May it please the King's most excellent Majesty
         Halley, Edmond, 1656-1742.
      
       
         
           1687
        
      
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         179866
         
           
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             May it please the King's most excellent Majesty
             Halley, Edmond, 1656-1742.
          
           12 p.
           
             s.n.,
             [London :
             1687]
          
           
             Caption title.
             Place and date of publication suggested by Wing (2nd ed.).
             Reproduction of original in: British Library.
          
        
      
    
     
       
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         eng
      
       
         
           Celestial mechanics -- Early works to 1800.
           Lunar theory -- Early works to 1800.
           Tides -- Early works to 1800.
        
      
    
     
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           May
           it
           Please
           THE
           KING'
           's
           MOST
           EXCELLENT
           MAJESTY
           .
        
         
           I
           Could
           not
           have
           presumed
           to
           approach
           your
           Majesties
           Royall
           Presence
           with
           a
           Book
           of
           this
           Nature
           ,
           had
           I
           not
           been
           assured
           that
           ,
           when
           the
           weighty
           Affairs
           of
           your
           Government
           permit
           it
           ,
           your
           Majesty
           has
           frequently
           shewn
           your self
           enclined
           to
           favour
           Mechanical
           and
           Philosophical
           Discoveries
           :
           And
           I
           may
           be
           bold
           to
           say
           ,
           that
           if
           ever
           Book
           was
           worthy
           the
           favourable
           acceptance
           of
           a
           Prince
           ,
           this
           wherein
           so
           many
           and
           so
           great
           Discoveries
           concerning
           the
           constitution
           of
           the
           Visible
           World
           are
           made
           out
           ,
           and
           put
           past
           dispute
           ,
           must
           needs
           be
           grateful
           to
           your
           Majesty
           ;
           especially
           being
           the
           Labours
           of
           a
           worthy
           Subject
           of
           your
           own
           ,
           and
           a
           Member
           of
           that
           
             Royall
             Society
          
           founded
           by
           your
           late
           Royall
           Brother
           ,
           for
           the
           advancement
           of
           Natural
           Knowledge
           ,
           and
           which
           now
           Flourishes
           ●nder
           your
           Majesties
           most
           Gracious
           Protection
           .
        
         
         
         
         
           But
           being
           sensible
           of
           the
           little
           Leisure
           which
           Care
           of
           the
           Publick
           leaves
           to
           Princes
           ,
           I
           believed
           it
           necessary
           to
           present
           with
           the
           Book
           a
           short
           Extract
           of
           the
           Matters
           conteined
           ,
           together
           with
           a
           Specimen
           thereof
           ,
           in
           the
           genuine
           Solution
           of
           the
           Cause
           of
           the
           Tides
           in
           the
           Ocean
           ;
           a
           thing
           frequently
           attempted
           ,
           but
           till
           now
           without
           success
           :
           Whereby
           your
           Majesty
           may
           judge
           of
           the
           rest
           of
           the
           performances
           of
           the
           Author
           .
        
         
           The
           sole
           Principle
           upon
           which
           this
           Author
           proceeds
           to
           explain
           most
           of
           the
           great
           and
           surprising
           appearances
           of
           Nature
           ,
           is
           no
           other
           than
           that
           of
           Gravity
           ,
           whereby
           in
           the
           Earth
           all
           Bodies
           have
           a
           tendency
           towards
           its
           Center
           ;
           as
           is
           most
           evident
           :
           and
           from
           undoubted
           Arguments
           it
           s
           proved
           ,
           that
           there
           is
           such
           a
           Gravitation
           towards
           the
           Centers
           of
           the
           Sun
           ,
           Moon
           and
           all
           the
           Planets
           .
        
         
           From
           this
           principle
           ,
           as
           a
           necessary
           consequence
           ,
           follows
           the
           Sphaerical
           Figure
           of
           the
           Earth
           and
           Sea
           ,
           and
           of
           all
           the
           other
           Caelestial
           Bodies
           :
           and
           tho'
           the
           tenacity
           and
           firmness
           of
           the
           Solid
           Parts
           support
           the
           inequalities
           of
           the
           Land
           above
           the
           level
           ;
           yet
           the
           Fluids
           ,
           pressing
           equally
           and
           easily
           yeilding
           to
           each
           other
           ,
           soon
           restore
           the
           Aequilibrium
           ,
           if
           disturbed
           ,
           and
           maintain
           the
           exact
           Figure
           of
           the
           Globe
           .
        
         
           Now
           this
           force
           of
           Descent
           of
           Bodies
           towards
           the
           Center
           is
           not
           in
           all
           places
           alike
           ,
           but
           is
           still
           less
           and
           less
           ,
           as
           the
           distance
           from
           the
           Center
           encreases
           :
           and
           in
           this
           Book
           it
           is
           demonstrated
           ,
           that
           this
           force
           decreases
           as
           the
           Square
           of
           the
           distance
           increases
           ;
           that
           is
           ,
           the
           weight
           of
           Bodies
           and
           the
           force
           of
           their
           Fall
           is
           less
           ,
           in
           parts
           more
           removed
           from
           the
           Center
           ,
           in
           the
           proportion
           of
           the
           squares
           of
           the
           distance
           .
           So
           as
           for
           Example
           ,
           a
           Tun
           weight
           on
           the
           surface
           of
           the
           Earth
           ,
           if
           it
           were
           raised
           to
           the
           height
           of
           4000
           miles
           ,
           which
           I
           suppose
           the
           semidiameter
           of
           the
           Earth
           ,
           would
           weigh
           but
           ¼
           of
           a
           Tun
           or
           5
           hundred
           weight
           :
           if
           to
           12000
           miles
           or
           3
           semidiameters
           from
           the
           surface
           ,
           that
           is
           4
           from
           the
           center
           ,
           it
           would
           weigh
           but
           1
           /
           16
           part
           of
           the
           weight
           on
           the
           surface
           ,
           or
           a
           hundred
           and
           quarter
           :
           So
           that
           it
           would
           be
           as
           easy
           for
           the
           strength
           of
           
           a
           man
           ,
           at
           that
           height
           ,
           to
           carry
           a
           Tun
           weight
           ,
           as
           here
           to
           carry
           a
           hundred
           and
           quarter
           .
           And
           in
           the
           same
           proportion
           does
           the
           Velocities
           of
           the
           fall
           of
           Bodies
           decrease
           :
           for
           whereas
           on
           the
           surface
           of
           the
           Earth
           all
           things
           fall
           16
           foot
           in
           a
           second
           ,
           at
           one
           semidiameter
           above
           this
           fall
           is
           but
           4
           foot
           ;
           and
           at
           3
           semidiameters
           ,
           or
           4
           from
           the
           center
           it
           is
           but
           1
           /
           16
           of
           the
           fall
           at
           the
           surface
           ,
           or
           but
           one
           foot
           in
           a
           second
           :
           and
           at
           greater
           distances
           both
           weight
           and
           fall
           become
           very
           small
           ,
           but
           yet
           at
           all
           given
           distances
           is
           still
           some
           thing
           ,
           tho'
           the
           effect
           become
           insensible
           .
           At
           the
           distance
           of
           the
           Moon
           (
           which
           I
           will
           suppose
           60
           semidiameters
           of
           the
           Earth
           )
           3600
           pounds
           weigh
           but
           one
           pound
           ,
           and
           the
           fall
           of
           Bodies
           is
           but
           16
           /
           3600
           of
           a
           foot
           in
           a
           second
           ,
           or
           16
           foot
           in
           a
           minute
           ;
           that
           is
           ,
           a
           body
           so
           far
           off
           descends
           in
           a
           minute
           no
           more
           than
           the
           same
           at
           the
           surface
           of
           the
           Earth
           would
           do
           in
           a
           second
           of
           Time.
           
        
         
           As
           was
           said
           before
           ,
           the
           same
           force
           decreasing
           after
           the
           same
           manner
           is
           evidently
           found
           in
           the
           Sun
           ,
           Moon
           and
           all
           the
           Planets
           ;
           but
           more
           especially
           in
           the
           Sun
           ,
           whose
           force
           is
           prodigious
           ;
           becoming
           sensible
           even
           in
           the
           immense
           distance
           of
           Saturn
           :
           This
           gives
           room
           to
           suspect
           that
           the
           force
           of
           Gravity
           is
           in
           the
           Celestial
           Globes
           proportional
           to
           the
           quantity
           of
           Matter
           in
           each
           of
           them
           :
           and
           the
           Sun
           being
           at
           least
           ten
           thousand
           times
           as
           bigg
           as
           the
           Earth
           ,
           its
           Gravitation
           or
           attracting
           Force
           ,
           is
           found
           to
           be
           at
           least
           ten
           thousand
           times
           as
           much
           as
           that
           of
           the
           Earth
           ,
           acting
           on
           Bodies
           at
           the
           same
           distances
           .
        
         
           This
           law
           of
           the
           decrease
           of
           Gravity
           being
           demonstratively
           proved
           ,
           and
           put
           past
           contradiction
           ;
           the
           Author
           with
           great
           Sagacity
           inquires
           into
           the
           necessary
           consequences
           of
           this
           Supposition
           ;
           whereby
           he
           finds
           the
           genuine
           cause
           of
           the
           several
           appearences
           in
           the
           Theory
           of
           the
           Moon
           and
           Planets
           ,
           and
           discovers
           the
           hitherto
           unknown
           laws
           of
           the
           Motion
           of
           Comets
           and
           of
           the
           Ebbing
           and
           Flowing
           of
           the
           Sea.
           Each
           of
           which
           are
           subjects
           that
           have
           heretofore
           taken
           up
           much
           larger
           Volumes
           ,
           but
           truth
           being
           uniforme
           and
           alwaies
           the
           same
           ,
           it
           is
           admirable
           to
           observe
           how
           
           easily
           and
           how
           satisfactorily
           Solutions
           are
           given
           in
           very
           abstruse
           and
           difficult
           matters
           ,
           when
           once
           true
           and
           genuine
           Principles
           are
           obtained
           :
           And
           on
           the
           other
           hand
           it
           may
           be
           wondred
           that
           ,
           notwithstanding
           the
           great
           facility
           of
           truth
           ,
           and
           the
           perplexity
           and
           nonconsequences
           that
           alwaies
           attend
           erronious
           suppositions
           ,
           these
           great
           discoveries
           should
           have
           escaped
           the
           Acute
           disquisitions
           of
           the
           best
           Philosophical
           Heads
           of
           all
           past
           ages
           ,
           and
           be
           reserved
           to
           be
           recorded
           to
           Posterity
           ,
           among
           the
           Glorious
           Acquisitions
           your
           Nations
           justly
           promise
           themselves
           ,
           during
           the
           course
           of
           your
           Majesties
           happy
           Reign
           over
           us
           :
        
         
           The
           Theory
           of
           the
           Motion
           of
           the
           primary
           Planets
           is
           here
           shewn
           to
           be
           nothing
           else
           ,
           but
           the
           contemplation
           of
           the
           Curve
           Lines
           which
           Bodies
           cast
           with
           a
           given
           velocity
           ,
           in
           a
           given
           direction
           ,
           and
           at
           the
           same
           time
           drawn
           towards
           the
           Sun
           by
           its
           gravitating
           Power
           ,
           would
           describe
           .
           Or
           ,
           which
           is
           all
           one
           ,
           that
           the
           Orbs
           of
           the
           Planets
           are
           such
           Curve
           Lines
           as
           a
           shot
           from
           a
           Gun
           describes
           in
           the
           Air
           ,
           being
           cast
           according
           to
           the
           direction
           of
           the
           Piece
           ,
           but
           bent
           into
           a
           crooked
           Line
           by
           the
           supervening
           tendency
           towards
           the
           Earths
           Center
           :
           And
           the
           Planets
           being
           supposed
           to
           be
           projected
           with
           a
           given
           force
           ,
           and
           attracted
           towards
           the
           Sun
           ,
           after
           the
           aforesaid
           manner
           ,
           are
           here
           proved
           to
           describe
           such
           Figures
           as
           answer
           punctually
           to
           all
           that
           the
           Industry
           of
           this
           and
           the
           last
           Age
           has
           observed
           in
           the
           Planetary
           Motions
           .
           So
           that
           it
           appears
           that
           there
           is
           no
           need
           of
           solid
           Orbs
           and
           Intelligences
           ,
           as
           the
           Ancients
           imagined
           ,
           nor
           yet
           of
           Vortices
           or
           Whirlpools
           of
           the
           Celestial
           Matter
           ,
           as
           
             Des
             Cartes
          
           supposes
           ;
           but
           the
           whole
           affair
           is
           simply
           and
           Mechanicall
           performed
           ,
           upon
           the
           sole
           supposition
           of
           a
           gravitation
           towards
           the
           Sun
           ;
           which
           cannot
           be
           denied
           .
        
         
           The
           Motion
           of
           Comets
           is
           here
           shewn
           to
           be
           compounded
           of
           the
           same
           Elements
           ,
           and
           not
           to
           differ
           from
           Planets
           ,
           but
           in
           their
           greater
           swiftness
           ,
           whereby
           overpowering
           the
           gravity
           that
           should
           hold
           them
           to
           the
           Sun
           ,
           as
           it
           does
           the
           Planets
           ,
           they
           flie
           off
           againe
           ,
           and
           distance
           themselves
           from
           the
           Sun
           and
           Earth
           ,
           so
           that
           they
           soon
           are
           
           out
           of
           sight
           :
           and
           the
           fewness
           and
           inaccuracy
           of
           the
           observations
           Antiquity
           has
           left
           us
           ,
           are
           not
           sufficient
           to
           determine
           whether
           the
           same
           Comet
           ever
           return
           again
           .
           But
           this
           Author
           has
           shewn
           how
           Geometrically
           to
           determine
           the
           Orb
           of
           a
           Comet
           from
           observations
           ,
           and
           to
           finde
           his
           distance
           from
           the
           Earth
           and
           Sun
           ,
           which
           was
           never
           before
           done
           .
        
         
           The
           third
           thing
           here
           done
           is
           the
           Theory
           of
           the
           Moon
           ,
           all
           the
           Inequalities
           of
           whose
           motion
           are
           proved
           to
           arise
           from
           the
           same
           principles
           ,
           only
           here
           the
           effect
           of
           two
           centers
           operating
           on
           or
           attracting
           a
           projected
           body
           comes
           to
           be
           considered
           ;
           for
           the
           Moon
           tho'
           principally
           attracted
           by
           the
           Earth
           and
           moving
           round
           it
           ,
           does
           together
           with
           the
           Earth
           move
           round
           the
           Sun
           once
           in
           a
           Year
           ,
           and
           is
           according
           as
           she
           is
           nearer
           or
           farther
           from
           the
           Sun
           ,
           drawn
           by
           him
           more
           or
           less
           than
           the
           Center
           of
           the
           Earth
           ,
           about
           which
           she
           moves
           ;
           whence
           arise
           several
           irregularities
           in
           her
           motion
           ,
           of
           all
           which
           the
           Author
           in
           this
           Book
           ,
           with
           no
           less
           subtilty
           than
           Industry
           ,
           has
           given
           a
           full
           account
           .
           And
           tho'
           by
           reason
           of
           the
           great
           complication
           of
           the
           problem
           ,
           he
           has
           not
           yet
           been
           able
           to
           make
           it
           purely
           Geometrical
           ,
           t
           is
           to
           be
           hoped
           ,
           that
           in
           some
           farther
           Essay
           he
           may
           surmount
           the
           difficulty
           ,
           and
           having
           perfected
           the
           Theory
           of
           the
           Moon
           ,
           the
           long
           desired
           discovery
           of
           the
           Longitude
           (
           which
           at
           Sea
           is
           only
           practicable
           this
           way
           )
           may
           at
           length
           be
           brought
           to
           light
           ,
           to
           the
           great
           honour
           of
           your
           Majesty
           and
           advantage
           of
           your
           Subjects
           .
        
         
           All
           the
           surprizing
           Phenomena
           of
           the
           Flux
           and
           Reflux
           of
           the
           Sea
           are
           in
           like
           manner
           shewn
           to
           proceed
           from
           the
           same
           principle
           ;
           which
           I
           design
           more
           largely
           to
           insist
           on
           ,
           since
           the
           matter
           of
           fact
           is
           in
           this
           case
           much
           better
           known
           to
           your
           Majesty
           than
           in
           the
           foregoing
           .
        
         
           If
           the
           Earth
           were
           alone
           ,
           that
           is
           to
           say
           ,
           not
           affected
           by
           the
           actions
           of
           the
           Sun
           and
           Moon
           ,
           it
           is
           not
           to
           be
           doubted
           but
           the
           Ocean
           being
           equally
           pressed
           by
           the
           force
           of
           Gravity
           towards
           the
           center
           ,
           would
           continue
           in
           a
           perfect
           stagnation
           ,
           always
           at
           the
           same
           hight
           ,
           
           without
           ebbing
           or
           flowing
           ;
           But
           it
           being
           not
           to
           be
           denied
           that
           the
           Sun
           and
           Moon
           have
           a
           like
           principle
           of
           Gravitation
           towards
           their
           Centers
           ,
           and
           that
           the
           Earth
           is
           within
           the
           activity
           of
           their
           attractions
           ,
           it
           will
           plainly
           follow
           that
           the
           equality
           of
           the
           pressure
           of
           Gravity
           towards
           the
           Center
           will
           thereby
           be
           disturbed
           ;
           and
           tho'
           the
           smallness
           of
           these
           forces
           ,
           in
           respect
           of
           the
           Gravitation
           towards
           the
           Earths
           Center
           ,
           renders
           them
           altogether
           imperceptible
           by
           any
           experiments
           we
           can
           devise
           ,
           yet
           the
           Ocean
           being
           fluid
           and
           yeilding
           to
           the
           least
           force
           ,
           by
           its
           rising
           shews
           where
           it
           is
           less
           prest
           ,
           and
           where
           it
           is
           more
           prest
           by
           its
           sinking
           .
        
         
           Now
           if
           we
           suppose
           the
           force
           of
           the
           Moons
           attraction
           to
           decrease
           as
           the
           square
           of
           the
           distance
           from
           its
           Center
           increases
           (
           as
           in
           the
           Earth
           and
           other
           Celestial
           Bodies
           )
           we
           shall
           find
           ,
           that
           where
           the
           Moon
           is
           perpendicularly
           either
           above
           or
           below
           the
           Horizon
           ,
           either
           in
           Zenith
           or
           Nadir
           ,
           there
           the
           force
           of
           Gravity
           is
           most
           of
           all
           diminished
           ,
           and
           consequently
           that
           there
           the
           Ocean
           must
           necessarily
           swell
           by
           the
           coming
           in
           of
           the
           water
           from
           those
           parts
           where
           the
           pressure
           is
           greatest
           ,
           viz.
           in
           those
           places
           where
           the
           Moon
           is
           near
           the
           Horizon
           :
           But
           that
           this
           may
           be
           the
           better
           understood
           ,
           I
           thought
           it
           needful
           to
           add
           the
           following
           Figure
           ,
           where
           M
           is
           the
           Moon
           ,
           E
           the
           Earth
           ,
           C
           its
           Center
           ,
           and
           Z
           the
           place
           where
           the
           Moon
           is
           in
           the
           Zenith
           ,
           N
           where
           in
           the
           Nadir
           .
        
         
         
           Now
           by
           the
           Hypothesis
           ,
           it
           is
           evident
           that
           the
           Water
           in
           Z
           being
           nearer
           ,
           is
           more
           drawn
           by
           the
           Moon
           than
           the
           Center
           of
           the
           Earth
           C
           ,
           and
           that
           again
           more
           than
           the
           water
           in
           N
           ,
           wherefore
           the
           water
           in
           Z
           has
           a
           tendency
           towards
           the
           Moon
           ,
           contrary
           to
           that
           of
           Gravity
           ,
           being
           equal
           to
           the
           excess
           of
           the
           Gravitation
           in
           Z
           above
           that
           in
           C
           :
           And
           in
           the
           other
           case
           ,
           the
           water
           in
           N
           ,
           tending
           
           less
           towards
           the
           Moon
           that
           the
           Center
           C
           ,
           is
           left
           behind
           ,
           by
           as
           much
           as
           is
           the
           difference
           of
           the
           Gravitations
           towards
           the
           Moon
           in
           C
           and
           N.
           This
           rightly
           understood
           ,
           it
           follows
           plainly
           that
           the
           Sea
           ,
           which
           otherwise
           would
           be
           Spherical
           ,
           upon
           the
           pressure
           of
           the
           Moon
           ,
           must
           form
           it self
           into
           a
           Spheroidal
           or
           Oval
           figure
           ,
           whose
           longest
           diameter
           is
           where
           the
           Moon
           is
           Vertical
           ,
           and
           shortest
           where
           she
           is
           in
           the
           Horizon
           ;
           and
           that
           the
           Moon
           shifting
           her
           position
           as
           she
           turns
           round
           the
           Earth
           once
           a
           day
           ,
           this
           Oval
           of
           water
           shifts
           with
           her
           ,
           occasioning
           thereby
           the
           two
           floods
           and
           ebbs
           observable
           in
           each
           25
           hours
           .
        
         
           And
           this
           may
           suffice
           as
           to
           the
           general
           cause
           of
           the
           Tides
           ;
           it
           remains
           now
           to
           shew
           how
           naturally
           this
           notion
           accounts
           for
           all
           the
           particulars
           that
           has
           been
           observed
           about
           them
           ;
           so
           that
           there
           can
           be
           no
           room
           left
           to
           doubt
           but
           that
           this
           is
           the
           true
           cause
           thereof
           .
        
         
           The
           Spring
           Tides
           upon
           the
           new
           and
           full
           Moons
           ,
           and
           Neap
           Tides
           on
           the
           Quarters
           are
           occasioned
           by
           the
           attractive
           force
           of
           the
           Sun
           in
           the
           new
           and
           full
           conspiring
           with
           the
           attraction
           of
           the
           Moon
           and
           producing
           a
           Tide
           by
           their
           united
           forces
           :
           whereas
           in
           the
           Quarters
           the
           Sun
           raises
           the
           water
           where
           the
           Moon
           depresses
           it
           ,
           and
           the
           contrary
           ;
           so
           as
           the
           Tides
           are
           made
           only
           by
           the
           difference
           of
           their
           attractions
           .
           That
           the
           force
           of
           the
           Sun
           is
           no
           greater
           in
           this
           case
           ,
           proceeds
           from
           the
           very
           small
           proportion
           the
           semidiameter
           of
           the
           Earth
           bares
           to
           the
           vast
           distance
           of
           the
           Sun.
           
        
         
           It
           is
           also
           observed
           that
           
             caeteris
             paribus
          
           the
           Aequinoctial
           Spring
           Tides
           in
           March
           and
           September
           ,
           or
           near
           them
           ,
           are
           the
           Highest
           ,
           and
           the
           Neap
           tides
           the
           Lowest
           ;
           which
           proceeds
           from
           the
           greater
           agitation
           of
           the
           Waters
           ,
           when
           the
           fluid
           Sphaeroid
           revolves
           about
           a
           great
           Circle
           of
           the
           Earth
           ,
           than
           when
           it
           turns
           about
           in
           a
           lesser
           Circle
           ;
           it
           being
           plain
           that
           if
           the
           Moon
           were
           constituted
           in
           the
           Pole
           and
           there
           stood
           ,
           that
           the
           Spheroid
           would
           have
           a
           fixt
           position
           ,
           and
           that
           it
           would
           be
           always
           high
           Water
           under
           the
           Poles
           ,
           and
           low
           Water
           every
           where
           under
           the
           Aequinoctial
           :
           and
           therefore
           the
           nearer
           the
           Moon
           approaches
           the
           Poles
           ,
           the
           less
           is
           the
           
           agitation
           of
           the
           Ocean
           :
           which
           is
           always
           greatest
           where
           the
           Moon
           is
           in
           the
           Aequinoctial
           ,
           or
           farthest
           distant
           from
           the
           Poles
           .
           Whence
           the
           Sun
           and
           Moon
           ,
           being
           either
           conjoyned
           or
           Opposite
           in
           the
           Aequinoctial
           ,
           produce
           the
           greatest
           Spring
           Tides
           ;
           and
           the
           subsequent
           Neap
           Tides
           ,
           being
           produced
           by
           the
           Tropical
           Moon
           in
           the
           Quarters
           ,
           are
           always
           the
           least
           Tides
           ;
           whereas
           in
           June
           and
           December
           the
           Spring
           Tides
           are
           made
           by
           the
           Tropical
           Sun
           and
           Moon
           ,
           and
           therefore
           less
           vigorous
           ;
           and
           the
           Neap
           Tides
           by
           the
           Aequinoctial
           Moon
           ,
           which
           therefore
           are
           the
           stronger
           ;
           hence
           it
           happens
           that
           the
           difference
           between
           the
           Spring
           and
           Neap
           Tides
           ,
           in
           these
           Months
           ,
           is
           much
           less
           considerable
           than
           in
           March
           and
           September
           .
           And
           the
           reason
           why
           the
           very
           Highest
           Spring
           Tides
           are
           found
           to
           be
           rather
           before
           the
           Vernal
           and
           after
           the
           Autumnal
           Equinox
           ,
           viz.
           in
           February
           and
           October
           ,
           than
           precisely
           upon
           them
           ,
           is
           because
           the
           Sun
           is
           nearer
           the
           Earth
           in
           the
           Winter
           Months
           ,
           and
           so
           comes
           to
           have
           a
           greater
           effect
           in
           producing
           the
           Tides
           .
        
         
           Hitherto
           we
           have
           considered
           such
           affections
           of
           the
           Tides
           as
           are
           Universal
           ,
           without
           relation
           to
           particular
           cases
           ;
           what
           follows
           from
           the
           differing
           Latitudes
           of
           places
           ,
           will
           be
           easily
           understood
           by
           the
           following
           figure
           .
        
         
         
           But
           the
           motions
           hitherto
           mentioned
           are
           somewhat
           altered
           by
           the
           libration
           of
           the
           water
           ,
           whereby
           tho'
           the
           Action
           of
           the
           Luminaries
           should
           cease
           ,
           the
           Flux
           and
           Reflux
           of
           the
           Sea
           would
           for
           some
           time
           continue
           :
           This
           conservation
           of
           the
           impressed
           motion
           diminishes
           the
           differences
           that
           otherwise
           would
           be
           between
           two
           consequent
           Tides
           ,
           and
           is
           the
           reason
           why
           the
           highest
           Spring-Tides
           are
           not
           percisely
           on
           the
           new
           and
           full
           Moons
           ,
           nor
           the
           Neapes
           on
           the
           Quarters
           ;
           but
           generally
           they
           are
           the
           third
           Tides
           after
           them
           ,
           and
           sometimes
           later
           .
        
         
         
           All
           these
           things
           would
           regularly
           come
           to
           pass
           ,
           if
           the
           whole
           Earth
           were
           covered
           with
           Sea
           very
           deep
           ;
           but
           by
           reason
           of
           the
           sholeness
           of
           some
           places
           ,
           and
           the
           narrowness
           of
           the
           Streights
           by
           which
           the
           Tides
           are
           in
           many
           cases
           propagated
           ;
           there
           arises
           a
           great
           diversity
           in
           the
           effect
           ,
           and
           not
           to
           be
           accounted
           for
           without
           an
           exact
           knowledg
           of
           all
           the
           circumstances
           of
           the
           places
           ,
           as
           of
           the
           position
           of
           the
           Land
           ,
           and
           the
           breadth
           and
           depth
           of
           the
           Channels
           by
           which
           the
           Tide
           flows
           ;
           for
           a
           very
           slow
           and
           imperceptible
           motion
           of
           the
           whole
           body
           of
           the
           water
           ,
           where
           it
           is
           (
           for
           example
           )
           2
           miles
           deep
           ,
           will
           suffice
           to
           raise
           its
           surface
           10
           or
           12
           feet
           in
           a
           Tides
           time
           ;
           whereas
           if
           the
           same
           quantity
           of
           water
           were
           to
           be
           conveied
           upon
           a
           channel
           of
           40
           fathoms
           deep
           ,
           it
           would
           require
           a
           very
           great
           stream
           to
           effect
           it
           ,
           in
           so
           large
           Inlets
           as
           are
           the
           Channel
           of
           England
           and
           the
           
             German
             Ocean
          
           ;
           whence
           the
           Tide
           is
           found
           to
           set
           strongest
           in
           those
           places
           where
           the
           Sea
           grows
           nar●owest
           ;
           the
           same
           quantity
           of
           water
           being
           to
           pass
           through
           a
           smaller
           passage
           :
           this
           is
           most
           evident
           in
           the
           Streights
           between
           Portland
           and
           
             Cape
             de
             Hague
          
           in
           Normandy
           ,
           where
           the
           Tide
           runs
           like
           a
           sluice
           ;
           and
           it
           would
           be
           yet
           more
           between
           Dover
           and
           Calais
           ,
           if
           the
           Tide
           coming
           about
           the
           Island
           from
           the
           North
           did
           not
           check
           it
           .
           And
           this
           force
           being
           once
           impressed
           upon
           the
           water
           ,
           continues
           to
           carry
           it
           about
           the
           level
           of
           the
           ordinary
           hight
           in
           the
           Ocean
           ,
           particularly
           where
           the
           water
           meets
           a
           direct
           obstacle
           ,
           as
           it
           is
           at
           St.
           Malo's
           ;
           and
           where
           it
           enters
           into
           a
           long
           channell
           ,
           which
           running
           far
           into
           the
           land
           ,
           grows
           very
           streight
           at
           its
           extremity
           ;
           as
           it
           is
           in
           the
           Severn-Sea
           at
           Chepstow
           and
           Bristol
           .
        
         
           This
           sholeness
           of
           the
           Sea
           and
           the
           intercurrent
           Continents
           are
           the
           reason
           that
           in
           the
           open
           Ocean
           the
           time
           of
           high
           water
           is
           not
           at
           the
           Moons
           appulse
           to
           the
           Meridian
           ,
           but
           always
           some
           hours
           after
           it
           ;
           as
           it
           is
           observed
           upon
           all
           the
           West
           Coast
           of
           Europe
           and
           Africa
           ,
           from
           Ireland
           to
           the
           Cape
           of
           Good-Hope
           :
           in
           all
           which
           a
           S.
           W.
           Moon
           makes
           high
           Water
           ;
           and
           the
           same
           is
           reported
           to
           be
           on
           the
           West
           side
           of
           America
           .
           But
           it
           would
           be
           endless
           to
           accont
           
           for
           all
           those
           particularities
           ,
           which
           are
           consequences
           of
           this
           Hypothesis
           ;
           as
           why
           Lakes
           ,
           such
           as
           the
           
             Caspian
             Sea
          
           ;
           and
           Mediterranian-Seas
           such
           as
           the
           Black-Sea
           ,
           the
           Streights
           and
           Baltick
           ,
           have
           no
           sensible
           Tides
           :
           For
           Lakes
           having
           no
           communication
           with
           the
           Ocean
           ,
           can
           neither
           encrease
           nor
           diminish
           their
           Water
           ,
           whereby
           to
           rise
           and
           fall
           ;
           and
           Seas
           that
           communicate
           by
           such
           narrow
           Inletts
           and
           are
           of
           so
           immense
           an
           extent
           ,
           cannot
           in
           a
           few
           hours
           time
           receive
           or
           empty
           Water
           enough
           to
           raise
           or
           sink
           their
           Surface
           any
           thing
           sensibly
           .
        
         
           Lastly
           to
           demonstrate
           the
           excellency
           of
           this
           Doctrine
           ,
           the
           example
           of
           the
           Tides
           in
           the
           Port
           of
           Tunking
           in
           China
           ,
           which
           are
           so
           extraordinary
           and
           differing
           from
           all
           others
           wee
           have
           yet
           heard
           of
           ,
           may
           suffice
           .
           In
           this
           Port
           there
           is
           but
           one
           Flood
           and
           Ebb
           in
           24
           hours
           ;
           and
           twice
           in
           each
           Month
           ,
           viz.
           when
           the
           Moon
           is
           near
           the
           Equinoctial
           ,
           there
           is
           no
           Tide
           at
           all
           ,
           but
           the
           Water
           is
           stagnant
           ;
           but
           with
           the
           Moons
           declination
           there
           begins
           a
           Tide
           which
           is
           greatest
           when
           she
           is
           in
           the
           Tropical
           Signs
           :
           only
           with
           this
           difference
           ,
           that
           when
           the
           Moon
           is
           to
           the
           Northward
           of
           the
           Aequinoctial
           ,
           it
           flows
           when
           she
           is
           above
           the
           Earth
           ,
           and
           Ebbs
           when
           she
           is
           under
           ,
           so
           as
           to
           make
           high
           Water
           at
           Moons
           setting
           ,
           and
           low
           Water
           at
           Moons
           rising
           :
           But
           on
           the
           contrary
           the
           Moon
           being
           to
           the
           Southward
           makes
           high
           water
           at
           rising
           and
           low
           water
           at
           setting
           ,
           it
           Ebbing
           all
           the
           time
           she
           is
           above
           the
           Horizon
           .
           As
           may
           be
           seen
           more
           at
           large
           in
           the
           
             Philosophical
             Transaction
          
           Num.
           162.
           
        
         
           The
           Cause
           of
           this
           odd
           Appearance
           is
           proposed
           by
           Mr.
           Newton
           ,
           to
           be
           from
           the
           concurrence
           of
           two
           Tides
           ;
           the
           one
           propagated
           in
           six
           hours
           out
           of
           the
           great
           South-Sea
           ,
           along
           the
           Coast
           of
           China
           ;
           the
           other
           out
           of
           the
           Indian-Sea
           ,
           from
           between
           the
           Islands
           ,
           in
           twelve
           hours
           ,
           along
           the
           Coast
           of
           Malacca
           and
           Cambodia
           .
           The
           one
           of
           these
           Tides
           ,
           being
           produced
           in
           North
           Latitude
           ,
           is
           ,
           as
           has
           been
           said
           ,
           greater
           ,
           when
           the
           Moon
           being
           to
           the
           North
           of
           the
           Equator
           is
           above
           the
           Earth
           ,
           and
           less
           when
           she
           is
           under
           the
           
           Earth
           ;
           and
           contrarywise
           the
           other
           Tide
           that
           comes
           out
           of
           the
           Indian-Sea
           ,
           being
           raised
           in
           South
           Latitude
           ,
           is
           greater
           when
           the
           Moon
           declining
           to
           the
           South
           is
           above
           the
           Earth
           ,
           and
           less
           when
           she
           is
           under
           the
           Earth
           :
           so
           that
           of
           these
           Tides
           alternately
           greater
           and
           lesser
           ,
           there
           comes
           alwaies
           successively
           two
           of
           the
           greater
           and
           two
           of
           the
           lesser
           together
           every
           day
           ;
           and
           the
           high-water
           falls
           alwais
           between
           the
           times
           of
           the
           arrival
           of
           the
           two
           greater
           Floods
           ,
           and
           the
           low-water
           between
           the
           arrival
           of
           the
           two
           lesser
           Floods
           .
           And
           the
           Moon
           coming
           to
           the
           Equinoctial
           ,
           and
           the
           alternate
           Floods
           becoming
           equal
           ,
           this
           Tide
           ceases
           and
           the
           Water
           stagnates
           :
           but
           when
           she
           has
           passed
           to
           the
           other
           side
           of
           the
           Equator
           ,
           those
           Floods
           which
           in
           the
           former
           order
           were
           the
           least
           ,
           now
           becoming
           the
           greatest
           ,
           that
           that
           before
           was
           the
           time
           of
           high
           water
           now
           becomes
           the
           low-water
           ,
           and
           the
           converse
           .
           So
           that
           the
           whole
           appearence
           of
           these
           strange
           Tides
           ,
           is
           without
           any
           forcing
           naturally
           deduced
           from
           these
           principles
           ,
           and
           is
           a
           great
           argument
           of
           the
           certainty
           of
           the
           whole
           Theory
           .
        
         
           If
           by
           reason
           of
           the
           difficulty
           of
           the
           Matter
           ,
           there
           be
           any
           thing
           herein
           not
           sufficiently
           explained
           ,
           or
           if
           there
           be
           any
           material
           thing
           observable
           in
           the
           Tides
           that
           I
           have
           omitted
           ,
           wherein
           your
           Majesty
           shall
           desire
           to
           be
           satisfied
           ,
           I
           doubt
           not
           but
           if
           your
           Majesty
           shall
           please
           to
           suffer
           me
           to
           be
           admited
           to
           the
           honour
           of
           your
           
             Royal
             Presence
          
           ,
           I
           may
           be
           able
           to
           give
           such
           an
           account
           thereof
           as
           may
           be
           to
           your
           Majesties
           full
           content
           .