
             then
             water
             .
             Whereas
             ,
             when
             the
             solid
             was
             that
             alone
             which
             cover'd
             and
             stop'd
             the
             hole
             ,
             there
             was
             a
             manifest
             Reason
             why
             it
             should
             be
             forcibly
             thrust
             downwards
             by
             the
             weight
             of
             the
             incumbent
             water
             
               B
               C.
            
             For
             ,
             in
             that
             case
             ,
             there
             was
             no
             water
             underneath
             it
             at
             A
             ,
             to
             support
             the
             solid
             ;
             and
             ,
             by
             its
             pressure
             upward
             ,
             to
             enable
             it
             to
             resist
             so
             great
             a
             weight
             .
          
           
             And
             this
             ,
             (
             to
             hint
             that
             upon
             the
             by
             )
             may
             perchance
             help
             us
             to
             guess
             at
             the
             reason
             of
             what
             Geographers
             relate
             of
             the
             Lake
             Asphaltites
             in
             Judea
             ,
             (
             in
             case
             the
             matter
             of
             fact
             be
             true
             ,
             )
             That
             this
             dead
             Sea
             (
             as
             they
             also
             call
             it
             )
             will
             not
             suffer
             any
             living
             creature
             to
             sinck
             in
             
             it
             .
             For
             the
             Body
             of
             a
             Man
             (
             and
             for
             ought
             we
             know
             of
             other
             Animals
             ,
             )
             is
             not
             much
             heavier
             
               in
               specie
            
             then
             common
             fresh
             water
             :
             Now
             if
             in
             this
             Lake
             (
             that
             stands
             where
             Sodom
             and
             Gomorrah
             did
             ,
             before
             those
             impious
             Regions
             were
             destroy'd
             by
             fire
             from
             Heaven
             ,
             )
             we
             suppose
             ,
             (
             which
             the
             nature
             of
             the
             Soyle
             ,
             and
             the
             Sacred
             Story
             makes
             probable
             enough
             )
             That
             the
             water
             abounds
             with
             Saline
             or
             Sulphurous
             Corpuscles
             ;
             (
             the
             former
             helping
             the
             later
             to
             associate
             with
             the
             water
             ,
             as
             we
             see
             in
             sope
             consisting
             of
             salt
             and
             oyle
             ,
             and
             in
             Chymical
             mixtures
             of
             Alcalis
             and
             Brimstone
             dissoluble
             in
             water
             )
             the
             Liquor
             may
             have
             its
             gravity
             so
             augmented
             ,
             as
             to
             become
             heavier
             
               in
               specie
            
             then
             the
             body
             of
             an
             animal
             .
             For
             I
             have
             learned
             of
             a
             Light
             Swimmer
             ,
             that
             he
             could
             hardly
             begin
             to
             Dive
             in
             salt
             water
             ,
             though
             he
             easily
             could
             in
             fresh
             .
             And
             't
             is
             not
             difficult
             to
             make
             a
             Brine
             
             or
             Lixivium
             (
             which
             are
             but
             Solutions
             of
             salt
             in
             water
             ,
             )
             heavy
             enough
             to
             keep
             up
             an
             egg
             from
             sincking
             .
             And
             ,
             not
             only
             barely
             by
             dissolving
             a
             metalline
             body
             in
             a
             saline
             Menstruum
             ,
             without
             otherwise
             thickning
             the
             Liquor
             ,
             I
             have
             brought
             solid
             pieces
             of
             Amber
             it self
             to
             swim
             upon
             it
             :
             but
             I
             have
             try'd
             that
             certain
             saline
             Solutions
             ,
             which
             I
             elsewhere
             mention
             ;
             nay
             ,
             and
             a
             distill'd
             Liquor
             ,
             (
             I
             us'd
             defleam'd
             oyle
             of
             Vitriol
             )
             without
             any
             thing
             dissolv'd
             in
             it
             ,
             would
             do
             the
             same
             thing
             ;
             by
             reason
             of
             the
             numerous
             ,
             though
             minute
             ,
             Corpuscles
             of
             salt
             and
             sulphur
             ,
             that
             it
             abounds
             with
             .
          
           
             There
             remains
             but
             one
             solution
             more
             of
             our
             Hydrostatical
             probleme
             ,
             that
             I
             think
             worth
             mentioning
             ,
             and
             that
             is
             given
             by
             the
             Learned
             Stevinus
             in
             these
             words
             ,
          
           
             Omni
             pressu
             quo
             Corpus
             dolore
             afficitur
             ,
             pars
             aliqua
             Corporis
             luxatur
             ;
             sed
             isto
             
             pressu
             nulla
             Corporis
             pars
             luxatur
             ,
             isto
             igitur
             pressu
             Corpus
             dolore
             nullo
             afficitur
             .
             Assumptio
             syllogismi
             manifesta
             est
             ,
             nam
             si
             pars
             aliqua
             ,
             ut
             caro
             ,
             sanguis
             ,
             humor
             ,
             aut
             quodlibet
             denique
             membrum
             luxaretur
             ,
             
             in
             alium
             locum
             concedat
             necesse
             esset
             :
             
             atqui
             locus
             ille
             non
             est
             extra
             Corpus
             ;
             
             cum
             aqua
             undiquaque
             aequali
             pressu
             circumfusa
             sit
             (
             quod
             vero
             pars
             ima
             ,
             
             per
             11.
             propositionem
             Hydrostaticorum
             ,
             
             paulo
             validius
             prematur
             superiori
             ,
             id
             hoc
             casu
             nullius
             momenti
             est
             ,
             quia
             tantula
             differentia
             partem
             nullam
             sua
             sede
             dimovere
             potest
             )
             neque
             item
             intra
             ipsum
             Corpus
             concedit
             ,
             cum
             istic
             Corpore
             omnia
             oppleta
             
             sint
             ,
             unde
             singulae
             partes
             singulis
             partibus
             aequaliter
             resistunt
             ,
             namque
             aqua
             undiquaque
             eadem
             ratione
             Corpus
             totum
             circumstat
             .
             Quare
             cum
             locus
             is
             nec
             intra
             ,
             nec
             extra
             Corpus
             sit
             ;
             absurdum
             ,
             imo
             impossibile
             fuerit
             ,
             partem
             ullam
             suo
             loco
             emoveri
             ,
             ideoque
             nec
             Corpus
             hic
             afficitur
             dolore
             .
          
           
             This
             Solution
             of
             Stevinus
             ,
             I
             esteem
             preferrible
             by
             farr
             ,
             to
             those
             that
             are
             wont
             to
             be
             given
             of
             this
             difficult
             Probleme
             :
             But
             yet
             ,
             the
             Phaenomenon
             seems
             to
             me
             to
             have
             still
             somewhat
             in
             it
             of
             strange
             .
             'T
             is
             true
             ,
             that
             if
             the
             Question
             were
             only
             that
             which
             some
             put
             ,
             viz.
             Why
             the
             body
             of
             a
             Diver
             ,
             when
             it
             is
             near
             the
             bottom
             of
             the
             Sea
             ,
             is
             not
             press'd
             down
             by
             so
             vast
             a
             weight
             of
             water
             ,
             as
             is
             incumbent
             on
             it
             ;
             It
             might
             be
             rationally
             answer'd
             ,
             That
             the
             weight
             of
             so
             much
             water
             ,
             as
             leans
             upon
             the
             body
             ,
             is
             not
             sustein'd
             by
             the
             force
             of
             the
             body
             it self
             ,
             but
             by
             that
             of
             the
             water
             which
             is
             under
             it
             .
             For
             ,
             
             by
             the
             Experiments
             and
             Explications
             ,
             we
             have
             annexed
             to
             some
             of
             the
             foregoing
             Paradoxes
             ,
             it
             appears
             ,
             That
             the
             subjacent
             water
             ,
             by
             its
             pressure
             upwards
             ,
             is
             able
             ,
             not
             only
             to
             support
             the
             weight
             of
             the
             incumbent
             water
             ,
             but
             so
             far
             to
             exceed
             it
             ,
             that
             it
             would
             not
             only
             support
             the
             immers'd
             body
             ,
             and
             the
             incumbent
             water
             ,
             but
             buoy
             up
             the
             body
             ,
             if
             it
             were
             never
             so
             little
             lighter
             
               in
               specie
            
             then
             water
             .
             And
             as
             for
             what
             Stevinus
             insinuates
             ,
             That
             ,
             when
             the
             water
             presses
             the
             body
             every
             way
             ,
             that
             pressure
             is
             not
             felt
             ,
             though
             it
             would
             be
             ,
             in
             case
             it
             press'd
             upon
             some
             parts
             ,
             and
             not
             upon
             others
             ;
             I
             am
             of
             the
             same
             opinion
             too
             ;
             and
             ,
             to
             prove
             it
             ,
             shall
             not
             make
             use
             of
             the
             example
             he
             proposes
             ,
             in
             the
             words
             immediately
             following
             those
             of
             his
             ,
             I
             just
             now
             recited
             :
             (
             For
             I
             doubt
             ,
             that
             example
             is
             rather
             a
             supposition
             ,
             then
             a
             try'd
             thing
             ;
             )
             but
             by
             an
             Experiment
             which
             may
             be
             easily
             
             made
             ,
             and
             has
             diverse
             times
             been
             so
             ,
             in
             our
             Pneumatical
             Engine
             .
             For
             ,
             though
             the
             aire
             be
             a
             heavy
             fluid
             ,
             and
             though
             ,
             whilst
             it
             uniformely
             presses
             the
             whole
             superficies
             of
             the
             body
             ,
             we
             feel
             not
             the
             pressure
             of
             it
             .
             And
             though
             ,
             for
             this
             reason
             ,
             you
             may
             lay
             the
             palm
             of
             your
             hand
             upon
             the
             open
             orifice
             of
             a
             small
             brass
             Cylinder
             ,
             apply'd
             to
             the
             Engine
             instead
             of
             a
             Receiver
             ,
             without
             any
             hurt
             ;
             Yet
             when
             ,
             by
             pumping
             ,
             the
             aire
             that
             was
             before
             under
             the
             palm
             of
             your
             hand
             ,
             is
             withdrawn
             ,
             and
             consequently
             can
             no
             longer
             help
             to
             support
             your
             hand
             ,
             against
             the
             pressure
             of
             the
             external
             and
             incumbent
             aire
             ;
             the
             external
             aire
             will
             lean
             so
             heavy
             upon
             the
             back
             of
             your
             hand
             ,
             that
             you
             will
             imagine
             some
             ponderous
             weight
             is
             lay'd
             upon
             it
             .
             And
             I
             remember
             by
             such
             an
             Experiment
             ,
             I
             have
             not
             onely
             had
             my
             hand
             put
             to
             much
             pain
             ,
             but
             have
             had
             the
             back
             of
             it
             so
             bent
             downward
             ,
             as
             if
             it
             were
             going
             to
             be
             broken
             .
          
           
           
             But
             though
             such
             considerations
             ,
             as
             these
             ,
             may
             much
             lessen
             the
             difficulty
             of
             our
             phaenomenon
             ,
             whose
             cause
             is
             inquired
             into
             ;
             Yet
             still
             it
             seems
             somewhat
             odd
             to
             me
             ,
             That
             (
             since
             't
             is
             evident
             from
             the
             nature
             of
             the
             thing
             ,
             and
             by
             Stevinus's
             his
             confession
             ,
             that
             there
             is
             a
             vast
             pressure
             of
             water
             against
             every
             part
             of
             the
             body
             ,
             whose
             endeavour
             tends
             inward
             ,
             )
             so
             exceedingly
             forcible
             a
             pressure
             ,
             (
             which
             thrusts
             ,
             for
             instance
             ,
             the
             Muscles
             of
             the
             Arms
             and
             Thighs
             against
             the
             Bones
             ,
             the
             Skin
             and
             Flesh
             of
             the
             Thorax
             against
             the
             Ribs
             ,
             )
             should
             not
             put
             the
             Dives
             to
             any
             sensible
             pain
             ;
             As
             I
             find
             not
             (
             by
             one
             that
             I
             examin'd
             )
             that
             it
             dos
             ;
             (
             Though
             this
             man
             told
             me
             ,
             he
             stay'd
             a
             good
             while
             at
             the
             depth
             of
             betwixt
             80
             and
             100
             foot
             under
             the
             Sea
             water
             ,
             which
             is
             heavier
             then
             fresh
             water
             ;
             )
             For
             ,
             that
             which
             Stevinus's
             Explication
             will
             only
             showis
             ,
             That
             there
             must
             be
             no
             manifest
             
             dislocation
             of
             the
             greater
             parts
             of
             the
             Body
             ;
             whereas
             the
             bare
             compression
             of
             two
             small
             parts
             ,
             one
             against
             another
             ,
             is
             sufficient
             to
             produce
             a
             sense
             of
             pain
             .
          
           
             But
             it
             seems
             ,
             the
             Texture
             of
             the
             bodyes
             of
             Animals
             is
             better
             able
             to
             resist
             the
             pressure
             of
             an
             every
             way
             ambient
             fluid
             ,
             then
             ,
             if
             we
             were
             not
             taught
             by
             experience
             ,
             we
             should
             imagine
             .
             And
             therefore
             ,
             to
             satisfie
             those
             that
             (
             secluding
             the
             Question
             about
             the
             sense
             of
             pain
             ,
             )
             think
             it
             an
             abundantly
             sufficient
             Argument
             ,
             (
             to
             prove
             ,
             that
             bodyes
             immers'd
             under
             water
             ,
             are
             not
             compress'd
             by
             it
             ;
             )
             That
             Divers
             are
             not
             oppress'd
             ,
             and
             ev'n
             crush'd
             ▪
             by
             so
             vast
             a
             load
             of
             water
             ,
             (
             amounting
             ,
             by
             Stevinus's
             computation
             ,
             to
             many
             thousands
             of
             pounds
             )
             as
             is
             incumbent
             on
             them
             .
             We
             will
             add
             ,
             that
             though
             an
             Experiment
             ,
             propos'd
             by
             Monsieur
             Paschal
             to
             this
             purpose
             ,
             were
             such
             ,
             
             that
             at
             first
             sight
             I
             said
             that
             it
             would
             not
             succeed
             ,
             (
             and
             was
             not
             upon
             tryal
             mistaken
             in
             my
             conjecture
             ;
             )
             yet
             it
             gave
             me
             the
             occasion
             to
             make
             another
             ,
             which
             will
             ,
             I
             hope
             ,
             fully
             make
             out
             the
             thing
             I
             design'd
             it
             for
             .
          
           
             The
             Ingenious
             Monsieur
             Paschal
             would
             perswade
             his
             Readers
             ,
             that
             if
             into
             a
             glass
             Vessel
             ,
             with
             luke-warm
             water
             in
             it
             ,
             you
             cast
             a
             flie
             ;
             and
             ,
             by
             a
             Rammer
             ,
             forcibly
             press
             that
             water
             ,
             you
             shall
             not
             be
             able
             to
             kill
             ,
             or
             hurt
             the
             flie
             .
             VVhich
             ,
             says
             he
             ,
             will
             live
             as
             well
             ,
             and
             walk
             up
             and
             down
             as
             lively
             ,
             in
             luke-warme
             water
             ,
             as
             in
             the
             aire
             .
             But
             ,
             upon
             tryal
             with
             a
             strong
             flie
             ,
             the
             Animal
             was
             (
             as
             we
             expected
             ,
             )
             presently
             drowned
             ,
             and
             so
             made
             moveless
             ,
             by
             the
             luke-warm
             water
             .
          
           
             Wherefore
             we
             substituted
             another
             Experiment
             ,
             that
             we
             knew
             would
             not
             only
             succeed
             ,
             (
             as
             you
             will
             presently
             see
             it
             will
             do
             ,
             )
             but
             teach
             us
             how
             great
             a
             
             pressure
             the
             included
             Animal
             must
             have
             been
             expos'd
             to
             .
             VVe
             took
             then
             a
             somewhat
             slender
             Cylindrical
             pipe
             of
             Glass
             ,
             
             seal'd
             at
             one
             end
             ,
             and
             open
             at
             the
             other
             ;
             and
             to
             this
             we
             fitted
             a
             Rammer
             ,
             which
             (
             by
             the
             help
             of
             some
             thongs
             of
             soft
             leather
             ,
             that
             were
             carefully
             wound
             about
             it
             )
             did
             so
             exactly
             fill
             the
             pipe
             that
             it
             could
             not
             easily
             be
             mov'd
             to
             and
             fro
             ;
             and
             would
             suffer
             neither
             water
             ,
             nor
             aire
             ,
             to
             get
             by
             betwixt
             it
             ,
             and
             the
             internal
             surface
             of
             the
             Glass
             .
             VVe
             also
             provided
             some
             small
             Tad-poles
             (
             or
             Gyrini
             )
             about
             an
             Inch
             long
             or
             less
             ;
             which
             sort
             of
             Animals
             we
             made
             choice
             of
             before
             any
             other
             ,
             partly
             because
             they
             could
             ,
             by
             reason
             of
             their
             smalness
             ,
             swim
             freely
             to
             &
             fro
             in
             so
             little
             water
             as
             our
             pipe
             contain'd
             ;
             &
             partly
             because
             those
             Creatures
             ,
             being
             as
             yet
             but
             in
             their
             Infancy
             ,
             were
             more
             tender
             ,
             and
             ,
             consequently
             ,
             far
             
             more
             expos'd
             to
             be
             injur'd
             by
             compression
             ,
             then
             other
             Animals
             of
             the
             same
             Bulk
             ,
             but
             come
             to
             their
             full
             age
             and
             growth
             ,
             would
             be
             ,
             (
             as
             indeed
             such
             young
             Tad-poles
             are
             so
             soft
             and
             tender
             ,
             that
             they
             seem
             ,
             in
             comparison
             to
             the
             bigger
             sort
             of
             flies
             ,
             to
             be
             but
             organiz'd
             Gelly
             .
             )
             One
             of
             these
             Tadpoles
             being
             put
             into
             the
             water
             ,
             and
             some
             Inches
             of
             aire
             being
             left
             in
             the
             pipe
             ,
             for
             the
             use
             anon
             to
             be
             mention'd
             ;
             the
             water
             and
             aire
             ,
             and
             consequently
             the
             Tadpole
             ,
             were
             by
             the
             intrusion
             of
             the
             plug
             or
             rammer
             ,
             with
             as
             great
             a
             force
             as
             a
             man
             was
             able
             to
             imploy
             ,
             violently
             compress'd
             ;
             and
             yet
             ,
             though
             the
             Tadpole
             seem'd
             to
             be
             compress'd
             into
             a
             little
             less
             Bulk
             then
             it
             was
             of
             before
             ,
             it
             swom
             freely
             up
             and
             down
             the
             water
             ,
             without
             forbearing
             sometimes
             to
             ascend
             to
             the
             very
             top
             ,
             though
             the
             Instrument
             were
             held
             perpendicular
             to
             the
             Horizon
             .
             Nor
             did
             it
             clearly
             appear
             to
             
             us
             ,
             That
             the
             little
             Animal
             was
             injur'd
             by
             this
             compression
             ;
             and
             most
             manifest
             it
             is
             ,
             he
             was
             not
             crush'd
             to
             death
             ,
             or
             sensibly
             hurt
             by
             it
             .
          
           
             And
             having
             repeated
             this
             Experiment
             several
             times
             ,
             &
             with
             Tadpoles
             of
             differing
             ages
             ;
             we
             may
             ,
             I
             presume
             ,
             safely
             conclude
             ,
             That
             the
             Texture
             of
             Animals
             is
             so
             strong
             ,
             that
             ,
             though
             water
             be
             allowed
             to
             weigh
             upon
             water
             ,
             yet
             a
             Diver
             ought
             not
             to
             be
             opprest
             by
             It
             :
             Since
             ,
             whether
             or
             no
             water
             weighs
             in
             water
             ,
             't
             is
             manifest
             that
             in
             our
             Experiment
             ,
             the
             water
             ,
             and
             consequently
             the
             Tadpole
             ,
             was
             very
             forcibly
             by
             an
             External
             Agent
             compress'd
             betwixt
             the
             violently
             condens'd
             aire
             ,
             and
             the
             rammer
             .
             And
             ,
             by
             the
             notice
             we
             took
             of
             the
             quantity
             of
             aire
             before
             the
             compression
             began
             ,
             and
             that
             to
             which
             it
             was
             reduc'd
             by
             compression
             ;
             The
             moderatest
             estimate
             we
             could
             make
             ,
             was
             ,
             That
             it
             was
             reduc'd
             into
             an
             eighth
             ,
             or
             
             tenth
             part
             of
             it's
             former
             space
             ;
             and
             so
             (
             according
             to
             what
             we
             have
             elswhere
             prov'd
             )
             the
             pressure
             that
             was
             upon
             the
             aire
             ,
             (
             and
             consequently
             upon
             the
             water
             ,
             and
             the
             included
             Tadpole
             ,
             )
             was
             as
             great
             as
             that
             of
             a
             Cylinder
             of
             water
             of
             above
             200
             if
             not
             300
             foot
             high
             .
             And
             yet
             all
             this
             weight
             being
             unable
             to
             oppress
             ,
             or
             so
             much
             as
             manifestly
             to
             hurt
             ,
             the
             tender
             Tadpole
             (
             which
             a
             very
             small
             weight
             would
             suffice
             to
             have
             crush'd
             ,
             if
             it
             prest
             only
             upon
             one
             part
             of
             it
             ,
             and
             not
             upon
             the
             other
             )
             we
             may
             thence
             learn
             the
             Truth
             of
             what
             we
             have
             been
             endeavouring
             to
             evince
             :
             That
             though
             water
             be
             allowed
             to
             press
             against
             water
             ,
             and
             all
             immers'd
             Bodys
             ;
             yet
             a
             Diver
             may
             very
             well
             remaine
             unoppress'd
             at
             a
             great
             depth
             under
             water
             ,
             as
             long
             as
             the
             pressure
             of
             it
             is
             uniforme
             against
             all
             the
             parts
             expos'd
             thereunto
             .
          
           
             FINIS
             .
          
        
      
       
         
         
           
           
           
           
           
           
           
           
           
        
      
    
     
       
         Notes, typically marginal, from the original text
         
           Notes for div A28989-e170
           
             *
             About
             this
             passage
             ,
             See
             the
             Publisher
             ,
             to
             the
             Reader
             .
          
           
             *
             Chiefly
             ,
             in
             several
             places
             of
             the
             unpublish'd
             part
             of
             the
             Treatise
             of
             the
             osefulness
             of
             Experimental
             Philosophy
             .
          
           
             *
             An
             Account
             of
             this
             passage
             also
             ,
             may
             be
             had
             from
             the
             Publishers
             Advertisement
             to
             the
             Reader
             .
          
        
         
           Notes for div A28989-e900
           
             *
             That
             excellent
             Mathematician
             the
             Learned
             Dr
             
               Wallis
               ,
               Savilian
               Professor
               of
               Geometry
               .
            
          
           
             This
             Experiment
             and
             the
             Explication
             of
             it
             ,
             if
             to
             some
             they
             should
             here
             seem
             somewhat
             obscure
             ,
             will
             be
             easily
             understood
             by
             the
             Figures
             and
             Explications
             belonging
             to
             the
             first
             ensuing
             Paradoxe
             .
          
           
             See
             the
             second
             Figure
             .
          
           
             In
             certain
             ,
             Notes
             upon
             some
             of
             the
             Physics-mechanical
             Experiments
             ,
             touching
             the
             Aire
             .
          
           
             Fig.
             3.
             
          
           
             Fig.
             1.
             2.
             
          
           
             Fig.
             4.
             
          
           
             Fig.
             5.
             
          
           
             See
             PARADOX
             the
             sixth
             .
          
           
             Fig.
             6.
             
          
           
             Fig.
             8.
             
          
           
             Figur
             .
             9.
             
          
           
             Fig.
             10.
             
          
           
             Fig.
             11.
             
          
           
             See
             Fig.
             12.
             
          
           
             Fig.
             13.
             
          
           
             Fig.
             14.
             
          
           
             See
             the
             Proof
             of
             the
             11.
             
             Paradox
             .
          
           
             Fig.
             15.
             
          
           
             Fig.
             16.
             
          
           
             Fig.
             17.
             
          
           
             Fig.
             18.
             
          
           
             In
             the
             Physico-Mechanical
             Experiments
             .
          
           
             Fig.
             19.
             
          
           
             *
             The
             word
             ,
             about
             ,
             is
             added
             ,
             because
             indeed
             the
             Author
             ,
             as
             he
             elsewhere
             delivers
             ,
             did
             by
             exact
             scales
             find
             Brass
             to
             weigh
             between
             eight
             or
             nine
             times
             as
             much
             as
             water
             ;
             but
             judg'd
             it
             needless
             to
             his
             present
             Argument
             ,
             and
             inconvenient
             to
             take
             notice
             of
             the
             fraction
             .
          
           
             Fig.
             20.
             
          
           
             In
             the
             History
             of
             fluidity
             &
             firmness
             
          
           
             Second
             Tome
             lettre
             32.
             
          
           
             Fig.
             22.
             
          
           
             Stevinus
             Hydrostat
             .
             Lib.
             5.
             pag.
             149.
             
          
           
             Sed
             Exemple
             clarius
             ita
             intelliges
             ,
             este
             ABCD
             aqua
             ,
             cujus
             fundum
             
          
           
             D
             C
             ▪
             in
             quo
             foramen
             E
             habeat
             Epistimeus
             sibi
             iesertum
             ,
             cui
             Dorso
             incumbat
             Homo
             F
             ,
             Quae
             cum
             ita
             fiat
             ,
             ab
             aqua
             pondere
             ipsi
             insidente
             nulla
             pars
             Corporis
             luxari
             poterit
             ,
             cum
             aqua
             ,
             ut
             dictus
             est
             ,
             undiquaque
             aqualiter
             urgeat
             .
          
           
             Fig.
             23.
             
          
           
             Si
             vero
             ejus
             veritatem
             explorare
             libeat
             ,
             eximito
             Epistemiun
             ,
             tumque
             tergum
             nulla
             re
             fultum
             sustinebitur
             ,
             ut
             in
             locis
             cateris
             ,
             ideoque
             istic
             tanto
             pressu
             afficietur
             ,
             quantus
             tertio
             exemple
             secunda
             propositionis
             hujus
             demonstratus
             est
             :
             vidquantam
             efficit
             columna
             aquea
             cujus
             Basis
             sit
             foramica
             E
             ,
             altitudo
             autem
             eadem
             quae
             aqua
             ipsi
             insidentis
             .
             Quo
             exemplo
             propositi
             veritas
             manifeste
             declaratur
             .
          
           
             Fig.
             24.