Sciothericum telescopicum, or, A new contrivance of adapting a telescope to an horizontal dial for observing the moment of time by day or night useful in all astronomical observations, and for regulating and adjusting curious pendulum-watches and other time-keepers, with proper tables requisite thereto / by William Molyneux ...
         Molyneux, William, 1656-1698.
      
       
         
           1686
        
      
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         ESTC R10281
         12533872
         ocm 12533872
         62821
         
           
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             Sciothericum telescopicum, or, A new contrivance of adapting a telescope to an horizontal dial for observing the moment of time by day or night useful in all astronomical observations, and for regulating and adjusting curious pendulum-watches and other time-keepers, with proper tables requisite thereto / by William Molyneux ...
             Molyneux, William, 1656-1698.
          
           [10], 54, [37] p., 1 folded leaf of plates.
           
             Printed by Andrew Crook and Samuel Helsham ..., and are to be sold by W. Norman ..., and S. Helsham and El. Dobson ...,
             Dublin :
             1686.
          
           
             This item appears at reel 769:2 incorrectly identified as Wing M2406, and at reel 1729:25 as Wing M2406A.
             Reproduction of original in Huntington Library.
          
        
      
    
     
       
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           Time measurements -- Early works to 1800.
           Astronomical instruments.
        
      
    
     
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           Sciothericum
           Telescopicum
           ;
           OR
           ,
           A
           New
           Contrivance
           of
           Adapting
           a
           TELESCOPE
           TO
           AN
           Horizontal
           Dial
           FOR
           OBSERVING
           The
           moment
           of
           Time
           by
           Day
           or
           Night
           :
           Useful
           in
           all
           
             Astronomical
             Observations
          
           ,
           and
           for
           Regulating
           and
           Adjusting
           Curious
           Pendulum-Watches
           and
           other
           Time-Keepers
           ,
           With
           proper
           Tables
           Requisite
           thereto
           .
        
         
           By
           
             William
             Molyneux
          
           
             Esq
          
           Fellow
           of
           the
           
             Royal
             Society
          
           ,
           and
           of
           that
           in
           Dublin
           .
        
         
           DVBLIN
           ,
           Printed
           by
           
             Andrew
             Crook
          
           and
           
             Samuel
             Helsham
          
           ,
           at
           the
           Printing-House
           on
           Ormond-Key
           ;
           and
           are
           to
           be
           sold
           by
           
             W.
             Norman
          
           in
           Dame-street
           ,
           and
           
             S.
             Helsham
          
           and
           
             El.
             Dobson
          
           Booksellers
           in
           Castle-street
           ,
           1686.
           
        
      
       
         
         
         
           TO
           HIS
           EXCELLENCY
           Henry
           Earl
           of
           Clarendon
           ,
           LORD
           Lieutenant
           General
           ,
           AND
           GENERAL
           GOVERNOUR
           OF
           His
           MAJESTIES
           Kingdom
           OF
           IRELAND
           .
        
         
           THe
           great
           Honour
           Your
           Excellency
           was
           pleased
           to
           shew
           Our
           Society
           in
           accepting
           Our
           Congratulation
           at
           Your
           happy
           Arrival
           and
           Settlement
           in
           the
           Government
           of
           this
           Kingdom
           ,
           and
           in
           giving
           us
           Your
           Incouragement
           in
           prosecuting
           our
           
             Philosophical
             Designs
          
           ,
           
           does
           necessarily
           require
           from
           us
           all
           possible
           Returns
           of
           Gratitude
           .
           And
           though
           what
           I
           now
           Present
           
             Your
             Excellency
          
           may
           seem
           unfit
           to
           begin
           withal
           ,
           yet
           I
           could
           not
           omit
           this
           opportunity
           of
           expressing
           to
           
             Your
             Lordship
          
           the
           deep
           sense
           I
           have
           of
           
             Your
             Favours
          
           to
           us
           ,
           and
           to
           Philosophy
           .
           And
           certainly
           ,
           my
           Lord
           ,
           
             True
             Philosophy
          
           does
           highly
           deserve
           Encouragement
           from
           the
           Wise
           ,
           the
           Great
           ,
           and
           Powerful
           ;
           the
           most
           
             Learned
             Universities
          
           have
           at
           all
           times
           made
           
             Natural
             Philosophy
          
           and
           Mathematicks
           a
           great
           Branch
           of
           their
           Literature
           ,
           and
           we
           see
           how
           universaly
           
             Academick
             Knowledge
          
           has
           been
           approved
           of
           by
           the
           great
           Encouragement
           and
           large
           Priviledges
           the
           Schools
           have
           received
           from
           our
           
             Wisest
             Princes
          
           ,
           and
           by
           the
           general
           agreement
           of
           the
           most
           sober
           and
           
             considerate
             men
          
           ,
           in
           sending
           their
           Youth
           to
           receive
           their
           Education
           therein
           .
           This
           shews
           how
           universaly
           
             Philosophick
             Learning
          
           has
           been
           approved
           ;
           and
           the
           only
           Question
           that
           can
           be
           raised
           at
           present
           is
           ,
           Whether
           the
           
             Natural
             Philosophy
          
           formerly
           professed
           in
           the
           Schools
           ,
           or
           that
           which
           is
           at
           present
           prosecuted
           by
           the
           Societies
           lately
           Instituted
           in
           several
           the
           most
           noted
           parts
           of
           Europe
           ,
           be
           the
           
             True
             Philosophy
          
           ,
           or
           method
           of
           
             Investigating
             Nature
          
           .
           But
           surely
           this
           will
           be
           no
           longer
           a
           doubt
           ,
           when
           we
           consider
           how
           unsatisfactory
           were
           the
           
             ancient
             Notions
             of
             Philosophy
          
           ,
           which
           then
           consisted
           rather
           in
           Disputes
           ,
           and
           Verbose
           empty
           Stuff
           ,
           than
           in
           any
           Curious
           Discovery
           of
           
             Natures
             Actions
          
           .
           If
           a
           man
           could
           prove
           Pro
           and
           Con
           ,
           whatever
           was
           proposed
           ,
           and
           maintain
           
           this
           Dispute
           for
           two
           or
           three
           hours
           by
           vain
           Distinctions
           and
           idle
           Evasions
           ,
           he
           presently
           gain'd
           the
           Name
           of
           a
           Philosopher
           ,
           tho
           all
           the
           while
           he
           had
           no
           manner
           of
           Notions
           in
           his
           Brain
           answerable
           to
           those
           senseless
           words
           he
           threw
           out
           .
           I
           would
           fain
           know
           ,
           what
           Notion
           any
           man
           has
           of
           Light
           upon
           pronouncing
           the
           definition
           of
           it
           ,
           
             Actus
             Perspicui
             quatenus
             Perspicuum
          
           ,
           does
           he
           hereby
           in
           the
           least
           understand
           any
           of
           the
           properties
           of
           Light
           ,
           or
           how
           't
           is
           affected
           by
           Refraction
           or
           Reflection
           ?
           or
           does
           this
           Definition
           lead
           him
           to
           improve
           Light
           for
           the
           advancement
           and
           help
           of
           our
           senses
           ,
           or
           other
           advantage
           of
           mankind
           ?
           And
           now
           ,
           
             my
             Lord
          
           ,
           if
           this
           kind
           of
           Philosophy
           which
           formerly
           fill'd
           our
           Schools
           were
           look'd
           upon
           as
           deserving
           the
           Favour
           of
           the
           Great
           ,
           how
           much
           more
           shall
           the
           present
           useful
           Enquiries
           of
           the
           Ingenious
           deserve
           Incouragement
           ?
           But
           that
           this
           may
           be
           made
           a
           little
           more
           evident
           (
           though
           I
           am
           perswaded
           't
           is
           sufficiently
           manifest
           already
           to
           
             Your
             Excellencys
          
           Discerning
           Judgment
           )
           I
           shall
           crave
           leave
           to
           be
           more
           particular
           in
           this
           matter
           ;
           And
           I
           shall
           begin
           with
           one
           of
           the
           most
           Considerable
           and
           Vniversal
           Concerns
           of
           
             Mans
             Life
          
           ,
           I
           mean
           Navigation
           ,
           wherein
           the
           Philosophy
           of
           the
           Moderns
           has
           been
           very
           much
           Exercised
           ;
           The
           Magnet
           by
           its
           Caprichious
           Variations
           is
           at
           present
           in
           several
           parts
           of
           the
           World
           rendred
           almost
           useless
           ;
           but
           diligent
           search
           is
           daily
           made
           after
           its
           Vagarys
           ,
           that
           we
           may
           not
           be
           deprived
           of
           the
           unspeakable
           benefit
           of
           one
           of
           the
           most
           surprising
           Phenomenas
           in
           Nature
           .
           Certainly
           men
           might
           
           have
           Disputed
           from
           Age
           to
           Age
           of
           
             Sympathy
             ,
             Antipathy
          
           ,
           and
           the
           
             Occult
             Qualities
          
           of
           the
           Loadstone
           ,
           before
           they
           should
           ever
           arrive
           to
           the
           Knowledge
           or
           Rectification
           of
           one
           of
           these
           Exorbitances
           ,
           which
           diligent
           
             Experimental
             Philosophy
          
           presently
           discovers
           ,
           and
           further
           Experiments
           may
           hope
           to
           Rectify
           .
           In
           relation
           likewise
           no
           Navigation
           are
           all
           the
           Enquiries
           into
           the
           Theory
           of
           the
           Tides
           ,
           and
           the
           
             Moons
             motion
          
           ,
           all
           the
           Endeavours
           for
           the
           Longitude
           ,
           and
           the
           Diligence
           used
           to
           Rectify
           Astronomy
           .
           The
           Philosophy
           of
           Hydraulicks
           and
           Hydrostaticks
           tends
           to
           the
           great
           Emolument
           and
           Pleasure
           of
           Mankind
           ,
           no
           place
           being
           habitable
           without
           Water
           ,
           and
           Curious
           Fountains
           adorn
           the
           Gardens
           and
           Houses
           of
           the
           Greatest
           Princes
           .
           Agriculture
           ,
           and
           the
           Philosophy
           relating
           to
           Earth
           and
           Vegitation
           ,
           is
           of
           universal
           extent
           over
           the
           face
           of
           the
           World
           ;
           and
           how
           mightily
           it
           has
           been
           lately
           prosecuted
           ,
           is
           evident
           from
           the
           Incomparable
           Works
           of
           Mr.
           Evelyn
           and
           others
           .
           By
           the
           
             Doctrine
             of
             Light
          
           ,
           and
           the
           Properties
           thereof
           ,
           our
           most
           Noble
           Sense
           has
           been
           Improved
           to
           an
           Acuteness
           some
           thousands
           of
           degrees
           beyond
           its
           natural
           Abilities
           ;
           and
           the
           Telescope
           and
           Microscope
           discover
           to
           us
           new
           Worlds
           and
           Animals
           ,
           extending
           the
           Creation
           farther
           than
           't
           was
           possible
           for
           the
           Ancients
           to
           imagine
           .
           There
           is
           no
           state
           of
           Life
           that
           is
           not
           concern'd
           in
           Meteorology
           ,
           or
           the
           
             Philosophy
             of
             the
             Weather
          
           .
           And
           all
           that
           have
           heard
           of
           the
           late
           contrived
           
             Baroscopes
             ,
             Hygroscopes
             ,
             Thermoters
          
           ,
           &c.
           may
           plainly
           perceive
           what
           Endeavours
           have
           been
           made
           towards
           it
           ,
           and
           their
           success
           .
        
         
         
           I
           might
           proceed
           on
           ,
           and
           fill
           a
           Volume
           with
           Instances
           to
           Your
           Excellency
           of
           the
           usefulness
           of
           an
           Active
           
             Experimental
             Philosophy
          
           ;
           but
           I
           stop
           my
           hand
           ,
           and
           shall
           only
           declare
           in
           short
           ,
           that
           from
           this
           alone
           we
           are
           to
           expect
           advancements
           in
           the
           most
           important
           concerns
           of
           humane
           life
           ;
           the
           Virtues
           of
           
             Animals
             ,
             Plants
          
           and
           Minerals
           for
           the
           health
           of
           mans
           Body
           ,
           Architecture
           Civil
           and
           Military
           for
           the
           pleasure
           and
           security
           of
           his
           life
           ;
           all
           kind
           of
           Machines
           and
           Movements
           for
           the
           increase
           and
           due
           application
           of
           his
           strength
           ,
           proceed
           from
           this
           kind
           of
           Philosophy
           ,
           which
           consists
           in
           Actions
           ,
           not
           in
           Words
           ,
           and
           prosecutes
           and
           sometimes
           
             Improves
             Nature
          
           by
           the
           same
           steps
           that
           she
           her self
           acts
           by
           .
           And
           indeed
           ,
           my
           Lord
           ,
           if
           we
           consider
           Nature
           as
           an
           Active
           Principle
           ,
           we
           must
           needs
           acknowledge
           that
           she
           is
           to
           be
           prosecuted
           by
           Action
           ,
           and
           not
           by
           
             Verbose
             Disputes
          
           ;
           There
           is
           nothing
           that
           the
           mind
           of
           man
           will
           not
           find
           something
           to
           say
           for
           or
           against
           all
           day
           long
           ;
           and
           therefore
           of
           the
           School-Disputes
           there
           is
           no
           end
           ;
           but
           Experiment
           is
           matter
           of
           Fact
           ,
           and
           strikes
           the
           Senses
           so
           forcibly
           ,
           that
           there
           is
           no
           opposing
           it
           .
           Who
           is
           it
           that
           will
           now
           question
           the
           force
           of
           Gun-powder
           ,
           or
           whether
           the
           Mercury
           rise
           and
           fall
           in
           the
           Baroscope
           at
           fair
           or
           foul
           Weather
           ?
        
         
           'T
           is
           therefore
           this
           
             Philosophy
             (
             may
             it
             please
             Your
             Excellency
             )
          
           that
           deserves
           Favour
           and
           Incouragement
           from
           the
           Powerful
           and
           Wise
           ;
           and
           as
           God
           has
           made
           all
           things
           in
           
             number
             ,
             measure
          
           ,
           and
           weight
           ,
           that
           Learning
           which
           teaches
           us
           the
           affections
           
           of
           number
           and
           measure
           ,
           as
           being
           the
           Foundation
           on
           which
           
             true
             Philosophy
          
           is
           to
           be
           superstructed
           ,
           is
           chiefly
           to
           be
           respected
           .
           There
           is
           no
           part
           of
           Philosophy
           wherein
           the
           Mathematicks
           are
           not
           deeply
           ingredient
           ,
           and
           on
           them
           depend
           the
           
             Arts
             of
             War
          
           as
           the
           
             Delights
             of
             Peace
          
           ,
           and
           even
           Sacred
           Theology
           it self
           is
           in
           a
           great
           measure
           beholding
           hereto
           for
           its
           help
           ,
           if
           we
           consider
           how
           far
           the
           Chronology
           of
           the
           
             Holy
             Scriptures
          
           is
           help'd
           out
           by
           Astronomy
           ,
           and
           the
           Doctrine
           of
           Eclipses
           .
        
         
           And
           as
           I
           have
           presumed
           to
           detain
           
             Your
             Excellency
          
           thus
           long
           ,
           in
           declaring
           how
           
             true
             Philosophy
          
           deserves
           Your
           Protection
           ,
           so
           give
           me
           leave
           to
           add
           one
           word
           more
           in
           declaring
           how
           
             Your
             Excellency
          
           deserves
           the
           Tutelage
           of
           true
           Philosophy
           .
           Your
           
             Illustrious
             Father
          
           ,
           of
           Happy
           Memory
           ,
           was
           no
           unactive
           
             Speculative
             Philosopher
          
           ,
           but
           was
           zealous
           and
           forward
           in
           promoting
           the
           Noble
           Design
           of
           the
           
             Royal
             Society
          
           ,
           as
           appears
           to
           his
           immortal
           Praise
           in
           their
           
             Incomparable
             History
          
           ,
           and
           by
           their
           Electing
           him
           ,
           and
           his
           willing
           Complyance
           to
           be
           their
           Protector
           .
           Neither
           did
           he
           only
           countenance
           Philosophy
           by
           his
           Authority
           and
           Favour
           ,
           but
           actually
           drew
           the
           Sword
           in
           its
           defence
           against
           the
           great
           
             Sea
             Monster
          
           that
           would
           have
           destroy'd
           the
           Virgin
           ;
           as
           is
           manifest
           from
           his
           Learned
           and
           
             Ingenious
             Treatise
          
           against
           the
           Leviathan
           .
           All
           the
           World
           that
           know
           
             Your
             Lordship
          
           ,
           must
           acknowledge
           that
           this
           and
           other
           his
           extraordinary
           Virtues
           are
           entail'd
           on
           
             Your
             Excellency
          
           ,
           who
           has
           not
           buried
           the
           Talent
           in
           a
           Napkin
           ,
           but
           improved
           
           it
           to
           an
           high
           degree
           .
           
             Your
             Excellency
          
           has
           Honoured
           the
           
             Royal
             Society
          
           by
           being
           one
           of
           their
           Number
           ,
           and
           their
           
             last
             years
             Council
          
           was
           compleated
           by
           Your
           being
           one
           of
           them
           .
           So
           that
           upon
           all
           occasions
           
             Your
             Excellency
          
           has
           shewn
           Your Self
           a
           zealous
           Patron
           of
           Learning
           and
           Ingenuity
           ;
           and
           though
           I
           dare
           not
           on
           either
           score
           challenge
           
             Your
             Excellency's
             Protection
          
           of
           what
           I
           here
           present
           You
           ,
           for
           I
           am
           afraid
           to
           trust
           my
           own
           Judgment
           in
           my
           own
           Concern
           ;
           yet
           I
           will
           presume
           to
           implore
           
             Your
             Favour
          
           towards
           it
           as
           't
           is
           new
           ,
           and
           not
           disliked
           by
           some
           
             Ingenious
             Men
          
           to
           whom
           I
           have
           shewn
           it
           .
           Whether
           it
           may
           deserve
           
             Your
             Excellency's
          
           Countenance
           for
           its
           Vse
           and
           Advantage
           ,
           I
           leave
           to
           Your
           own
           discerning
           Thought
           ,
           after
           
             Your
             Lordship
          
           is
           pleased
           to
           consider
           what
           I
           offer
           in
           the
           First
           and
           Second
           Chapters
           .
           However
           ,
           this
           I
           will
           venture
           to
           assert
           before-hand
           ,
           that
           as
           Clocks
           or
           Time-keepers
           by
           Wheels
           and
           Weights
           have
           been
           an
           ancient
           Invention
           ,
           (
           if
           we
           believe
           
             Severinus
             Boethius
          
           to
           be
           the
           first
           Author
           of
           them
           ,
           't
           is
           above
           1100
           years
           ago
           )
           yet
           in
           these
           later
           days
           they
           have
           received
           a
           most
           high
           advancement
           (
           to
           the
           immortal
           glory
           of
           
             M
             nsr
             Hugens
          
           .
           )
           by
           the
           addition
           of
           a
           plain
           and
           simple
           Swag
           or
           Pendulum
           ;
           since
           the
           days
           of
           Hezekiah
           ,
           wherein
           we
           first
           find
           Dials
           mentioned
           ,
           I
           have
           not
           heard
           of
           a
           more
           plain
           and
           easy
           addition
           for
           the
           advancement
           of
           Dials
           ,
           and
           inlarging
           and
           ascertaining
           their
           Vse
           ,
           than
           what
           I
           here
           propose
           .
           And
           though
           I
           shall
           not
           be
           so
           vain
           ,
           as
           to
           expect
           its
           sudden
           propagation
           ,
           or
           any
           great
           Glory
           from
           the
           Contrivance
           ;
           
           yet
           if
           I
           can
           be
           so
           happy
           as
           thereby
           to
           Divert
           and
           Please
           
             Your
             Excellency
          
           ,
           and
           in
           some
           measure
           to
           purchase
           Your
           Favour
           ,
           't
           is
           the
           highest
           Ambition
           of
        
         
           
             Your
             Excellencies
             Most
             Obedient
             Humble
             Servant
             ,
             WILL.
             MOLYNEVX
             .
          
           
             Dublin
             ,
             
               April
               17.
               1686.
               
            
          
        
      
    
     
       
         
         
           Sciothericum
           Telescopicum
           ,
           OR
           ,
           A
           New
           Contrivance
           of
           Adapting
           a
           Telescope
           To
           a
           large
           Horizontal
           Dial
           ,
           for
           observing
           the
           moment
           of
           Time
           by
           Day
           or
           Night
           .
        
         
           
             CHAP.
             I.
             The
             Vse
             and
             Advantages
             of
             this
             Contrivance
             .
          
           
             EVery
             one
             the
             least
             versed
             in
             Astronomy
             ,
             does
             know
             of
             what
             great
             Concernment
             the
             Observation
             of
             the
             exact
             Moment
             of
             Time
             is
             therein
             .
             Without
             this
             no
             Celestial
             Observation
             can
             be
             performed
             Accurately
             ,
             and
             Astronomy
             is
             like
             to
             receive
             but
             little
             advancements
             .
             Hereby
             the
             
               Tables
               Astronomical
            
             are
             approved
             or
             rejected
             ,
             and
             Calculations
             found
             true
             or
             false
             .
             So
             that
             whatever
             advantages
             we
             propose
             to
             our selves
             by
             a
             Correct
             Astronomy
             ,
             we
             shall
             find
             our
             present
             Indeavour
             to
             be
             helpful
             towards
             them
             .
             And
             certainly
             there
             are
             some
             signal
             uses
             expected
             from
             it
             ,
             since
             so
             many
             
               Kings
               ,
               Princes
               ,
               States
            
             ,
             and
             Learned
             Men
             in
             all
             Ages
             ,
             particularly
             our
             late
             and
             our
             present
             Soveraign
             of
             Great-Brittain
             ,
             The
             present
             
               French
               King
            
             ,
             and
             formerly
             some
             Kings
             
             of
             Denmark
             ,
             have
             been
             at
             such
             great
             expences
             both
             of
             
               Time
               ,
               Labour
            
             ,
             and
             Charges
             ,
             for
             the
             advancement
             thereof
             .
             But
             I
             shall
             pass
             by
             all
             other
             excellent
             uses
             that
             are
             expected
             from
             an
             
               Accurate
               Theory
            
             of
             the
             motions
             of
             the
             
               Heavenly
               Bodies
            
             ,
             and
             shall
             only
             insist
             on
             one
             particular
             ,
             wherein
             the
             Observation
             of
             the
             exact
             Moment
             of
             Time
             does
             more
             immediately
             tend
             to
             the
             use
             of
             mankind
             .
             We
             all
             know
             how
             universaly
             the
             whole
             World
             is
             concern'd
             in
             Navigation
             and
             Commerce
             ,
             by
             Ships
             flying
             before
             the
             winds
             ,
             and
             floating
             on
             the
             
               Seas
               ;
               Nation
            
             converses
             with
             Nation
             ,
             as
             every
             man
             with
             another
             by
             words
             flying
             in
             the
             Air
             ;
             by
             this
             ,
             Civility
             ,
             Learning
             ,
             and
             all
             Politeness
             is
             propagated
             ;
             we
             are
             made
             acquainted
             with
             one
             anothers
             
               Laws
               ,
               Constitutions
            
             and
             Manners
             ,
             we
             mutually
             reap
             the
             Fruits
             of
             each
             others
             Countrys
             ,
             and
             are
             no
             longer
             Strangers
             ,
             but
             Fellow-Citizens
             of
             the
             World.
             And
             for
             all
             these
             advantages
             (
             at
             least
             for
             our
             more
             securely
             reaping
             these
             benefits
             )
             we
             are
             in
             a
             great
             measure
             ,
             if
             not
             wholly
             ,
             beholding
             to
             Astronomy
             .
             For
             whoever
             has
             but
             inquired
             into
             the
             first
             Rudiments
             of
             that
             Science
             ,
             does
             very
             well
             know
             ,
             how
             far
             the
             determination
             of
             the
             Longitude
             of
             places
             ,
             and
             consequently
             the
             advancement
             of
             Geography
             and
             Navigation
             depends
             thereon
             .
             But
             whether
             this
             be
             attempted
             by
             Eclipses
             of
             the
             
               Sun
               ,
               Moon
            
             ,
             or
             Stars
             ,
             or
             by
             the
             Immersions
             and
             Emersions
             of
             
             Jupiter's
             Satellits
             into
             or
             from
             his
             shadow
             ,
             or
             by
             the
             
               Pendulum
               Clock
            
             ,
             at
             Sea
             ,
             &c.
             
             In
             
             all
             these
             methods
             the
             Observation
             of
             the
             exact
             Moment
             of
             time
             is
             necessary
             ,
             for
             otherwise
             the
             Horary
             distance
             of
             the
             place
             of
             Observation
             ,
             and
             consequently
             the
             distance
             on
             the
             Aequator
             ,
             or
             Longitude
             ,
             from
             an
             assigned
             place
             shall
             be
             uncertain
             .
          
        
         
           
             CHAP.
             II.
             Of
             the
             Methods
             used
             for
             observing
             the
             Exact
             Moment
             of
             Time
             ,
             and
             their
             Inconveniencies
             and
             Troubles
             .
          
           
             THE
             common
             ways
             used
             by
             Astronomers
             for
             observing
             the
             Time
             are
             ,
             either
             by
             Dials
             ,
             or
             by
             taking
             the
             
               Suns
               Altitude
            
             by
             day
             ,
             or
             by
             the
             Altitude
             of
             fixt
             Stars
             by
             night
             ,
             taken
             by
             large
             and
             accurate
             Instruments
             ;
             or
             by
             observing
             the
             Altitude
             and
             Azimuth
             of
             the
             Sun
             or
             Stars
             ,
             or
             lastly
             by
             the
             transits
             of
             Sun
             or
             Stars
             cross
             the
             Meridian
             ,
             or
             the
             coming
             of
             some
             of
             the
             
               Circum-Polar
               Stars
            
             in
             the
             same
             Vertical
             with
             the
             Pole-Star
             .
             All
             these
             methods
             have
             their
             inconveniences
             ,
             or
             at
             least
             ,
             are
             attended
             with
             far
             greater
             trouble
             than
             that
             which
             I
             shall
             propose
             .
          
           
             And
             first
             for
             Dials
             ,
             unless
             they
             be
             very
             large
             they
             will
             not
             admit
             of
             divisions
             so
             minute
             ,
             as
             are
             requisite
             to
             the
             nice
             determination
             of
             the
             Time
             ,
             as
             into
             minutes
             ,
             half-minutes
             ,
             and
             quarter-minutes
             .
             And
             when
             they
             are
             so
             large
             as
             to
             admit
             such
             ,
             the
             uncertain
             shadow
             that
             is
             cast
             from
             a
             long
             
             Gnomon
             renders
             them
             useless
             for
             such
             niceness
             ;
             for
             though
             your
             Dial
             have
             on
             it
             every
             quarter-minute
             ,
             the
             most
             accurate
             eye
             cannot
             tell
             where
             the
             shadow
             determines
             to
             a
             minute
             .
             Another
             grand
             defect
             of
             Dials
             is
             ,
             that
             they
             serve
             only
             in
             the
             day-time
             ,
             and
             that
             too
             ,
             when
             the
             Sun
             shines
             out
             intensely
             .
             So
             that
             for
             the
             night
             (
             which
             is
             the
             chief
             time
             of
             
               Astronomical
               Observation
               )
               Dials
            
             are
             perfectly
             useless
             .
          
           
             Perhaps
             I
             need
             say
             no
             more
             to
             recommend
             my
             present
             contrivance
             ,
             then
             to
             assert
             that
             it
             clearly
             takes
             off
             both
             these
             inconveniences
             .
             For
             thereby
             the
             larger
             the
             Dial
             is
             ,
             and
             the
             more
             minute
             the
             divisions
             are
             ,
             the
             more
             accurately
             is
             the
             Time
             observed
             .
             A
             long
             Gnomon
             in
             our
             way
             hinders
             not
             at
             all
             ,
             nor
             is
             there
             any
             uncertainty
             from
             a
             Penumbra
             .
             And
             moreover
             't
             is
             adapted
             as
             well
             to
             serve
             by
             the
             Stars
             at
             night
             ,
             as
             by
             the
             Sun
             in
             the
             day
             ,
             and
             gives
             the
             hour
             almost
             by
             inspection
             at
             a
             Star
             ,
             as
             at
             the
             Sun.
             And
             withal
             has
             this
             advantage
             ,
             that
             when
             the
             Sun
             is
             over-clouded
             ,
             so
             as
             but
             just
             to
             be
             seen
             faintly
             ,
             and
             casts
             no
             shadow
             at
             all
             on
             a
             Dial
             ;
             yet
             in
             our
             way
             ,
             if
             he
             be
             in
             the
             least
             perceivable
             by
             the
             eye
             ,
             the
             Time
             may
             be
             exactly
             told
             by
             him
             .
          
           
             I
             cannot
             say
             that
             there
             are
             inconveniences
             in
             observing
             the
             Time
             ,
             by
             taking
             the
             Sun
             or
             Stars
             Altitudes
             and
             Azimuths
             by
             day
             and
             night
             ;
             and
             yet
             if
             we
             reckon
             trouble
             an
             inconvenience
             ,
             these
             methods
             are
             not
             free
             from
             it
             .
             For
             ,
             besides
             the
             difficulty
             
             and
             charge
             of
             obtaining
             Instruments
             large
             and
             accurate
             enough
             for
             doing
             these
             ,
             and
             the
             dexterity
             and
             long
             practice
             that
             is
             requisite
             for
             rightly
             managing
             them
             :
             This
             method
             is
             attended
             by
             the
             trouble
             of
             Calculating
             the
             most
             difficult
             of
             oblique
             spherical
             Triangles
             ,
             viz.
             that
             wherein
             three
             sides
             are
             given
             to
             find
             an
             Angle
             ;
             and
             this
             ,
             if
             the
             observation
             be
             by
             the
             Altitude
             of
             the
             Sun
             in
             day-time
             ;
             for
             by
             the
             Altitudes
             of
             Stars
             by
             night
             ,
             the
             Calculation
             is
             yet
             more
             tedious
             and
             troublesome
             .
             And
             if
             so
             ,
             what
             a
             toil
             must
             it
             be
             to
             suppute
             twenty
             or
             thirty
             of
             these
             in
             a
             night
             ?
             Besides
             ,
             the
             Altitudes
             of
             the
             Sun
             towards
             the
             meridian
             alter
             so
             slowly
             ,
             that
             for
             a
             good
             while
             both
             before
             and
             after
             noon
             ,
             't
             is
             not
             safe
             to
             rely
             upon
             them
             .
             This
             inconvenience
             indeed
             is
             something
             remedied
             at
             the
             Stars
             ,
             where
             I
             can
             choose
             those
             that
             are
             of
             a
             proper
             Altitude
             ,
             and
             conveniently
             remote
             from
             the
             Meridian
             ,
             and
             the
             observation
             of
             the
             Azimuth
             remedies
             the
             other
             uncertainty
             proceeding
             from
             their
             vicinity
             to
             the
             Meridian
             .
             But
             ,
             as
             I
             said
             before
             ,
             the
             trouble
             of
             Calculation
             attends
             the
             observation
             either
             of
             Altitudes
             or
             Azimuths
             ;
             whereas
             the
             Instrument
             I
             propose
             ,
             does
             the
             matter
             with
             the
             greatest
             certainty
             ,
             and
             greatest
             ease
             imaginable
             .
             There
             is
             requisite
             therein
             ,
             besides
             a
             plain
             and
             simple
             observation
             ,
             no
             Calculation
             by
             Triangles
             ,
             or
             any
             other
             Operation
             ,
             save
             only
             the
             addition
             and
             substraction
             of
             two
             or
             three
             small
             numbers
             ,
             to
             be
             had
             in
             the
             
             Tables
             ready
             Calculated
             ;
             and
             that
             too
             ,
             only
             when
             the
             observation
             is
             by
             the
             Stars
             at
             night
             .
          
           
             The
             methods
             of
             observing
             the
             Time
             by
             the
             appulses
             of
             the
             Sun
             or
             fixt
             Stars
             to
             the
             Meridian
             ,
             or
             the
             Circum-Polars
             coming
             in
             the
             same
             Vertical
             with
             the
             Pole
             ,
             are
             plain
             ,
             simple
             ,
             and
             easy
             .
             We
             have
             the
             first
             described
             by
             Riccioli
             in
             his
             
               Almagestum
               Novum
               ,
               Lib.
               5.
               
               Cap.
               15.
               
               Prob.
            
             8.
             where
             he
             shews
             us
             how
             to
             perform
             it
             by
             his
             
               Triangulum
               Filare
            
             .
             The
             latter
             way
             is
             described
             by
             Sir
             
               Jonas
               Moore
            
             in
             his
             
               Compendium
               Mathematicum
               ,
               p.
            
             118.
             and
             more
             fully
             in
             the
             Royal
             Almanacks
             for
             the
             years
             1676
             ,
             1677
             ,
             1678.
             
             And
             I
             have
             by
             me
             Tables
             laboriously
             and
             carefully
             Calculated
             by
             my
             esteemed
             Friend
             
               Henry
               Osburn
            
             
               Esq
            
             and
             excellent
             Astronomer
             and
             Mathematician
             for
             Dublin
             and
             other
             Latitudes
             in
             Ireland
             to
             years
             lately
             past
             ,
             and
             to
             come
             ,
             which
             are
             to
             be
             used
             in
             this
             way
             .
             But
             ,
             though
             both
             these
             ways
             (
             as
             I
             said
             before
             )
             are
             very
             plain
             and
             easy
             ,
             yet
             they
             serve
             rather
             to
             rectifie
             Watches
             and
             other
             Time-keepers
             ,
             then
             to
             shew
             the
             Time
             themselves
             throughout
             the
             whole
             course
             of
             an
             observation
             ;
             as
             ,
             suppose
             it
             were
             an
             Eclipse
             of
             the
             Moon
             ,
             perhaps
             when
             a
             spot
             either
             immerges
             or
             emerges
             into
             or
             from
             the
             shadow
             ,
             there
             is
             not
             at
             that
             very
             instant
             ,
             and
             perhaps
             will
             not
             be
             for
             many
             minutes
             after
             ,
             a
             Star
             in
             the
             Meridian
             ,
             or
             under
             the
             Pole-star
             ,
             to
             tell
             me
             the
             moment
             of
             that
             time
             .
          
           
             But
             what
             I
             propose
             does
             as
             constantly
             (
             and
             not
             
             by
             fits
             )
             shew
             ,
             and
             follow
             the
             time
             ,
             if
             duly
             managed
             ,
             as
             the
             Hand
             of
             a
             well-going
             Pendulum-Watch
             indicates
             the
             hour
             ;
             that
             is
             to
             say
             ,
             it
             tells
             you
             the
             present
             minute
             ,
             and
             quarter
             of
             a
             minute
             ,
             whenever
             you
             are
             pleased
             to
             look
             ,
             as
             well
             as
             any
             other
             ,
             past
             ,
             or
             to
             come
             .
          
        
         
           
             CHAP.
             III.
             A
             Description
             of
             the
             Instrument
             .
          
           
             THE
             contrivance
             of
             this
             Instrument
             consists
             in
             making
             a
             very
             large
             
               Horizontal
               Dial
            
             ,
             adapted
             to
             your
             proper
             Latitude
             ,
             and
             capable
             of
             receiving
             divisions
             into
             minutes
             ,
             and
             parts
             of
             a
             minute
             ,
             fitted
             with
             a
             large
             ,
             strong
             ,
             and
             double
             Gnomon
             ;
             I
             call
             that
             a
             double
             Gnomon
             that
             casts
             the
             morning-shadow
             from
             its
             Western-edge
             ,
             and
             the
             afternoon-shadow
             from
             its
             Eastern-edge
             ,
             and
             the
             noon-shadow
             by
             its
             thickness
             .
             This
             Dial
             is
             to
             be
             furnished
             with
             two
             pair
             of
             Sights
             or
             Rulers
             ;
             one
             to
             serve
             in
             the
             morning
             ,
             or
             for
             Stars
             on
             the
             Eastern-side
             of
             the
             Meridian
             ,
             t'other
             to
             serve
             in
             the
             afternoon
             ,
             or
             for
             Stars
             on
             the
             Western-side
             of
             the
             Meridian
             .
             Each
             of
             these
             pair
             consists
             of
             two
             movable
             Rulers
             ,
             one
             I
             will
             call
             the
             Horizontal-Ruler
             ,
             t'other
             the
             Gnomonick-Ruler
             ,
             or
             Stile-Ruler
             .
             These
             two
             Rulers
             are
             to
             be
             so
             adapted
             ,
             that
             their
             two
             edges
             that
             are
             next
             
             the
             Gnomon
             ,
             may
             be
             perpetually
             in
             the
             same
             plane
             with
             each
             other
             ,
             and
             at
             the
             time
             of
             observation
             ,
             that
             they
             both
             may
             be
             in
             the
             same
             plane
             with
             their
             correspondent
             edge
             of
             the
             Gnomon
             .
             On
             the
             Stile-Ruler
             are
             fixt
             Telescopick
             Sights
             ,
             and
             the
             cross
             hairs
             in
             their
             due
             place
             .
             But
             all
             this
             will
             be
             made
             plainer
             by
             the
             first
             Figure
             ,
             in
             which
             I
             shall
             represent
             that
             Instrument
             which
             by
             my
             directions
             was
             made
             in
             London
             in
             the
             Summer
             1685
             by
             
               Richard
               Whitehead
            
             Math.
             Inst
             .
             Maker
             ,
             who
             took
             the
             directions
             from
             my self
             ,
             but
             made
             the
             Instrument
             in
             my
             absence
             .
          
           
             The
             first
             Figure
             represents
             the
             Instrument
             in
             Perspective
             ,
             having
             one
             pair
             of
             its
             Rulers
             in
             a
             posture
             of
             observation
             ;
             t'other
             pair
             lying
             carelesly
             on
             the
             plane
             of
             the
             Dial.
             'T
             is
             a
             large
             Octogonal
             Brass-plate
             ,
             clear'd
             in
             the
             middle
             ,
             except
             only
             the
             cross-bars
             zzz
             of
             the
             same
             piece
             with
             the
             Plate
             ,
             left
             for
             strengthning
             the
             Instrument
             ,
             and
             receiving
             the
             Stile
             ,
             the
             Plate
             is
             of
             a
             moderate
             thickness
             about
             15
             /
             100
             of
             an
             inch
             ,
             the
             Diameter
             of
             the
             largest
             circle
             it
             receives
             is
             18
             inches
             ,
             't
             is
             supported
             from
             the
             plane
             on
             which
             it
             stands
             about
             three
             quarters
             of
             an
             inch
             by
             three
             brass-feet
             2.
             2.
             2.
             the
             bredth
             of
             the
             limb
             for
             receiving
             the
             Figures
             and
             Divisions
             ,
             is
             2
             1
             /
             2
             inches
             .
             The
             thickness
             or
             bredth
             of
             the
             face
             of
             the
             Stile
             malb
             is
             7
             /
             10
             of
             an
             inch
             .
             The
             Divisions
             actually
             expressed
             upon
             it
             are
             hours
             ,
             half
             hours
             ,
             quarters
             ,
             five
             minutes
             ,
             minutes
             ,
             and
             half
             minutes
             ,
             
             and
             one
             may
             easily
             judge
             of
             the
             third
             part
             of
             an
             half
             minute
             ,
             that
             is
             ,
             10
             seconds
             .
             Down
             along
             the
             face
             of
             the
             Stile
             (
             some
             perhaps
             will
             call
             it
             the
             back
             of
             the
             Cock
             )
             there
             runs
             a
             deep
             Groove
             ,
             to
             receive
             the
             screw
             
               m.
               l.
            
             which
             screw
             ,
             by
             turning
             the
             handle
             n
             ,
             raises
             and
             lets
             down
             the
             Nut
             op
             ,
             on
             which
             the
             Stile-Ruler
             ef
             rests
             ,
             and
             is
             thereby
             raised
             and
             let
             down
             ,
             as
             the
             Sun
             or
             Star
             requires
             .
             This
             Nut
             op
             is
             furnish'd
             with
             a
             Return'd
             Fork
             ,
             meerly
             to
             keep
             the
             Stile-Ruler
             from
             an
             accidental
             fall
             ,
             if
             any
             thing
             should
             chance
             to
             move
             it
             rudely
             .
             But
             I
             shall
             describe
             this
             Nut
             
               o.
               p.
            
             presently
             by
             it self
             .
             The
             screw
             
               m.
               l.
            
             is
             fixt
             both
             at
             top
             m
             and
             bottom
             l
             ,
             so
             that
             it
             only
             is
             to
             be
             turn'd
             round
             by
             the
             handle
             n.
             the
             Stile
             is
             fixt
             most
             strongly
             by
             the
             screws
             ,
             
               q.
               r.
            
             I
             come
             next
             to
             describe
             the
             Rulers
             ,
             and
             first
             for
             the
             Horizontal
             Ruler
             cd
             ,
             this
             turns
             most
             truly
             upon
             the
             Center
             of
             the
             hour-lines
             and
             divisions
             at
             k
             ,
             and
             has
             so
             much
             of
             the
             root
             of
             the
             Stile
             clear'd
             off
             ,
             as
             its
             thickness
             requires
             to
             permit
             its
             motion
             freely
             ;
             the
             line
             cd
             of
             this
             Ruler
             crosses
             the
             Center
             most
             exactly
             ,
             and
             the
             edge
             cd
             is
             neatly
             cypher'd
             off
             (
             as
             the
             Workmen
             call
             it
             .
             )
             Wherefore
             the
             right
             line
             ab
             of
             the
             Stile
             ,
             and
             the
             line
             of
             the
             under-edge
             of
             the
             
               Horizontal
               Ruler
               cd
            
             ,
             meeting
             ,
             and
             crossing
             perpetually
             in
             the
             same
             point
             k
             ,
             they
             shall
             be
             always
             in
             the
             same
             plain
             ,
             (
             by
             
               Prop.
               2.
               
               Eucl.
            
             11.
             
             Book
             .
             )
          
           
             To
             the
             other
             end
             of
             this
             
               Horizontal
               Ruler
            
             there
             
             is
             adapted
             the
             Stile-Ruler
             ef
             ,
             which
             by
             means
             of
             the
             joynt
             vxy
             (
             which
             I
             shall
             describe
             by
             it self
             )
             obeys
             two
             several
             motions
             ,
             viz.
             one
             upwards
             and
             downwards
             ,
             as
             govern'd
             by
             the
             Nut
             and
             screw
             on
             the
             Stile
             ;
             and
             t'other
             Eastward
             and
             Westward
             ,
             according
             to
             the
             Azimuth
             ,
             or
             as
             it
             follows
             the
             Horizontal
             Ruler
             .
             And
             in
             these
             two
             motions
             ,
             't
             is
             so
             contrived
             ,
             that
             the
             line
             cd
             and
             ef
             may
             perpetually
             cross
             each
             other
             in
             one
             and
             the
             same
             Center
             at
             y.
             Hence
             it
             comes
             to
             pass
             ,
             that
             the
             right
             line
             cd
             ,
             and
             the
             right
             line
             ef
             ,
             are
             always
             in
             the
             same
             plain
             .
             Wherefore
             laying
             the
             line
             ef
             to
             the
             edge
             of
             the
             Stile
             ,
             the
             three
             lines
             
               ab
               ,
               cd
               ,
               ef
            
             ,
             are
             in
             the
             same
             plain
             ;
             and
             consequently
             directing
             the
             line
             ef
             to
             the
             Center
             of
             the
             Sun
             ,
             the
             edge
             of
             the
             Gnomon
             ,
             and
             the
             edges
             cd
             and
             ef
             of
             the
             Rulers
             are
             in
             the
             plain
             of
             the
             shadow
             ;
             and
             therefore
             the
             Ruler
             cd
             cuts
             the
             division
             on
             the
             limb
             of
             the
             Dial-Plate
             ,
             where
             the
             shadow
             would
             cut
             it
             .
          
           
             To
             the
             Stile-Ruler
             are
             fixt
             ,
             the
             Eye-glass
             at
             h
             ,
             the
             Ring
             that
             carries
             the
             cross
             hairs
             at
             g
             ,
             and
             the
             Object-glass
             at
             i
             ;
             The
             manner
             of
             adjusting
             all
             which
             ,
             I
             shall
             shew
             presently
             .
          
           
             But
             I
             must
             not
             forget
             to
             mention
             the
             Artificer
             ,
             whose
             hands
             were
             imploy'd
             in
             this
             Instrument
             ,
             Mr.
             
               Richard
               Whitehead
            
             living
             in
             Gunpowder-Alley
             in
             Shoo-Lane
             ,
             by
             
               Fleetstreet
               ,
               London
            
             ,
             a
             most
             exact
             and
             careful
             Workman
             ,
             of
             whose
             skill
             and
             curiosity
             in
             
             making
             Mathematical
             Instruments
             ,
             I
             have
             more
             than
             this
             one
             instance
             ;
             And
             I
             dare
             venture
             to
             recommend
             any
             Gentleman
             to
             him
             ,
             as
             a
             most
             exact
             performer
             .
          
        
         
           
             CHAP.
             IV.
             Of
             the
             Stile-Nut
             ,
             and
             Ruler-Joynt
             .
          
           
             IN
             the
             foregoing
             Chapter
             I
             have
             promised
             a
             particular
             description
             of
             some
             of
             the
             forementioned
             parts
             belonging
             to
             this
             contrivance
             ;
             and
             first
             of
             the
             Nut
             
               op
               (
               Fig.
               1.
            
             )
             This
             I
             have
             represented
             by
             it self
             in
             
               Fig.
               2.
               ss
            
             is
             the
             Stile-screw
             passing
             through
             the
             Nut
             n
             ,
             which
             is
             lined
             with
             a
             female-screw
             ;
             this
             Nut
             slides
             in
             the
             Groove
             along
             the
             face
             of
             the
             Gnomon
             ,
             so
             that
             the
             whole
             thickness
             of
             the
             screw
             lies
             under
             the
             said
             face
             :
             
               p
               p
            
             are
             two
             arms
             that
             clasp
             the
             Stile
             to
             make
             the
             motion
             of
             this
             Nut
             more
             even
             and
             steady
             .
             fab
             is
             the
             Return'd
             Fork
             to
             keep
             the
             Rulers
             ,
             when
             they
             are
             supported
             on
             this
             Nut
             ,
             from
             any
             accidental
             fall
             ,
             and
             is
             very
             useful
             when
             the
             Horizontal
             Ruler
             is
             removed
             far
             from
             the
             Meridian
             .
             And
             least
             at
             any
             time
             ,
             either
             of
             the
             Returns
             ab
             ,
             may
             stand
             in
             the
             way
             of
             either
             of
             the
             Rulers
             motions
             ,
             the
             parts
             ab
             are
             movable
             at
             a
             by
             a
             riveted
             joynt
             ,
             and
             may
             be
             turn'd
             clearly
             downward
             out
             
             of
             the
             way
             ,
             as
             at
             
               ac
               ,
               ac
            
             .
             At
             a
             there
             may
             be
             fixt
             a
             small
             gentle
             spring
             ,
             that
             may
             lightly
             bear
             the
             edge
             of
             the
             Ruler
             constantly
             to
             the
             edge
             of
             the
             Stile
             ;
             but
             this
             contrivance
             is
             not
             on
             my
             Instrument
             ,
             though
             it
             may
             be
             easily
             added
             .
          
           
             The
             several
             parts
             of
             the
             Ruler-joynt
             (
             which
             indeed
             is
             the
             most
             curious
             piece
             of
             Mechanicks
             about
             the
             whole
             Instrument
             ,
             and
             on
             which
             the
             whole
             affair
             does
             chiefly
             depend
             )
             are
             represented
             all
             apart
             in
             Figures
             by
             themselves
             .
             Fig.
             3.
             shews
             the
             outward
             end
             of
             the
             Horizontal
             Ruler
             ,
             aaa
             are
             the
             holes
             that
             admit
             the
             screws
             which
             fasten
             it
             to
             the
             other
             parts
             of
             the
             joynt
             ,
             particularly
             to
             the
             socket
             shewn
             in
             Fig.
             5
             ,
             6
             ,
             7
             ,
             8.
             at
             
               aaa
               .
               Fig.
            
             4.
             shews
             the
             other
             end
             of
             the
             Horizontal
             Ruler
             ,
             where
             it
             turns
             on
             the
             Pin
             in
             the
             Center
             of
             the
             Dial
             at
             the
             root
             of
             the
             Stile
             (
             at
             
               k
               Fig.
               1.
            
             )
          
           
             Fig.
             5.
             expresses
             the
             appearance
             of
             the
             joynt
             ,
             when
             discover'd
             of
             
               Fig.
               3.
               ,
               ihi
            
             is
             a
             perfect
             hinge
             ,
             the
             Center
             of
             whose
             motion
             is
             in
             the
             line
             
               fh
               ,
               iii
            
             that
             part
             of
             the
             hinge
             belonging
             to
             the
             Ruler
             ,
             hhh
             that
             part
             belonging
             to
             the
             Tumbler
             or
             Nut
             expressed
             in
             
               Fig.
               7.
               hhh
               .
               aaa
            
             the
             socket
             wherein
             the
             Timbler
             hhh
             moves
             round
             and
             truly
             on
             the
             Center
             at
             middle
             h
             ,
             which
             also
             is
             in
             the
             Center
             of
             the
             hinges
             motion
             .
             This
             socket
             aaa
             is
             represented
             in
             
               Fig.
               8.
               bb
            
             are
             the
             screw-holes
             for
             the
             Ring
             and
             Snout
             of
             the
             Eye-glass
             .
          
           
             Fig
             6
             shews
             the
             under-side
             of
             Fig.
             5.
             where
             the
             
             same
             parts
             are
             marked
             with
             the
             same
             letters
             ;
             c
             is
             the
             round
             Pin
             of
             the
             same
             piece
             with
             the
             Nut
             hhh
             :
             This
             is
             more
             plain
             in
             Fig.
             7
             ,
             this
             Pin
             turns
             truly
             in
             the
             hole
             of
             the
             socket
             c
             in
             Fig.
             8.
             whilst
             the
             Nut
             hhh
             of
             Fig.
             7.
             rests
             and
             turns
             on
             the
             bottom
             of
             the
             said
             socket
             
               hhh
               Fig.
            
             8.
             
             This
             Nut
             is
             kept
             close
             in
             the
             socket
             ,
             and
             there
             made
             to
             move
             steadily
             and
             truly
             by
             the
             Pin
             e
             and
             springing
             Plate
             
               d
               Fig.
            
             6.
             and
             9.
             which
             Pin
             e
             passes
             over
             the
             Plate
             d
             through
             the
             Pin
             of
             the
             Nut
             c.
             
          
        
         
           
             CHAP.
             V.
             Of
             the
             Telescopick
             Sights
             ,
             and
             their
             true
             Adjusting
             .
          
           
             FOr
             the
             true
             adjusting
             of
             the
             Telescopick
             Sights
             
               hgi
               (
               Fig.
               1.
            
             )
             to
             the
             Stile-Ruler
             ef
             ,
             there
             are
             three
             things
             requisite
             .
             But
             first
             I
             must
             advertise
             ,
             that
             the
             Stile-Ruler
             ef
             ought
             to
             be
             so
             strengthned
             ,
             that
             as
             it
             rests
             on
             the
             Nut
             op
             ,
             it
             may
             not
             at
             all
             bend
             ,
             but
             that
             the
             line
             ef
             may
             be
             one
             right
             line
             as
             nigh
             as
             possible
             .
             But
             in
             this
             particular
             the
             greatest
             niceness
             is
             not
             requisite
             ,
             for
             if
             the
             Ruler
             chance
             a
             little
             to
             deviate
             from
             its
             exact
             straightness
             ,
             I
             shall
             shew
             a
             way
             of
             rectifying
             the
             error
             by
             the
             cross-hairs
             or
             Mensurator
             .
          
           
             The
             first
             thing
             requisite
             to
             the
             placing
             of
             the
             Telescopick
             Sights
             is
             ,
             that
             the
             ring
             g
             ,
             that
             carries
             
             the
             cross-hairs
             or
             other
             Mensurator
             ,
             be
             at
             a
             due
             and
             exact
             distance
             from
             the
             Object-glass
             i.
             This
             distance
             is
             to
             be
             exactly
             the
             total
             length
             of
             the
             Object-glass
             ;
             but
             that
             we
             may
             get
             this
             total
             length
             more
             accurately
             than
             by
             any
             admeasurement
             ,
             the
             Eye-glass
             and
             Object-glass
             being
             adapted
             together
             ,
             and
             placing
             the
             Mensurator
             in
             the
             ring
             g
             between
             the
             Object-glass
             and
             Eye-glass
             at
             the
             distance
             of
             the
             Focus
             of
             the
             said
             Eye-glass
             ,
             let
             us
             look
             at
             some
             object
             distant
             4
             or
             5
             miles
             ,
             and
             moving
             your
             eye
             before
             the
             Eye-glass
             ,
             observe
             whether
             the
             Mensurator
             seems
             to
             move
             upon
             the
             said
             object
             ;
             for
             if
             it
             do
             ,
             then
             the
             Mensurator
             is
             not
             at
             its
             exact
             distance
             from
             the
             Object-glass
             ,
             but
             the
             Object-glass
             is
             to
             be
             removed
             farther
             or
             nigher
             ,
             till
             the
             eye
             looking
             at
             such
             a
             distant
             object
             ,
             and
             moving
             before
             the
             Eye-glass
             ,
             perceives
             the
             Mensurator
             as
             it
             were
             fixt
             and
             immovable
             on
             the
             object
             .
             If
             in
             raising
             the
             eye
             ,
             the
             object
             seem
             to
             fall
             down
             on
             the
             Mensurator
             ,
             or
             in
             depressing
             the
             eye
             ,
             the
             object
             seem
             to
             rise
             on
             the
             Mensurator
             ,
             then
             is
             the
             Object-glass
             too
             nigh
             the
             Mensurator
             .
             But
             if
             in
             raising
             the
             eye
             ,
             the
             object
             seem
             to
             rise
             on
             the
             Mensurator
             ;
             or
             in
             depressing
             the
             eye
             ,
             the
             object
             seem
             to
             fall
             on
             the
             Mensurator
             ,
             then
             is
             the
             Object-glass
             too
             far
             from
             the
             Mensurator
             .
             All
             which
             will
             be
             evident
             from
             the
             10
             Fig.
             wherein
             let
             AB
             be
             a
             distant
             object
             ,
             whose
             middle
             point
             C
             is
             projected
             by
             the
             Object-glass
             D
             at
             k
             ,
             let
             mn1
             be
             the
             Mensurator
             
             to
             which
             the
             Object-glass
             is
             too
             nigh
             ,
             and
             mn2
             the
             Mensurator
             from
             which
             the
             Object-glass
             is
             too
             far
             ,
             
               e
               ,
               f
               ,
               g
            
             ,
             the
             eye
             placed
             at
             three
             different
             postures
             ;
             in
             case
             of
             the
             first
             mensurator
             ,
             if
             the
             eye
             rise
             from
             e
             to
             f
             it
             perceives
             the
             point
             k
             depressed
             from
             1
             to
             h
             ;
             or
             if
             the
             eye
             fall
             from
             e
             to
             g
             ,
             it
             perceives
             the
             point
             k
             raised
             from
             1
             to
             l
             ;
             and
             here
             the
             mensurator
             is
             too
             nigh
             the
             Object-glass
             .
             But
             in
             case
             of
             the
             second
             Mensurator
             ,
             if
             the
             eye
             rise
             from
             e
             to
             f
             ,
             the
             point
             k
             seems
             to
             rise
             on
             the
             Mensurator
             from
             2
             to
             r
             ;
             or
             if
             the
             eye
             fall
             from
             e
             to
             g
             ,
             it
             perceives
             the
             point
             k
             fallen
             from
             2
             to
             s
             ,
             and
             in
             this
             case
             the
             Mensurator
             is
             too
             distant
             from
             the
             Object-glass
             ;
             but
             if
             the
             mensurator
             be
             exactly
             in
             the
             Focus
             at
             k
             ,
             let
             the
             eye
             rise
             or
             fall
             ,
             the
             mensurator
             seems
             fixt
             and
             steddy
             upon
             the
             object
             .
             And
             this
             is
             the
             first
             thing
             requisite
             to
             the
             adjusting
             of
             these
             Sights
             .
          
           
             This
             Affair
             is
             usually
             so
             well
             adjusted
             by
             the
             Workmen
             ,
             and
             when
             once
             adjusted
             ,
             is
             never
             alterable
             ,
             that
             I
             need
             shew
             no
             way
             of
             providing
             for
             it
             .
             But
             in
             short
             ,
             it
             may
             easily
             be
             provided
             for
             ,
             by
             making
             the
             holes
             for
             the
             screws
             ,
             that
             fixt
             the
             Object-glass-ring
             to
             the
             Stile-Ruler
             ,
             long
             slits
             ,
             so
             as
             to
             slip
             forwards
             and
             backwards
             on
             the
             necks
             of
             the
             screws
             ;
             and
             when
             the
             Object-glass
             is
             at
             its
             right
             posture
             ,
             the
             screw-heads
             may
             pinch
             and
             fix
             the
             Ring
             steddily
             .
          
           
             The
             next
             requisite
             is
             ,
             that
             the
             line
             of
             Collimation
             from
             the
             mensurator
             through
             the
             Object-glass
             ,
             and
             
             so
             to
             the
             object
             ,
             run
             parallel
             to
             the
             line
             ef
             of
             the
             Stile-Ruler
             .
             This
             Parallelism
             consists
             in
             two
             manner
             of
             ways
             ,
             first
             ,
             that
             the
             mensurator
             be
             neither
             more
             to
             the
             right
             or
             left-hand
             than
             requisite
             ;
             or
             secondly
             ,
             that
             it
             be
             neither
             higher
             or
             lower
             than
             it
             ought
             .
             The
             first
             error
             makes
             the
             Azimuths
             be
             shewn
             false
             ,
             and
             the
             second
             error
             makes
             the
             Altitudes
             be
             shewn
             false
             :
             but
             an
             Horizontal
             Dial
             tells
             the
             time
             by
             both
             Altitude
             and
             Azimuth
             ;
             therefore
             both
             these
             are
             to
             be
             taken
             care
             of
             .
          
           
             And
             first
             for
             the
             Fabrick
             of
             the
             Ring
             g
             ,
             that
             carries
             the
             mensurator
             ;
             this
             is
             so
             to
             be
             order'd
             ,
             that
             first
             the
             Ring
             may
             be
             moved
             more
             to
             the
             right
             or
             left-hand
             ,
             and
             there
             to
             be
             fixt
             ;
             and
             secondly
             ,
             that
             the
             mensurator
             may
             be
             raised
             or
             depressed
             according
             as
             is
             requisite
             ,
             and
             there
             fixt
             .
             The
             first
             is
             obtain'd
             by
             making
             the
             holes
             for
             the
             screws
             ,
             whereby
             this
             Ring
             g
             is
             fixt
             to
             the
             Stile-Ruler
             ,
             long
             slits
             ,
             so
             that
             they
             may
             slip
             on
             the
             necks
             of
             the
             screws
             before
             the
             Eye-glass
             ,
             and
             when
             they
             are
             in
             their
             right
             posture
             ,
             may
             be
             pinched
             close
             by
             the
             screw-heads
             ,
             and
             there
             fixt
             .
             Thus
             therefore
             we
             give
             the
             mensurator
             a
             motion
             to
             the
             right
             or
             left-hand
             ,
             by
             which
             't
             is
             brought
             to
             shew
             the
             Azimuth
             right
             ,
             as
             I
             shall
             declare
             presently
             .
             Next
             ,
             that
             the
             mensurator
             may
             be
             raised
             or
             depressed
             ,
             instead
             of
             cross-hairs
             in
             the
             Ring
             g
             ,
             let
             there
             be
             placed
             therein
             a
             very
             strong
             Steel-needle
             ,
             that
             may
             end
             in
             a
             most
             fine
             slender
             point
             :
             this
             needle
             
             is
             to
             be
             a
             screw
             almost
             its
             whole
             length
             nigh
             to
             its
             smaller
             end
             ,
             and
             to
             be
             screw'd
             through
             the
             top
             of
             the
             Ring
             g
             ,
             so
             that
             its
             smaller
             end
             may
             pass
             through
             the
             center
             of
             the
             Ring
             ;
             by
             screwing
             or
             unscrewing
             of
             this
             Needle
             ,
             we
             depress
             or
             raise
             its
             fine
             point
             in
             the
             Ring
             .
             And
             thus
             much
             for
             the
             contrivance
             or
             Fabrick
             of
             the
             Ring
             .
          
           
             I
             come
             now
             to
             shew
             the
             way
             of
             managing
             these
             two
             motions
             in
             the
             Mensurator
             ,
             so
             as
             to
             bring
             it
             to
             its
             true
             posture
             ,
             and
             there
             fix
             it
             .
             And
             first
             for
             rectifying
             the
             Mensurator
             so
             as
             to
             shew
             the
             true
             Azimuth
             .
             There
             are
             two
             manner
             of
             ways
             for
             doing
             this
             .
             The
             first
             is
             more
             troublesome
             and
             tedious
             ,
             but
             being
             most
             universal
             to
             the
             fixing
             of
             
               Telescopick
               Sights
            
             on
             all
             Rulers
             ,
             I
             shall
             here
             describe
             it
             .
             In
             Fig.
             11.
             let
             ABCD
             represent
             a
             Ruler
             ,
             whose
             edge
             or
             side
             AC
             is
             exactly
             parallel
             to
             its
             side
             BD.
             To
             make
             a
             Ruler
             thus
             parallel
             ,
             is
             not
             difficult
             to
             a
             good
             Artificer
             ;
             but
             I
             shall
             shew
             how
             to
             try
             whether
             these
             sides
             are
             parallel
             or
             not
             .
             E
             is
             the
             Object-glass
             ,
             F
             the
             
               Mensurator
               ,
               G
            
             the
             Eye-glass
             .
             On
             a
             plain
             Board
             strike
             two
             round
             Brass-pins
             ,
             as
             suppose
             at
             H
             and
             I
             ,
             to
             these
             apply
             the
             side
             of
             the
             
               Ruler
               BD
            
             ,
             so
             as
             it
             may
             rest
             against
             the
             pins
             ,
             which
             are
             therefore
             not
             clearly
             buried
             into
             the
             Board
             ,
             but
             stand
             out
             about
             1
             /
             10
             of
             an
             inch
             :
             then
             look
             through
             the
             Glasses
             ,
             and
             observe
             where
             the
             mensurator
             falls
             on
             an
             object
             distant
             a
             mile
             or
             two
             .
             Then
             remove
             the
             Ruler
             ,
             and
             apply
             its
             other
             
             side
             AC
             to
             the
             other
             side
             of
             the
             pins
             HI
             ,
             and
             observe
             whether
             the
             mensurator
             falls
             on
             the
             same
             point
             of
             the
             object
             as
             before
             .
             If
             it
             do
             so
             ,
             then
             are
             the
             sides
             of
             the
             
               Ruler
               AC
               ,
               BD
            
             parallel
             ;
             if
             not
             ,
             then
             the
             sides
             are
             not
             parallel
             .
             The
             reason
             that
             so
             remote
             an
             object
             must
             be
             chosen
             ,
             is
             ,
             that
             the
             bredth
             of
             the
             Ruler
             may
             subsend
             an
             inconsiderable
             Angle
             in
             a
             circle
             ,
             whose
             Radius
             is
             the
             distance
             of
             the
             object
             .
             Having
             found
             the
             sides
             of
             the
             Ruler
             to
             be
             parallel
             ,
             the
             next
             thing
             is
             ,
             to
             make
             the
             line
             of
             Sight
             ,
             or
             line
             of
             
               Collimation
               LK
            
             parallel
             to
             these
             sides
             ,
             for
             therein
             consists
             the
             first
             rectification
             of
             our
             Stile-Ruler
             .
             The
             method
             of
             doing
             this
             is
             much
             the
             same
             with
             what
             immediately
             precedes
             ,
             but
             requires
             another
             disposition
             of
             our
             pins
             ;
             for
             now
             we
             are
             to
             raise
             our
             plain
             Board
             so
             as
             to
             stand
             edge-wise
             ,
             nigh
             perpendicular
             to
             the
             Horizon
             ,
             and
             the
             pins
             must
             stand
             an
             inch
             or
             more
             out
             from
             the
             Board
             ,
             almost
             parallel
             to
             the
             Horizon
             ;
             then
             resting
             the
             under-side
             of
             the
             Ruler
             on
             the
             pins
             ,
             and
             applying
             its
             edge
             to
             the
             plain
             Board
             ,
             observe
             the
             point
             of
             a
             remote
             object
             whereon
             the
             mensurator
             falls
             ;
             in
             this
             posture
             the
             Glasses
             stand
             uppermost
             ,
             or
             on
             the
             upper-side
             of
             the
             Ruler
             ,
             and
             over-look
             the
             pins
             .
             Then
             remove
             the
             Ruler
             ,
             and
             hang
             the
             other
             side
             thereof
             on
             the
             pins
             ,
             that
             now
             the
             Glasses
             may
             be
             on
             the
             underside
             the
             Ruler
             ,
             or
             under-look
             the
             pins
             ,
             and
             resting
             the
             edge
             against
             the
             plain
             Board
             ,
             observe
             whether
             
             the
             mensurator
             fall
             on
             the
             same
             point
             as
             before
             ;
             if
             it
             do
             ,
             then
             is
             the
             line
             of
             
               Collimation
               LK
            
             parallel
             to
             the
             sides
             
               AC
               ,
               BD
            
             ;
             if
             it
             do
             not
             ,
             but
             falls
             to
             the
             right-hand
             apparently
             of
             the
             said
             object
             ,
             then
             is
             the
             mensurator
             to
             be
             removed
             (
             by
             means
             of
             the
             screws
             and
             slits
             in
             its
             Ring
             )
             to
             the
             left-hand
             :
             the
             contrary
             requiring
             the
             contrary
             .
             And
             thus
             by
             frequent
             repetitions
             and
             trials
             we
             at
             last
             bring
             all
             to
             rights
             .
             The
             most
             convenient
             Board
             or
             Table
             for
             this
             Operation
             ,
             is
             a
             Surveyors
             Plain-table
             ;
             for
             these
             being
             usually
             made
             true
             ,
             and
             readily
             and
             steddily
             obeying
             all
             motions
             and
             postures
             ,
             and
             are
             easily
             fixt
             thereat
             ;
             they
             are
             to
             be
             chosen
             before
             any
             other
             .
             Note
             also
             that
             the
             pins
             to
             be
             used
             with
             this
             or
             such
             like
             Table
             ,
             are
             to
             be
             strong
             brass-wire
             ,
             which
             having
             its
             roundness
             from
             its
             drawing
             ,
             is
             sure
             to
             have
             its
             sides
             parallel
             .
             By
             this
             method
             ,
             the
             line
             of
             sight
             of
             any
             Cylindrical
             or
             square
             Telescope
             may
             be
             made
             to
             run
             parallel
             to
             its
             sides
             ,
             for
             finding
             the
             Declination
             of
             the
             Magnet
             according
             to
             the
             methods
             lately
             proposed
             by
             
               Monsieur
               Hautefeville
            
             ,
             and
             M
             nsr
             .
             Sturmius
             ,
             in
             the
             Journal
             
               des
               Scavans
               23.
               
               Aug.
            
             1683.
             and
             in
             the
             
               Acta
               Lipsiae
               ,
               An.
               1684.
               mens
               .
               Decemb.
            
             and
             for
             want
             of
             this
             method
             ,
             what
             
               M
               nsr
               .
               Sturmius
            
             says
             in
             the
             foresaid
             
               Act.
               Lips
               .
               pag.
            
             579.
             is
             very
             defective
             .
             For
             thus
             he
             ,
             
               Sola
               tubi
               locatio
               ut
               axis
               visionis
               per
               medias
               lentes
               excurrens
               meridianae
               lineae
               exacte
               respondeat
               difficultatis
               quippiam
               habere
               videbatur
               ,
               verum
               &
               huic
               infirmitati
               praesens
               ,
               uti
               
               credo
               ,
               inventum
               est
               remedium
               ,
               &c.
               
            
             And
             the
             remedy
             he
             tell
             us
             is
             ,
             that
             the
             Tube
             be
             made
             a
             parallelipiped
             of
             Wood
             or
             Brass
             ;
             for
             then
             ,
             says
             he
             ,
             applying
             the
             side
             of
             your
             Tube
             to
             the
             
               meridian
               line
            
             ,
             the
             Axis
             of
             vision
             will
             be
             parallel
             to
             the
             said
             
               meridian
               line
            
             .
             But
             I
             must
             crave
             leave
             to
             deny
             this
             ,
             unless
             first
             it
             be
             rectified
             ,
             so
             that
             this
             Axis
             runs
             parallel
             to
             the
             side
             of
             the
             Tube
             ,
             which
             he
             was
             not
             aware
             of
             :
             and
             this
             is
             to
             be
             done
             by
             the
             method
             I
             have
             just
             now
             proposed
             ,
             which
             serves
             likewise
             in
             many
             other
             Occasions
             ,
             Experiments
             and
             Practises
             ,
             wherein
             a
             Ruler
             with
             
               Telescopick
               Sights
            
             is
             requisite
             .
          
           
             The
             second
             method
             for
             effecting
             this
             said
             rectification
             ,
             is
             more
             easily
             applicable
             to
             our
             Dials
             ,
             and
             withal
             is
             sufficiently
             accurate
             ,
             as
             doing
             the
             business
             to
             10″
             or
             15″
             seconds
             of
             time
             at
             utmost
             ,
             and
             by
             a
             careful
             and
             curious
             eye
             ,
             may
             do
             it
             to
             half
             that
             or
             less
             .
             Place
             the
             Dial
             so
             before
             the
             Sun
             ,
             that
             as
             nigh
             as
             possibly
             the
             eye
             can
             judge
             ,
             the
             Gnomon
             may
             be
             equally
             enlightned
             on
             both
             sides
             ,
             that
             is
             ,
             that
             the
             shadow
             of
             the
             Stile
             may
             fall
             exactly
             on
             12
             a
             Clock
             ,
             or
             the
             
               meridian
               line
            
             of
             the
             Dial.
             This
             perhaps
             will
             be
             said
             by
             some
             to
             be
             no
             fair
             proceeding
             ,
             because
             in
             this
             we
             cannot
             tell
             where
             the
             shadow
             does
             exactly
             determine
             ,
             and
             that
             this
             being
             one
             of
             the
             inconveniences
             our
             Dial
             pretends
             to
             remedy
             ,
             if
             we
             rectify
             our
             Dial
             by
             supposing
             we
             can
             determine
             that
             ;
             &
             if
             afterwards
             we
             determine
             
             that
             by
             supposing
             our
             
               Dial
               rectified
            
             ,
             it
             will
             seem
             a
             circle
             in
             Argumentation
             ,
             but
             yet
             I
             say
             ,
             they
             that
             will
             try
             it
             ,
             will
             find
             it
             otherwise
             ;
             for
             I
             can
             place
             the
             Dial
             so
             ,
             that
             the
             shadow
             from
             the
             thickness
             of
             the
             Stile
             ,
             or
             at
             least
             the
             Penumbra
             from
             both
             the
             Stiles
             edges
             ,
             shall
             so
             equally
             fall
             upon
             the
             12
             a
             Clock-lines
             ,
             that
             10″
             seconds
             of
             time
             ,
             or
             less
             ,
             shall
             sensibly
             alter
             the
             equality
             .
             And
             't
             is
             not
             the
             same
             case
             in
             telling
             when
             this
             shadow
             comes
             to
             an
             equality
             on
             both
             the
             12
             a
             Clock-lines
             ,
             as
             in
             telling
             when
             the
             shadow
             of
             one
             of
             the
             single
             edges
             of
             the
             Gnomon
             comes
             to
             any
             of
             the
             other
             hour-lines
             .
             For
             in
             the
             first
             case
             I
             am
             only
             to
             judge
             by
             comparison
             ,
             when
             the
             shadow
             is
             come
             as
             much
             to
             one
             of
             the
             12
             a
             Clock-lines
             as
             to
             th'
             other
             ;
             but
             in
             the
             latter
             case
             I
             am
             to
             judge
             positively
             without
             comparison
             .
             Wherefore
             having
             the
             Dial
             in
             this
             posture
             ,
             bring
             the
             Horizontal
             and
             Stile-Rulers
             just
             to
             12
             a
             Clock
             on
             the
             Dial-Plate
             ,
             and
             observe
             whether
             your
             Mensurator
             divide
             the
             Sun
             equally
             into
             an
             Eastern
             and
             Western
             half
             ;
             if
             it
             do
             so
             ,
             then
             is
             your
             Mensurator
             right
             ;
             if
             not
             ,
             the
             mensurator
             is
             to
             be
             moved
             something
             to
             the
             right
             or
             left
             hand
             ,
             as
             is
             requisite
             ,
             till
             at
             last
             by
             frequent
             repetitions
             and
             tryals
             we
             obtain
             our
             desire
             .
             And
             thus
             much
             shall
             suffice
             concerning
             the
             rectification
             of
             the
             mensurator
             to
             the
             right
             or
             left
             hand
             ,
             so
             as
             to
             shew
             the
             Azimuths
             truly
             .
             I
             shall
             only
             take
             notice
             ,
             that
             when
             one
             pair
             of
             the
             Rulers
             is
             rectified
             ,
             the
             other
             
             pair
             is
             easily
             rectified
             by
             them
             ;
             for
             bring
             the
             rectified
             pair
             to
             the
             12
             a
             Clock-line
             on
             the
             Dial
             ,
             and
             move
             the
             whole
             body
             of
             the
             Dial
             ,
             till
             you
             get
             the
             center
             of
             the
             Sun
             ,
             or
             any
             〈◊〉
             on
             the
             mensurator
             ,
             then
             immediately
             bring
             the
             unrectified
             pair
             of
             Rulers
             to
             the
             12
             a
             Clock-line
             on
             their
             side
             ,
             and
             if
             the
             Sun
             or
             Star
             be
             not
             exactly
             on
             the
             mensurator
             on
             this
             pair
             ,
             the
             Mensurator
             is
             false
             ,
             and
             must
             be
             rectified
             ,
             as
             is
             requisite
             :
             but
             this
             being
             plain
             to
             the
             meanest
             capacity
             versed
             in
             these
             matters
             ,
             I
             shall
             insist
             no
             longer
             thereon
             .
          
           
             But
             I
             proceed
             to
             the
             other
             Rectification
             of
             the
             Mensurator
             for
             rightly
             telling
             the
             Altitudes
             ,
             as
             I
             have
             said
             before
             .
             And
             tho
             there
             be
             not
             so
             very
             great
             exactness
             required
             herein
             ,
             especially
             in
             telling
             the
             time
             by
             the
             Sun
             or
             Stars
             when
             nigh
             the
             Meridian
             ;
             yet
             a
             gross
             error
             herein
             must
             not
             be
             allow'd
             .
             This
             likewise
             is
             to
             be
             performed
             much
             after
             the
             same
             method
             with
             the
             former
             Rectifications
             ,
             for
             't
             is
             but
             contriving
             some
             way
             for
             inverting
             the
             Ruler
             ,
             so
             that
             its
             errors
             of
             this
             kind
             may
             be
             perceived
             ,
             as
             by
             our
             former
             Inversions
             we
             discovered
             the
             errors
             of
             another
             kind
             .
             But
             to
             make
             this
             a
             little
             more
             plain
             ,
             this
             error
             consists
             in
             the
             line
             of
             Sight
             not
             running
             parallel
             with
             the
             under-side
             of
             the
             Ruler
             ;
             wherefore
             if
             we
             have
             (
             suppose
             )
             a
             Deal-board
             whose
             two
             faces
             are
             exactly
             parallel
             ,
             and
             this
             Board
             be
             raised
             and
             fixt
             
             so
             as
             to
             lye
             steddily
             along
             one
             of
             its
             edges
             ,
             and
             on
             each
             face
             of
             the
             Board
             there
             were
             a
             ledge
             to
             support
             the
             Ruler
             ;
             and
             the
             Ruler
             be
             applyed
             by
             its
             under-side
             to
             one
             face
             of
             the
             Board
             ,
             and
             the
             object
             marked
             out
             by
             the
             Mensurator
             ,
             diligently
             observed
             ;
             and
             then
             the
             Ruler
             applyed
             by
             the
             same
             under-side
             to
             the
             other
             face
             of
             the
             Board
             :
             If
             the
             same
             object
             be
             now
             cut
             as
             formerly
             ,
             ly
             ,
             all
             is
             right
             ;
             if
             not
             ,
             the
             Mensurator
             (
             being
             such
             as
             I
             have
             formerly
             described
             )
             must
             be
             screw'd
             or
             unscrew'd
             ,
             so
             that
             the
             fine
             point
             thereof
             may
             be
             lower
             or
             higher
             in
             the
             Ring
             ,
             according
             as
             is
             requisite
             .
          
           
             Another
             more
             easy
             way
             of
             discovering
             and
             rectifying
             this
             Error
             to
             sufficient
             accuracy
             ,
             is
             thus
             :
             After
             you
             have
             by
             the
             former
             methods
             brought
             the
             Mensurator
             ,
             and
             thereby
             the
             Ruler
             ,
             to
             shew
             the
             true
             Azimuth
             ;
             observe
             the
             time
             by
             the
             Dial
             when
             the
             Sun
             is
             very
             far
             removed
             from
             the
             Meridian
             ,
             as
             early
             in
             the
             morning
             ;
             and
             at
             the
             same
             time
             observe
             by
             a
             good
             Pendulum
             Clock
             the
             hour
             ,
             minute
             ,
             and
             second
             ;
             and
             note
             the
             difference
             between
             the
             Dial
             and
             Clock
             .
             Proceed
             thus
             to
             make
             an
             observation
             every
             quarter
             of
             an
             hour
             through
             the
             whole
             morning
             ,
             still
             noting
             the
             differences
             :
             And
             because
             we
             may
             well
             suppose
             that
             a
             good
             Pendulum
             Clock
             in
             so
             short
             a
             course
             of
             time
             goes
             equally
             ,
             these
             differences
             should
             be
             always
             equal
             ;
             but
             if
             they
             are
             unequal
             ,
             then
             the
             Mensurator
             shews
             
             the
             Altitudes
             falsely
             .
             As
             for
             instance
             ,
             suppose
             I
             find
             that
             approaching
             towards
             Noon
             these
             differences
             decrease
             ,
             then
             does
             the
             Mensurator
             on
             the
             
               Telescopick
               Ruler
            
             shew
             the
             Altitudes
             too
             little
             ,
             and
             therefore
             must
             be
             order'd
             so
             as
             to
             shew
             them
             more
             :
             if
             I
             find
             them
             increase
             ,
             the
             contrary
             is
             to
             be
             done
             .
             The
             reason
             of
             this
             is
             plain
             ,
             for
             an
             
               Horizontal
               Dial
            
             shews
             the
             time
             as
             well
             by
             the
             Altitudes
             as
             Azimuths
             ;
             but
             as
             the
             time
             approaches
             towards
             Noon
             ,
             the
             Altitudes
             are
             less
             concern'd
             in
             the
             matter
             than
             the
             Azimuths
             ;
             and
             so
             less
             and
             less
             ,
             till
             just
             at
             Noon
             the
             time
             is
             not
             at
             all
             shewn
             by
             the
             Altitude
             ,
             but
             solely
             by
             the
             Azimuth
             .
             And
             consequently
             ,
             if
             there
             be
             any
             error
             in
             the
             time
             arising
             from
             a
             false
             Altitude
             ,
             it
             will
             appear
             by
             comparing
             two
             times
             or
             more
             together
             ;
             some
             ,
             wherein
             the
             Altitudes
             are
             much
             concern'd
             ,
             and
             others
             ,
             wherein
             the
             Altitudes
             are
             little
             or
             not
             at
             all
             concern'd
             ;
             but
             such
             times
             are
             ,
             early
             in
             the
             morning
             ,
             and
             towards
             noon
             .
          
        
         
           
             CHAP.
             VI.
             The
             Way
             of
             Setting
             this
             Dial.
             
          
           
             TO
             the
             true
             Setting
             of
             this
             Dial
             ,
             there
             are
             two
             things
             requisite
             ;
             First
             ,
             that
             the
             plain
             of
             the
             Dial
             be
             in
             an
             exact
             Horizontal
             posture
             ,
             this
             
             is
             easily
             obtain'd
             by
             accurate
             levels
             ,
             which
             are
             so
             common
             ,
             that
             I
             shall
             mention
             nothing
             further
             hereof
             .
             The
             second
             requisite
             is
             ,
             that
             the
             meridian
             or
             12
             a
             Clock-line
             of
             the
             Dial
             be
             in
             an
             exact
             meridian
             line
             .
             This
             indeed
             is
             one
             of
             the
             chief
             particulars
             that
             we
             are
             to
             take
             care
             of
             ,
             for
             thereon
             depends
             the
             accuracy
             of
             the
             whole
             .
             But
             that
             we
             may
             not
             over-turn
             or
             neglect
             the
             whole
             affair
             for
             the
             difficulty
             of
             this
             one
             particular
             ,
             I
             shall
             shew
             that
             this
             is
             no
             such
             insuperable
             hardship
             as
             may
             be
             imagin'd
             .
             Let
             us
             therefore
             consider
             ,
             that
             what
             is
             here
             alledged
             as
             a
             difficulty
             in
             this
             Dial
             ,
             may
             as
             well
             be
             made
             against
             the
             large
             
               Azimuthal
               Quadrants
            
             used
             by
             Astronomers
             ,
             and
             their
             observations
             of
             
               meridional
               Altitudes
            
             ,
             and
             transits
             through
             the
             
               Meridian
               ;
               Ricciolis
               Triangulum
               Filare
            
             described
             
               Almag
               .
               Nov.
               Lib.
               5.
               
               Cap.
               15.
               
               Probl.
            
             8.
             and
             all
             Enquiries
             after
             the
             Declination
             of
             the
             Magnet
             are
             to
             no
             purpose
             ;
             for
             these
             wholly
             proceed
             on
             the
             discovery
             of
             an
             exact
             
               meridian
               line
            
             .
             And
             indeed
             there
             are
             ways
             sufficiently
             accurate
             described
             by
             several
             for
             finding
             the
             true
             meridian
             .
             Amongst
             others
             ,
             Hevelius
             in
             the
             first
             Part
             of
             his
             
               Machinia
               Caelestis
               ,
               Chap.
            
             16.
             has
             many
             contrivances
             :
             And
             I
             shall
             presently
             set
             down
             an
             Instrument
             and
             way
             of
             my
             own
             for
             doing
             it
             ,
             inferior
             ,
             I
             think
             ,
             to
             none
             .
             But
             let
             us
             a
             little
             consider
             ,
             how
             much
             a
             meridian
             line
             must
             be
             erronious
             ,
             to
             make
             a
             true
             Dial
             apply'd
             to
             it
             to
             err
             a
             minute
             in
             time
             ;
             and
             this
             in
             our
             latitude
             of
             Dublin
             
             will
             be
             12
             minutes
             of
             a
             Quadrant
             to
             make
             the
             Dial
             err
             a
             minute
             in
             time
             about
             noon
             ;
             and
             for
             so
             much
             error
             in
             the
             meridian
             line
             the
             Dial
             shall
             err
             less
             than
             a
             minute
             in
             time
             about
             5
             and
             6
             a
             Clock
             ,
             as
             is
             manifest
             to
             those
             that
             understand
             calculating
             hour
             distances
             for
             an
             Horizontal
             plain
             .
             Now
             't
             is
             a
             very
             rude
             way
             indeed
             that
             will
             not
             take
             a
             meridian
             line
             more
             accurately
             than
             to
             half
             or
             quarter
             12
             minutes
             error
             .
          
           
             But
             last
             of
             all
             ,
             (
             clearly
             to
             take
             off
             this
             difficulty
             ,
             )
             if
             it
             be
             allowed
             that
             there
             is
             any
             most
             accurate
             way
             of
             telling
             the
             time
             of
             day
             or
             night
             ,
             as
             by
             the
             Altitude
             of
             the
             Sun
             or
             Stars
             taken
             by
             large
             and
             curious
             Instruments
             ,
             and
             Calculating
             thereby
             ;
             I
             say
             ,
             by
             such
             a
             way
             as
             this
             I
             will
             set
             my
             Dial
             ,
             and
             then
             surely
             it
             will
             be
             granted
             to
             be
             in
             a
             true
             Meridian
             .
             And
             perhaps
             this
             very
             hint
             may
             shew
             as
             accurate
             a
             way
             as
             any
             in
             the
             World
             for
             finding
             a
             meridian
             line
             ;
             for
             the
             12
             a
             Clock
             line
             of
             a
             large
             and
             true
             Dial
             that
             is
             Set
             by
             such
             an
             accurate
             observation
             must
             needs
             lye
             in
             a
             true
             meridian
             line
             .
          
           
             But
             I
             am
             mindful
             of
             my
             promise
             ,
             Viz.
             
          
        
         
           
           
             CHAP.
             VII
             .
             For
             Finding
             a
             Meridian
             Line
             .
          
           
             THis
             is
             perform'd
             by
             means
             of
             the
             Instrument
             represented
             
               Fig.
               12.
               
               ABC
            
             is
             a
             Triangle
             .
             (
             That
             which
             I
             have
             made
             is
             of
             Wood
             ,
             but
             a
             good
             Mathematical-Instrument-maker
             would
             make
             one
             much
             better
             of
             Brass
             .
             )
             AB
             I
             call
             the
             Perpendicular
             side
             ,
             BC
             the
             Horizontal
             side
             ;
             in
             the
             end
             of
             the
             Horizontal
             side
             at
             E
             there
             is
             a
             screw
             ,
             and
             from
             the
             said
             Horizontal
             side
             there
             strikes
             out
             a
             short
             arm
             D
             ,
             in
             which
             also
             there
             is
             a
             screw
             ;
             this
             arm
             D
             keeps
             the
             Instrument
             steddy
             from
             tottering
             .
             By
             means
             of
             these
             two
             screws
             at
             D
             and
             E
             ,
             the
             side
             AB
             is
             brought
             to
             its
             exact
             perpendicularity
             ;
             but
             especially
             by
             means
             of
             the
             screw
             D
             ,
             the
             edge
             xz
             of
             the
             side
             AB
             is
             brought
             to
             stand
             exactly
             in
             the
             same
             Vertical
             plain
             with
             the
             edge
             mn
             of
             the
             side
             BC
             ,
             and
             this
             by
             help
             of
             a
             Plum-line
             .
             F
             is
             a
             plate
             of
             Brass
             ,
             having
             in
             it
             a
             center-hole
             in
             the
             line
             
               m
               ,
               n
            
             continued
             .
             G
             is
             a
             round
             ,
             slender
             ,
             but
             strong
             Brass-pin
             arising
             perpendicularly
             from
             the
             face
             
               mn
               .
               1
               ,
               2
               ,
               3
               ,
               4
               ,
               5
               ,
               &c.
            
             are
             round
             Brass-pins
             that
             rise
             and
             stick
             out
             from
             the
             face
             xz
             ,
             at
             what
             distances
             we
             please
             .
             This
             Instrument
             being
             placed
             truly
             on
             an
             exquisite
             Horizontal
             plain
             ,
             
             so
             that
             its
             end
             E
             may
             something
             over-stretch
             the
             plain
             ,
             and
             turning
             steddily
             on
             a
             pin
             in
             the
             center-hole
             F
             ,
             lay
             a
             Ruler
             adapted
             with
             
               Telescopick
               Sights
            
             over
             the
             pin
             G
             ,
             and
             any
             of
             the
             other
             1
             ,
             2
             ,
             3
             ,
             &c.
             as
             is
             found
             most
             convenient
             and
             agreeable
             to
             the
             Altitude
             of
             the
             Sun
             or
             Stars
             you
             observe
             by
             ,
             at
             convenient
             times
             both
             before
             and
             after
             Noon
             .
             'T
             is
             therefore
             requisite
             that
             in
             the
             under-side
             of
             your
             
               Telescopick
               Ruler
            
             towards
             the
             end
             next
             the
             eye
             ,
             there
             be
             fixt
             a
             pin
             ,
             that
             resting
             on
             the
             pin
             G
             may
             keep
             the
             Ruler
             from
             slipping
             down
             in
             this
             declining
             posture
             .
             Let
             us
             then
             suppose
             that
             about
             9
             a
             Clock
             in
             the
             morning
             on
             the
             Summer
             Solstice
             ,
             the
             
               Telescopick
               Ruler
            
             resting
             on
             the
             pin
             G
             ,
             and
             the
             third
             pin
             in
             the
             perpendicular
             side
             takes
             the
             Suns
             Altitude
             exactly
             ,
             then
             on
             the
             Horizontal
             plain
             draw
             a
             line
             along
             the
             face
             
               m
               ,
               n.
            
             Again
             ,
             let
             us
             suppose
             that
             the
             Ruler
             removed
             upwards
             to
             the
             fourth
             pin
             ,
             and
             there
             resting
             ,
             takes
             the
             Suns
             Altitude
             the
             same
             morning
             about
             half
             an
             hour
             after
             9
             ;
             then
             by
             the
             face
             mn
             let
             us
             draw
             another
             line
             on
             the
             Horizontal
             plain
             ,
             and
             so
             let
             us
             proceed
             to
             elevate
             the
             Ruler
             on
             other
             pins
             ,
             to
             make
             observations
             at
             10
             ,
             at
             half
             an
             hour
             after
             10
             the
             same
             morning
             ,
             still
             drawing
             lines
             on
             the
             Horizontal
             plain
             at
             each
             observation
             .
          
           
             Then
             again
             in
             the
             afternoon
             let
             us
             descend
             by
             the
             same
             steps
             or
             pins
             ,
             by
             which
             we
             rise
             in
             the
             morning
             ,
             diligently
             observing
             when
             the
             Sun
             
             comes
             to
             the
             corresponding
             Altitudes
             ,
             and
             drawing
             lines
             as
             before
             .
             Here
             we
             shall
             have
             three
             or
             four
             observations
             made
             in
             the
             morning
             ,
             and
             as
             many
             in
             the
             afternoon
             .
             Then
             bisecting
             these
             Angles
             from
             the
             point
             F
             ,
             if
             all
             their
             bisections
             are
             coincident
             in
             the
             same
             right
             line
             ,
             we
             are
             sure
             that
             line
             is
             a
             true
             meridian
             line
             .
          
           
             What
             is
             here
             said
             of
             the
             Sun
             ,
             and
             of
             observing
             by
             it
             at
             the
             Summer
             Solstice
             ,
             may
             be
             accommodated
             to
             the
             taking
             a
             meridian
             line
             at
             any
             time
             of
             the
             year
             by
             some
             fixt
             Stars
             ,
             that
             being
             removed
             about
             2
             or
             3
             hours
             from
             the
             Meridian
             ,
             have
             Altitude
             convenient
             ;
             though
             in
             choosing
             of
             a
             great
             Altitude
             there
             is
             no
             great
             nicety
             ;
             for
             if
             Refraction
             do
             interpose
             in
             the
             morning-observation
             ;
             it
             interposes
             as
             much
             in
             the
             afternoon-observation
             ;
             so
             that
             't
             is
             as
             if
             it
             did
             not
             interpose
             at
             all
             .
             And
             here
             we
             have
             a
             way
             of
             finding
             a
             Meridian
             line
             by
             the
             Stars
             at
             night
             ,
             which
             is
             of
             no
             small
             advantage
             ,
             they
             being
             not
             subject
             to
             sudden
             alteration
             of
             their
             Declination
             ,
             and
             consequently
             this
             method
             may
             be
             practised
             at
             all
             times
             of
             the
             year
             .
          
           
             And
             indeed
             if
             we
             are
             careful
             to
             have
             all
             things
             exact
             ,
             viz.
             an
             exact
             Horizontal
             plain
             ,
             the
             face
             xz
             in
             an
             exact
             Vertical
             with
             the
             face
             mn
             ,
             the
             
               Telescopick
               Ruler
            
             and
             its
             Sights
             exactly
             adjusted
             by
             the
             methods
             in
             the
             foregoing
             5th
             Chapt.
             and
             be
             very
             diligent
             and
             accurate
             in
             observing
             the
             true
             Altitudes
             ,
             this
             method
             of
             finding
             a
             
               meridian
               line
            
             will
             
             appear
             inferior
             to
             none
             that
             has
             yet
             been
             proposed
             .
          
           
             Such
             a
             plain
             
               Telescopick
               Ruler
            
             as
             is
             expressed
             in
             the
             11th
             .
             Figure
             ,
             of
             a
             convenient
             length
             ,
             is
             sufficient
             in
             this
             practice
             .
          
        
         
           
             CHAP.
             VIII
             .
             The
             Manner
             of
             observing
             the
             Time
             ,
             and
             exactly
             determining
             it
             by
             the
             Sun
             or
             Stars
             .
          
           
             ALL
             things
             being
             rightly
             adjusted
             ,
             and
             the
             Dial
             placed
             in
             an
             exact
             level
             or
             Horizontal
             posture
             ,
             and
             by
             a
             true
             meridian
             line
             ,
             look
             at
             the
             Sun
             through
             the
             Telescopick
             or
             Stile-Ruler
             ,
             and
             bring
             the
             Mensurator
             upon
             the
             Suns
             center
             ,
             then
             shall
             the
             
               Horizontal
               Ruler
            
             cut
             the
             hour
             ,
             minute
             ,
             and
             part
             of
             a
             minute
             most
             exactly
             .
             But
             for
             Setting
             ,
             or
             finding
             the
             error
             of
             a
             Clock
             ,
             the
             best
             way
             is
             to
             bring
             the
             
               Horizontal
               Ruler
            
             to
             some
             full
             Division
             ,
             as
             ,
             to
             some
             compleat
             minute
             ;
             and
             by
             rightly
             managing
             the
             Stile-screw
             and
             Nut
             ,
             and
             Stile-Ruler
             ,
             observe
             when
             the
             center
             of
             the
             Sun
             and
             Mensurator
             come
             together
             ,
             for
             that
             is
             the
             exact
             time
             to
             which
             you
             placed
             the
             
               Horizontal
               Ruler
            
             .
             And
             indeed
             through
             the
             
               Telescopick
               Sights
            
             we
             shall
             perceive
             the
             motion
             of
             the
             Sun
             so
             very
             quick
             ,
             that
             we
             may
             determine
             its
             being
             on
             and
             off
             the
             mensurator
             to
             2
             beats
             of
             a
             
             second
             Pendulum
             .
             So
             that
             if
             it
             be
             granted
             me
             that
             I
             can
             bring
             and
             settle
             the
             Horizontal-Ruler
             to
             a
             full
             division
             exactly
             ,
             and
             not
             to
             err
             in
             placing
             it
             thereat
             over
             3
             ,
             5
             ,
             or
             7
             seconds
             ,
             I
             can
             determine
             the
             time
             of
             day
             or
             night
             to
             3
             ,
             5
             ,
             or
             7
             seconds
             .
             But
             if
             this
             great
             exactness
             will
             not
             be
             allow'd
             me
             ,
             I
             say
             it
             is
             not
             on
             the
             account
             of
             any
             fault
             in
             the
             Theory
             of
             this
             contrivance
             ,
             which
             I
             dare
             assert
             to
             be
             most
             accurate
             in
             it self
             ,
             but
             on
             the
             account
             of
             the
             workmanship
             or
             deficiency
             of
             some
             of
             its
             parts
             .
             And
             that
             strikes
             not
             at
             the
             Inventer
             ;
             let
             those
             that
             use
             them
             ,
             and
             adjust
             them
             ,
             look
             to
             their
             truness
             in
             all
             particulars
             .
          
           
             The
             way
             of
             using
             this
             Dial
             at
             the
             Stars
             by
             night
             is
             much
             the
             same
             ,
             only
             for
             these
             there
             are
             requisite
             the
             Tables
             ,
             at
             the
             end
             of
             this
             Book
             ,
             of
             the
             Sun
             and
             Stars
             temporary
             
               Right
               Ascensions
            
             .
             In
             looking
             at
             ,
             or
             observing
             a
             Star
             through
             the
             
               Telescopick
               Ruler
            
             ,
             the
             
               Horizontal
               Ruler
            
             cuts
             the
             said
             Stars
             horary
             distance
             from
             the
             Meridian
             ,
             but
             then
             the
             hours
             are
             to
             be
             counted
             by
             the
             smaller
             Figures
             on
             the
             in-side
             of
             the
             limb
             .
             Thus
             ,
             suppose
             I
             observe
             a
             Star
             ,
             and
             find
             the
             
               Horizontal
               Ruler
            
             cut
             the
             ten
             a
             Clock
             line
             to
             which
             the
             great
             Figure
             of
             X
             is
             affixt
             ,
             the
             horary
             distance
             of
             that
             Star
             from
             the
             Meridian
             is
             22
             hours
             ,
             that
             is
             ,
             twenty
             two
             hours
             are
             elapsed
             since
             that
             Star
             was
             last
             in
             our
             meridian
             ,
             though
             really
             the
             Star
             be
             but
             2
             hours
             to
             the
             East
             of
             our
             meridian
             .
             This
             premised
             ,
             the
             great
             Rule
             
             for
             telling
             the
             time
             by
             the
             Stars
             is
             this
             ;
             
               To
               the
               Stars
               horary
               distance
               from
               the
               meridian
               ,
               add
               the
               Stars
               temporary
               Right
               Ascension
               ,
               and
               from
               the
               Sum
               substract
               the
               Suns
               Right
               Ascension
               ,
               the
               remainder
               (
               rejecting
               24
               hours
               if
               need
               be
               )
               gives
               the
               hour
               ,
               minute
               ,
               &c.
               of
               the
               night
               .
            
          
           
             I
             shall
             declare
             this
             by
             an
             Example
             .
             
               Anno
               1686.
               
               April
            
             the
             5th
             .
             between
             9
             and
             10
             a
             Clock
             at
             night
             I
             desire
             to
             know
             the
             exact
             time
             .
             I
             observe
             by
             
               Spica
               Virginis
            
             ,
             and
             find
             (
             suppose
             )
             its
             horary
             distance
             from
             the
             
               meridian
               22
               h.
               03′
               15″
            
             .
             The
             temporary
             
               Right
               Ascension
            
             of
             that
             Star
             for
             that
             year
             is
             ,
             13
             
               h.
               08′
               .
               46″
            
             ,
             this
             added
             to
             the
             foresaid
             horary
             distance
             ,
             the
             sum
             is
             35
             h.
             12′
             .
             01″
             .
             At
             the
             same
             time
             the
             Suns
             place
             is
             ♈
             .
             26°
             13′
             59″
             .
             Therefore
             its
             
               Right
               Ascension
            
             in
             time
             by
             the
             following
             Tables
             ,
             is
             1
             h.
             37′
             .
             17″
             .
             this
             substracted
             from
             the
             foresaid
             sum
             (
             and
             rejecting
             24
             hours
             )
             leaves
             9
             h.
             34′
             44″
             .
             the
             exact
             time
             of
             night
             .
             The
             reason
             and
             demonstration
             of
             this
             method
             depends
             on
             Astronomical
             Principles
             ,
             which
             at
             present
             I
             must
             not
             undertake
             to
             illustrate
             ,
             but
             are
             obvious
             enough
             to
             those
             that
             are
             versed
             in
             that
             Science
             ,
             and
             will
             be
             very
             plain
             to
             those
             that
             consider
             the
             way
             of
             Calculating
             the
             hour
             of
             the
             night
             by
             the
             Altitude
             of
             a
             Star
             given
             ,
             according
             to
             the
             most
             Learned
             and
             Ingenious
             
               Pere
               Tacquets
            
             Illustration
             thereof
             in
             his
             Astronomy
             ,
             
               Lib.
               5.
               
               Cap.
               4.
               
               Num.
            
             45.
             
          
           
             And
             though
             there
             are
             other
             ways
             of
             ordering
             the
             foregoing
             Data
             ,
             for
             getting
             the
             hour
             of
             the
             
             night
             ,
             yet
             what
             I
             propose
             is
             as
             plain
             and
             easy
             as
             any
             ,
             and
             less
             embarras
             to
             the
             mind
             .
          
           
             But
             here
             I
             must
             not
             omit
             one
             particular
             ,
             and
             that
             is
             ,
             that
             by
             our
             present
             contrivance
             ,
             the
             
               Right
               Ascension
            
             ,
             or
             place
             in
             the
             Aequator
             of
             any
             Star
             ,
             is
             most
             easily
             and
             accurately
             obtained
             .
             How
             difficult
             and
             troublesome
             't
             is
             to
             obtain
             the
             
               Right
               Ascension
            
             of
             Stars
             ,
             is
             known
             to
             Astronomers
             ,
             and
             will
             appear
             to
             those
             that
             consult
             the
             forementioned
             
               Tacquet
               Astionom
               .
               Lib.
               5.
               
               Cap.
               1.
               num
               .
            
             4
             ,
             5.
             but
             by
             this
             Instrument
             ,
             and
             a
             truly
             rectify'd
             Pendulum
             Clock
             ,
             the
             business
             is
             easily
             perform'd
             :
             For
             ,
             from
             the
             sum
             of
             the
             Suns
             
               Right
               Ascension
            
             ,
             and
             hour
             of
             the
             night
             (
             known
             by
             the
             Clock
             )
             substract
             the
             Stars
             hour
             on
             the
             Dial
             ,
             the
             remainder
             is
             the
             Stars
             
               Right
               Ascension
            
             in
             time
             ,
             which
             converted
             into
             degrees
             and
             minutes
             ,
             shews
             the
             Aequatorian
             distance
             of
             the
             Star
             from
             the
             first
             point
             of
             ♈
             ,
             or
             its
             
               Right
               Ascension
            
             .
          
        
         
           
             CHAP.
             IX
             .
             Of
             the
             Tables
             of
             the
             Suns
             and
             Stars
             Temporary
             Right
             Ascensions
             .
          
           
             THe
             Table
             of
             the
             Stars
             
               Right
               Ascensions
            
             in
             time
             is
             plain
             enough
             of
             it self
             .
             'T
             is
             computed
             to
             the
             year
             1686
             ,
             and
             will
             serve
             for
             ten
             years
             to
             come
             without
             the
             error
             of
             half
             a
             minute
             .
             
             'T
             is
             according
             to
             
             Riccioli's
             Catalogue
             of
             sixt
             Stars
             in
             his
             
               Astronomia
               Reformata
            
             .
             It
             consists
             of
             5
             Columns
             ,
             the
             first
             contains
             the
             Magnitudes
             ,
             the
             second
             shews
             the
             
               Greek
               Letters
            
             by
             which
             each
             Star
             is
             marked
             in
             
               Bayers
               Vranometria
            
             Printed
             at
             Ausburg
             ,
             1603.
             
             The
             third
             has
             the
             numbers
             by
             which
             each
             Star
             is
             noted
             in
             
             Tiho's
             Catalogue
             ,
             which
             is
             followed
             by
             most
             Authors
             ,
             but
             is
             to
             be
             found
             particularly
             in
             
               Tichonis
               Brahe
               Astronomiae
               Instauratae
               Progymnasmata
               ,
               pag.
            
             258.
             and
             at
             the
             end
             of
             the
             
               Rudolphine
               Tables
            
             published
             by
             Kepler
             .
             The
             fourth
             Column
             contains
             the
             Stars
             names
             ,
             as
             they
             are
             in
             
             Bayer's
             Vranometria
             ;
             and
             also
             after
             each
             name
             we
             express
             the
             common
             name
             in
             English
             ,
             and
             as
             they
             are
             to
             be
             found
             on
             our
             common
             Globes
             .
             And
             here
             we
             must
             not
             wonder
             to
             find
             that
             called
             Right
             or
             Left
             in
             the
             Latin
             names
             of
             Bayer
             ,
             that
             is
             called
             Left
             or
             Right
             in
             the
             English
             common
             names
             ;
             as
             for
             instance
             ,
             
               Herculis
               Humerus
               Dexter
            
             ,
             is
             in
             English
             ,
             the
             
               left
               shoulder
               of
               Hercules
            
             .
             For
             the
             reason
             of
             this
             will
             appear
             plain
             to
             those
             that
             consider
             the
             Constellations
             of
             Bayer
             ,
             and
             the
             common
             Constellations
             on
             our
             Globes
             .
             And
             I
             thought
             it
             not
             amiss
             to
             take
             all
             this
             care
             ,
             and
             express
             all
             these
             marks
             for
             the
             sake
             of
             those
             that
             are
             not
             so
             well
             versed
             in
             the
             appearance
             of
             the
             Firmament
             ,
             that
             they
             may
             the
             readier
             find
             out
             ,
             and
             not
             so
             easily
             mistake
             any
             of
             the
             forementioned
             Stars
             .
             The
             fifth
             and
             last
             Column
             expresses
             
             the
             
               Right
               Ascension
            
             in
             time
             of
             each
             Star
             to
             the
             present
             year
             1686.
             
          
           
             The
             Tables
             of
             the
             Suns
             
               Right
               Ascension
            
             in
             time
             require
             the
             Suns
             place
             to
             be
             had
             from
             some
             good
             Tables
             or
             Ephemerides
             .
             They
             consist
             of
             four
             Columns
             ,
             the
             first
             contains
             every
             degree
             and
             10
             minutes
             of
             the
             Suns
             place
             ,
             the
             second
             contains
             the
             hours
             appropriated
             to
             the
             signs
             between
             the
             Vernal
             and
             
               Autumnal
               Equinox
            
             ,
             the
             third
             shews
             the
             hours
             appropriated
             to
             the
             signs
             between
             the
             Autumnal
             and
             
               Vernal
               Equinox
            
             ;
             and
             the
             fourth
             and
             last
             shews
             the
             parts
             of
             an
             hour
             ,
             that
             is
             ,
             minutes
             and
             seconds
             ,
             that
             are
             common
             to
             the
             opposite
             signs
             .
             By
             the
             side
             of
             each
             division
             are
             expressed
             the
             differences
             between
             every
             10
             minutes
             of
             the
             Suns
             place
             ,
             for
             more
             ready
             making
             proportion
             .
             For
             Example
             ,
             suppose
             the
             Suns
             place
             were
             ♈
             .
             25°
             .
             10″
             I
             find
             its
             
               Right
               Ascension
            
             1
             h.
             33′
             15″
             .
             But
             if
             his
             place
             were
             ♎
             25°
             .
             10″
             .
             the
             
               Right
               Ascension
            
             would
             be
             13
             h.
             33′
             .
             15″
             .
             Where
             we
             see
             33′
             .
             15″
             .
             common
             to
             both
             places
             .
             But
             suppose
             I
             find
             by
             a
             good
             Ephemeris
             the
             Suns
             place
             about
             my
             required
             time
             to
             be
             ♈
             25°
             .
             15″
             then
             by
             making
             proportion
             I
             find
             by
             the
             Tables
             the
             
               Right
               Ascension
            
             to
             be
             1
             h.
             33′
             .
             34″
             .
             For
             I
             say
             if
             10′
             (
             the
             common
             difference
             of
             the
             minutes
             )
             give
             38″
             ,
             what
             shall
             5′
             (
             the
             difference
             between
             10′
             and
             15′
             )
             give
             ,
             and
             it
             will
             be
             19″
             ,
             which
             added
             to
             1
             h.
             33′
             .
             15″
             .
             makes
             1
             h.
             33′
             34″
             .
          
           
             I
             know
             the
             common
             way
             for
             giving
             the
             Suns
             
             
               Right
               Ascension
            
             is
             by
             making
             a
             Table
             of
             the
             days
             of
             the
             month
             ,
             and
             giving
             the
             Suns
             
               Right
               Ascension
            
             to
             the
             days
             .
             But
             this
             way
             ,
             if
             it
             be
             general
             ,
             and
             not
             appropriated
             to
             a
             certain
             year
             ,
             is
             not
             accurate
             to
             a
             minute
             or
             two
             :
             and
             if
             it
             be
             adapted
             to
             a
             certain
             year
             ,
             't
             is
             not
             general
             ,
             and
             will
             not
             serve
             another
             time
             .
             Whereas
             our
             Tables
             of
             the
             Suns
             
               Right
               Ascension
            
             are
             general
             ,
             most
             accurate
             to
             a
             second
             ,
             and
             perpetual
             .
          
        
         
           
             CHAP.
             X.
             Concerning
             the
             Astronomical
             Equation
             of
             Time
             ,
             and
             the
             Tables
             thereof
             .
          
           
             BEing
             now
             upon
             the
             business
             of
             Time
             ,
             and
             the
             accurate
             observation
             thereof
             ,
             so
             as
             thereby
             to
             regulate
             curious
             Time-keepers
             ;
             it
             will
             not
             be
             improper
             to
             our
             subject
             to
             speak
             something
             of
             the
             Inequality
             of
             natural
             Days
             ;
             a
             matter
             that
             has
             exercised
             the
             thoughts
             of
             all
             Astronomers
             in
             all
             ages
             :
             And
             though
             all
             have
             allowed
             that
             there
             really
             is
             such
             an
             Inequality
             ,
             yet
             they
             have
             much
             disagreed
             in
             assigning
             its
             quantity
             ,
             or
             demonstrating
             the
             reason
             and
             affections
             thereof
             ;
             till
             at
             last
             our
             most
             Learned
             and
             Ingenious
             English
             Astronomer
             ,
             and
             my
             Honoured
             Friend
             Mr.
             
               John
               Flamsteed
               Math.
               Regius
            
             ,
             has
             determined
             the
             Controversy
             ,
             
             and
             by
             most
             evident
             demonstrations
             has
             put
             the
             matter
             beyond
             further
             dispute
             ,
             clearly
             evincing
             both
             the
             Reasons
             ,
             Affections
             ,
             and
             Quantity
             of
             this
             Inequality
             .
             His
             Dissertation
             concerning
             this
             is
             annex'd
             and
             publish'd
             at
             the
             end
             of
             the
             
               Opera
               Posthuma
               Jeremiae
               Horroxcii
               ,
               Lond.
            
             1673.
             4
             to
             .
             From
             which
             (
             with
             my
             esteemed
             Friend's
             leave
             )
             I
             shall
             present
             the
             Reader
             with
             the
             following
             Schemes
             and
             Demonstrations
             .
          
           
             On
             account
             of
             the
             Suns
             Excentricity
             from
             the
             center
             of
             the
             Earths
             
               Annual
               Orbit
            
             ,
             the
             Diurnal
             motion
             of
             the
             Earth
             is
             sometimes
             faster
             ,
             and
             sometimes
             slower
             than
             the
             mean
             motion
             ,
             and
             consequently
             the
             apparent
             Day
             is
             sometimes
             longer
             ,
             and
             sometimes
             shorter
             than
             the
             mean
             Day
             .
             Which
             Inequality
             ,
             and
             the
             Quantity
             of
             the
             difference
             of
             the
             equal
             or
             mean
             Day
             from
             the
             apparent
             ,
             is
             thus
             demonstrated
             from
             the
             13
             Figure
             ,
             according
             to
             the
             
               Copernican
               System
            
             .
          
           
             Let
             ABPN
             be
             the
             great
             Orbit
             in
             which
             the
             Earth
             is
             yearly
             carried
             about
             the
             Sun
             ,
             the
             center
             hereof
             is
             
               C
               ,
               A
            
             the
             Aphelion
             ,
             or
             the
             Earths
             place
             at
             Noon
             on
             that
             day
             that
             it
             is
             in
             its
             Aphelion
             ,
             suppose
             the
             18th
             .
             of
             
               June
               .
               B
            
             the
             Earths
             place
             at
             Noon
             the
             day
             following
             .
             AL
             an
             assigned
             Meridian
             of
             the
             Earth
             .
             The
             arch
             AB
             ,
             or
             the
             angle
             ACB
             ,
             the
             mean
             motion
             of
             the
             Earth
             from
             the
             Noon
             of
             a
             given
             day
             to
             the
             Noon
             of
             the
             day
             following
             .
             L
             a
             point
             in
             the
             given
             Meridian
             turn'd
             to
             the
             Sun
             ;
             which
             
             point
             ,
             whilst
             the
             Earth
             is
             carried
             in
             its
             Orbit
             from
             A
             to
             B
             ,
             is
             rould
             by
             the
             
               diurnal
               circumvolution
            
             of
             the
             Earth
             from
             L
             through
             O
             in
             the
             first
             place
             A
             to
             d
             in
             the
             second
             place
             B
             ;
             to
             which
             place
             ,
             when
             the
             said
             point
             arrives
             ,
             't
             is
             manifest
             that
             the
             Earth
             has
             performed
             a
             compleat
             revolution
             about
             its
             own
             Axis
             ;
             because
             the
             
               meridian
               Bd
            
             ,
             in
             this
             its
             second
             posture
             at
             B
             ,
             is
             made
             parallel
             to
             AL
             it
             s
             yesterdays
             posture
             at
             A.
             But
             it
             is
             not
             yet
             apparent
             Noon
             ,
             till
             the
             same
             point
             of
             the
             Earth
             by
             its
             revolution
             by
             brought
             to
             e
             ,
             where
             't
             is
             turn'd
             directly
             opposite
             to
             the
             Sun
             ,
             who
             governs
             the
             Civil
             Days
             .
             And
             that
             this
             time
             is
             not
             the
             same
             with
             the
             Caelestial
             or
             equal
             Noon
             ,
             will
             be
             proved
             ,
             not
             only
             because
             the
             Earth
             has
             not
             yet
             performed
             its
             mean
             motion
             above
             its
             revolution
             ,
             (
             tho
             this
             were
             a
             sufficient
             argument
             )
             but
             also
             because
             the
             diurnal
             motions
             about
             the
             Sun
             ,
             and
             consequently
             the
             returns
             of
             any
             certain
             meridian
             to
             him
             ,
             are
             very
             unequal
             ;
             neither
             can
             they
             possibly
             be
             equal
             in
             respect
             of
             any
             point
             about
             which
             the
             Earth
             is
             not
             carried
             equally
             ,
             as
             is
             sufficiently
             manifest
             from
             the
             inspection
             of
             the
             Scheme
             only
             .
             Wherefore
             the
             mean
             Noon
             and
             equal
             Time
             respects
             the
             point
             of
             the
             mean
             motion
             
               (
               that
               is
               the
               center
               of
               the
               Orbit
               C
               )
            
             and
             in
             our
             present
             instance
             is
             then
             when
             the
             meridian
             carried
             from
             e
             arrives
             at
             f
             ,
             where
             't
             is
             directly
             opposite
             to
             the
             center
             of
             the
             
               Orbit
               C.
            
             And
             when
             it
             has
             gained
             this
             posture
             ,
             the
             Earth
             has
             
             performed
             its
             mean
             motion
             above
             a
             revolution
             requisite
             to
             compleat
             a
             mean
             day
             .
             For
             the
             arch
             df
             or
             the
             angle
             dBf
             is
             equal
             to
             the
             angle
             ACB
             the
             mean
             diurnal
             motion
             of
             the
             Earth
             .
             Also
             the
             arch
             de
             ,
             which
             the
             Earth
             ,
             or
             any
             meridian
             therein
             ,
             must
             pass
             more
             than
             a
             revolution
             before
             it
             be
             apparent
             Noon
             ,
             is
             equal
             to
             the
             angle
             ASB
             the
             apparent
             motion
             of
             the
             Earth
             at
             the
             Sun.
             From
             whence
             't
             is
             evident
             ,
             that
             the
             arch
             ef
             ,
             which
             the
             circumference
             of
             the
             rouling
             Earth
             performs
             between
             the
             apparent
             and
             mean
             Noon
             ,
             and
             which
             shews
             the
             difference
             between
             the
             apparent
             and
             mean
             Day
             ,
             is
             equal
             to
             the
             angle
             SBC
             ,
             which
             is
             the
             Equation
             of
             the
             Orbit
             .
             Wherefore
             the
             Prosthaphaereses
             of
             the
             Orbit
             resolved
             into
             parts
             of
             time
             ,
             shall
             be
             the
             Aequations
             of
             time
             ;
             which
             Aequations
             ,
             throughout
             this
             semicircle
             of
             Anomoly
             are
             negative
             ,
             or
             to
             be
             substracted
             from
             the
             apparent
             time
             ,
             for
             herein
             the
             mean
             Noon
             succeeds
             the
             apparent
             .
          
           
             In
             like
             manner
             ,
             if
             we
             take
             the
             opposite
             parts
             of
             the
             Scheme
             ,
             and
             consider
             the
             Earth
             in
             its
             Perihelion
             .
             The
             point
             g
             ,
             or
             the
             
               meridian
               ng
            
             ,
             being
             made
             parallel
             to
             its
             yesterdays
             posture
             ,
             't
             is
             plain
             that
             the
             Earth
             has
             performed
             one
             compleat
             revolution
             .
             This
             point
             being
             carried
             to
             h
             ,
             where
             't
             is
             opposite
             to
             the
             center
             of
             the
             Orbit
             ,
             't
             is
             now
             mean
             Noon
             ;
             for
             the
             arch
             gh
             ,
             or
             the
             angle
             gNh
             equal
             to
             the
             mean
             diurnal
             motion
             of
             the
             Earth
             ,
             is
             passed
             over
             .
             But
             it
             is
             not
             yet
             apparent
             Noon
             ,
             till
             the
             
             Earth
             by
             its
             rouling
             brings
             the
             same
             meridian
             to
             k
             ,
             where
             't
             is
             directly
             opposite
             to
             the
             Sun.
             From
             whence
             't
             is
             manifest
             that
             the
             apparent
             Day
             exceeds
             the
             mean
             by
             so
             much
             time
             as
             is
             requisite
             for
             the
             earth
             to
             pass
             the
             arch
             hk
             ,
             which
             arch
             is
             equal
             to
             the
             angle
             CNS
             the
             Prosthapheresis
             of
             the
             Orbit
             :
             wherefore
             resolving
             this
             into
             time
             ,
             we
             have
             the
             Aequation
             of
             time
             ,
             which
             throughout
             this
             semicircle
             of
             Anomoly
             is
             affirmative
             ,
             or
             to
             be
             added
             to
             the
             apparent
             time
             ,
             because
             herein
             the
             mean
             Noon
             precedes
             the
             apparent
             .
          
           
             'T
             is
             manifest
             from
             what
             foregoes
             ,
             that
             if
             the
             Sun
             were
             in
             the
             center
             of
             the
             great
             Orbit
             ,
             and
             the
             Earths
             Axis
             were
             not
             inclined
             to
             its
             path
             or
             way
             ,
             there
             would
             be
             no
             Inequality
             of
             time
             ,
             but
             the
             mean
             Day
             and
             apparent
             would
             be
             equal
             .
             Moreover
             ,
             if
             there
             were
             no
             excentricity
             of
             the
             Sun
             from
             the
             center
             of
             the
             Orbit
             ,
             but
             there
             were
             the
             usual
             inclination
             of
             the
             Earths
             Axis
             to
             the
             Orbit
             ,
             tho
             there
             would
             no
             Inequality
             of
             time
             arise
             such
             as
             is
             shewn
             in
             the
             foregoing
             demonstration
             ;
             yet
             there
             would
             arise
             another
             Inequality
             from
             the
             said
             inclination
             of
             the
             Earths
             Axis
             ,
             or
             as
             the
             Ptolomaicks
             would
             express
             it
             ,
             from
             the
             inclination
             of
             the
             Ecliptick
             to
             the
             Aequator
             ;
             the
             quantity
             and
             affections
             of
             which
             Inequality
             is
             thus
             shewn
             by
             the
             Analemma
             .
          
           
             In
             
               Fig.
               14.
               
               PCF
            
             is
             a
             Quadrant
             of
             the
             
               Solstitial
               Colure
               ,
               P
            
             the
             
               Pole
               ,
               AF
            
             a
             Radius
             of
             the
             
               Aequator
               ,
               CA
            
             a
             
             Radius
             of
             the
             
               Ecliptick
               ,
               A
            
             the
             Equinoctial
             point
             ,
             or
             the
             place
             of
             the
             Sun
             in
             the
             beginning
             of
             ♈
             at
             noon
             on
             some
             certain
             day
             ,
             ☉
             the
             Suns
             place
             at
             noon
             the
             day
             following
             ;
             through
             which
             place
             striking
             the
             arch
             
               P
               ☉
               B
               perpendicular
            
             to
             the
             
               Aequator
               ,
               A
            
             ☉
             will
             express
             the
             diurnal
             motion
             of
             the
             Sun
             ,
             and
             AB
             its
             
               Right
               ascension
            
             ,
             or
             the
             arch
             of
             the
             Aequator
             that
             Culminates
             with
             the
             Sun.
             Which
             arch
             ,
             seeing
             't
             is
             one
             of
             the
             sides
             of
             a
             Right-angled
             
               Triangle
               A
               ☉
               B
            
             ,
             cannot
             be
             equal
             to
             the
             Hypotenuse
             ,
             that
             is
             ,
             to
             the
             Suns
             motion
             A
             ☉
             .
             Wherefore
             seeing
             the
             revolutions
             of
             the
             Aequator
             ,
             and
             of
             its
             equal
             or
             like
             parts
             ,
             are
             equable
             ,
             and
             performed
             in
             equal
             times
             ,
             but
             the
             Sun
             in
             passing
             equal
             parts
             of
             the
             Ecliptick
             applies
             to
             the
             meridian
             with
             unequal
             parts
             of
             the
             Aequator
             ;
             it
             necessarily
             follows
             that
             the
             solar
             days
             are
             unequal
             .
             And
             that
             the
             difference
             between
             the
             Suns
             true
             place
             and
             its
             
               Right
               ascension
            
             being
             converted
             into
             time
             ,
             is
             the
             true
             Aequation
             of
             time
             arising
             from
             this
             cause
             .
             Which
             Aequation
             ,
             in
             the
             first
             and
             third
             Quadrants
             of
             the
             Zodiack
             is
             to
             be
             substracted
             from
             the
             apparent
             time
             ,
             for
             in
             them
             the
             longitude
             of
             the
             Sun
             from
             the
             next
             Equinoctial
             point
             passes
             the
             meridian
             sooner
             than
             a
             like
             arch
             projected
             in
             the
             Aequator
             .
             But
             in
             the
             2d
             and
             
               4th
               Quadrants
            
             of
             the
             Zodiack
             this
             Aequation
             is
             to
             be
             added
             to
             the
             apparent
             time
             to
             get
             the
             mean
             ;
             for
             in
             these
             the
             longitude
             of
             the
             Sun
             from
             the
             Aequinox
             passes
             the
             meridian
             later
             than
             the
             like
             Arch
             projected
             in
             the
             
             Aequator
             .
             For
             example
             ,
             let
             the
             longitude
             of
             the
             Sun
             from
             the
             first
             point
             of
             ♈
             be
             ☉
             A.
             0°
             .
             59′
             .
             08″
             .
             it
             s
             
               Right
               ascension
            
             ,
             or
             the
             arch
             of
             the
             
               Aequator
               culminating
            
             therewith
             AB
             will
             be
             0°
             .
             54′
             .
             13″
             .
             their
             difference
             4′
             .
             55″
             .
             being
             converted
             into
             time
             is
             00
             h
             00′
             .
             19″
             .
             40‴
             ,
             and
             by
             so
             much
             is
             the
             apparent
             day
             shorter
             than
             the
             mean.
             This
             therefore
             is
             the
             Aequation
             of
             time
             arising
             from
             this
             cause
             ,
             and
             is
             negative
             ,
             or
             to
             be
             substracted
             from
             the
             apparent
             time
             ,
             to
             obtain
             the
             mean
             time
             ;
             for
             the
             longitude
             of
             the
             Sun
             arrives
             at
             the
             meridian
             sooner
             than
             a
             like
             arch
             projected
             in
             the
             Aequator
             .
          
           
             Here
             are
             therefore
             demonstrated
             two
             sorts
             of
             Aequations
             of
             time
             arising
             from
             two
             different
             causes
             ,
             if
             they
             are
             both
             to
             be
             added
             ,
             or
             both
             to
             be
             substracted
             ,
             their
             sum
             is
             to
             be
             added
             or
             substracted
             ;
             but
             if
             one
             be
             to
             be
             added
             ,
             and
             t'other
             substracted
             ,
             their
             difference
             according
             to
             the
             nature
             of
             the
             greatest
             is
             to
             be
             added
             or
             substracted
             to
             or
             from
             the
             apparent
             time
             to
             get
             the
             mean.
             
          
           
             And
             thus
             far
             I
             have
             presumed
             to
             borrow
             from
             my
             Learned
             and
             Ingenious
             Friend's
             Discourse
             ;
             which
             is
             sufficient
             ,
             I
             think
             ,
             to
             put
             this
             matter
             out
             of
             all
             dispute
             .
          
           
             After
             clearing
             the
             Theory
             of
             this
             Doctrine
             ,
             I
             come
             next
             to
             apply
             it
             to
             practice
             in
             regulating
             curious
             Time-keepers
             ,
             which
             indeed
             are
             very
             often
             abused
             for
             want
             of
             the
             due
             consideration
             and
             right
             application
             of
             this
             Aequation
             of
             time
             .
             For
             
             at
             some
             time
             of
             the
             year
             it
             happens
             that
             if
             our
             Watches
             or
             
               Oscillating
               Pendulums
            
             do
             not
             differ
             above
             a
             quarter
             of
             an
             hour
             from
             the
             time
             shew'd
             by
             the
             Sun
             or
             Stars
             ,
             they
             are
             false
             ,
             and
             need
             a
             correction
             .
             And
             the
             reason
             of
             this
             is
             plain
             ,
             for
             if
             a
             Pendulum-Watch
             goes
             true
             ,
             it
             goes
             equal
             ,
             that
             is
             ,
             one
             24
             hours
             at
             any
             time
             of
             the
             year
             ,
             is
             as
             long
             as
             another
             24
             hours
             at
             any
             other
             time
             of
             the
             year
             ,
             and
             this
             perpetually
             and
             constantly
             ;
             that
             is
             ,
             all
             Watches
             that
             go
             true
             ,
             measure
             the
             equal
             or
             mean
             time
             ,
             and
             consequently
             ought
             to
             differ
             from
             the
             apparent
             time
             shewn
             by
             a
             Sun-dial
             or
             other
             Instrument
             ,
             as
             much
             as
             is
             the
             Aequation
             of
             time
             in
             excess
             or
             defect
             ;
             but
             the
             Aequation
             of
             time
             is
             sometimes
             above
             a
             quarter
             of
             an
             hour
             ,
             therefore
             so
             much
             ought
             a
             good-going
             Pendulum-watch
             to
             differ
             sometimes
             from
             the
             Sun
             ,
             if
             it
             be
             rightly
             adjusted
             .
             But
             this
             will
             be
             more
             evident
             by
             explaining
             the
             Tables
             .
             These
             are
             calculated
             by
             the
             foregoing
             Theory
             ,
             and
             will
             serve
             very
             well
             for
             these
             20
             years
             to
             come
             ;
             though
             it
             must
             be
             confest
             ,
             that
             to
             have
             them
             most
             accurate
             ,
             these
             Tables
             ought
             to
             be
             Calculated
             for
             every
             year
             ,
             as
             is
             manifest
             to
             those
             that
             consider
             the
             foregoing
             Theory
             .
             Yet
             I
             say
             ,
             these
             will
             serve
             very
             well
             for
             20
             years
             to
             come
             ,
             without
             any
             considerable
             error
             .
             Some
             few
             seconds
             error
             there
             may
             be
             ,
             and
             he
             that
             desires
             them
             more
             exact
             ,
             may
             be
             at
             the
             pains
             of
             Calculating
             them
             himself
             ;
             the
             method
             whereof
             he
             may
             find
             laid
             down
             
             in
             the
             forementioned
             Treatise
             at
             the
             end
             of
             
             Horrox's
             Works
             ;
             or
             in
             Mr.
             
               Flamsteed's
               Doctrine
               of
               the
               Sphere
            
             publish'd
             in
             
               Sir
               J.
               Moore
               's
               System
               of
               Mathematicks
               .
            
             We
             see
             there
             are
             only
             four
             days
             in
             the
             year
             on
             which
             the
             aequations
             of
             days
             cease
             ,
             that
             is
             ,
             the
             apparent
             and
             mean
             time
             are
             then
             the
             same
             ,
             viz.
             on
             the
             4th
             .
             of
             
               April
               ,
               June
            
             the
             
               6th
               .
               Aug.
            
             the
             21st
             .
             and
             Decemb.
             13.
             
             If
             on
             any
             of
             these
             days
             we
             Set
             a
             wellregulated
             Pendulum-watch
             to
             the
             apparent
             time
             shewn
             by
             the
             Sun
             or
             Stars
             ,
             on
             any
             day
             afterwards
             ,
             it
             ought
             to
             differ
             from
             the
             apparent
             time
             shewn
             by
             the
             Sun
             so
             much
             as
             is
             the
             Aequation
             of
             time
             in
             the
             Table
             .
             If
             the
             Aequation
             is
             to
             be
             substracted
             ,
             the
             Pendulum
             ought
             to
             be
             so
             much
             slower
             than
             (
             or
             behind
             )
             the
             Sun
             ;
             if
             the
             Aequation
             is
             to
             be
             added
             ,
             the
             Pendulum
             ought
             to
             be
             so
             much
             faster
             than
             (
             or
             before
             )
             the
             Sun.
             For
             upon
             any
             day
             of
             the
             year
             observing
             the
             time
             exactly
             by
             Sun
             or
             Stars
             ,
             that
             time
             is
             the
             apparent
             time
             ,
             and
             to
             gain
             the
             mean
             time
             which
             ought
             to
             be
             shewn
             by
             the
             Clock
             ,
             we
             are
             to
             add
             too
             or
             to
             substract
             from
             the
             said
             apparent
             time
             ,
             the
             Aequation
             answering
             to
             the
             day
             of
             our
             observation
             .
             Suppose
             for
             instance
             ,
             on
             the
             4th
             of
             April
             I
             observe
             the
             time
             by
             the
             Sun
             ,
             here
             because
             the
             Aequation
             ceases
             ,
             the
             apparent
             and
             mean
             time
             are
             the
             same
             ,
             and
             therefore
             I
             am
             to
             set
             my
             Clock
             to
             the
             exact
             and
             full
             time
             ,
             as
             the
             Sun
             or
             Stars
             shew
             it
             ;
             but
             if
             the
             Pendulum
             go
             exactly
             true
             ,
             and
             it
             move
             to
             the
             4th
             of
             May
             ,
             I
             shall
             find
             it
             4′
             .
             17″
             behind
             
             the
             Sun
             ,
             for
             so
             much
             is
             the
             aequation
             on
             the
             4th
             of
             May
             to
             be
             substracted
             from
             the
             apparent
             time
             of
             the
             Sun
             to
             gain
             the
             mean
             time
             of
             the
             Clock
             ;
             that
             is
             ,
             when
             the
             Sun
             shews
             it
             to
             be
             9
             a
             Clock
             in
             the
             morning
             ,
             the
             Clock
             ought
             to
             be
             but
             8h
             .
             55′
             .
             43″
             .
             And
             if
             I
             find
             the
             Pendulum
             more
             or
             less
             behind
             the
             Sun
             ,
             it
             has
             not
             gone
             truly
             as
             it
             ought
             ,
             but
             the
             Pendulum
             or
             swagg
             is
             to
             be
             lengthned
             or
             shortned
             as
             is
             requisite
             to
             make
             it
             gain
             or
             lose
             the
             difference
             betwixt
             the
             time
             shewn
             by
             the
             Clock
             ,
             and
             8h
             .
             55′
             .
             43″
             .
             in
             30
             days
             elapsed
             between
             the
             4th
             of
             April
             ,
             and
             4th
             of
             May
             ;
             according
             to
             a
             Table
             ,
             whose
             use
             I
             shall
             declare
             presently
             .
             But
             if
             the
             Movement
             be
             exquisitely
             true
             ,
             if
             it
             go
             to
             the
             6th
             of
             June
             ,
             it
             will
             again
             shew
             the
             same
             time
             with
             the
             Sun
             or
             Stars
             ,
             for
             then
             again
             the
             Aequation
             is
             nothing
             .
             And
             if
             it
             go
             onwards
             exactly
             to
             the
             3d
             of
             August
             ,
             it
             will
             be
             4′
             .
             18″
             .
             before
             the
             Sun
             ;
             for
             at
             that
             time
             so
             much
             is
             the
             aequation
             to
             be
             added
             to
             the
             apparent
             time
             to
             make
             it
             the
             mean.
             'Till
             again
             on
             the
             24th
             of
             October
             the
             Watch
             ought
             to
             be
             16′
             .
             4″
             .
             behind
             the
             Sun
             ,
             for
             so
             much
             is
             the
             aequation
             on
             that
             day
             to
             be
             substracted
             .
          
           
             Wherefore
             if
             at
             any
             time
             we
             set
             our
             Pendulum-Watch
             in
             order
             to
             rectify
             it
             ,
             and
             bring
             it
             exactly
             to
             measure
             the
             mean
             day
             ,
             we
             are
             to
             add
             to
             or
             substract
             from
             the
             apparent
             time
             shewn
             by
             the
             Sun
             so
             much
             as
             is
             the
             aequation
             of
             days
             at
             the
             time
             we
             set
             it
             .
             For
             example
             ,
             at
             noon
             ,
             or
             just
             when
             
             the
             Sun
             is
             in
             the
             Meridian
             on
             the
             9th
             of
             the
             September
             ,
             that
             is
             ,
             when
             the
             apparent
             time
             is
             exactly
             12
             a
             Clock
             ,
             I
             set
             my
             Watch
             ,
             the
             aequation
             is
             then
             6′
             .
             26″
             .
             subtr
             .
             Wherefore
             I
             set
             my
             Watch
             to
             11h
             .
             53′
             .
             34″
             .
             Which
             ,
             if
             it
             go
             right
             ,
             that
             is
             equally
             as
             it
             ought
             ,
             on
             the
             9th
             of
             October
             will
             be
             14′
             .
             52″
             .
             behind
             the
             the
             Sun
             ;
             if
             it
             be
             either
             more
             or
             less
             behind
             or
             before
             the
             Sun
             ,
             it
             has
             gone
             false
             ,
             and
             is
             to
             be
             rectified
             by
             lengthning
             or
             shortning
             the
             Pendulum
             as
             much
             as
             is
             requisite
             to
             make
             it
             gain
             or
             lose
             the
             difference
             between
             14′
             .
             52″
             behind
             the
             Sun
             and
             its
             error
             whatever
             it
             is
             in
             30
             days
             time
             elapsed
             between
             the
             9th
             of
             Septemb.
             and
             9th
             of
             Octob.
             But
             if
             at
             any
             other
             time
             of
             the
             year
             we
             set
             our
             Watch
             when
             the
             aequation
             is
             to
             be
             added
             ,
             we
             must
             put
             it
             so
             much
             before
             the
             Sun
             as
             is
             the
             aequation
             .
             But
             this
             is
             plain
             enough
             without
             further
             Illustration
             .
          
           
             Of
             the
             certainty
             and
             exactness
             of
             this
             aequation
             of
             time
             ,
             I
             have
             made
             a
             most
             convincing
             Experiment
             by
             an
             exquisitely
             rectified
             Pendulum-Clock
             ,
             which
             I
             bought
             from
             Mr.
             
               Richard
               Jarrat
            
             Watch-maker
             in
             
               Lothbury
               ,
               London
            
             ,
             whom
             I
             can
             therefore
             recommend
             for
             his
             honesty
             and
             ability
             .
          
           
             And
             because
             I
             have
             spoken
             in
             this
             Chapter
             of
             lengthning
             or
             shortning
             of
             a
             Pendulum
             ,
             so
             as
             to
             make
             it
             go
             slower
             or
             faster
             so
             much
             in
             a
             certain
             time
             ;
             for
             doing
             this
             more
             regularly
             ,
             and
             not
             by
             guess
             ,
             I
             have
             here
             added
             a
             Table
             adapted
             to
             a
             Pendulum
             
             that
             
               Vibrates
               seconds
            
             ,
             which
             is
             supposed
             to
             be
             39.2
             .
             inches
             long
             .
             Sir
             
               Jonas
               Moore
            
             in
             his
             
               Mathematical
               Compendium
               ,
               pag.
            
             113.
             gives
             us
             such
             a
             Table
             as
             this
             ,
             but
             whether
             by
             the
             fault
             of
             the
             Printer
             or
             Calculator
             't
             is
             very
             erronious
             ,
             as
             any
             one
             may
             find
             that
             will
             be
             at
             the
             pains
             to
             examine
             it
             by
             the
             following
             Rules
             for
             Calculating
             these
             Tables
             .
             The
             Rule
             is
             ,
             
               the
               lengths
               of
               Pendulums
               are
               to
               each
               other
               reciprocally
               as
               the
               squares
               of
               their
               vibrations
               in
               the
               same
               time
               .
            
             Thus
             ,
             if
             a
             Pendulum
             39.2
             inches
             long
             vibrate
             60
             times
             in
             a
             minute
             ,
             how
             oft
             will
             a
             Pendulum
             9.8
             
               (
               viz.
            
             quarter
             of
             39.2
             )
             inches
             vibrate
             in
             a
             minute
             ?
             by
             the
             foregoing
             Rule
             the
             proportion
             stands
             thus
             ,
             9.8
             :
             39.2
             :
             :
             3600
             :
             14400
             ,
             whose
             square
             Root
             is
             120
             ;
             therefore
             a
             Pendulum
             9.8
             will
             vibrate
             120
             times
             in
             a
             minute
             .
             So
             if
             it
             be
             required
             how
             oft
             a
             Pendulum
             39.0
             inches
             vibrates
             in
             a
             minute
             ,
             the
             Analogy
             will
             be
             this
             ,
             39.0
             :
             39.2
             :
             :
             3600
             :
             3618.
             whose
             square
             Root
             is
             60.15
             .
             that
             is
             ,
             a
             Pendulum
             39.0
             inches
             long
             vibrates
             in
             a
             minute
             60
             times
             ,
             and
             15
             hundreds
             of
             a
             vibration
             more
             than
             60
             times
             .
             So
             that
             multiplying
             15
             hundreds
             of
             a
             vibration
             by
             1440
             the
             number
             of
             minutes
             in
             24
             hours
             ,
             we
             get
             the
             number
             of
             vibrations
             which
             a
             Pendulum
             39.0
             inches
             long
             vibrates
             in
             a
             day
             more
             than
             one
             of
             39.2
             ;
             and
             seeing
             each
             vibration
             of
             the
             Pendulum
             in
             a
             Clock
             adapted
             for
             it
             ,
             sets
             the
             hand
             forward
             a
             second
             ,
             by
             knowing
             the
             number
             of
             vibrations
             which
             a
             Pendulum
             39.0
             inches
             long
             performs
             in
             a
             
             day
             more
             than
             a
             Pendulum
             39.2
             inches
             long
             ,
             we
             may
             know
             the
             number
             of
             seconds
             which
             it
             will
             advance
             the
             Index
             of
             the
             Clock
             forward
             more
             than
             one
             39.2
             inches
             long
             .
             And
             by
             these
             Rules
             are
             the
             following
             Tables
             Calculated
             .
          
           
             
               
                 
                   1
                
                 
                   2
                
                 
                   3
                
                 
                   4
                
              
               
                 
                   38.7
                
                 
                   60″
                   .
                   3863
                
                 
                   9′
                   .
                   16″
                   .
                   16‴
                
                 
                   1′
                   .
                   52″
                   06‴
                
              
               
                 
                   38.8
                
                 
                   60.3084
                
                 
                   7.
                   24.
                   10
                
                 
                   1.
                   51.
                   40
                
              
               
                 
                   38.9
                
                 
                   60.2309
                
                 
                   5.
                   32.
                   30
                
                 
                   1.
                   51.
                   20
                
              
               
                 
                   39.0
                
                 
                   60.1536
                
                 
                   3.
                   41.
                   10
                
                 
                   1.
                   50.
                   40
                
              
               
                 
                   39.1
                
                 
                   60.0766
                
                 
                   1.
                   50.
                   20
                
                 
                   1.
                   50.
                   20
                
              
               
                 
                   39.2
                
                 
                   60.0000
                
                 
                   0.
                   00.
                   00
                
                 
                    
                
              
               
                 
                   39.3
                
                 
                   59.9236
                
                 
                   1.
                   50.
                   00
                
                 
                   1.
                   50.
                   00
                
              
               
                 
                   39.4
                
                 
                   59.8475
                
                 
                   3.
                   39.
                   36
                
                 
                   1.
                   49.
                   36
                
              
               
                 
                   39.5
                
                 
                   59.7717
                
                 
                   5.
                   28.
                   45
                
                 
                   1.
                   49.
                   09
                
              
               
                 
                   39.6
                
                 
                   59.6962
                
                 
                   7.
                   17.
                   30
                
                 
                   1.
                   48.
                   45
                
              
               
                 
                   39.7
                
                 
                   59.6210
                
                 
                   9.
                   05.
                   45
                
                 
                   1.
                   48.
                   15
                
              
            
          
           
             The
             first
             Column
             has
             in
             the
             middle
             the
             length
             of
             the
             Pendulum
             39.2
             ;
             upwards
             it
             diminisheth
             one
             tenth
             ,
             and
             downwards
             it
             increaseth
             one
             tenth
             .
             The
             second
             Column
             is
             the
             vibrations
             and
             parts
             of
             a
             Vibration
             performed
             in
             a
             minute
             by
             the
             lengths
             
             in
             the
             first
             .
             The
             third
             Column
             is
             the
             minutes
             and
             seconds
             that
             these
             lengthnings
             and
             shortnings
             of
             the
             Pendulum
             will
             cause
             in
             a
             day
             ,
             and
             are
             gotten
             by
             multiplying
             1440′
             the
             minutes
             in
             a
             day
             by
             the
             Decimals
             above
             or
             under
             60″
             .
             The
             4th
             and
             last
             Column
             are
             the
             differences
             of
             the
             3d.
             The
             like
             Table
             may
             be
             made
             to
             any
             length
             of
             a
             Pendulum
             ,
             respect
             being
             had
             to
             the
             foregoing
             Rule
             .
          
           
             I
             shall
             conclude
             all
             relating
             to
             my
             Dial
             with
             the
             Calculation
             of
             hours
             and
             minutes
             for
             an
             
               Horizontal
               Dial
            
             for
             the
             latitude
             of
             
               Dublin
               53°
               .
               20′
            
             .
             Which
             I
             believe
             will
             not
             be
             unacceptable
             to
             those
             that
             design
             curious
             Dials
             for
             that
             place
             .
          
           
             The
             Tables
             follow
             amongst
             the
             others
             .
          
        
         
           
             CHAP.
             XI
             .
             Of
             the
             Tables
             of
             the
             Circumpolar
             Stars
             ,
             their
             Calculation
             and
             Vses
             .
          
           
             I
             Shall
             here
             ,
             as
             a
             conclusion
             to
             this
             Work
             ,
             add
             something
             concerning
             very
             useful
             Tables
             for
             shewing
             the
             time
             of
             night
             very
             accurately
             ,
             and
             other
             operations
             by
             the
             Circumpolars
             ,
             or
             Stars
             that
             never
             set
             in
             our
             latitude
             of
             Dublin
             .
             Such
             Tables
             as
             these
             we
             have
             mentioned
             in
             Sir
             J.
             Moore
             's
             
               Mathematical
               Compendium
               p.
            
             118
             ,
             119.
             but
             they
             are
             for
             the
             latitude
             of
             London
             ;
             neither
             does
             he
             give
             us
             all
             their
             
             uses
             ,
             or
             the
             method
             of
             Calculating
             them
             for
             other
             places
             .
             I
             shall
             do
             both
             in
             this
             place
             ,
             and
             first
             for
             their
             use
             .
          
           
             In
             any
             Northern
             Window
             ,
             or
             other
             convenient
             place
             ,
             hang
             up
             a
             good
             weighty
             Plummet
             by
             a
             fine
             and
             even
             silk
             or
             silver-wire
             ,
             then
             placing
             your
             eye
             at
             some
             distance
             behind
             this
             thred
             ,
             that
             is
             ,
             to
             the
             South
             thereof
             ,
             observe
             when
             any
             of
             the
             Stars
             mentioned
             in
             the
             Table
             are
             cut
             by
             this
             thred
             at
             the
             same
             time
             with
             the
             
               Pole-Star
               .
               From
               the
               Stars
               Right
               ascension
               in
               the
               Table
               (
               adding
               24
               hours
               if
               need
               be
               )
               substract
               the
               Suns
               right
               ascension
               ,
               the
               remainder
               gives
               the
               hour
               ,
               minute
               ,
               and
               second
               of
               the
               night
               .
            
             The
             Tables
             consist
             of
             6
             Colums
             ,
             the
             first
             shews
             the
             Magnitudes
             ;
             the
             second
             contains
             the
             Stars
             names
             ,
             as
             they
             are
             described
             on
             our
             common
             
               English
               Globes
            
             ;
             the
             third
             shews
             the
             
               Right
               ascension
            
             of
             the
             Mid-heaven
             in
             time
             ,
             when
             any
             of
             these
             Stars
             come
             in
             the
             same
             Vertical
             with
             the
             Pole-Star
             ,
             by
             which
             (
             working
             according
             to
             the
             foregoing
             Rule
             )
             we
             find
             the
             hour
             of
             the
             night
             ;
             the
             fourth
             Column
             gives
             the
             difference
             in
             time
             between
             the
             coming
             of
             any
             of
             these
             Stars
             under
             the
             Pole-star
             ,
             and
             their
             coming
             under
             the
             Pole
             it self
             .
             Some
             of
             these
             Stars
             pass
             the
             Meridian
             ,
             or
             come
             under
             the
             Pole
             before
             they
             come
             under
             the
             Pole-Star
             ,
             such
             as
             are
             all
             the
             Stars
             whose
             
               Right
               ascensions
            
             are
             above
             9°
             .
             14′
             .
             10″
             ,
             and
             under
             189°
             .
             14′
             .
             10″
             .
             And
             of
             these
             we
             say
             nothing
             in
             this
             place
             ,
             only
             they
             are
             all
             marked
             in
             the
             Table
             
             with
             E
             ,
             as
             having
             their
             Azimuth
             when
             under
             the
             
               Pole-star
               Eastward
            
             .
             But
             of
             these
             Stars
             in
             this
             Catalogue
             which
             pass
             the
             Meridian
             ,
             or
             come
             under
             the
             Pole
             after
             they
             have
             left
             the
             Vertical
             of
             the
             Pole-star
             ,
             we
             make
             this
             following
             use
             .
             All
             these
             are
             marked
             in
             the
             sixth
             Column
             with
             W
             ,
             as
             having
             a
             
               Western
               Azimuth
            
             when
             they
             are
             under
             the
             Pole-star
             .
             Wherefore
             placing
             a
             second
             line
             and
             plummet
             behind
             ,
             or
             to
             the
             South
             of
             the
             former
             ,
             then
             observe
             by
             the
             first
             when
             any
             of
             these
             Stars
             come
             under
             the
             Pole-star
             ,
             and
             by
             a
             Pendulum
             from
             that
             instant
             count
             the
             time
             in
             this
             fourth
             Column
             ,
             and
             placing
             your
             eye
             now
             behind
             both
             the
             lines
             ,
             just
             at
             the
             end
             of
             your
             count
             by
             gently
             moving
             this
             last
             thred
             ,
             make
             them
             both
             cut
             the
             Star
             you
             count
             for
             ,
             then
             are
             these
             two
             lines
             exactly
             in
             the
             meridian
             ;
             and
             is
             a
             curious
             way
             for
             finding
             a
             
               Meridian
               line
            
             .
             The
             fifth
             and
             sixth
             Columns
             serve
             for
             the
             same
             use
             ;
             for
             when
             any
             of
             these
             Stars
             are
             under
             the
             Pole-star
             ,
             making
             your
             two
             lines
             cut
             both
             Pole-star
             and
             t'other
             ,
             these
             two
             lines
             hang
             so
             far
             out
             of
             the
             
               Meridian
               line
            
             ,
             as
             is
             the
             Azimuth
             expressed
             in
             the
             Table
             ,
             which
             Azimuth
             is
             shewn
             to
             be
             East
             or
             West
             by
             the
             6th
             Column
             .
             Wherefore
             this
             angle
             being
             set
             off
             from
             the
             found
             line
             ,
             shews
             the
             true
             Meridian
             .
             And
             we
             may
             observe
             ,
             that
             there
             are
             three
             stars
             expressed
             in
             the
             Table
             ,
             which
             being
             under
             the
             pole-star
             are
             insensibly
             nigh
             the
             Meridian
             ,
             these
             are
             
               Cassiopeid's
               Hipp
               ,
               Cor
               Caroli
            
             ,
             and
             Aliot
             
             or
             the
             
               Great
               Bears
               Rump
            
             .
             Wherefore
             whenever
             we
             have
             any
             of
             these
             under
             the
             pole-star
             ,
             we
             may
             by
             it
             find
             a
             
               Meridian
               line
            
             without
             any
             sensible
             error
             .
             Another
             use
             that
             we
             may
             make
             of
             this
             Table
             ,
             is
             for
             the
             true
             adjusting
             of
             Hour-glasses
             and
             other
             Time-keepers
             ,
             as
             
               Pendulum-Watches
               ,
               &c.
            
             for
             trying
             their
             going
             ,
             and
             bringing
             them
             to
             their
             right
             measure
             .
             Thus
             we
             shall
             find
             it
             just
             four
             hours
             (
             wanting
             one
             second
             )
             between
             the
             coming
             of
             
               Cor
               Caroli
            
             ,
             and
             the
             
               24th
               Star
            
             of
             Draco
             (
             in
             
               Tich
               .
               Catal.
            
             )
             under
             the
             Pole-star
             ;
             for
             when
             
               Cor
               Caroli
            
             is
             under
             the
             pole-star
             ,
             the
             
               Right
               Ascension
            
             of
             the
             Mid-heaven
             in
             time
             is
             
               00h
               .
               36′
               .
               44″
            
             .
             And
             when
             the
             24th
             of
             Draco
             is
             under
             the
             pole-star
             ,
             the
             
               mid-heavens
               temporary
               Right
               Ascension
            
             is
             
               4h
               .
               36′
               .
               43″
            
             .
             their
             difference
             is
             
               3h
               .
               59′
               .
               59″
            
             .
             which
             wants
             only
             one
             second
             of
             four
             hours
             .
             Note
             that
             this
             24th
             of
             Draco
             is
             marked
             in
             Bayer
             by
             .
          
           
             I
             come
             now
             to
             shew
             the
             method
             of
             Calculating
             this
             Table
             ,
             for
             which
             see
             the
             15
             and
             16
             Figures
             .
             Wherein
             axbp
             is
             the
             circle
             described
             by
             the
             
               pole-star
               x
            
             round
             the
             
               pole
               p
               ,
               z
            
             the
             
               Zenith
               ,
               zn
            
             the
             meridian
             ,
             whose
             North
             part
             is
             
               pn
               ,
               s
            
             is
             any
             other
             
               Circumpolar
               stars
               ,
               zxs
            
             a
             
               Vertical
               circle
               ,
               hn
            
             the
             
               Horizon
               ,
               aeq
            
             the
             
               Aequator
               ,
               po
            
             the
             
               Axis
               Mundi
            
             .
             There
             are
             here
             given
             (
             or
             at
             least
             may
             be
             known
             from
             the
             Tables
             )
             px
             the
             Complement
             of
             the
             
               pole-stars
               Declination
               ,
               ps
            
             the
             Complement
             of
             the
             other
             
               stars
               Declination
               ,
               xps
            
             the
             difference
             of
             the
             
               Right
               Ascensions
            
             
             of
             the
             pole-star
             ,
             and
             other
             star
             ,
             also
             zp
             the
             Complement
             of
             the
             
               Poles
               Elevation
            
             .
             Wherefore
             ,
             in
             the
             
               Triangle
               spx
            
             ,
             having
             
               sp
               ,
               px
            
             ,
             and
             the
             angle
             spx
             ,
             we
             may
             find
             the
             angle
             sxp
             ;
             and
             having
             that
             ,
             we
             have
             the
             angle
             pxz
             ,
             for
             this
             is
             the
             Complement
             of
             sxp
             to
             180
             degrees
             .
             Then
             in
             the
             
               Triangle
               zpx
            
             ,
             we
             have
             
               zp
               ,
               px
            
             ,
             and
             the
             angle
             pxz
             ,
             to
             find
             the
             angle
             pzx
             ,
             which
             is
             the
             Azimuth
             that
             these
             two
             Stars
             have
             ,
             when
             they
             come
             in
             the
             same
             Vertical
             ,
             and
             makes
             the
             fifth
             Column
             in
             our
             Table
             .
             And
             from
             the
             same
             Data
             ,
             we
             may
             find
             the
             angle
             zpx
             .
             Therefore
             in
             the
             
               Triangle
               zps
            
             ,
             we
             have
             found
             the
             angle
             zps
             ,
             for
             zps
             is
             equal
             to
             the
             sum
             of
             zpx
             and
             spx
             .
             Now
             the
             difference
             between
             zps
             and
             180
             degrees
             is
             equal
             to
             the
             difference
             in
             time
             between
             the
             Star
             s
             coming
             under
             the
             Pole-star
             and
             coming
             ,
             under
             the
             Pole
             ,
             or
             its
             being
             in
             the
             Meridian
             ,
             and
             consequently
             its
             having
             its
             own
             
               Right
               Ascension
            
             ,
             or
             its
             Complement
             ;
             and
             this
             makes
             the
             fourth
             Column
             in
             our
             Table
             .
             Now
             this
             difference
             in
             time
             between
             the
             Pole
             and
             Pole-star
             being
             added
             to
             or
             substracted
             from
             the
             true
             
               Right
               Ascension
            
             of
             the
             Star
             s
             in
             time
             ,
             gives
             the
             
               Right
               Ascension
            
             in
             time
             of
             the
             Star
             s
             (
             or
             of
             the
             mid-heaven
             )
             when
             't
             is
             under
             the
             Pole-star
             ;
             and
             this
             makes
             our
             third
             Column
             in
             the
             Table
             .
             The
             Rule
             to
             know
             when
             this
             difference
             in
             time
             between
             the
             Pole
             and
             Pole-star
             is
             to
             be
             added
             ,
             and
             when
             to
             be
             substracted
             ,
             will
             be
             evident
             by
             observing
             ,
             that
             all
             such
             Stars
             whose
             
               Right
               
               Ascensions
            
             are
             above
             the
             
               Right
               Ascension
            
             of
             the
             Pole-star
             (
             for
             the
             year
             ,
             as
             for
             1680
             )
             9°
             .
             14′
             .
             10″
             ,
             and
             under
             189°
             .
             14′
             .
             10″
             .
             pass
             the
             meridian
             before
             they
             come
             under
             the
             Pole-star
             ;
             all
             the
             other
             semicircle
             ,
             contrarily
             ;
             for
             if
             the
             Star
             pass
             the
             meridian
             before
             it
             comes
             under
             the
             Pole-star
             ,
             this
             difference
             in
             time
             between
             the
             Pole
             and
             Pole-star
             is
             to
             be
             added
             to
             the
             
               Right
               Ascension
            
             of
             the
             Star
             ;
             if
             the
             contrary
             ,
             't
             is
             to
             be
             substracted
             .
          
           
             FINIS
             .
          
        
         
           
           
             TABLES
             OF
             THE
             Suns
             Right
             Ascension
             in
             Time
             TO
             EVERY
             Ten
             Minutes
             of
             the
             ECLIPTICK
             .
          
           
             
             
               
                 
                   
                     D.
                     m.
                     
                  
                   
                     ♈
                     H
                  
                   
                     ♎
                     H
                  
                   
                     Com.
                     ′
                     Pts
                     ″
                  
                   
                     X
                  
                
                 
                   
                     0.0
                  
                   
                     0
                  
                   
                     12
                  
                   
                     0.0
                  
                
                 
                   
                     10
                  
                   
                     0
                  
                   
                     12
                  
                   
                     0.37
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     ″
                  
                
                 
                   
                     20
                  
                   
                     0
                  
                   
                     12
                  
                   
                     1.13
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     37
                  
                
                 
                   
                     30
                  
                   
                     0
                  
                   
                     12
                  
                   
                     1.50
                  
                
                 
                   
                     40
                  
                   
                     0
                  
                   
                     12
                  
                   
                     2.27
                  
                
                 
                   
                     50
                  
                   
                     0
                  
                   
                     12
                  
                   
                     3.3
                  
                
                 
                   
                     1.0
                  
                   
                     0
                  
                   
                     12
                  
                   
                     3.40
                  
                
                 
                   
                     10
                  
                   
                     0
                  
                   
                     12
                  
                   
                     4.17
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     ″
                  
                
                 
                   
                     20
                  
                   
                     0
                  
                   
                     12
                  
                   
                     4.53
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     37
                  
                
                 
                   
                     30
                  
                   
                     0
                  
                   
                     12
                  
                   
                     5.30
                  
                
                 
                   
                     40
                  
                   
                     0
                  
                   
                     12
                  
                   
                     6.7
                  
                
                 
                   
                     50
                  
                   
                     0
                  
                   
                     12
                  
                   
                     6.43
                  
                
                 
                   
                     2.0
                  
                   
                     0
                  
                   
                     12
                  
                   
                     7.20
                  
                
                 
                   
                     10
                  
                   
                     0
                  
                   
                     12
                  
                   
                     7.57
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     ″
                  
                
                 
                   
                     20
                  
                   
                     0
                  
                   
                     12
                  
                   
                     8.33
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     ″
                  
                
                 
                   
                     30
                  
                   
                     0
                  
                   
                     12
                  
                   
                     9
                     10
                  
                
                 
                   
                     40
                  
                   
                     0
                  
                   
                     12
                  
                   
                     9
                     46
                  
                
                 
                   
                     50
                  
                   
                     0
                  
                   
                     12
                  
                   
                     10.23
                  
                
                 
                   
                     3.0
                  
                   
                     0
                  
                   
                     12
                  
                   
                     11.0
                  
                
                 
                   
                     10
                  
                   
                     0
                  
                   
                     12
                  
                   
                     11.37
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     11
                  
                
                 
                   
                     20
                  
                   
                     0
                  
                   
                     12
                  
                   
                     12.13
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     37
                  
                
                 
                   
                     30
                  
                   
                     0
                  
                   
                     12
                  
                   
                     12.50
                  
                
                 
                   
                     40
                  
                   
                     0
                  
                   
                     12
                  
                   
                     13.26
                  
                
                 
                   
                     50
                  
                   
                     0
                  
                   
                     12
                  
                   
                     14.3
                  
                
                 
                   
                     4.0
                  
                   
                     0
                  
                   
                     0
                  
                   
                     12
                  
                   
                     14.40
                  
                
                 
                   
                     10
                  
                   
                     0
                  
                   
                     12
                  
                   
                     15.17
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     11
                  
                
                 
                   
                     20
                  
                   
                     0
                  
                   
                     12
                  
                   
                     15.53
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     37
                  
                
                 
                   
                     30
                  
                   
                     0
                  
                   
                     12
                  
                   
                     16.30
                  
                
                 
                   
                     40
                  
                   
                     0
                  
                   
                     12
                  
                   
                     17.6
                  
                
                 
                   
                     50
                  
                   
                     0
                  
                   
                     12
                  
                   
                     17.43
                  
                
                 
                   
                     5.0
                  
                   
                     0
                  
                   
                     12
                  
                   
                     18.20
                  
                
                 
                   
                     10
                  
                   
                     0
                  
                   
                     12
                  
                   
                     18.57
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     11
                  
                
                 
                   
                     20
                  
                   
                     0
                  
                   
                     12
                  
                   
                     19.33
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     37
                  
                
                 
                   
                     30
                  
                   
                     0
                  
                   
                     12
                  
                   
                     20.10
                  
                
                 
                   
                     40
                  
                   
                     0
                  
                   
                     12
                  
                   
                     20.46
                  
                
                 
                   
                     50
                  
                   
                     0
                  
                   
                     12
                  
                   
                     21.23
                  
                
                 
                   
                     6.0
                  
                   
                     0
                  
                   
                     12
                  
                   
                     22.0
                  
                
                 
                   
                     10
                  
                   
                     0
                  
                   
                     12
                  
                   
                     22.37
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     11
                  
                
                 
                   
                     20
                  
                   
                     0
                  
                   
                     12
                  
                   
                     23.13
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     37
                  
                
                 
                   
                     30
                  
                   
                     0
                  
                   
                     12
                  
                   
                     23.50
                  
                
                 
                   
                     40
                  
                   
                     0
                  
                   
                     12
                  
                   
                     24.26
                  
                
                 
                   
                     50
                  
                   
                     0
                  
                   
                     12
                  
                   
                     25.3
                  
                
                 
                   
                     7.0
                  
                   
                     0
                  
                   
                     12
                  
                   
                     25.41
                  
                
                 
                   
                     10
                  
                   
                     0
                  
                   
                     12
                  
                   
                     26.18
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     11
                  
                
                 
                   
                     20
                  
                   
                     0
                  
                   
                     12
                  
                   
                     26.55
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     37
                  
                
                 
                   
                     30
                  
                   
                     0
                  
                   
                     12
                  
                   
                     27.32
                  
                
                 
                   
                     40
                  
                   
                     0
                  
                   
                     12
                  
                   
                     28.9
                  
                
                 
                   
                     50
                  
                   
                     0
                  
                   
                     12
                  
                   
                     28.46
                  
                
                 
                   
                     8.0
                  
                   
                     0
                  
                   
                     12
                  
                   
                     29.23
                  
                
                 
                   
                     10
                  
                   
                     0
                  
                   
                     12
                  
                   
                     30.0
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     11
                  
                
                 
                   
                     20
                  
                   
                     0
                  
                   
                     12
                  
                   
                     30.36
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     37
                  
                
                 
                   
                     30
                  
                   
                     0
                  
                   
                     12
                  
                   
                     31.13
                  
                
                 
                   
                     40
                  
                   
                     0
                  
                   
                     12
                  
                   
                     31.50
                  
                
                 
                   
                     50
                  
                   
                     0
                  
                   
                     12
                  
                   
                     32.26
                  
                
                 
                   
                     9.0
                  
                   
                     0
                  
                   
                     12
                  
                   
                     33.3
                  
                
                 
                   
                     10
                  
                   
                     0
                  
                   
                     12
                  
                   
                     33.40
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     11
                  
                
                 
                   
                     20
                  
                   
                     0
                  
                   
                     12
                  
                   
                     34.16
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     37
                  
                
                 
                   
                     30
                  
                   
                     0
                  
                   
                     12
                  
                   
                     34.53
                  
                
                 
                   
                     40
                  
                   
                     0
                  
                   
                     12
                  
                   
                     35.30
                  
                
                 
                   
                     50
                  
                   
                     0
                  
                   
                     12
                  
                   
                     36.7
                  
                
                 
                 
                   
                     10.0
                  
                   
                     0
                  
                   
                     12
                  
                   
                     36
                     44
                  
                
                 
                   
                     10
                  
                   
                     0
                  
                   
                     12
                  
                   
                     37.21
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     ″
                  
                
                 
                   
                     20
                  
                   
                     0
                  
                   
                     12
                  
                   
                     37.58
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     37
                  
                
                 
                   
                     30
                  
                   
                     0
                  
                   
                     12
                  
                   
                     38.35
                  
                
                 
                   
                     40
                  
                   
                     0
                  
                   
                     12
                  
                   
                     39
                     12
                  
                
                 
                   
                     50
                  
                   
                     0
                  
                   
                     12
                  
                   
                     39
                     49
                  
                
                 
                   
                     11.0
                  
                   
                     0
                  
                   
                     12
                  
                   
                     40.26
                  
                
                 
                   
                     10
                  
                   
                     0
                  
                   
                     12
                  
                   
                     41.
                     ●3
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     ″
                  
                
                 
                   
                     20
                  
                   
                     0
                  
                   
                     12
                  
                   
                     41.40
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     37
                  
                
                 
                   
                     30
                  
                   
                     0
                  
                   
                     12
                  
                   
                     42.17
                  
                
                 
                   
                     40
                  
                   
                     0
                  
                   
                     12
                  
                   
                     42.54
                  
                
                 
                   
                     50
                  
                   
                     0
                  
                   
                     12
                  
                   
                     43
                     31
                  
                
                 
                   
                     12.0
                  
                   
                     0
                  
                   
                     12
                  
                   
                     44.7
                  
                
                 
                   
                     10
                  
                   
                     0
                  
                   
                     12
                  
                   
                     44
                     44
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     ″
                  
                
                 
                   
                     20
                  
                   
                     0
                  
                   
                     12
                  
                   
                     45.21
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     37
                  
                
                 
                   
                     30
                  
                   
                     0
                  
                   
                     12
                  
                   
                     45.58
                  
                
                 
                   
                     40
                  
                   
                     0
                  
                   
                     12
                  
                   
                     46
                     35
                  
                
                 
                   
                     50
                  
                   
                     0
                  
                   
                     12
                  
                   
                     47.12
                  
                
                 
                   
                     13.0
                  
                   
                     0
                  
                   
                     12
                  
                   
                     47.49
                  
                
                 
                   
                     10
                  
                   
                     0
                  
                   
                     12
                  
                   
                     48.26
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     ″
                  
                
                 
                   
                     20
                  
                   
                     0
                  
                   
                     12
                  
                   
                     49
                     03
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     37
                  
                
                 
                   
                     30
                  
                   
                     0
                  
                   
                     12
                  
                   
                     49
                     40
                  
                
                 
                   
                     40
                  
                   
                     0
                  
                   
                     12
                  
                   
                     50.17
                  
                
                 
                   
                     50
                  
                   
                     0
                  
                   
                     12
                  
                   
                     50.54
                  
                
                 
                   
                     14.0
                  
                   
                     0
                  
                   
                     12
                  
                   
                     51.31
                  
                
                 
                   
                     10
                  
                   
                     0
                  
                   
                     12
                  
                   
                     52.8
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     ″
                  
                
                 
                   
                     20
                  
                   
                     0
                  
                   
                     12
                  
                   
                     52.45
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     37
                  
                
                 
                   
                     30
                  
                   
                     0
                  
                   
                     12
                  
                   
                     53.22
                  
                
                 
                   
                     40
                  
                   
                     0
                  
                   
                     12
                  
                   
                     53.59
                  
                
                 
                   
                     50
                  
                   
                     0
                  
                   
                     12
                  
                   
                     54.36
                  
                
                 
                   
                     15.0
                  
                   
                     0
                  
                   
                     12
                  
                   
                     55
                     .
                     1●
                  
                
                 
                   
                     10
                  
                   
                     0
                  
                   
                     12
                  
                   
                     55.50
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     ″
                  
                
                 
                   
                     20
                  
                   
                     0
                  
                   
                     12
                  
                   
                     56.27
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     37
                  
                
                 
                   
                     30
                  
                   
                     0
                  
                   
                     12
                  
                   
                     57.
                     ●4
                  
                
                 
                   
                     40
                  
                   
                     0
                  
                   
                     12
                  
                   
                     57
                     .
                     4●
                  
                
                 
                   
                     50
                  
                   
                     0
                  
                   
                     12
                  
                   
                     58.19
                  
                
                 
                   
                     16.0
                  
                   
                     0
                  
                   
                     12
                  
                   
                     58
                     .
                     5●
                  
                
                 
                   
                     10
                  
                   
                     0
                  
                   
                     12
                  
                   
                     59
                     .
                     3●
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     ″
                  
                
                 
                   
                     20
                  
                   
                     1
                  
                   
                     13
                  
                   
                     00.
                     ●0
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     37
                  
                
                 
                   
                     30
                  
                   
                     1
                  
                   
                     13
                  
                   
                     00.47
                  
                
                 
                   
                     40
                  
                   
                     1
                  
                   
                     13
                  
                   
                     1.
                     24
                  
                
                 
                   
                     50
                  
                   
                     1
                  
                   
                     13
                  
                   
                     2.2
                  
                
                 
                   
                     17
                     0
                  
                   
                     1
                  
                   
                     13
                  
                   
                     2
                     .
                     3●
                  
                
                 
                   
                     10
                  
                   
                     1
                  
                   
                     13
                  
                   
                     3.16
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     ″
                  
                
                 
                   
                     20
                  
                   
                     1
                  
                   
                     13
                  
                   
                     3.53
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     37
                  
                
                 
                   
                     30
                  
                   
                     1
                  
                   
                     13
                  
                   
                     4
                     30
                  
                
                 
                   
                     40
                  
                   
                     1
                  
                   
                     13
                  
                   
                     5.7
                  
                
                 
                   
                     50
                  
                   
                     1
                  
                   
                     13
                  
                   
                     5.45
                  
                
                 
                   
                     18.0
                  
                   
                     1
                  
                   
                     13
                  
                   
                     6.22
                  
                
                 
                   
                     10
                  
                   
                     1
                  
                   
                     13
                  
                   
                     6.59
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     ″
                  
                
                 
                   
                     20
                  
                   
                     1
                  
                   
                     13
                  
                   
                     7
                     37
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     37
                  
                
                 
                   
                     30
                  
                   
                     1
                  
                   
                     13
                  
                   
                     8.14
                  
                
                 
                   
                     40
                  
                   
                     1
                  
                   
                     13
                  
                   
                     8
                     52
                  
                
                 
                   
                     50
                  
                   
                     1
                  
                   
                     13
                  
                   
                     9
                     29
                  
                
                 
                   
                     19.0
                  
                   
                     1
                  
                   
                     13
                  
                   
                     10.6
                  
                
                 
                   
                     10
                  
                   
                     1
                  
                   
                     13
                  
                   
                     10.43
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     ″
                  
                
                 
                   
                     20
                  
                   
                     1
                  
                   
                     13
                  
                   
                     11.21
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     37
                  
                
                 
                   
                     30
                  
                   
                     1
                  
                   
                     13
                  
                   
                     11.58
                  
                
                 
                   
                     40
                  
                   
                     1
                  
                   
                     13
                  
                   
                     12.36
                  
                
                 
                   
                     50
                  
                   
                     1
                  
                   
                     13
                  
                   
                     13.13
                  
                
                 
                 
                   
                     20.0
                  
                   
                     1
                  
                   
                     13
                  
                   
                     13.50
                  
                
                 
                   
                     10
                  
                   
                     1
                  
                   
                     13
                  
                   
                     14.27
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     ″
                  
                
                 
                   
                     20
                  
                   
                     1
                  
                   
                     13
                  
                   
                     15.5
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     38
                  
                
                 
                   
                     30
                  
                   
                     1
                  
                   
                     13
                  
                   
                     15.42
                  
                
                 
                   
                     40
                  
                   
                     1
                  
                   
                     13
                  
                   
                     16.20
                  
                
                 
                   
                     50
                  
                   
                     1
                  
                   
                     13
                  
                   
                     16.57
                  
                
                 
                   
                     21.0
                  
                   
                     1
                  
                   
                     13
                  
                   
                     17.34
                  
                
                 
                   
                     10
                  
                   
                     1
                  
                   
                     13
                  
                   
                     18.12
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     ″
                  
                
                 
                   
                     20
                  
                   
                     1
                  
                   
                     13
                  
                   
                     18.50
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     38
                  
                
                 
                   
                     30
                  
                   
                     1
                  
                   
                     13
                  
                   
                     19.27
                  
                
                 
                   
                     40
                  
                   
                     1
                  
                   
                     13
                  
                   
                     20.5
                  
                
                 
                   
                     50
                  
                   
                     1
                  
                   
                     13
                  
                   
                     20.43
                  
                
                 
                   
                     22.0
                  
                   
                     1
                  
                   
                     13
                  
                   
                     21.19
                  
                
                 
                   
                     10
                  
                   
                     1
                  
                   
                     13
                  
                   
                     21.57
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     ″
                  
                
                 
                   
                     20
                  
                   
                     1
                  
                   
                     13
                  
                   
                     22.35
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     39
                  
                
                 
                   
                     30
                  
                   
                     1
                  
                   
                     13
                  
                   
                     23.12
                  
                
                 
                   
                     40
                  
                   
                     1
                  
                   
                     13
                  
                   
                     23.50
                  
                
                 
                   
                     50
                  
                   
                     1
                  
                   
                     13
                  
                   
                     24.28
                  
                
                 
                   
                     23.0
                  
                   
                     1
                  
                   
                     13
                  
                   
                     25.5
                  
                
                 
                   
                     10
                  
                   
                     1
                  
                   
                     13
                  
                   
                     25.42
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     ″
                  
                
                 
                   
                     20
                  
                   
                     1
                  
                   
                     13
                  
                   
                     26.20
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     39
                  
                
                 
                   
                     30
                  
                   
                     1
                  
                   
                     13
                  
                   
                     26.57
                  
                
                 
                   
                     50
                  
                   
                     1
                  
                   
                     13
                  
                   
                     27.35
                  
                
                 
                   
                     50
                  
                   
                     1
                  
                   
                     13
                  
                   
                     28.13
                  
                
                 
                   
                     24.0
                  
                   
                     1
                  
                   
                     13
                  
                   
                     28.50
                  
                
                 
                   
                     10
                  
                   
                     1
                  
                   
                     13
                  
                   
                     29.28
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     ″
                  
                
                 
                   
                     20
                  
                   
                     1
                  
                   
                     13
                  
                   
                     30.6
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     39
                  
                
                 
                   
                     30
                  
                   
                     1
                  
                   
                     13
                  
                   
                     30.44
                  
                
                 
                   
                     40
                  
                   
                     1
                  
                   
                     13
                  
                   
                     31.22
                  
                
                 
                   
                     50
                  
                   
                     1
                  
                   
                     13
                  
                   
                     32.0
                  
                
                 
                   
                     25.0
                  
                   
                     1
                  
                   
                     13
                  
                   
                     32.37
                  
                
                 
                   
                     10
                  
                   
                     1
                  
                   
                     13
                  
                   
                     33.15
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     ″
                  
                
                 
                   
                     20
                  
                   
                     1
                  
                   
                     13
                  
                   
                     33.53
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     38
                  
                
                 
                   
                     30
                  
                   
                     1
                  
                   
                     13
                  
                   
                     34.31
                  
                
                 
                   
                     40
                  
                   
                     1
                  
                   
                     13
                  
                   
                     35.9
                  
                
                 
                   
                     50
                  
                   
                     1
                  
                   
                     13
                  
                   
                     35.46
                  
                
                 
                   
                     26.0
                  
                   
                     1
                  
                   
                     13
                  
                   
                     36.24
                  
                
                 
                   
                     10
                  
                   
                     1
                  
                   
                     13
                  
                   
                     37.2
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     ″
                  
                
                 
                   
                     20
                  
                   
                     1
                  
                   
                     13
                  
                   
                     37.40
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     38
                  
                
                 
                   
                     30
                  
                   
                     1
                  
                   
                     13
                  
                   
                     38.18
                  
                
                 
                   
                     40
                  
                   
                     1
                  
                   
                     13
                  
                   
                     38.56
                  
                
                 
                   
                     50
                  
                   
                     1
                  
                   
                     13
                  
                   
                     39.33
                  
                
                 
                   
                     27.0
                  
                   
                     1
                  
                   
                     13
                  
                   
                     40.11
                  
                
                 
                   
                     10
                  
                   
                     1
                  
                   
                     13
                  
                   
                     40.49
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     ″
                  
                
                 
                   
                     20
                  
                   
                     1
                  
                   
                     13
                  
                   
                     41.27
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     38
                  
                
                 
                   
                     30
                  
                   
                     1
                  
                   
                     13
                  
                   
                     42.5
                  
                
                 
                   
                     40
                  
                   
                     1
                  
                   
                     13
                  
                   
                     42.43
                  
                
                 
                   
                     50
                  
                   
                     1
                  
                   
                     13
                  
                   
                     43.21
                  
                
                 
                   
                     28.0
                  
                   
                     1
                  
                   
                     13
                  
                   
                     43.59
                  
                
                 
                   
                     10
                  
                   
                     1
                  
                   
                     13
                  
                   
                     44.37
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     ″
                  
                
                 
                   
                     20
                  
                   
                     1
                  
                   
                     13
                  
                   
                     45.15
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     38
                  
                
                 
                   
                     30
                  
                   
                     1
                  
                   
                     13
                  
                   
                     45.53
                  
                
                 
                   
                     40
                  
                   
                     1
                  
                   
                     13
                  
                   
                     46.31
                  
                
                 
                   
                     50
                  
                   
                     1
                  
                   
                     13
                  
                   
                     47.9
                  
                
                 
                   
                     29.0
                  
                   
                     1
                  
                   
                     13
                  
                   
                     47.47
                  
                
                 
                   
                     10
                  
                   
                     1
                  
                   
                     13
                  
                   
                     48.25
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     ″
                  
                
                 
                   
                     20
                  
                   
                     1
                  
                   
                     13
                  
                   
                     49.03
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     39
                  
                
                 
                   
                     30
                  
                   
                     1
                  
                   
                     13
                  
                   
                     50.41
                  
                
                 
                   
                     40
                  
                   
                     1
                  
                   
                     13
                  
                   
                     51.19
                  
                
                 
                   
                     50
                  
                   
                     1
                  
                   
                     13
                  
                   
                     51.58
                  
                
              
               
               
                 
                   
                     D.
                     m.
                     
                  
                   
                     ♉
                     H
                  
                   
                     ♏
                     H
                  
                   
                     Com.
                     ′
                     Pts.
                     ″
                  
                
                 
                   
                     0.0
                  
                   
                     1
                  
                   
                     13
                  
                   
                     51.36
                  
                
                 
                   
                     10
                  
                   
                     1
                  
                   
                     13
                  
                   
                     52.14
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     ″
                  
                
                 
                   
                     20
                  
                   
                     1
                  
                   
                     13
                  
                   
                     52.52
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     38
                  
                
                 
                   
                     30
                  
                   
                     1
                  
                   
                     13
                  
                   
                     53.30
                  
                
                 
                   
                     40
                  
                   
                     1
                  
                   
                     13
                  
                   
                     54.8
                  
                
                 
                   
                     50
                  
                   
                     1
                  
                   
                     13
                  
                   
                     54.47
                  
                
                 
                   
                     1.0
                  
                   
                     1
                  
                   
                     13
                  
                   
                     55.25
                  
                
                 
                   
                     10
                  
                   
                     1
                  
                   
                     13
                  
                   
                     56.4
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     ″
                  
                
                 
                   
                     20
                  
                   
                     1
                  
                   
                     13
                  
                   
                     56.42
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     38
                  
                
                 
                   
                     30
                  
                   
                     1
                  
                   
                     13
                  
                   
                     57.21
                  
                
                 
                   
                     40
                  
                   
                     1
                  
                   
                     13
                  
                   
                     57.59
                  
                
                 
                   
                     50
                  
                   
                     1
                  
                   
                     13
                  
                   
                     58.38
                  
                
                 
                   
                     2.0
                  
                   
                     1
                  
                   
                     13
                  
                   
                     59.15
                  
                
                 
                   
                     10
                  
                   
                     1
                  
                   
                     13
                  
                   
                     59.54
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     ″
                  
                
                 
                   
                     20
                  
                   
                     2
                  
                   
                     14
                  
                   
                     0.32
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     39
                  
                
                 
                   
                     30
                  
                   
                     2
                  
                   
                     14
                  
                   
                     1.11
                  
                
                 
                   
                     40
                  
                   
                     2
                  
                   
                     14
                  
                   
                     1.49
                  
                
                 
                   
                     50
                  
                   
                     2
                  
                   
                     14
                  
                   
                     2.27
                  
                
                 
                   
                     3.0
                  
                   
                     2
                  
                   
                     14
                  
                   
                     3.6
                  
                
                 
                   
                     10
                  
                   
                     2
                  
                   
                     14
                  
                   
                     3.45
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     ″
                  
                
                 
                   
                     20
                  
                   
                     2
                  
                   
                     14
                  
                   
                     4.23
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     39
                  
                
                 
                   
                     30
                  
                   
                     2
                  
                   
                     14
                  
                   
                     5.1
                  
                
                 
                   
                     50
                  
                   
                     2
                  
                   
                     14
                  
                   
                     5.39
                  
                
                 
                   
                     50
                  
                   
                     2
                  
                   
                     14
                  
                   
                     6.18
                  
                
                 
                   
                     4.0
                  
                   
                     2
                  
                   
                     14
                  
                   
                     6.57
                  
                
                 
                   
                     10
                  
                   
                     2
                  
                   
                     14
                  
                   
                     7.36
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     ″
                  
                
                 
                   
                     20
                  
                   
                     2
                  
                   
                     14
                  
                   
                     8.15
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     39
                  
                
                 
                   
                     30
                  
                   
                     2
                  
                   
                     14
                  
                   
                     8.53
                  
                
                 
                   
                     40
                  
                   
                     2
                  
                   
                     14
                  
                   
                     9.32
                  
                
                 
                   
                     50
                  
                   
                     2
                  
                   
                     14
                  
                   
                     10.11
                  
                
                 
                   
                     5.0
                  
                   
                     2
                  
                   
                     14
                  
                   
                     10.49
                  
                
                 
                   
                     10
                  
                   
                     2
                  
                   
                     14
                  
                   
                     11.28
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     ″
                  
                
                 
                   
                     20
                  
                   
                     2
                  
                   
                     14
                  
                   
                     12.7
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     39
                  
                
                 
                   
                     30
                  
                   
                     2
                  
                   
                     14
                  
                   
                     12.46
                  
                
                 
                   
                     40
                  
                   
                     2
                  
                   
                     14
                  
                   
                     13.25
                  
                
                 
                   
                     50
                  
                   
                     2
                  
                   
                     14
                  
                   
                     14.4
                  
                
                 
                   
                     6.0
                  
                   
                     2
                  
                   
                     14
                  
                   
                     14.42
                  
                
                 
                   
                     10
                  
                   
                     2
                  
                   
                     14
                  
                   
                     15.21
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     ″
                  
                
                 
                   
                     20
                  
                   
                     2
                  
                   
                     14
                  
                   
                     16.0
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     39
                  
                
                 
                   
                     30
                  
                   
                     2
                  
                   
                     14
                  
                   
                     16.39
                  
                
                 
                   
                     40
                  
                   
                     2
                  
                   
                     14
                  
                   
                     17.18
                  
                
                 
                   
                     50
                  
                   
                     2
                  
                   
                     14
                  
                   
                     17.57
                  
                
                 
                   
                     7.0
                  
                   
                     2
                  
                   
                     14
                  
                   
                     18.35
                  
                
                 
                   
                     10
                  
                   
                     2
                  
                   
                     14
                  
                   
                     19.14
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     ″
                  
                
                 
                   
                     20
                  
                   
                     2
                  
                   
                     14
                  
                   
                     19.53
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     39
                  
                
                 
                   
                     30
                  
                   
                     2
                  
                   
                     14
                  
                   
                     20.32
                  
                
                 
                   
                     40
                  
                   
                     2
                  
                   
                     14
                  
                   
                     21.11
                  
                
                 
                   
                     50
                  
                   
                     2
                  
                   
                     14
                  
                   
                     21.50
                  
                
                 
                   
                     8.0
                  
                   
                     2
                  
                   
                     14
                  
                   
                     22.29
                  
                
                 
                   
                     10
                  
                   
                     2
                  
                   
                     14
                  
                   
                     23.8
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     ″
                  
                
                 
                   
                     20
                  
                   
                     2
                  
                   
                     14
                  
                   
                     23.47
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     39
                  
                
                 
                   
                     30
                  
                   
                     2
                  
                   
                     14
                  
                   
                     24.26
                  
                
                 
                   
                     40
                  
                   
                     2
                  
                   
                     14
                  
                   
                     25.5
                  
                
                 
                   
                     50
                  
                   
                     2
                  
                   
                     14
                  
                   
                     25.44
                  
                
                 
                   
                     9.0
                  
                   
                     2
                  
                   
                     14
                  
                   
                     26.24
                  
                
                 
                   
                     10
                  
                   
                     2
                  
                   
                     14
                  
                   
                     27.3
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     ″
                  
                
                 
                   
                     20
                  
                   
                     2
                  
                   
                     14
                  
                   
                     27.41
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     39
                  
                
                 
                   
                     30
                  
                   
                     2
                  
                   
                     14
                  
                   
                     28.20
                  
                
                 
                   
                     40
                  
                   
                     2
                  
                   
                     14
                  
                   
                     28.59
                  
                
                 
                   
                     50
                  
                   
                     2
                  
                   
                     14
                  
                   
                     29.38
                  
                
                 
                 
                   
                     10.0
                  
                   
                     2
                  
                   
                     14
                  
                   
                     30.19
                  
                
                 
                   
                     10
                  
                   
                     2
                  
                   
                     14
                  
                   
                     30.59
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     ″
                  
                
                 
                   
                     20
                  
                   
                     2
                  
                   
                     14
                  
                   
                     31.38
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     39
                  
                
                 
                   
                     30
                  
                   
                     2
                  
                   
                     14
                  
                   
                     32.17
                  
                
                 
                   
                     40
                  
                   
                     2
                  
                   
                     14
                  
                   
                     33.7
                  
                
                 
                   
                     50
                  
                   
                     2
                  
                   
                     14
                  
                   
                     33.46
                  
                
                 
                   
                     11.0
                  
                   
                     2
                  
                   
                     14
                  
                   
                     34.15
                  
                
                 
                   
                     10
                  
                   
                     2
                  
                   
                     14
                  
                   
                     34.54
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     ″
                  
                
                 
                   
                     20
                  
                   
                     2
                  
                   
                     14
                  
                   
                     35.34
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     39
                  
                
                 
                   
                     30
                  
                   
                     2
                  
                   
                     14
                  
                   
                     36.13
                  
                
                 
                   
                     40
                  
                   
                     2
                  
                   
                     14
                  
                   
                     36.51
                  
                
                 
                   
                     50
                  
                   
                     2
                  
                   
                     14
                  
                   
                     37.31
                  
                
                 
                   
                     12.0
                  
                   
                     2
                  
                   
                     14
                  
                   
                     38.11
                  
                
                 
                   
                     10
                  
                   
                     2
                  
                   
                     14
                  
                   
                     38.51
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     ″
                  
                
                 
                   
                     20
                  
                   
                     2
                  
                   
                     14
                  
                   
                     39.31
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     40
                  
                
                 
                   
                     30
                  
                   
                     2
                  
                   
                     14
                  
                   
                     40.11
                  
                
                 
                   
                     40
                  
                   
                     2
                  
                   
                     14
                  
                   
                     40.51
                  
                
                 
                   
                     50
                  
                   
                     2
                  
                   
                     14
                  
                   
                     41.31
                  
                
                 
                   
                     13.0
                  
                   
                     2
                  
                   
                     14
                  
                   
                     42.9
                  
                
                 
                   
                     10
                  
                   
                     2
                  
                   
                     14
                  
                   
                     42.49
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     ″
                  
                
                 
                   
                     20
                  
                   
                     2
                  
                   
                     14
                  
                   
                     43.29
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     40
                  
                
                 
                   
                     30
                  
                   
                     2
                  
                   
                     14
                  
                   
                     44.8
                  
                
                 
                   
                     40
                  
                   
                     2
                  
                   
                     14
                  
                   
                     44.48
                  
                
                 
                   
                     50
                  
                   
                     2
                  
                   
                     14
                  
                   
                     45.27
                  
                
                 
                   
                     14.0
                  
                   
                     2
                  
                   
                     14
                  
                   
                     46.7
                  
                
                 
                   
                     10
                  
                   
                     2
                  
                   
                     14
                  
                   
                     46.47
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     ″
                  
                
                 
                   
                     20
                  
                   
                     2
                  
                   
                     14
                  
                   
                     47.27
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     40
                  
                
                 
                   
                     30
                  
                   
                     2
                  
                   
                     14
                  
                   
                     48.6
                  
                
                 
                   
                     40
                  
                   
                     2
                  
                   
                     14
                  
                   
                     48.46
                  
                
                 
                   
                     50
                  
                   
                     2
                  
                   
                     14
                  
                   
                     49.25
                  
                
                 
                   
                     15.0
                  
                   
                     2
                  
                   
                     14
                  
                   
                     50.5
                  
                
                 
                   
                     10
                  
                   
                     2
                  
                   
                     14
                  
                   
                     50.45
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     ″
                  
                
                 
                   
                     20
                  
                   
                     2
                  
                   
                     14
                  
                   
                     51.25
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     40
                  
                
                 
                   
                     30
                  
                   
                     2
                  
                   
                     14
                  
                   
                     52.5
                  
                
                 
                   
                     40
                  
                   
                     2
                  
                   
                     14
                  
                   
                     52.45
                  
                
                 
                   
                     50
                  
                   
                     2
                  
                   
                     14
                  
                   
                     53.25
                  
                
                 
                   
                     16.0
                  
                   
                     2
                  
                   
                     14
                  
                   
                     54.5
                  
                
                 
                   
                     10
                  
                   
                     2
                  
                   
                     14
                  
                   
                     54.45
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     ″
                  
                
                 
                   
                     20
                  
                   
                     2
                  
                   
                     14
                  
                   
                     55.25
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     40
                  
                
                 
                   
                     30
                  
                   
                     2
                  
                   
                     14
                  
                   
                     56.5
                  
                
                 
                   
                     40
                  
                   
                     2
                  
                   
                     14
                  
                   
                     56.45
                  
                
                 
                   
                     50
                  
                   
                     2
                  
                   
                     14
                  
                   
                     57.25
                  
                
                 
                   
                     17.0
                  
                   
                     2
                  
                   
                     14
                  
                   
                     58.5
                  
                
                 
                   
                     10
                  
                   
                     2
                  
                   
                     14
                  
                   
                     58.45
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     ″
                  
                
                 
                   
                     20
                  
                   
                     2
                  
                   
                     14
                  
                   
                     59.25
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     40
                  
                
                 
                   
                     30
                  
                   
                     3
                  
                   
                     15
                  
                   
                     0.5
                  
                
                 
                   
                     40
                  
                   
                     3
                  
                   
                     15
                  
                   
                     0.46
                  
                
                 
                   
                     50
                  
                   
                     3
                  
                   
                     15
                  
                   
                     1.26
                  
                
                 
                   
                     18.0
                  
                   
                     3
                  
                   
                     15
                  
                   
                     2.6
                  
                
                 
                   
                     10
                  
                   
                     3
                  
                   
                     15
                  
                   
                     2.46
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     ″
                  
                
                 
                   
                     20
                  
                   
                     3
                  
                   
                     15
                  
                   
                     3.27
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     40
                  
                
                 
                   
                     30
                  
                   
                     3
                  
                   
                     15
                  
                   
                     4.7
                  
                
                 
                   
                     40
                  
                   
                     3
                  
                   
                     15
                  
                   
                     4.47
                  
                
                 
                   
                     50
                  
                   
                     3
                  
                   
                     15
                  
                   
                     5.28
                  
                
                 
                   
                     19.0
                  
                   
                     3
                  
                   
                     15
                  
                   
                     6.8
                  
                
                 
                   
                     10
                  
                   
                     3
                  
                   
                     15
                  
                   
                     6.49
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     ″
                  
                
                 
                   
                     20
                  
                   
                     3
                  
                   
                     15
                  
                   
                     7.29
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     40
                  
                
                 
                   
                     30
                  
                   
                     3
                  
                   
                     15
                  
                   
                     8.10
                  
                
                 
                   
                     40
                  
                   
                     3
                  
                   
                     15
                  
                   
                     8.50
                  
                
                 
                   
                     50
                  
                   
                     3
                  
                   
                     15
                  
                   
                     9.30
                  
                
                 
                 
                   
                     20.0
                  
                   
                     3
                  
                   
                     15
                  
                   
                     10.10
                  
                
                 
                   
                     10
                  
                   
                     3
                  
                   
                     15
                  
                   
                     10.51
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     ″
                  
                
                 
                   
                     20
                  
                   
                     3
                  
                   
                     15
                  
                   
                     11.30
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     41
                  
                
                 
                   
                     30
                  
                   
                     3
                  
                   
                     15
                  
                   
                     12.11
                  
                
                 
                   
                     40
                  
                   
                     3
                  
                   
                     15
                  
                   
                     12.51
                  
                
                 
                   
                     50
                  
                   
                     3
                  
                   
                     15
                  
                   
                     13.32
                  
                
                 
                   
                     21.0
                  
                   
                     3
                  
                   
                     15
                  
                   
                     14.13
                  
                
                 
                   
                     10
                  
                   
                     3
                  
                   
                     15
                  
                   
                     14.53
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     ″
                  
                
                 
                   
                     20
                  
                   
                     3
                  
                   
                     15
                  
                   
                     15.34
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     41
                  
                
                 
                   
                     30
                  
                   
                     3
                  
                   
                     15
                  
                   
                     16.15
                  
                
                 
                   
                     40
                  
                   
                     3
                  
                   
                     15
                  
                   
                     16.55
                  
                
                 
                   
                     50
                  
                   
                     3
                  
                   
                     15
                  
                   
                     17.36
                  
                
                 
                   
                     22.0
                  
                   
                     3
                  
                   
                     15
                  
                   
                     18.17
                  
                
                 
                   
                     10
                  
                   
                     3
                  
                   
                     15
                  
                   
                     18.58
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     ″
                  
                
                 
                   
                     20
                  
                   
                     3
                  
                   
                     15
                  
                   
                     19.39
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     41
                  
                
                 
                   
                     30
                  
                   
                     3
                  
                   
                     15
                  
                   
                     20.20
                  
                
                 
                   
                     40
                  
                   
                     3
                  
                   
                     15
                  
                   
                     21.1
                  
                
                 
                   
                     50
                  
                   
                     3
                  
                   
                     15
                  
                   
                     21.41
                  
                
                 
                   
                     23.0
                  
                   
                     3
                  
                   
                     15
                  
                   
                     22.22
                  
                
                 
                   
                     10
                  
                   
                     3
                  
                   
                     15
                  
                   
                     23.03
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     ″
                  
                
                 
                   
                     20
                  
                   
                     3
                  
                   
                     15
                  
                   
                     23.44
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     41
                  
                
                 
                   
                     30
                  
                   
                     3
                  
                   
                     15
                  
                   
                     24.25
                  
                
                 
                   
                     40
                  
                   
                     3
                  
                   
                     15
                  
                   
                     25.06
                  
                
                 
                   
                     50
                  
                   
                     3
                  
                   
                     15
                  
                   
                     25.47
                  
                
                 
                   
                     24.0
                  
                   
                     3
                  
                   
                     15
                  
                   
                     26.27
                  
                
                 
                   
                     10
                  
                   
                     3
                  
                   
                     15
                  
                   
                     27.08
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     ″
                  
                
                 
                   
                     20
                  
                   
                     5
                  
                   
                     15
                  
                   
                     27.49
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     41
                  
                
                 
                   
                     30
                  
                   
                     3
                  
                   
                     15
                  
                   
                     28.30
                  
                
                 
                   
                     40
                  
                   
                     3
                  
                   
                     15
                  
                   
                     29.11
                  
                
                 
                   
                     50
                  
                   
                     3
                  
                   
                     15
                  
                   
                     29.52
                  
                
                 
                   
                     25.0
                  
                   
                     3
                  
                   
                     15
                  
                   
                     30.33
                  
                
                 
                   
                     10
                  
                   
                     3
                  
                   
                     15
                  
                   
                     31.14
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     ″
                  
                
                 
                   
                     20
                  
                   
                     3
                  
                   
                     15
                  
                   
                     31.55
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     41
                  
                
                 
                   
                     30
                  
                   
                     3
                  
                   
                     15
                  
                   
                     32.36
                  
                
                 
                   
                     40
                  
                   
                     3
                  
                   
                     15
                  
                   
                     33.17
                  
                
                 
                   
                     50
                  
                   
                     3
                  
                   
                     15
                  
                   
                     33.58
                  
                
                 
                   
                     26.0
                  
                   
                     3
                  
                   
                     15
                  
                   
                     34
                     40
                  
                
                 
                   
                     10
                  
                   
                     3
                  
                   
                     15
                  
                   
                     35.21
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     ″
                  
                
                 
                   
                     20
                  
                   
                     3
                  
                   
                     15
                  
                   
                     36.02
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     41
                  
                
                 
                   
                     30
                  
                   
                     3
                  
                   
                     15
                  
                   
                     36.44
                  
                
                 
                   
                     40
                  
                   
                     3
                  
                   
                     15
                  
                   
                     37
                     25
                  
                
                 
                   
                     50
                  
                   
                     3
                  
                   
                     15
                  
                   
                     38.06
                  
                
                 
                   
                     27.0
                  
                   
                     3
                  
                   
                     15
                  
                   
                     38
                     47
                  
                
                 
                   
                     10
                  
                   
                     3
                  
                   
                     15
                  
                   
                     39.29
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     ″
                  
                
                 
                   
                     20
                  
                   
                     3
                  
                   
                     15
                  
                   
                     40.11
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     41
                  
                
                 
                   
                     30
                  
                   
                     3
                  
                   
                     15
                  
                   
                     40
                     53
                  
                
                 
                   
                     40
                  
                   
                     3
                  
                   
                     15
                  
                   
                     41.34
                  
                
                 
                   
                     50
                  
                   
                     3
                  
                   
                     15
                  
                   
                     42.15
                  
                
                 
                   
                     28.0
                  
                   
                     3
                  
                   
                     15
                  
                   
                     42.55
                  
                
                 
                   
                     10
                  
                   
                     3
                  
                   
                     15
                  
                   
                     43.37
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     ″
                  
                
                 
                   
                     20
                  
                   
                     3
                  
                   
                     15
                  
                   
                     44.19
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     41
                  
                
                 
                   
                     30
                  
                   
                     3
                  
                   
                     15
                  
                   
                     45
                     01
                  
                
                 
                   
                     40
                  
                   
                     3
                  
                   
                     15
                  
                   
                     45.43
                  
                
                 
                   
                     50
                  
                   
                     3
                  
                   
                     15
                  
                   
                     46.21
                  
                
                 
                   
                     29.0
                  
                   
                     3
                  
                   
                     15
                  
                   
                     47.4
                  
                
                 
                   
                     10
                  
                   
                     3
                  
                   
                     15
                  
                   
                     47.46
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     ″
                  
                
                 
                   
                     20
                  
                   
                     3
                  
                   
                     15
                  
                   
                     48.28
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     42
                  
                
                 
                   
                     30
                  
                   
                     3
                  
                   
                     15
                  
                   
                     49
                     10
                  
                
                 
                   
                     40
                  
                   
                     3
                  
                   
                     15
                  
                   
                     49.52
                  
                
                 
                   
                     50
                  
                   
                     3
                  
                   
                     15
                  
                   
                     50.33
                  
                
              
               
               
                 
                   
                     D.
                     m.
                     
                  
                   
                     ♊
                     H.
                     
                  
                   
                     ♐
                     H.
                     
                  
                   
                     Com.
                     ′
                     Pts.
                     ″
                  
                
                 
                   
                     0.0
                  
                   
                     3
                  
                   
                     15
                  
                   
                     51.14
                  
                
                 
                   
                     10
                  
                   
                     3
                  
                   
                     15
                  
                   
                     51.56
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     ″
                  
                
                 
                   
                     20
                  
                   
                     3
                  
                   
                     15
                  
                   
                     52.37
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     42
                  
                
                 
                   
                     30
                  
                   
                     3
                  
                   
                     15
                  
                   
                     53.19
                  
                
                 
                   
                     40
                  
                   
                     3
                  
                   
                     15
                  
                   
                     54.
                     ●0
                  
                
                 
                   
                     50
                  
                   
                     3
                  
                   
                     15
                  
                   
                     54
                     42
                  
                
                 
                   
                     1.0
                  
                   
                     3
                  
                   
                     15
                  
                   
                     55.24
                  
                
                 
                   
                     10
                  
                   
                     3
                  
                   
                     15
                  
                   
                     56.
                     ●6
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     ″
                  
                
                 
                   
                     20
                  
                   
                     3
                  
                   
                     15
                  
                   
                     56.47
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     42
                  
                
                 
                   
                     30
                  
                   
                     3
                  
                   
                     15
                  
                   
                     57.29
                  
                
                 
                   
                     40
                  
                   
                     3
                  
                   
                     15
                  
                   
                     58.10
                  
                
                 
                   
                     50
                  
                   
                     3
                  
                   
                     15
                  
                   
                     58.52
                  
                
                 
                   
                     2.0
                  
                   
                     3
                  
                   
                     15
                  
                   
                     59.35
                  
                
                 
                   
                     10
                  
                   
                     4
                  
                   
                     16
                  
                   
                     00.17
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     ″
                  
                
                 
                   
                     20
                  
                   
                     4
                  
                   
                     16
                  
                   
                     00.59
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     42
                  
                
                 
                   
                     30
                  
                   
                     4
                  
                   
                     16
                  
                   
                     01.40
                  
                
                 
                   
                     40
                  
                   
                     4
                  
                   
                     16
                  
                   
                     2●
                     .
                     22
                  
                
                 
                   
                     50
                  
                   
                     4
                  
                   
                     16
                  
                   
                     3.4
                  
                
                 
                   
                     3.0
                  
                   
                     4
                  
                   
                     16
                  
                   
                     3.46
                  
                
                 
                   
                     10
                  
                   
                     4
                  
                   
                     16
                  
                   
                     4.28
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     ″
                  
                
                 
                   
                     20
                  
                   
                     4
                  
                   
                     16
                  
                   
                     5.9
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     42
                  
                
                 
                   
                     30
                  
                   
                     4
                  
                   
                     16
                  
                   
                     5.51
                  
                
                 
                   
                     40
                  
                   
                     4
                  
                   
                     16
                  
                   
                     6.33
                  
                
                 
                   
                     50
                  
                   
                     4
                  
                   
                     16
                  
                   
                     7.15
                  
                
                 
                   
                     4.0
                  
                   
                     4
                  
                   
                     16
                  
                   
                     7.59
                  
                
                 
                   
                     10
                  
                   
                     4
                  
                   
                     16
                  
                   
                     8.41
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     ″
                  
                
                 
                   
                     20
                  
                   
                     4
                  
                   
                     16
                  
                   
                     9.23
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     42
                  
                
                 
                   
                     30
                  
                   
                     4
                  
                   
                     16
                  
                   
                     10.5
                  
                
                 
                   
                     40
                  
                   
                     4
                  
                   
                     16
                  
                   
                     10.47
                  
                
                 
                   
                     50
                  
                   
                     4
                  
                   
                     16
                  
                   
                     11.29
                  
                
                 
                   
                     5.0
                  
                   
                     4
                  
                   
                     16
                  
                   
                     12.11
                  
                
                 
                   
                     10
                  
                   
                     4
                  
                   
                     16
                  
                   
                     12.53
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     ″
                  
                
                 
                   
                     20
                  
                   
                     4
                  
                   
                     16
                  
                   
                     13
                     35
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     42
                  
                
                 
                   
                     30
                  
                   
                     4
                  
                   
                     16
                  
                   
                     14.17
                  
                
                 
                   
                     40
                  
                   
                     4
                  
                   
                     16
                  
                   
                     14
                     59
                  
                
                 
                   
                     50
                  
                   
                     4
                  
                   
                     16
                  
                   
                     15.41
                  
                
                 
                   
                     6.0
                  
                   
                     4
                  
                   
                     16
                  
                   
                     16.25
                  
                
                 
                   
                     10
                  
                   
                     4
                  
                   
                     16
                  
                   
                     17.7
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     ″
                  
                
                 
                   
                     20
                  
                   
                     4
                  
                   
                     16
                  
                   
                     17.50
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     42
                  
                
                 
                   
                     30
                  
                   
                     4
                  
                   
                     16
                  
                   
                     18.32
                  
                
                 
                   
                     40
                  
                   
                     4
                  
                   
                     16
                  
                   
                     19.15
                  
                
                 
                   
                     50
                  
                   
                     4
                  
                   
                     16
                  
                   
                     19.57
                  
                
                 
                   
                     7.0
                  
                   
                     4
                  
                   
                     16
                  
                   
                     20.39
                  
                
                 
                   
                     10
                  
                   
                     4
                  
                   
                     16
                  
                   
                     21.21
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     ″
                  
                
                 
                   
                     20
                  
                   
                     4
                  
                   
                     16
                  
                   
                     22.4
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     43
                  
                
                 
                   
                     30
                  
                   
                     4
                  
                   
                     16
                  
                   
                     22.47
                  
                
                 
                   
                     40
                  
                   
                     4
                  
                   
                     19
                  
                   
                     23.30
                  
                
                 
                   
                     50
                  
                   
                     4
                  
                   
                     16
                  
                   
                     24.12
                  
                
                 
                   
                     8.0
                  
                   
                     4
                  
                   
                     16
                  
                   
                     24.54
                  
                
                 
                   
                     10
                  
                   
                     4
                  
                   
                     16
                  
                   
                     25.36
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     ″
                  
                
                 
                   
                     20
                  
                   
                     4
                  
                   
                     16
                  
                   
                     26.19
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     43
                  
                
                 
                   
                     30
                  
                   
                     4
                  
                   
                     16
                  
                   
                     27.1
                  
                
                 
                   
                     40
                  
                   
                     4
                  
                   
                     16
                  
                   
                     27.44
                  
                
                 
                   
                     50
                  
                   
                     4
                  
                   
                     16
                  
                   
                     28.26
                  
                
                 
                   
                     9.0
                  
                   
                     4
                  
                   
                     16
                  
                   
                     29.9
                  
                
                 
                   
                     10
                  
                   
                     4
                  
                   
                     16
                  
                   
                     29.51
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     ″
                  
                
                 
                   
                     20
                  
                   
                     4
                  
                   
                     16
                  
                   
                     30.34
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     43
                  
                
                 
                   
                     30
                  
                   
                     4
                  
                   
                     16
                  
                   
                     31.16
                  
                
                 
                   
                     40
                  
                   
                     4
                  
                   
                     16
                  
                   
                     31.59
                  
                
                 
                   
                     50
                  
                   
                     4
                  
                   
                     16
                  
                   
                     32.42
                  
                
                 
                 
                   
                     10.0
                  
                   
                     4
                  
                   
                     16
                  
                   
                     33.25
                  
                
                 
                   
                     10
                  
                   
                     4
                  
                   
                     16
                  
                   
                     34.8
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     ″
                  
                
                 
                   
                     20
                  
                   
                     4
                  
                   
                     16
                  
                   
                     34.51
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     43
                  
                
                 
                   
                     30
                  
                   
                     4
                  
                   
                     16
                  
                   
                     35.34
                  
                
                 
                   
                     40
                  
                   
                     4
                  
                   
                     16
                  
                   
                     36.15
                  
                
                 
                   
                     50
                  
                   
                     4
                  
                   
                     16
                  
                   
                     36.58
                  
                
                 
                   
                     11.0
                  
                   
                     4
                  
                   
                     16
                  
                   
                     37.41
                  
                
                 
                   
                     10
                  
                   
                     4
                  
                   
                     16
                  
                   
                     38.24
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     ″
                  
                
                 
                   
                     20
                  
                   
                     4
                  
                   
                     16
                  
                   
                     39.7
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     43
                  
                
                 
                   
                     30
                  
                   
                     4
                  
                   
                     16
                  
                   
                     39.49
                  
                
                 
                   
                     40
                  
                   
                     4
                  
                   
                     16
                  
                   
                     40.32
                  
                
                 
                   
                     50
                  
                   
                     4
                  
                   
                     16
                  
                   
                     41.14
                  
                
                 
                   
                     12.0
                  
                   
                     4
                  
                   
                     16
                  
                   
                     41.57
                  
                
                 
                   
                     10
                  
                   
                     4
                  
                   
                     16
                  
                   
                     42.40
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     ″
                  
                
                 
                   
                     20
                  
                   
                     4
                  
                   
                     16
                  
                   
                     43.23
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     43
                  
                
                 
                   
                     30
                  
                   
                     4
                  
                   
                     16
                  
                   
                     44.05
                  
                
                 
                   
                     40
                  
                   
                     4
                  
                   
                     16
                  
                   
                     44.48
                  
                
                 
                   
                     50
                  
                   
                     4
                  
                   
                     16
                  
                   
                     45.31
                  
                
                 
                   
                     13.0
                  
                   
                     4
                  
                   
                     16
                  
                   
                     46.15
                  
                
                 
                   
                     10
                  
                   
                     4
                  
                   
                     16
                  
                   
                     46.58
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     ″
                  
                
                 
                   
                     20
                  
                   
                     4
                  
                   
                     16
                  
                   
                     47.41
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     43
                  
                
                 
                   
                     30
                  
                   
                     4
                  
                   
                     16
                  
                   
                     48.23
                  
                
                 
                   
                     40
                  
                   
                     4
                  
                   
                     16
                  
                   
                     49.5
                  
                
                 
                   
                     50
                  
                   
                     4
                  
                   
                     16
                  
                   
                     49.48
                  
                
                 
                   
                     14.0
                  
                   
                     4
                  
                   
                     16
                  
                   
                     50.32
                  
                
                 
                   
                     10
                  
                   
                     4
                  
                   
                     16
                  
                   
                     51.15
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     ″
                  
                
                 
                   
                     20
                  
                   
                     4
                  
                   
                     16
                  
                   
                     51.58
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     43
                  
                
                 
                   
                     30
                  
                   
                     4
                  
                   
                     16
                  
                   
                     52.41
                  
                
                 
                   
                     40
                  
                   
                     4
                  
                   
                     16
                  
                   
                     53.23
                  
                
                 
                   
                     50
                  
                   
                     4
                  
                   
                     16
                  
                   
                     54.5
                  
                
                 
                   
                     15.0
                  
                   
                     4
                  
                   
                     16
                  
                   
                     54.51
                  
                
                 
                   
                     10
                  
                   
                     4
                  
                   
                     16
                  
                   
                     55.34
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     ″
                  
                
                 
                   
                     20
                  
                   
                     4
                  
                   
                     16
                  
                   
                     56.17
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     43
                  
                
                 
                   
                     30
                  
                   
                     4
                  
                   
                     16
                  
                   
                     57.00
                  
                
                 
                   
                     40
                  
                   
                     4
                  
                   
                     16
                  
                   
                     57.43
                  
                
                 
                   
                     50
                  
                   
                     4
                  
                   
                     16
                  
                   
                     58.26
                  
                
                 
                   
                     16.0
                  
                   
                     4
                  
                   
                     16
                  
                   
                     59.9
                  
                
                 
                   
                     10
                  
                   
                     4
                  
                   
                     16
                  
                   
                     59.52
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     ″
                  
                
                 
                   
                     20
                  
                   
                     5
                  
                   
                     6
                  
                   
                     00.35
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     43
                  
                
                 
                   
                     30
                  
                   
                     5
                  
                   
                     6
                  
                   
                     1.18
                  
                
                 
                   
                     40
                  
                   
                     5
                  
                   
                     6
                  
                   
                     2.01
                  
                
                 
                   
                     50
                  
                   
                     5
                  
                   
                     6
                  
                   
                     2.44
                  
                
                 
                   
                     17.0
                  
                   
                     5
                  
                   
                     17
                  
                   
                     3.28
                  
                
                 
                   
                     10
                  
                   
                     5
                  
                   
                     17
                  
                   
                     4.11
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     ″
                  
                
                 
                   
                     20
                  
                   
                     5
                  
                   
                     17
                  
                   
                     4.54
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     43
                  
                
                 
                   
                     30
                  
                   
                     5
                  
                   
                     17
                  
                   
                     5.37
                  
                
                 
                   
                     40
                  
                   
                     5
                  
                   
                     17
                  
                   
                     6.20
                  
                
                 
                   
                     50
                  
                   
                     5
                  
                   
                     17
                  
                   
                     7.04
                  
                
                 
                   
                     18.0
                  
                   
                     5
                  
                   
                     17
                  
                   
                     7.48
                  
                
                 
                   
                     10
                  
                   
                     5
                  
                   
                     17
                  
                   
                     8.31
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     ″
                  
                
                 
                   
                     20
                  
                   
                     5
                  
                   
                     17
                  
                   
                     9.14
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     43
                  
                
                 
                   
                     30
                  
                   
                     5
                  
                   
                     17
                  
                   
                     9.58
                  
                
                 
                   
                     40
                  
                   
                     5
                  
                   
                     17
                  
                   
                     10.41
                  
                
                 
                   
                     50
                  
                   
                     5
                  
                   
                     17
                  
                   
                     11.24
                  
                
                 
                   
                     19.0
                  
                   
                     5
                  
                   
                     17
                  
                   
                     12.8
                  
                
                 
                   
                     10
                  
                   
                     5
                  
                   
                     17
                  
                   
                     12.52
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     ″
                  
                
                 
                   
                     20
                  
                   
                     5
                  
                   
                     17
                  
                   
                     13.35
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     43
                  
                
                 
                   
                     30
                  
                   
                     5
                  
                   
                     17
                  
                   
                     14.18
                  
                
                 
                   
                     40
                  
                   
                     5
                  
                   
                     17
                  
                   
                     15.01
                  
                
                 
                   
                     50
                  
                   
                     5
                  
                   
                     17
                  
                   
                     15.44
                  
                
                 
                 
                   
                     20.0
                  
                   
                     5
                  
                   
                     17
                  
                   
                     16.28
                  
                
                 
                   
                     10
                  
                   
                     5
                  
                   
                     17
                  
                   
                     17.12
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     ″
                  
                
                 
                   
                     20
                  
                   
                     5
                  
                   
                     17
                  
                   
                     17.55
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     44
                  
                
                 
                   
                     30
                  
                   
                     5
                  
                   
                     17
                  
                   
                     18.39
                  
                
                 
                   
                     40
                  
                   
                     5
                  
                   
                     17
                  
                   
                     19.23
                  
                
                 
                   
                     50
                  
                   
                     5
                  
                   
                     17
                  
                   
                     20.5
                  
                
                 
                   
                     21.0
                  
                   
                     5
                  
                   
                     17
                  
                   
                     20.48
                  
                
                 
                   
                     10
                  
                   
                     5
                  
                   
                     17
                  
                   
                     21.32
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     ″
                  
                
                 
                   
                     20
                  
                   
                     5
                  
                   
                     17
                  
                   
                     22
                     15
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     44
                  
                
                 
                   
                     30
                  
                   
                     5
                  
                   
                     17
                  
                   
                     22.59
                  
                
                 
                   
                     40
                  
                   
                     5
                  
                   
                     17
                  
                   
                     23.42
                  
                
                 
                   
                     50
                  
                   
                     5
                  
                   
                     17
                  
                   
                     24.26
                  
                
                 
                   
                     22.0
                  
                   
                     5
                  
                   
                     17
                  
                   
                     25.9
                  
                
                 
                   
                     10
                  
                   
                     5
                  
                   
                     17
                  
                   
                     25
                     53
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     ″
                  
                
                 
                   
                     20
                  
                   
                     5
                  
                   
                     17
                  
                   
                     26.37
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     44
                  
                
                 
                   
                     30
                  
                   
                     5
                  
                   
                     17
                  
                   
                     27.21
                  
                
                 
                   
                     40
                  
                   
                     5
                  
                   
                     17
                  
                   
                     28
                     04
                  
                
                 
                   
                     50
                  
                   
                     5
                  
                   
                     17
                  
                   
                     28.47
                  
                
                 
                   
                     23.0
                  
                   
                     5
                  
                   
                     17
                  
                   
                     29.30
                  
                
                 
                   
                     10
                  
                   
                     5
                  
                   
                     17
                  
                   
                     30.14
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     ″
                  
                
                 
                   
                     20
                  
                   
                     5
                  
                   
                     17
                  
                   
                     30.58
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     44
                  
                
                 
                   
                     30
                  
                   
                     5
                  
                   
                     17
                  
                   
                     31.41
                  
                
                 
                   
                     40
                  
                   
                     5
                  
                   
                     17
                  
                   
                     32.25
                  
                
                 
                   
                     50
                  
                   
                     5
                  
                   
                     17
                  
                   
                     33.08
                  
                
                 
                   
                     24.0
                  
                   
                     5
                  
                   
                     17
                  
                   
                     33.51
                  
                
                 
                   
                     10
                  
                   
                     5
                  
                   
                     17
                  
                   
                     34.35
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     ″
                  
                
                 
                   
                     20
                  
                   
                     5
                  
                   
                     17
                  
                   
                     35.18
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     44
                  
                
                 
                   
                     30
                  
                   
                     5
                  
                   
                     17
                  
                   
                     36
                     02
                  
                
                 
                   
                     40
                  
                   
                     5
                  
                   
                     17
                  
                   
                     36.46
                  
                
                 
                   
                     50
                  
                   
                     5
                  
                   
                     17
                  
                   
                     37.30
                  
                
                 
                   
                     25.0
                  
                   
                     5
                  
                   
                     17
                  
                   
                     38.12
                  
                
                 
                   
                     10
                  
                   
                     5
                  
                   
                     17
                  
                   
                     38.56
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     ″
                  
                
                 
                   
                     20
                  
                   
                     5
                  
                   
                     17
                  
                   
                     39.39
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     44
                  
                
                 
                   
                     30
                  
                   
                     5
                  
                   
                     17
                  
                   
                     40.23
                  
                
                 
                   
                     40
                  
                   
                     5
                  
                   
                     17
                  
                   
                     41.06
                  
                
                 
                   
                     50
                  
                   
                     5
                  
                   
                     17
                  
                   
                     41.50
                  
                
                 
                   
                     26.0
                  
                   
                     5
                  
                   
                     17
                  
                   
                     42.33
                  
                
                 
                   
                     10
                  
                   
                     5
                  
                   
                     17
                  
                   
                     43.17
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     ″
                  
                
                 
                   
                     20
                  
                   
                     5
                  
                   
                     17
                  
                   
                     44.00
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     44
                  
                
                 
                   
                     30
                  
                   
                     5
                  
                   
                     17
                  
                   
                     44.44
                  
                
                 
                   
                     40
                  
                   
                     5
                  
                   
                     17
                  
                   
                     45.27
                  
                
                 
                   
                     50
                  
                   
                     5
                  
                   
                     17
                  
                   
                     46.11
                  
                
                 
                   
                     27.0
                  
                   
                     5
                  
                   
                     17
                  
                   
                     46.55
                  
                
                 
                   
                     10
                  
                   
                     5
                  
                   
                     17
                  
                   
                     47.39
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     ″
                  
                
                 
                   
                     20
                  
                   
                     5
                  
                   
                     17
                  
                   
                     48.22
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     44
                  
                
                 
                   
                     30
                  
                   
                     5
                  
                   
                     17
                  
                   
                     49.06
                  
                
                 
                   
                     40
                  
                   
                     5
                  
                   
                     17
                  
                   
                     49.49
                  
                
                 
                   
                     50
                  
                   
                     5
                  
                   
                     17
                  
                   
                     50.33
                  
                
                 
                   
                     28.0
                  
                   
                     5
                  
                   
                     17
                  
                   
                     51.17
                  
                
                 
                   
                     10
                  
                   
                     5
                  
                   
                     17
                  
                   
                     52.01
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     ″
                  
                
                 
                   
                     20
                  
                   
                     5
                  
                   
                     17
                  
                   
                     52
                     44
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     44
                  
                
                 
                   
                     30
                  
                   
                     5
                  
                   
                     17
                  
                   
                     53.27
                  
                
                 
                   
                     40
                  
                   
                     5
                  
                   
                     17
                  
                   
                     54.11
                  
                
                 
                   
                     50
                  
                   
                     5
                  
                   
                     17
                  
                   
                     54.54
                  
                
                 
                   
                     29.0
                  
                   
                     5
                  
                   
                     17
                  
                   
                     55.38
                  
                
                 
                   
                     10
                  
                   
                     5
                  
                   
                     17
                  
                   
                     56.22
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     ″
                  
                
                 
                   
                     20
                  
                   
                     5
                  
                   
                     17
                  
                   
                     57
                     06
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     44
                  
                
                 
                   
                     30
                  
                   
                     5
                  
                   
                     17
                  
                   
                     57
                     49
                  
                
                 
                   
                     40
                  
                   
                     5
                  
                   
                     17
                  
                   
                     58.33
                  
                
                 
                   
                     50
                  
                   
                     5
                  
                   
                     17
                  
                   
                     59.16
                  
                
              
               
               
                 
                   
                     D.
                     m.
                     
                  
                   
                     ♋
                     H
                  
                   
                     ♑
                     H
                  
                   
                     Com.
                     ′
                     pts
                     .
                     ″
                  
                
                 
                   
                     0.0
                  
                   
                     6
                  
                   
                     18
                  
                   
                     0.0
                  
                
                 
                   
                     10
                  
                   
                     6
                  
                   
                     18
                  
                   
                     00.44
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     ″
                  
                
                 
                   
                     20
                  
                   
                     6
                  
                   
                     18
                  
                   
                     1.27
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     44
                  
                
                 
                   
                     30
                  
                   
                     6
                  
                   
                     18
                  
                   
                     2
                     01
                  
                
                 
                   
                     40
                  
                   
                     6
                  
                   
                     18
                  
                   
                     2.44
                  
                
                 
                   
                     50
                  
                   
                     6
                  
                   
                     18
                  
                   
                     3.28
                  
                
                 
                   
                     1.0
                  
                   
                     6
                  
                   
                     18
                  
                   
                     4.22
                  
                
                 
                   
                     10
                  
                   
                     6
                  
                   
                     18
                  
                   
                     5.06
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     ″
                  
                
                 
                   
                     20
                  
                   
                     6
                  
                   
                     18
                  
                   
                     5.50
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     44
                  
                
                 
                   
                     30
                  
                   
                     6
                  
                   
                     18
                  
                   
                     6.34
                  
                
                 
                   
                     40
                  
                   
                     6
                  
                   
                     18
                  
                   
                     7
                     18
                  
                
                 
                   
                     50
                  
                   
                     6
                  
                   
                     18
                  
                   
                     8.02
                  
                
                 
                   
                     2.0
                  
                   
                     6
                  
                   
                     18
                  
                   
                     8.43
                  
                
                 
                   
                     10
                  
                   
                     6
                  
                   
                     18
                  
                   
                     9.26
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     ″
                  
                
                 
                   
                     20
                  
                   
                     6
                  
                   
                     18
                  
                   
                     10.10
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     44
                  
                
                 
                   
                     30
                  
                   
                     6
                  
                   
                     18
                  
                   
                     10.54
                  
                
                 
                   
                     40
                  
                   
                     6
                  
                   
                     18
                  
                   
                     11.37
                  
                
                 
                   
                     50
                  
                   
                     6
                  
                   
                     18
                  
                   
                     12.20
                  
                
                 
                   
                     3.0
                  
                   
                     6
                  
                   
                     18
                  
                   
                     13.5
                  
                
                 
                   
                     10
                  
                   
                     6
                  
                   
                     18
                  
                   
                     13.49
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     ″
                  
                
                 
                   
                     20
                  
                   
                     6
                  
                   
                     18
                  
                   
                     14.32
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     44
                  
                
                 
                   
                     30
                  
                   
                     6
                  
                   
                     18
                  
                   
                     15.16
                  
                
                 
                   
                     40
                  
                   
                     6
                  
                   
                     18
                  
                   
                     15.59
                  
                
                 
                   
                     50
                  
                   
                     6
                  
                   
                     18
                  
                   
                     16.43
                  
                
                 
                   
                     4.0
                  
                   
                     6
                  
                   
                     18
                  
                   
                     17.27
                  
                
                 
                   
                     10
                  
                   
                     6
                  
                   
                     18
                  
                   
                     18.11
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     ″
                  
                
                 
                   
                     20
                  
                   
                     6
                  
                   
                     18
                  
                   
                     18.54
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     44
                  
                
                 
                   
                     30
                  
                   
                     6
                  
                   
                     18
                  
                   
                     19
                     38
                  
                
                 
                   
                     40
                  
                   
                     6
                  
                   
                     18
                  
                   
                     20.22
                  
                
                 
                   
                     50
                  
                   
                     6
                  
                   
                     18
                  
                   
                     21.05
                  
                
                 
                   
                     5.0
                  
                   
                     6
                  
                   
                     18
                  
                   
                     21.48
                  
                
                 
                   
                     10
                  
                   
                     6
                  
                   
                     18
                  
                   
                     22.31
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     ″
                  
                
                 
                   
                     20
                  
                   
                     6
                  
                   
                     18
                  
                   
                     23.15
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     44
                  
                
                 
                   
                     30
                  
                   
                     6
                  
                   
                     18
                  
                   
                     23.59
                  
                
                 
                   
                     40
                  
                   
                     6
                  
                   
                     18
                  
                   
                     24.
                     ●2
                  
                
                 
                   
                     50
                  
                   
                     6
                  
                   
                     18
                  
                   
                     25.25
                  
                
                 
                   
                     6.0
                  
                   
                     6
                  
                   
                     18
                  
                   
                     26.
                     ●9
                  
                
                 
                   
                     10
                  
                   
                     6
                  
                   
                     18
                  
                   
                     26.53
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     ″
                  
                
                 
                   
                     20
                  
                   
                     6
                  
                   
                     18
                  
                   
                     27.37
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     44
                  
                
                 
                   
                     30
                  
                   
                     6
                  
                   
                     11
                  
                   
                     28.20
                  
                
                 
                   
                     40
                  
                   
                     6
                  
                   
                     18
                  
                   
                     29.04
                  
                
                 
                   
                     50
                  
                   
                     6
                  
                   
                     18
                  
                   
                     29.47
                  
                
                 
                   
                     7.0
                  
                   
                     6
                  
                   
                     18
                  
                   
                     30.30
                  
                
                 
                   
                     10
                  
                   
                     6
                  
                   
                     18
                  
                   
                     31.14
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     ″
                  
                
                 
                   
                     20
                  
                   
                     6
                  
                   
                     18
                  
                   
                     31.57
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     44
                  
                
                 
                   
                     30
                  
                   
                     6
                  
                   
                     18
                  
                   
                     32.41
                  
                
                 
                   
                     40
                  
                   
                     6
                  
                   
                     18
                  
                   
                     33.24
                  
                
                 
                   
                     50
                  
                   
                     6
                  
                   
                     18
                  
                   
                     34.17
                  
                
                 
                   
                     8.0
                  
                   
                     6
                  
                   
                     18
                  
                   
                     34.51
                  
                
                 
                   
                     10
                  
                   
                     6
                  
                   
                     18
                  
                   
                     35.34
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     ″
                  
                
                 
                   
                     20
                  
                   
                     6
                  
                   
                     18
                  
                   
                     36.18
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     44
                  
                
                 
                   
                     30
                  
                   
                     6
                  
                   
                     18
                  
                   
                     37.01
                  
                
                 
                   
                     40
                  
                   
                     6
                  
                   
                     18
                  
                   
                     37.45
                  
                
                 
                   
                     50
                  
                   
                     6
                  
                   
                     18
                  
                   
                     38.28
                  
                
                 
                   
                     9.0
                  
                   
                     6
                  
                   
                     18
                  
                   
                     39.11
                  
                
                 
                   
                     10
                  
                   
                     6
                  
                   
                     18
                  
                   
                     39.54
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     ″
                  
                
                 
                   
                     20
                  
                   
                     6
                  
                   
                     18
                  
                   
                     40.48
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     44
                  
                
                 
                   
                     30
                  
                   
                     6
                  
                   
                     18
                  
                   
                     41.31
                  
                
                 
                   
                     40
                  
                   
                     6
                  
                   
                     18
                  
                   
                     42.15
                  
                
                 
                   
                     50
                  
                   
                     6
                  
                   
                     18
                  
                   
                     42.58
                  
                
                 
                 
                   
                     10.0
                  
                   
                     6
                  
                   
                     18
                  
                   
                     43.32
                  
                
                 
                   
                     10
                  
                   
                     6
                  
                   
                     18
                  
                   
                     44.15
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     ″
                  
                
                 
                   
                     20
                  
                   
                     6
                  
                   
                     18
                  
                   
                     44.59
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     43
                  
                
                 
                   
                     30
                  
                   
                     6
                  
                   
                     18
                  
                   
                     45.42
                  
                
                 
                   
                     40
                  
                   
                     6
                  
                   
                     18
                  
                   
                     46.25
                  
                
                 
                   
                     50
                  
                   
                     6
                  
                   
                     18
                  
                   
                     47.
                     ●9
                  
                
                 
                   
                     11.0
                  
                   
                     6
                  
                   
                     18
                  
                   
                     47
                     52
                  
                
                 
                   
                     10
                  
                   
                     6
                  
                   
                     18
                  
                   
                     48.35
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     ″
                  
                
                 
                   
                     20
                  
                   
                     6
                  
                   
                     18
                  
                   
                     49.18
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     43
                  
                
                 
                   
                     30
                  
                   
                     6
                  
                   
                     18
                  
                   
                     50.2
                  
                
                 
                   
                     40
                  
                   
                     6
                  
                   
                     18
                  
                   
                     50.45
                  
                
                 
                   
                     50
                  
                   
                     6
                  
                   
                     18
                  
                   
                     51.29
                  
                
                 
                   
                     12.0
                  
                   
                     6
                  
                   
                     18
                  
                   
                     52.12
                  
                
                 
                   
                     10
                  
                   
                     6
                  
                   
                     18
                  
                   
                     52.55
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     ″
                  
                
                 
                   
                     20
                  
                   
                     6
                  
                   
                     18
                  
                   
                     53.38
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     43
                  
                
                 
                   
                     30
                  
                   
                     6
                  
                   
                     18
                  
                   
                     54
                     22
                  
                
                 
                   
                     40
                  
                   
                     6
                  
                   
                     18
                  
                   
                     55.5
                  
                
                 
                   
                     50
                  
                   
                     6
                  
                   
                     18
                  
                   
                     55.48
                  
                
                 
                   
                     13.0
                  
                   
                     6
                  
                   
                     18
                  
                   
                     56.31
                  
                
                 
                   
                     10
                  
                   
                     6
                  
                   
                     18
                  
                   
                     57.14
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     ″
                  
                
                 
                   
                     20
                  
                   
                     6
                  
                   
                     18
                  
                   
                     57.57
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     43
                  
                
                 
                   
                     30
                  
                   
                     6
                  
                   
                     18
                  
                   
                     58.41
                  
                
                 
                   
                     40
                  
                   
                     6
                  
                   
                     18
                  
                   
                     59.24
                  
                
                 
                   
                     50
                  
                   
                     7
                  
                   
                     19
                  
                   
                     0.7
                  
                
                 
                   
                     14.0
                  
                   
                     7
                  
                   
                     19
                  
                   
                     0.50
                  
                
                 
                   
                     10
                  
                   
                     7
                  
                   
                     19
                  
                   
                     1.33
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     ″
                  
                
                 
                   
                     20
                  
                   
                     7
                  
                   
                     19
                  
                   
                     2.16
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     43
                  
                
                 
                   
                     30
                  
                   
                     7
                  
                   
                     19
                  
                   
                     3.
                     ●0
                  
                
                 
                   
                     40
                  
                   
                     7
                  
                   
                     19
                  
                   
                     3.43
                  
                
                 
                   
                     50
                  
                   
                     7
                  
                   
                     19
                  
                   
                     4
                     26
                  
                
                 
                   
                     15.0
                  
                   
                     7
                  
                   
                     19
                  
                   
                     5.
                     ●9
                  
                
                 
                   
                     10
                  
                   
                     7
                  
                   
                     19
                  
                   
                     5.52
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     ″
                  
                
                 
                   
                     20
                  
                   
                     7
                  
                   
                     19
                  
                   
                     6.35
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     43
                  
                
                 
                   
                     30
                  
                   
                     7
                  
                   
                     19
                  
                   
                     7.18
                  
                
                 
                   
                     40
                  
                   
                     7
                  
                   
                     19
                  
                   
                     8.
                     ●1
                  
                
                 
                   
                     50
                  
                   
                     7
                  
                   
                     19
                  
                   
                     8.44
                  
                
                 
                   
                     16.0
                  
                   
                     7
                  
                   
                     19
                  
                   
                     9.27
                  
                
                 
                   
                     10
                  
                   
                     7
                  
                   
                     19
                  
                   
                     10.10
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     ″
                  
                
                 
                   
                     20
                  
                   
                     7
                  
                   
                     19
                  
                   
                     10.53
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     43
                  
                
                 
                   
                     30
                  
                   
                     7
                  
                   
                     19
                  
                   
                     11.36
                  
                
                 
                   
                     40
                  
                   
                     7
                  
                   
                     19
                  
                   
                     12.19
                  
                
                 
                   
                     50
                  
                   
                     7
                  
                   
                     19
                  
                   
                     13.2
                  
                
                 
                   
                     17.0
                  
                   
                     7
                  
                   
                     19
                  
                   
                     13.45
                  
                
                 
                   
                     10
                  
                   
                     7
                  
                   
                     19
                  
                   
                     14.28
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     ″
                  
                
                 
                   
                     20
                  
                   
                     7
                  
                   
                     19
                  
                   
                     15.11
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     43
                  
                
                 
                   
                     30
                  
                   
                     7
                  
                   
                     19
                  
                   
                     15.54
                  
                
                 
                   
                     40
                  
                   
                     7
                  
                   
                     19
                  
                   
                     16.36
                  
                
                 
                   
                     50
                  
                   
                     7
                  
                   
                     19
                  
                   
                     17.19
                  
                
                 
                   
                     18.0
                  
                   
                     7
                  
                   
                     19
                  
                   
                     18.
                     ●2
                  
                
                 
                   
                     10
                  
                   
                     7
                  
                   
                     19
                  
                   
                     18.45
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     ″
                  
                
                 
                   
                     20
                  
                   
                     7
                  
                   
                     19
                  
                   
                     19.28
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     43
                  
                
                 
                   
                     30
                  
                   
                     7
                  
                   
                     19
                  
                   
                     20.11
                  
                
                 
                   
                     40
                  
                   
                     7
                  
                   
                     19
                  
                   
                     20
                     53
                  
                
                 
                   
                     50
                  
                   
                     7
                  
                   
                     19
                  
                   
                     21.36
                  
                
                 
                   
                     19.0
                  
                   
                     7
                  
                   
                     19
                  
                   
                     22.19
                  
                
                 
                   
                     10
                  
                   
                     7
                  
                   
                     19
                  
                   
                     23.2
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     ″
                  
                
                 
                   
                     20
                  
                   
                     7
                  
                   
                     19
                  
                   
                     23.45
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     43
                  
                
                 
                   
                     30
                  
                   
                     7
                  
                   
                     19
                  
                   
                     24.27
                  
                
                 
                   
                     40
                  
                   
                     7
                  
                   
                     19
                  
                   
                     25.10
                  
                
                 
                   
                     50
                  
                   
                     7
                  
                   
                     19
                  
                   
                     25.53
                  
                
                 
                 
                   
                     20.0
                  
                   
                     7
                  
                   
                     19
                  
                   
                     26.35
                  
                
                 
                   
                     10
                  
                   
                     7
                  
                   
                     19
                  
                   
                     27.18
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     ″
                  
                
                 
                   
                     20
                  
                   
                     7
                  
                   
                     19
                  
                   
                     28.0
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     43
                  
                
                 
                   
                     30
                  
                   
                     7
                  
                   
                     19
                  
                   
                     28.43
                  
                
                 
                   
                     40
                  
                   
                     7
                  
                   
                     19
                  
                   
                     29.25
                  
                
                 
                   
                     50
                  
                   
                     7
                  
                   
                     19
                  
                   
                     30.8
                  
                
                 
                   
                     21.0
                  
                   
                     7
                  
                   
                     19
                  
                   
                     30.51
                  
                
                 
                   
                     10
                  
                   
                     7
                  
                   
                     19
                  
                   
                     31.34
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     ″
                  
                
                 
                   
                     20
                  
                   
                     7
                  
                   
                     19
                  
                   
                     32.16
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     43
                  
                
                 
                   
                     30
                  
                   
                     7
                  
                   
                     19
                  
                   
                     32.59
                  
                
                 
                   
                     40
                  
                   
                     7
                  
                   
                     19
                  
                   
                     33.41
                  
                
                 
                   
                     50
                  
                   
                     7
                  
                   
                     19
                  
                   
                     34
                     24
                  
                
                 
                   
                     22.0
                  
                   
                     7
                  
                   
                     19
                  
                   
                     35.6
                  
                
                 
                   
                     10
                  
                   
                     7
                  
                   
                     19
                  
                   
                     35.49
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     ″
                  
                
                 
                   
                     20
                  
                   
                     7
                  
                   
                     19
                  
                   
                     36.31
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     43
                  
                
                 
                   
                     30
                  
                   
                     7
                  
                   
                     19
                  
                   
                     37.14
                  
                
                 
                   
                     40
                  
                   
                     7
                  
                   
                     19
                  
                   
                     37
                     56
                  
                
                 
                   
                     50
                  
                   
                     7
                  
                   
                     19
                  
                   
                     38
                     39
                  
                
                 
                   
                     23.0
                  
                   
                     7
                  
                   
                     19
                  
                   
                     39.21
                  
                
                 
                   
                     10
                  
                   
                     7
                  
                   
                     19
                  
                   
                     40.3
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     ″
                  
                
                 
                   
                     20
                  
                   
                     7
                  
                   
                     19
                  
                   
                     40.46
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     42
                  
                
                 
                   
                     30
                  
                   
                     7
                  
                   
                     19
                  
                   
                     41
                     28
                  
                
                 
                   
                     40
                  
                   
                     7
                  
                   
                     19
                  
                   
                     42.10
                  
                
                 
                   
                     50
                  
                   
                     7
                  
                   
                     19
                  
                   
                     42.52
                  
                
                 
                   
                     24.0
                  
                   
                     7
                  
                   
                     19
                  
                   
                     43.35
                  
                
                 
                   
                     10
                  
                   
                     7
                  
                   
                     19
                  
                   
                     44.17
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     ″
                  
                
                 
                   
                     20
                  
                   
                     7
                  
                   
                     19
                  
                   
                     45.0
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     42
                  
                
                 
                   
                     30
                  
                   
                     7
                  
                   
                     19
                  
                   
                     45.42
                  
                
                 
                   
                     40
                  
                   
                     7
                  
                   
                     19
                  
                   
                     46.24
                  
                
                 
                   
                     50
                  
                   
                     7
                  
                   
                     19
                  
                   
                     47.7
                  
                
                 
                   
                     25.0
                  
                   
                     7
                  
                   
                     19
                  
                   
                     47.49
                  
                
                 
                   
                     10
                  
                   
                     7
                  
                   
                     19
                  
                   
                     48.31
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     ″
                  
                
                 
                   
                     20
                  
                   
                     7
                  
                   
                     19
                  
                   
                     49.13
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     42
                  
                
                 
                   
                     30
                  
                   
                     7
                  
                   
                     19
                  
                   
                     49.56
                  
                
                 
                   
                     40
                  
                   
                     7
                  
                   
                     19
                  
                   
                     50
                     38
                  
                
                 
                   
                     50
                  
                   
                     7
                  
                   
                     19
                  
                   
                     51.20
                  
                
                 
                   
                     26.0
                  
                   
                     7
                  
                   
                     19
                  
                   
                     52.01
                  
                
                 
                   
                     10
                  
                   
                     7
                  
                   
                     19
                  
                   
                     52
                     43
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     ″
                  
                
                 
                   
                     20
                  
                   
                     7
                  
                   
                     19
                  
                   
                     53.25
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     42
                  
                
                 
                   
                     30
                  
                   
                     7
                  
                   
                     19
                  
                   
                     54.
                     ●7
                  
                
                 
                   
                     40
                  
                   
                     7
                  
                   
                     19
                  
                   
                     54.50
                  
                
                 
                   
                     50
                  
                   
                     7
                  
                   
                     19
                  
                   
                     55.32
                  
                
                 
                   
                     27.0
                  
                   
                     7
                  
                   
                     19
                  
                   
                     56.13
                  
                
                 
                   
                     10
                  
                   
                     7
                  
                   
                     19
                  
                   
                     56.55
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     ″
                  
                
                 
                   
                     20
                  
                   
                     7
                  
                   
                     19
                  
                   
                     57.37
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     42
                  
                
                 
                   
                     30
                  
                   
                     7
                  
                   
                     19
                  
                   
                     58.20
                  
                
                 
                   
                     40
                  
                   
                     7
                  
                   
                     19
                  
                   
                     59.2
                  
                
                 
                   
                     50
                  
                   
                     7
                  
                   
                     19
                  
                   
                     59
                     43
                  
                
                 
                   
                     28.0
                  
                   
                     8
                  
                   
                     20
                  
                   
                     0.25
                  
                
                 
                   
                     10
                  
                   
                     8
                  
                   
                     20
                  
                   
                     1.7
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     ″
                  
                
                 
                   
                     20
                  
                   
                     8
                  
                   
                     20
                  
                   
                     1.49
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     42
                  
                
                 
                   
                     30
                  
                   
                     8
                  
                   
                     20
                  
                   
                     2.30
                  
                
                 
                   
                     40
                  
                   
                     8
                  
                   
                     20
                  
                   
                     3.12
                  
                
                 
                   
                     50
                  
                   
                     8
                  
                   
                     20
                  
                   
                     3.54
                  
                
                 
                   
                     29.0
                  
                   
                     8
                  
                   
                     20
                  
                   
                     4.36
                  
                
                 
                   
                     10
                  
                   
                     8
                  
                   
                     20
                  
                   
                     5.18
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     ″
                  
                
                 
                   
                     20
                  
                   
                     8
                  
                   
                     20
                  
                   
                     6.0
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     42
                  
                
                 
                   
                     30
                  
                   
                     8
                  
                   
                     20
                  
                   
                     6.41
                  
                
                 
                   
                     40
                  
                   
                     8
                  
                   
                     20
                  
                   
                     7.23
                  
                
                 
                   
                     50
                  
                   
                     8
                  
                   
                     20
                  
                   
                     8.4
                  
                
              
               
               
                 
                   
                     D.m.
                     
                  
                   
                     ♌
                     H
                  
                   
                     ♒
                     H
                  
                   
                     Com.
                     ′
                     Pts.
                     ″
                  
                
                 
                   
                     0.0
                  
                   
                     8
                  
                   
                     30
                  
                   
                     8.46
                  
                
                 
                   
                     10
                  
                   
                     8
                  
                   
                     20
                  
                   
                     9.28
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     ″
                  
                
                 
                   
                     20
                  
                   
                     8
                  
                   
                     20
                  
                   
                     10.10
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     42
                  
                
                 
                   
                     30
                  
                   
                     8
                  
                   
                     20
                  
                   
                     10.52
                  
                
                 
                   
                     40
                  
                   
                     8
                  
                   
                     20
                  
                   
                     11.34
                  
                
                 
                   
                     50
                  
                   
                     8
                  
                   
                     20
                  
                   
                     12.16
                  
                
                 
                   
                     1.0
                  
                   
                     8
                  
                   
                     20
                  
                   
                     12.55
                  
                
                 
                   
                     10
                  
                   
                     8
                  
                   
                     20
                  
                   
                     13.36
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     ″
                  
                
                 
                   
                     20
                  
                   
                     8
                  
                   
                     20
                  
                   
                     14.17
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     41
                  
                
                 
                   
                     30
                  
                   
                     8
                  
                   
                     20
                  
                   
                     14.58
                  
                
                 
                   
                     40
                  
                   
                     8
                  
                   
                     20
                  
                   
                     15.39
                  
                
                 
                   
                     50
                  
                   
                     8
                  
                   
                     20
                  
                   
                     16.20
                  
                
                 
                   
                     2.0
                  
                   
                     8
                  
                   
                     20
                  
                   
                     17.4
                  
                
                 
                   
                     10
                  
                   
                     8
                  
                   
                     20
                  
                   
                     17.45
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     ″
                  
                
                 
                   
                     20
                  
                   
                     8
                  
                   
                     20
                  
                   
                     18.26
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     41
                  
                
                 
                   
                     30
                  
                   
                     8
                  
                   
                     20
                  
                   
                     19.07
                  
                
                 
                   
                     40
                  
                   
                     8
                  
                   
                     20
                  
                   
                     19.48
                  
                
                 
                   
                     50
                  
                   
                     8
                  
                   
                     20
                  
                   
                     20.29
                  
                
                 
                   
                     3.0
                  
                   
                     8
                  
                   
                     20
                  
                   
                     21.12
                  
                
                 
                   
                     10
                  
                   
                     8
                  
                   
                     20
                  
                   
                     21.53
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     ″
                  
                
                 
                   
                     20
                  
                   
                     8
                  
                   
                     20
                  
                   
                     22.34
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     41
                  
                
                 
                   
                     30
                  
                   
                     8
                  
                   
                     20
                  
                   
                     23.15
                  
                
                 
                   
                     40
                  
                   
                     8
                  
                   
                     20
                  
                   
                     23.56
                  
                
                 
                   
                     50
                  
                   
                     8
                  
                   
                     20
                  
                   
                     24.37
                  
                
                 
                   
                     4.0
                  
                   
                     8
                  
                   
                     20
                  
                   
                     25.20
                  
                
                 
                   
                     10
                  
                   
                     8
                  
                   
                     20
                  
                   
                     16.01
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     ″
                  
                
                 
                   
                     20
                  
                   
                     8
                  
                   
                     20
                  
                   
                     26.42
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     41
                  
                
                 
                   
                     30
                  
                   
                     8
                  
                   
                     20
                  
                   
                     27.23
                  
                
                 
                   
                     40
                  
                   
                     8
                  
                   
                     20
                  
                   
                     28.04
                  
                
                 
                   
                     50
                  
                   
                     8
                  
                   
                     20
                  
                   
                     28.45
                  
                
                 
                   
                     5.0
                  
                   
                     8
                  
                   
                     20
                  
                   
                     29.27
                  
                
                 
                   
                     10
                  
                   
                     8
                  
                   
                     20
                  
                   
                     30
                     08
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     ″
                  
                
                 
                   
                     20
                  
                   
                     8
                  
                   
                     20
                  
                   
                     30.49
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     41
                  
                
                 
                   
                     30
                  
                   
                     8
                  
                   
                     20
                  
                   
                     31.30
                  
                
                 
                   
                     40
                  
                   
                     8
                  
                   
                     20
                  
                   
                     32.11
                  
                
                 
                   
                     50
                  
                   
                     8
                  
                   
                     20
                  
                   
                     32.52
                  
                
                 
                   
                     6.0
                  
                   
                     8
                  
                   
                     20
                  
                   
                     33.33
                  
                
                 
                   
                     10
                  
                   
                     8
                  
                   
                     20
                  
                   
                     34.14
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     ″
                  
                
                 
                   
                     20
                  
                   
                     8
                  
                   
                     20
                  
                   
                     34.55
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     41
                  
                
                 
                   
                     30
                  
                   
                     8
                  
                   
                     20
                  
                   
                     35.36
                  
                
                 
                   
                     40
                  
                   
                     8
                  
                   
                     20
                  
                   
                     36.17
                  
                
                 
                   
                     50
                  
                   
                     8
                  
                   
                     20
                  
                   
                     36.58
                  
                
                 
                   
                     7.0
                  
                   
                     8
                  
                   
                     20
                  
                   
                     37.38
                  
                
                 
                   
                     10
                  
                   
                     8
                  
                   
                     20
                  
                   
                     38.19
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     ″
                  
                
                 
                   
                     20
                  
                   
                     8
                  
                   
                     20
                  
                   
                     39.00
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     41
                  
                
                 
                   
                     30
                  
                   
                     8
                  
                   
                     20
                  
                   
                     39.41
                  
                
                 
                   
                     40
                  
                   
                     8
                  
                   
                     20
                  
                   
                     40.22
                  
                
                 
                   
                     50
                  
                   
                     8
                  
                   
                     20
                  
                   
                     41.03
                  
                
                 
                   
                     8.0
                  
                   
                     8
                  
                   
                     20
                  
                   
                     41.42
                  
                
                 
                   
                     10
                  
                   
                     8
                  
                   
                     20
                  
                   
                     42.23
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     ″
                  
                
                 
                   
                     20
                  
                   
                     8
                  
                   
                     20
                  
                   
                     43.04
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     41
                  
                
                 
                   
                     30
                  
                   
                     8
                  
                   
                     20
                  
                   
                     43.45
                  
                
                 
                   
                     40
                  
                   
                     8
                  
                   
                     20
                  
                   
                     44.26
                  
                
                 
                   
                     50
                  
                   
                     8
                  
                   
                     20
                  
                   
                     45.07
                  
                
                 
                   
                     9.0
                  
                   
                     8
                  
                   
                     20
                  
                   
                     45.46
                  
                
                 
                   
                     10
                  
                   
                     8
                  
                   
                     20
                  
                   
                     46.26
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     ″
                  
                
                 
                   
                     20
                  
                   
                     8
                  
                   
                     20
                  
                   
                     47.06
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     40
                  
                
                 
                   
                     30
                  
                   
                     8
                  
                   
                     20
                  
                   
                     47.46
                  
                
                 
                   
                     40
                  
                   
                     8
                  
                   
                     20
                  
                   
                     48.26
                  
                
                 
                   
                     50
                  
                   
                     8
                  
                   
                     20
                  
                   
                     49.06
                  
                
              
               
               
                 
                   
                     D.
                     m.
                     
                  
                   
                     ♌
                     H
                  
                   
                     ♒
                     H
                  
                   
                     Com.
                     ′
                     Pts.
                     ″
                  
                
                 
                   
                     10.0
                  
                   
                     8
                  
                   
                     30
                  
                   
                     49.50
                  
                
                 
                   
                     10
                  
                   
                     8
                  
                   
                     20
                  
                   
                     50.30
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     ″
                  
                
                 
                   
                     20
                  
                   
                     8
                  
                   
                     20
                  
                   
                     51.10
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     40
                  
                
                 
                   
                     30
                  
                   
                     8
                  
                   
                     20
                  
                   
                     51.50
                  
                
                 
                   
                     40
                  
                   
                     8
                  
                   
                     20
                  
                   
                     52.30
                  
                
                 
                   
                     50
                  
                   
                     8
                  
                   
                     20
                  
                   
                     53.10
                  
                
                 
                   
                     11.0
                  
                   
                     8
                  
                   
                     20
                  
                   
                     53.53
                  
                
                 
                   
                     10
                  
                   
                     8
                  
                   
                     20
                  
                   
                     54.33
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     ″
                  
                
                 
                   
                     20
                  
                   
                     8
                  
                   
                     20
                  
                   
                     55.13
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     40
                  
                
                 
                   
                     30
                  
                   
                     8
                  
                   
                     20
                  
                   
                     55.53
                  
                
                 
                   
                     40
                  
                   
                     8
                  
                   
                     20
                  
                   
                     56
                     33
                  
                
                 
                   
                     50
                  
                   
                     8
                  
                   
                     20
                  
                   
                     57.13
                  
                
                 
                   
                     12.0
                  
                   
                     8
                  
                   
                     20
                  
                   
                     57.55
                  
                
                 
                   
                     10
                  
                   
                     8
                  
                   
                     20
                  
                   
                     58.35
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     ″
                  
                
                 
                   
                     20
                  
                   
                     8
                  
                   
                     20
                  
                   
                     59.15
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     40
                  
                
                 
                   
                     30
                  
                   
                     8
                  
                   
                     20
                  
                   
                     59.55
                  
                
                 
                   
                     40
                  
                   
                     9
                  
                   
                     21
                  
                   
                     00.35
                  
                
                 
                   
                     50
                  
                   
                     9
                  
                   
                     21
                  
                   
                     1.15
                  
                
                 
                   
                     13.0
                  
                   
                     9
                  
                   
                     21
                  
                   
                     1.55
                  
                
                 
                   
                     10
                  
                   
                     9
                  
                   
                     21
                  
                   
                     2.35
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     ″
                  
                
                 
                   
                     20
                  
                   
                     9
                  
                   
                     21
                  
                   
                     3.15
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     40
                  
                
                 
                   
                     30
                  
                   
                     9
                  
                   
                     21
                  
                   
                     3.55
                  
                
                 
                   
                     40
                  
                   
                     9
                  
                   
                     21
                  
                   
                     4.35
                  
                
                 
                   
                     50
                  
                   
                     9
                  
                   
                     21
                  
                   
                     5.15
                  
                
                 
                   
                     14.0
                  
                   
                     9
                  
                   
                     21
                  
                   
                     5.35
                  
                
                 
                   
                     10
                  
                   
                     9
                  
                   
                     21
                  
                   
                     6.35
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     ″
                  
                
                 
                   
                     20
                  
                   
                     9
                  
                   
                     21
                  
                   
                     7.15
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     40
                  
                
                 
                   
                     30
                  
                   
                     9
                  
                   
                     21
                  
                   
                     7.55
                  
                
                 
                   
                     40
                  
                   
                     9
                  
                   
                     21
                  
                   
                     8.35
                  
                
                 
                   
                     50
                  
                   
                     9
                  
                   
                     21
                  
                   
                     9.15
                  
                
                 
                   
                     15.0
                  
                   
                     9
                  
                   
                     21
                  
                   
                     9.55
                  
                
                 
                   
                     10
                  
                   
                     9
                  
                   
                     21
                  
                   
                     10.35
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     ″
                  
                
                 
                   
                     20
                  
                   
                     9
                  
                   
                     21
                  
                   
                     11.15
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     40
                  
                
                 
                   
                     30
                  
                   
                     9
                  
                   
                     21
                  
                   
                     11.55
                  
                
                 
                   
                     40
                  
                   
                     9
                  
                   
                     21
                  
                   
                     12.35
                  
                
                 
                   
                     50
                  
                   
                     9
                  
                   
                     21
                  
                   
                     13.15
                  
                
                 
                   
                     16.0
                  
                   
                     9
                  
                   
                     21
                  
                   
                     13.53
                  
                
                 
                   
                     10
                  
                   
                     9
                  
                   
                     21
                  
                   
                     14.33
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     ″
                  
                
                 
                   
                     20
                  
                   
                     9
                  
                   
                     21
                  
                   
                     15.13
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     40
                  
                
                 
                   
                     30
                  
                   
                     9
                  
                   
                     21
                  
                   
                     15.53
                  
                
                 
                   
                     40
                  
                   
                     9
                  
                   
                     21
                  
                   
                     16.33
                  
                
                 
                   
                     50
                  
                   
                     9
                  
                   
                     21
                  
                   
                     17.13
                  
                
                 
                   
                     17.0
                  
                   
                     9
                  
                   
                     21
                  
                   
                     17.51
                  
                
                 
                   
                     10
                  
                   
                     9
                  
                   
                     21
                  
                   
                     18.31
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     ″
                  
                
                 
                   
                     20
                  
                   
                     9
                  
                   
                     21
                  
                   
                     19.11
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     40
                  
                
                 
                   
                     30
                  
                   
                     9
                  
                   
                     21
                  
                   
                     19.51
                  
                
                 
                   
                     40
                  
                   
                     9
                  
                   
                     21
                  
                   
                     20.31
                  
                
                 
                   
                     50
                  
                   
                     9
                  
                   
                     21
                  
                   
                     21.11
                  
                
                 
                   
                     18.0
                  
                   
                     9
                  
                   
                     21
                  
                   
                     21.48
                  
                
                 
                   
                     10
                  
                   
                     9
                  
                   
                     21
                  
                   
                     22.27
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     ″
                  
                
                 
                   
                     20
                  
                   
                     9
                  
                   
                     21
                  
                   
                     23.06
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     39
                  
                
                 
                   
                     30
                  
                   
                     9
                  
                   
                     21
                  
                   
                     23
                     45
                  
                
                 
                   
                     40
                  
                   
                     9
                  
                   
                     21
                  
                   
                     24.24
                  
                
                 
                   
                     50
                  
                   
                     9
                  
                   
                     21
                  
                   
                     25
                     03
                  
                
                 
                   
                     19.0
                  
                   
                     9
                  
                   
                     21
                  
                   
                     25.45
                  
                
                 
                   
                     10
                  
                   
                     9
                  
                   
                     21
                  
                   
                     26.24
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     ″
                  
                
                 
                   
                     20
                  
                   
                     9
                  
                   
                     21
                  
                   
                     27.03
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     39
                  
                
                 
                   
                     30
                  
                   
                     9
                  
                   
                     21
                  
                   
                     27.42
                  
                
                 
                   
                     40
                  
                   
                     9
                  
                   
                     21
                  
                   
                     28.21
                  
                
                 
                   
                     50
                  
                   
                     9
                  
                   
                     21
                  
                   
                     29.00
                  
                
                 
                 
                   
                     20.0
                  
                   
                     9
                  
                   
                     21
                  
                   
                     29.41
                  
                
                 
                   
                     10
                  
                   
                     9
                  
                   
                     21
                  
                   
                     30.20
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     ″
                  
                
                 
                   
                     20
                  
                   
                     9
                  
                   
                     21
                  
                   
                     30.59
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     39
                  
                
                 
                   
                     30
                  
                   
                     9
                  
                   
                     21
                  
                   
                     31.38
                  
                
                 
                   
                     40
                  
                   
                     9
                  
                   
                     21
                  
                   
                     32.17
                  
                
                 
                   
                     50
                  
                   
                     9
                  
                   
                     21
                  
                   
                     32.56
                  
                
                 
                   
                     21.0
                  
                   
                     9
                  
                   
                     21
                  
                   
                     33.36
                  
                
                 
                   
                     10
                  
                   
                     9
                  
                   
                     21
                  
                   
                     34.15
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     ″
                  
                
                 
                   
                     20
                  
                   
                     9
                  
                   
                     21
                  
                   
                     34.54
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     39
                  
                
                 
                   
                     30
                  
                   
                     9
                  
                   
                     21
                  
                   
                     35.33
                  
                
                 
                   
                     40
                  
                   
                     9
                  
                   
                     21
                  
                   
                     36.12
                  
                
                 
                   
                     50
                  
                   
                     9
                  
                   
                     21
                  
                   
                     36.51
                  
                
                 
                   
                     22.0
                  
                   
                     9
                  
                   
                     21
                  
                   
                     37.30
                  
                
                 
                   
                     10
                  
                   
                     9
                  
                   
                     21
                  
                   
                     38.9
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     ″
                  
                
                 
                   
                     20
                  
                   
                     9
                  
                   
                     21
                  
                   
                     38.48
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     39
                  
                
                 
                   
                     30
                  
                   
                     9
                  
                   
                     21
                  
                   
                     39.27
                  
                
                 
                   
                     40
                  
                   
                     9
                  
                   
                     21
                  
                   
                     40.06
                  
                
                 
                   
                     50
                  
                   
                     9
                  
                   
                     21
                  
                   
                     40.45
                  
                
                 
                   
                     23.0
                  
                   
                     9
                  
                   
                     21
                  
                   
                     41.24
                  
                
                 
                   
                     10
                  
                   
                     9
                  
                   
                     21
                  
                   
                     42.03
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     ″
                  
                
                 
                   
                     20
                  
                   
                     9
                  
                   
                     21
                  
                   
                     42.42
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     39
                  
                
                 
                   
                     30
                  
                   
                     9
                  
                   
                     21
                  
                   
                     43.21
                  
                
                 
                   
                     40
                  
                   
                     9
                  
                   
                     21
                  
                   
                     44.00
                  
                
                 
                   
                     50
                  
                   
                     9
                  
                   
                     21
                  
                   
                     44.39
                  
                
                 
                   
                     24.0
                  
                   
                     9
                  
                   
                     21
                  
                   
                     45.17
                  
                
                 
                   
                     10
                  
                   
                     9
                  
                   
                     21
                  
                   
                     45.56
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     ″
                  
                
                 
                   
                     20
                  
                   
                     9
                  
                   
                     21
                  
                   
                     46.35
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     39
                  
                
                 
                   
                     30
                  
                   
                     9
                  
                   
                     21
                  
                   
                     47.14
                  
                
                 
                   
                     40
                  
                   
                     9
                  
                   
                     21
                  
                   
                     47.53
                  
                
                 
                   
                     50
                  
                   
                     9
                  
                   
                     21
                  
                   
                     48.32
                  
                
                 
                   
                     25.0
                  
                   
                     9
                  
                   
                     21
                  
                   
                     49.11
                  
                
                 
                   
                     10
                  
                   
                     9
                  
                   
                     21
                  
                   
                     49
                     50
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     ″
                  
                
                 
                   
                     20
                  
                   
                     9
                  
                   
                     21
                  
                   
                     50.29
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     39
                  
                
                 
                   
                     30
                  
                   
                     9
                  
                   
                     21
                  
                   
                     51.08
                  
                
                 
                   
                     40
                  
                   
                     9
                  
                   
                     21
                  
                   
                     51.47
                  
                
                 
                   
                     50
                  
                   
                     9
                  
                   
                     21
                  
                   
                     52.26
                  
                
                 
                   
                     26.0
                  
                   
                     9
                  
                   
                     21
                  
                   
                     53.2
                  
                
                 
                   
                     10
                  
                   
                     9
                  
                   
                     21
                  
                   
                     53.41
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     ″
                  
                
                 
                   
                     20
                  
                   
                     9
                  
                   
                     21
                  
                   
                     54.9
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     39
                  
                
                 
                   
                     30
                  
                   
                     9
                  
                   
                     21
                  
                   
                     54
                     58
                  
                
                 
                   
                     40
                  
                   
                     9
                  
                   
                     21
                  
                   
                     55.36
                  
                
                 
                   
                     50
                  
                   
                     9
                  
                   
                     21
                  
                   
                     56.14
                  
                
                 
                   
                     27.0
                  
                   
                     9
                  
                   
                     21
                  
                   
                     56
                     53
                  
                
                 
                   
                     10
                  
                   
                     9
                  
                   
                     21
                  
                   
                     57.32
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     ″
                  
                
                 
                   
                     20
                  
                   
                     9
                  
                   
                     21
                  
                   
                     58.10
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     39
                  
                
                 
                   
                     30
                  
                   
                     9
                  
                   
                     21
                  
                   
                     58.49
                  
                
                 
                   
                     40
                  
                   
                     9
                  
                   
                     21
                  
                   
                     59.27
                  
                
                 
                   
                     50
                  
                   
                     10
                  
                   
                     22
                  
                   
                     00.06
                  
                
                 
                   
                     28.0
                  
                   
                     10
                  
                   
                     22
                  
                   
                     0.44
                  
                
                 
                   
                     10
                  
                   
                     10
                  
                   
                     22
                  
                   
                     1.22
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     ″
                  
                
                 
                   
                     20
                  
                   
                     10
                  
                   
                     22
                  
                   
                     2.00
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     38
                  
                
                 
                   
                     30
                  
                   
                     10
                  
                   
                     22
                  
                   
                     2.39
                  
                
                 
                   
                     40
                  
                   
                     10
                  
                   
                     22
                  
                   
                     3.17
                  
                
                 
                   
                     50
                  
                   
                     10
                  
                   
                     22
                  
                   
                     3.55
                  
                
                 
                   
                     29.0
                  
                   
                     10
                  
                   
                     22
                  
                   
                     4.34
                  
                
                 
                   
                     10
                  
                   
                     10
                  
                   
                     22
                  
                   
                     5.12
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     ″
                  
                
                 
                   
                     20
                  
                   
                     10
                  
                   
                     22
                  
                   
                     5.50
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     38
                  
                
                 
                   
                     30
                  
                   
                     10
                  
                   
                     22
                  
                   
                     6.29
                  
                
                 
                   
                     40
                  
                   
                     10
                  
                   
                     22
                  
                   
                     7.08
                  
                
                 
                   
                     50
                  
                   
                     10
                  
                   
                     22
                  
                   
                     7.46
                  
                
              
               
               
                 
                   
                     D.
                     m.
                     
                  
                   
                     ♍
                     H
                  
                   
                     ♓
                     H
                  
                   
                     Com.
                     ′
                     Pts.
                     ″
                  
                
                 
                   
                     0.0
                  
                   
                     10
                  
                   
                     22
                  
                   
                     8.24
                  
                
                 
                   
                     10
                  
                   
                     10
                  
                   
                     22
                  
                   
                     9.02
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     ″
                  
                
                 
                   
                     20
                  
                   
                     10
                  
                   
                     22
                  
                   
                     9.40
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     38
                  
                
                 
                   
                     30
                  
                   
                     10
                  
                   
                     22
                  
                   
                     10.19
                  
                
                 
                   
                     40
                  
                   
                     10
                  
                   
                     22
                  
                   
                     10.57
                  
                
                 
                   
                     50
                  
                   
                     10
                  
                   
                     22
                  
                   
                     11.35
                  
                
                 
                   
                     1.0
                  
                   
                     10
                  
                   
                     22
                  
                   
                     12.13
                  
                
                 
                   
                     10
                  
                   
                     10
                  
                   
                     22
                  
                   
                     12.51
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     ″
                  
                
                 
                   
                     20
                  
                   
                     10
                  
                   
                     22
                  
                   
                     13.29
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     38
                  
                
                 
                   
                     30
                  
                   
                     10
                  
                   
                     22
                  
                   
                     14.07
                  
                
                 
                   
                     40
                  
                   
                     10
                  
                   
                     22
                  
                   
                     14.45
                  
                
                 
                   
                     50
                  
                   
                     10
                  
                   
                     22
                  
                   
                     15.23
                  
                
                 
                   
                     2.0
                  
                   
                     10
                  
                   
                     22
                  
                   
                     16.1
                  
                
                 
                   
                     10
                  
                   
                     10
                  
                   
                     22
                  
                   
                     16.39
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     ″
                  
                
                 
                   
                     20
                  
                   
                     10
                  
                   
                     22
                  
                   
                     17.17
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     38
                  
                
                 
                   
                     30
                  
                   
                     10
                  
                   
                     22
                  
                   
                     17.55
                  
                
                 
                   
                     40
                  
                   
                     10
                  
                   
                     22
                  
                   
                     18.33
                  
                
                 
                   
                     50
                  
                   
                     10
                  
                   
                     22
                  
                   
                     19.11
                  
                
                 
                   
                     3.0
                  
                   
                     10
                  
                   
                     22
                  
                   
                     19.49
                  
                
                 
                   
                     10
                  
                   
                     10
                  
                   
                     22
                  
                   
                     20.27
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     ″
                  
                
                 
                   
                     20
                  
                   
                     10
                  
                   
                     22
                  
                   
                     21.05
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     38
                  
                
                 
                   
                     30
                  
                   
                     10
                  
                   
                     22
                  
                   
                     21.43
                  
                
                 
                   
                     40
                  
                   
                     10
                  
                   
                     22
                  
                   
                     22.21
                  
                
                 
                   
                     50
                  
                   
                     10
                  
                   
                     22
                  
                   
                     22.59
                  
                
                 
                   
                     4.0
                  
                   
                     10
                  
                   
                     22
                  
                   
                     23.36
                  
                
                 
                   
                     10
                  
                   
                     10
                  
                   
                     22
                  
                   
                     24.14
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     ″
                  
                
                 
                   
                     20
                  
                   
                     10
                  
                   
                     22
                  
                   
                     24.52
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     38
                  
                
                 
                   
                     30
                  
                   
                     10
                  
                   
                     22
                  
                   
                     25.30
                  
                
                 
                   
                     40
                  
                   
                     10
                  
                   
                     22
                  
                   
                     26.08
                  
                
                 
                   
                     50
                  
                   
                     10
                  
                   
                     22
                  
                   
                     26.46
                  
                
                 
                   
                     5.0
                  
                   
                     10
                  
                   
                     22
                  
                   
                     27.23
                  
                
                 
                   
                     10
                  
                   
                     10
                  
                   
                     22
                  
                   
                     28.01
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     ″
                  
                
                 
                   
                     20
                  
                   
                     10
                  
                   
                     22
                  
                   
                     28.39
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     38
                  
                
                 
                   
                     30
                  
                   
                     10
                  
                   
                     22
                  
                   
                     29.16
                  
                
                 
                   
                     40
                  
                   
                     10
                  
                   
                     22
                  
                   
                     29.54
                  
                
                 
                   
                     50
                  
                   
                     10
                  
                   
                     22
                  
                   
                     30.32
                  
                
                 
                   
                     6.0
                  
                   
                     10
                  
                   
                     22
                  
                   
                     31.9
                  
                
                 
                   
                     10
                  
                   
                     10
                  
                   
                     22
                  
                   
                     31.46
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     ″
                  
                
                 
                   
                     20
                  
                   
                     10
                  
                   
                     22
                  
                   
                     32.24
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     38
                  
                
                 
                   
                     30
                  
                   
                     10
                  
                   
                     22
                  
                   
                     33.01
                  
                
                 
                   
                     40
                  
                   
                     10
                  
                   
                     22
                  
                   
                     33.39
                  
                
                 
                   
                     50
                  
                   
                     10
                  
                   
                     22
                  
                   
                     34.17
                  
                
                 
                   
                     7.0
                  
                   
                     10
                  
                   
                     22
                  
                   
                     34.55
                  
                
                 
                   
                     10
                  
                   
                     10
                  
                   
                     22
                  
                   
                     35.33
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     ″
                  
                
                 
                   
                     20
                  
                   
                     10
                  
                   
                     22
                  
                   
                     36.10
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     38
                  
                
                 
                   
                     30
                  
                   
                     10
                  
                   
                     22
                  
                   
                     36.48
                  
                
                 
                   
                     40
                  
                   
                     10
                  
                   
                     22
                  
                   
                     37.25
                  
                
                 
                   
                     50
                  
                   
                     10
                  
                   
                     22
                  
                   
                     38.03
                  
                
                 
                   
                     8.0
                  
                   
                     10
                  
                   
                     22
                  
                   
                     38
                     40
                  
                
                 
                   
                     10
                  
                   
                     10
                  
                   
                     22
                  
                   
                     39.
                     ●8
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     ″
                  
                
                 
                   
                     20
                  
                   
                     10
                  
                   
                     22
                  
                   
                     39.56
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     38
                  
                
                 
                   
                     30
                  
                   
                     10
                  
                   
                     22
                  
                   
                     40
                     33
                  
                
                 
                   
                     40
                  
                   
                     10
                  
                   
                     22
                  
                   
                     41.10
                  
                
                 
                   
                     50
                  
                   
                     10
                  
                   
                     22
                  
                   
                     41.48
                  
                
                 
                   
                     9.0
                  
                   
                     10
                  
                   
                     22
                  
                   
                     42
                     25
                  
                
                 
                   
                     10
                  
                   
                     10
                  
                   
                     22
                  
                   
                     43.02
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     ″
                  
                
                 
                   
                     20
                  
                   
                     10
                  
                   
                     22
                  
                   
                     43.40
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     38
                  
                
                 
                   
                     30
                  
                   
                     10
                  
                   
                     22
                  
                   
                     44.17
                  
                
                 
                   
                     40
                  
                   
                     10
                  
                   
                     22
                  
                   
                     44.54
                  
                
                 
                   
                     50
                  
                   
                     10
                  
                   
                     22
                  
                   
                     45.32
                  
                
                 
                 
                   
                     10.0
                  
                   
                     10
                  
                   
                     22
                  
                   
                     46.10
                  
                
                 
                   
                     10
                  
                   
                     10
                  
                   
                     22
                  
                   
                     46.47
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     ″
                  
                
                 
                   
                     20
                  
                   
                     10
                  
                   
                     22
                  
                   
                     47.25
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     37
                  
                
                 
                   
                     30
                  
                   
                     10
                  
                   
                     22
                  
                   
                     48.03
                  
                
                 
                   
                     40
                  
                   
                     10
                  
                   
                     22
                  
                   
                     48.40
                  
                
                 
                   
                     50
                  
                   
                     10
                  
                   
                     22
                  
                   
                     49.17
                  
                
                 
                   
                     11.0
                  
                   
                     10
                  
                   
                     22
                  
                   
                     49.54
                  
                
                 
                   
                     10
                  
                   
                     10
                  
                   
                     22
                  
                   
                     50.31
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     ″
                  
                
                 
                   
                     20
                  
                   
                     10
                  
                   
                     22
                  
                   
                     51.09
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     37
                  
                
                 
                   
                     30
                  
                   
                     10
                  
                   
                     22
                  
                   
                     51.46
                  
                
                 
                   
                     40
                  
                   
                     10
                  
                   
                     22
                  
                   
                     52.23
                  
                
                 
                   
                     50
                  
                   
                     10
                  
                   
                     22
                  
                   
                     53.01
                  
                
                 
                   
                     12.0
                  
                   
                     10
                  
                   
                     22
                  
                   
                     53.38
                  
                
                 
                   
                     10
                  
                   
                     10
                  
                   
                     22
                  
                   
                     54.15
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     ″
                  
                
                 
                   
                     20
                  
                   
                     10
                  
                   
                     22
                  
                   
                     54.52
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     37
                  
                
                 
                   
                     30
                  
                   
                     10
                  
                   
                     22
                  
                   
                     55.29
                  
                
                 
                   
                     40
                  
                   
                     10
                  
                   
                     22
                  
                   
                     56.07
                  
                
                 
                   
                     50
                  
                   
                     10
                  
                   
                     22
                  
                   
                     56.44
                  
                
                 
                   
                     13.0
                  
                   
                     10
                  
                   
                     22
                  
                   
                     57.21
                  
                
                 
                   
                     10
                  
                   
                     10
                  
                   
                     22
                  
                   
                     57.58
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     ″
                  
                
                 
                   
                     20
                  
                   
                     10
                  
                   
                     22
                  
                   
                     58.34
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     37
                  
                
                 
                   
                     30
                  
                   
                     10
                  
                   
                     22
                  
                   
                     59.12
                  
                
                 
                   
                     40
                  
                   
                     10
                  
                   
                     22
                  
                   
                     59.49
                  
                
                 
                   
                     50
                  
                   
                     11
                  
                   
                     23
                  
                   
                     00.27
                  
                
                 
                   
                     14.0
                  
                   
                     11
                  
                   
                     23
                  
                   
                     1.4
                  
                
                 
                   
                     10
                  
                   
                     11
                  
                   
                     23
                  
                   
                     1.41
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     ″
                  
                
                 
                   
                     20
                  
                   
                     11
                  
                   
                     23
                  
                   
                     2.18
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     37
                  
                
                 
                   
                     30
                  
                   
                     11
                  
                   
                     23
                  
                   
                     2.55
                  
                
                 
                   
                     40
                  
                   
                     11
                  
                   
                     23
                  
                   
                     3.32
                  
                
                 
                   
                     50
                  
                   
                     11
                  
                   
                     23
                  
                   
                     4.09
                  
                
                 
                   
                     15.0
                  
                   
                     11
                  
                   
                     23
                  
                   
                     4.47
                  
                
                 
                   
                     10
                  
                   
                     11
                  
                   
                     23
                  
                   
                     5.24
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     ″
                  
                
                 
                   
                     20
                  
                   
                     11
                  
                   
                     23
                  
                   
                     6.01
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     37
                  
                
                 
                   
                     30
                  
                   
                     11
                  
                   
                     23
                  
                   
                     6.39
                  
                
                 
                   
                     40
                  
                   
                     11
                  
                   
                     23
                  
                   
                     7.16
                  
                
                 
                   
                     50
                  
                   
                     11
                  
                   
                     23
                  
                   
                     7.53
                  
                
                 
                   
                     16.0
                  
                   
                     11
                  
                   
                     23
                  
                   
                     8.29
                  
                
                 
                   
                     10
                  
                   
                     11
                  
                   
                     23
                  
                   
                     9.06
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     ″
                  
                
                 
                   
                     20
                  
                   
                     11
                  
                   
                     23
                  
                   
                     9.43
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     37
                  
                
                 
                   
                     30
                  
                   
                     11
                  
                   
                     23
                  
                   
                     10.20
                  
                
                 
                   
                     40
                  
                   
                     11
                  
                   
                     23
                  
                   
                     10.57
                  
                
                 
                   
                     50
                  
                   
                     11
                  
                   
                     23
                  
                   
                     11.34
                  
                
                 
                   
                     17.0
                  
                   
                     11
                  
                   
                     23
                  
                   
                     12.11
                  
                
                 
                   
                     10
                  
                   
                     11
                  
                   
                     23
                  
                   
                     12.48
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     ″
                  
                
                 
                   
                     20
                  
                   
                     11
                  
                   
                     23
                  
                   
                     13.25
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     37
                  
                
                 
                   
                     30
                  
                   
                     11
                  
                   
                     23
                  
                   
                     14.02
                  
                
                 
                   
                     40
                  
                   
                     11
                  
                   
                     23
                  
                   
                     14.39
                  
                
                 
                   
                     50
                  
                   
                     11
                  
                   
                     23
                  
                   
                     15.16
                  
                
                 
                   
                     18.0
                  
                   
                     11
                  
                   
                     23
                  
                   
                     15.53
                  
                
                 
                   
                     10
                  
                   
                     11
                  
                   
                     23
                  
                   
                     16.30
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     ″
                  
                
                 
                   
                     20
                  
                   
                     11
                  
                   
                     23
                  
                   
                     17.07
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     37
                  
                
                 
                   
                     30
                  
                   
                     11
                  
                   
                     23
                  
                   
                     17
                     44
                  
                
                 
                   
                     40
                  
                   
                     11
                  
                   
                     23
                  
                   
                     18.21
                  
                
                 
                   
                     50
                  
                   
                     11
                  
                   
                     23
                  
                   
                     18.58
                  
                
                 
                   
                     19.0
                  
                   
                     11
                  
                   
                     23
                  
                   
                     19.34
                  
                
                 
                   
                     10
                  
                   
                     11
                  
                   
                     23
                  
                   
                     20.11
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     ″
                  
                
                 
                   
                     20
                  
                   
                     11
                  
                   
                     23
                  
                   
                     20
                     48
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     37
                  
                
                 
                   
                     30
                  
                   
                     11
                  
                   
                     23
                  
                   
                     21.25
                  
                
                 
                   
                     40
                  
                   
                     11
                  
                   
                     23
                  
                   
                     22.02
                  
                
                 
                   
                     50
                  
                   
                     11
                  
                   
                     23
                  
                   
                     22
                     39
                  
                
                 
                 
                   
                     20.
                     0
                  
                   
                     11
                  
                   
                     23
                  
                   
                     23.16
                  
                
                 
                   
                     10
                  
                   
                     11
                  
                   
                     23
                  
                   
                     23.53
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     ″
                  
                
                 
                   
                     20
                  
                   
                     11
                  
                   
                     23
                  
                   
                     24.30
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     37
                  
                
                 
                   
                     30
                  
                   
                     11
                  
                   
                     23
                  
                   
                     25.07
                  
                
                 
                   
                     40
                  
                   
                     11
                  
                   
                     23
                  
                   
                     25.44
                  
                
                 
                   
                     50
                  
                   
                     11
                  
                   
                     23
                  
                   
                     26.21
                  
                
                 
                   
                     21.
                     0
                  
                   
                     11
                  
                   
                     23
                  
                   
                     26.56
                  
                
                 
                   
                     10
                  
                   
                     11
                  
                   
                     23
                  
                   
                     27.33
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     ″
                  
                
                 
                   
                     20
                  
                   
                     11
                  
                   
                     23
                  
                   
                     28.10
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     37
                  
                
                 
                   
                     30
                  
                   
                     11
                  
                   
                     23
                  
                   
                     28.46
                  
                
                 
                   
                     40
                  
                   
                     11
                  
                   
                     23
                  
                   
                     29.23
                  
                
                 
                   
                     50
                  
                   
                     11
                  
                   
                     23
                  
                   
                     30.00
                  
                
                 
                   
                     22.
                     0
                  
                   
                     11
                  
                   
                     23
                  
                   
                     30.37
                  
                
                 
                   
                     10
                  
                   
                     11
                  
                   
                     23
                  
                   
                     31.14
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     ″
                  
                
                 
                   
                     20
                  
                   
                     11
                  
                   
                     23
                  
                   
                     31.51
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     37
                  
                
                 
                   
                     30
                  
                   
                     11
                  
                   
                     23
                  
                   
                     32.27
                  
                
                 
                   
                     40
                  
                   
                     11
                  
                   
                     23
                  
                   
                     33.04
                  
                
                 
                   
                     50
                  
                   
                     11
                  
                   
                     23
                  
                   
                     33.41
                  
                
                 
                   
                     23.
                     0
                  
                   
                     11
                  
                   
                     23
                  
                   
                     34.18
                  
                
                 
                   
                     10
                  
                   
                     11
                  
                   
                     23
                  
                   
                     34
                     55
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     ″
                  
                
                 
                   
                     20
                  
                   
                     11
                  
                   
                     23
                  
                   
                     35.32
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     37
                  
                
                 
                   
                     30
                  
                   
                     11
                  
                   
                     23
                  
                   
                     36
                     08
                  
                
                 
                   
                     40
                  
                   
                     11
                  
                   
                     23
                  
                   
                     36.45
                  
                
                 
                   
                     50
                  
                   
                     11
                  
                   
                     23
                  
                   
                     37.22
                  
                
                 
                   
                     24.
                     0
                  
                   
                     11
                  
                   
                     23
                  
                   
                     37.59
                  
                
                 
                   
                     10
                  
                   
                     11
                  
                   
                     23
                  
                   
                     38.36
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     ″
                  
                
                 
                   
                     20
                  
                   
                     11
                  
                   
                     23
                  
                   
                     39.13
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     37
                  
                
                 
                   
                     30
                  
                   
                     11
                  
                   
                     23
                  
                   
                     39.59
                  
                
                 
                   
                     40
                  
                   
                     11
                  
                   
                     23
                  
                   
                     40.36
                  
                
                 
                   
                     50
                  
                   
                     11
                  
                   
                     23
                  
                   
                     41.13
                  
                
                 
                   
                     25.
                     0
                  
                   
                     11
                  
                   
                     23
                  
                   
                     41.40
                  
                
                 
                   
                     10
                  
                   
                     11
                  
                   
                     23
                  
                   
                     42.17
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     ″
                  
                
                 
                   
                     20
                  
                   
                     11
                  
                   
                     23
                  
                   
                     42.54
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     37
                  
                
                 
                   
                     30
                  
                   
                     11
                  
                   
                     23
                  
                   
                     43
                     30
                  
                
                 
                   
                     40
                  
                   
                     11
                  
                   
                     23
                  
                   
                     44
                     07
                  
                
                 
                   
                     50
                  
                   
                     11
                  
                   
                     23
                  
                   
                     44
                     43
                  
                
                 
                   
                     26.
                     0
                  
                   
                     11
                  
                   
                     23
                  
                   
                     45.20
                  
                
                 
                   
                     10
                  
                   
                     11
                  
                   
                     23
                  
                   
                     45.57
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     ″
                  
                
                 
                   
                     20
                  
                   
                     11
                  
                   
                     23
                  
                   
                     46.34
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     37
                  
                
                 
                   
                     30
                  
                   
                     11
                  
                   
                     23
                  
                   
                     47.10
                  
                
                 
                   
                     40
                  
                   
                     11
                  
                   
                     23
                  
                   
                     47.47
                  
                
                 
                   
                     50
                  
                   
                     11
                  
                   
                     23
                  
                   
                     48.23
                  
                
                 
                   
                     27.
                     0
                  
                   
                     11
                  
                   
                     23
                  
                   
                     49.0
                  
                
                 
                   
                     10
                  
                   
                     11
                  
                   
                     23
                  
                   
                     49.37
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     ″
                  
                
                 
                   
                     20
                  
                   
                     11
                  
                   
                     23
                  
                   
                     50.14
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     37
                  
                
                 
                   
                     30
                  
                   
                     11
                  
                   
                     23
                  
                   
                     50.50
                  
                
                 
                   
                     40
                  
                   
                     11
                  
                   
                     23
                  
                   
                     51.27
                  
                
                 
                   
                     50
                  
                   
                     11
                  
                   
                     23
                  
                   
                     52.03
                  
                
                 
                   
                     28.
                     0
                  
                   
                     11
                  
                   
                     23
                  
                   
                     52.40
                  
                
                 
                   
                     10
                  
                   
                     11
                  
                   
                     23
                  
                   
                     53.17
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     ″
                  
                
                 
                   
                     20
                  
                   
                     11
                  
                   
                     23
                  
                   
                     53.54
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     37
                  
                
                 
                   
                     30
                  
                   
                     11
                  
                   
                     23
                  
                   
                     54.30
                  
                
                 
                   
                     40
                  
                   
                     11
                  
                   
                     23
                  
                   
                     55.06
                  
                
                 
                   
                     50
                  
                   
                     11
                  
                   
                     23
                  
                   
                     55.43
                  
                
                 
                   
                     29.
                     0
                  
                   
                     11
                  
                   
                     23
                  
                   
                     56.20
                  
                
                 
                   
                     10
                  
                   
                     11
                  
                   
                     23
                  
                   
                     56.57
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     ″
                  
                
                 
                   
                     20
                  
                   
                     11
                  
                   
                     23
                  
                   
                     57
                     34
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     37
                  
                
                 
                   
                     30
                  
                   
                     11
                  
                   
                     23
                  
                   
                     58
                     10
                  
                
                 
                   
                     40
                  
                   
                     11
                  
                   
                     23
                  
                   
                     58.46
                  
                
                 
                   
                     50
                  
                   
                     11
                  
                   
                     23
                  
                   
                     59.23
                  
                
              
            
          
           
             
             
               
                 
                   A
                   Catalogue
                   of
                   some
                   Noted
                   fix'd
                   Stars
                   ,
                   with
                   their
                   Temporary
                   Right
                   Ascensions
                   to
                   the
                   Year
                   1686.
                   
                   The
                   first
                   Column
                   shews
                   their
                   Magnitudes
                   .
                   The
                   second
                   
                   Bayer's
                   Notes
                   .
                   The
                   third
                   the
                   Numbers
                   in
                   
                   Ticho's
                   Catalogue
                   .
                   The
                   fourth
                   
                   Bayer's
                   Latin
                   Names
                   ,
                   and
                   common
                   English
                   Names
                   .
                   The
                   fifth
                   their
                   Temporary
                   Right
                   Ascensions
                   .
                
                 
                   
                     Mag
                  
                   
                     Not.
                     Bay.
                     
                  
                   
                     Num
                     Cat.
                     Tich
                  
                   
                     Stars
                     Names
                     .
                  
                   
                     Rt.
                     Ascens
                     .
                     H.
                     ′
                     ″
                  
                
                 
                   
                     3
                  
                   
                     ι
                  
                   
                     21
                  
                   
                     In
                     Extremitate
                     Boreali
                     Caudae
                     Ceti
                  
                   
                     00.03.32
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     Northern
                     in
                     the
                     Whales
                     Tail
                  
                   
                      
                  
                
                 
                   
                     2
                  
                   
                     β
                  
                   
                     22
                  
                   
                     In
                     Extremitate
                     Australi
                     Caudae
                     Ceti
                  
                   
                     00.
                     28.
                     17
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     Southern
                     in
                     the
                     Whales
                     Tail
                  
                   
                      
                  
                
                 
                   
                     3
                  
                   
                     κ
                  
                   
                     16
                  
                   
                     Praecedens
                     in
                     Eductione
                     Caudae
                     Ceti
                  
                   
                     00.
                     54.
                     13
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     Western
                     in
                     the
                     Back
                     of
                     the
                     Whale
                  
                   
                      
                  
                
                 
                   
                     3
                  
                   
                     θ
                  
                   
                     15
                  
                   
                     Sequens
                     in
                     Eductione
                     Caudae
                     Ceti
                  
                   
                     01.
                     08.
                     40
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     Eastern
                     in
                     the
                     Back
                     of
                     the
                     Whale
                  
                   
                      
                  
                
                 
                   
                     3
                  
                   
                     ζ
                  
                   
                     14
                  
                   
                     In
                     medio
                     corpore
                     Ceti
                     trium
                     Septentrionalior
                  
                   
                     01.
                     36.
                     05
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     Northern
                     in
                     the
                     Whales
                     Beily
                  
                   
                      
                  
                
                 
                   
                     4
                  
                   
                     γ
                  
                   
                     1
                  
                   
                     Prima
                     Stella
                     Arietis
                  
                   
                     01.
                     36.
                     22
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     First
                     Star
                     of
                     Aries
                  
                   
                      
                  
                
                 
                   
                     4
                  
                   
                     β
                  
                   
                     2
                  
                   
                     In
                     sinistro
                     Cornu
                     Arietis
                  
                   
                     01.
                     37.
                     04
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     Second
                     Star
                     of
                     Aries
                  
                   
                      
                  
                
                 
                   
                     3
                  
                   
                     α
                  
                   
                     19
                  
                   
                     In
                     Nodo
                     Vinculorum
                     Piscium
                  
                   
                     01.
                     45.
                     49
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     Br
                     ⋆
                     in
                     the
                     Knot
                     of
                     the
                     Fishes
                     Line
                  
                   
                      
                  
                
                 
                   
                     3
                  
                   
                     α
                  
                   
                     14
                  
                   
                     Lucidae
                     Arietis
                  
                   
                     01.
                     49.
                     29
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     Bright
                     Star
                     of
                     Aries
                  
                   
                      
                  
                
                 
                   
                     3
                  
                   
                     δ
                  
                   
                     4
                  
                   
                     Trium
                     in
                     Collo
                     Ceti
                     Australior
                  
                   
                     02.
                     23.
                     43
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     In
                     the
                     Whales
                     Cheek
                  
                   
                      
                  
                
                 
                   
                     3
                  
                   
                     ι
                  
                   
                     10
                  
                   
                     Laeteris
                     Sequentis
                     Quadrilateri
                     Borea
                     in
                     Pectore
                     Ceti
                  
                   
                     02.
                     24.
                     40
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     On
                     the
                     Whales
                     Brest
                  
                   
                      
                  
                
                 
                   
                     3
                  
                   
                     γ
                  
                   
                     3
                  
                   
                     Media
                     Trium
                     in
                     Collo
                     Ceti
                  
                   
                     02.
                     27.
                     16
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     In
                     the
                     Whales
                     Mouth
                     .
                  
                   
                      
                  
                
                 
                 
                   
                     2
                  
                   
                     α
                  
                   
                     2
                  
                   
                     Lucida
                     in
                     Naribus
                     ,
                     Menkar
                     ,
                     Ceti
                  
                   
                     02.
                     45.
                     50
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     Whales
                     Jaw
                  
                   
                      
                  
                
                 
                   
                     3
                  
                   
                     α
                  
                   
                     32
                  
                   
                     Lucida
                     Pleiadum
                     Tauri
                  
                   
                     03.
                     29.
                     01
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     Brightest
                     of
                     the
                     Pleiades
                  
                   
                      
                  
                
                 
                   
                     3
                  
                   
                     γ
                  
                   
                     11
                  
                   
                     In
                     Vultu
                     Tauri
                     illa
                     in
                     Naribus
                  
                   
                     04.
                     01.
                     50
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     The
                     lowest
                     of
                     the
                     Hyades
                  
                   
                      
                  
                
                 
                   
                     3
                  
                   
                     ι
                  
                   
                     15
                  
                   
                     Ad
                     Oculum
                     Boreum
                     Tauri
                  
                   
                     04.
                     10.
                     08
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     North
                     Eye
                     of
                     Taurus
                  
                   
                      
                  
                
                 
                   
                     1
                  
                   
                     α
                  
                   
                     14
                  
                   
                     Tauri
                     Oculus
                     Austrinus
                     .
                     Aldebaran
                  
                   
                     04.
                     17.
                     56
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     Bulls
                     South
                     Eye
                  
                   
                      
                  
                
                 
                   
                     3
                  
                   
                     β
                  
                   
                     2
                  
                   
                     Supra
                     Pedem
                     Orionis
                     in
                     Flumine
                     Erid
                     .
                  
                   
                     04.
                     52.
                     32
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     Orions
                     Foot
                     in
                     Eridanus
                  
                   
                      
                  
                
                 
                   
                     1
                  
                   
                     β
                  
                   
                     35
                  
                   
                     Pes
                     Dexter
                     Orionis
                     .
                     Rigel
                  
                   
                     04.
                     59.
                     29
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     Bright
                     Star
                     in
                     Orions
                     Foot
                  
                   
                      
                  
                
                 
                   
                     2
                  
                   
                     β
                  
                   
                      
                  
                   
                     Tauri
                     Cornu
                     Septentrionale
                  
                   
                     05
                     06.
                     27
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     Bulls
                     North
                     Horn
                  
                   
                      
                  
                
                 
                   
                     2
                  
                   
                     γ
                  
                   
                     3
                  
                   
                     In
                     humero
                     Dextro
                     Orionis
                     Duarum
                     Borealior
                  
                   
                     05.
                     08.
                     22
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     First
                     or
                     left
                     Shoulder
                     of
                     Orion
                  
                   
                      
                  
                
                 
                   
                     2
                  
                   
                     δ
                  
                   
                     26
                  
                   
                     In
                     Baltheo
                     Orionis
                     Fulgentium
                     
                       3
                       um
                    
                     precedens
                  
                   
                     05.
                     15.
                     55
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     First
                     in
                     Orions
                     Belt
                  
                   
                      
                  
                
                 
                   
                     3
                  
                   
                     ζ
                  
                   
                     19
                  
                   
                     Extrema
                     Cornu
                     Australis
                     Tauri
                  
                   
                     05.
                     18.
                     50
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     Bulls
                     South
                     Horn
                  
                   
                      
                  
                
                 
                   
                     2
                  
                   
                     φ
                  
                   
                     27
                  
                   
                     Media
                     Balthei
                     Orionis
                  
                   
                     05.
                     20.
                     08
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     The
                     second
                     or
                     middle
                     in
                     Orions
                     Belt
                  
                   
                      
                  
                
                 
                   
                     2
                  
                   
                     ξ
                  
                   
                     28
                  
                   
                     Sequens
                     seu
                     tertia
                     Balthei
                     Orionis
                  
                   
                     05.
                     24.
                     30
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     Third
                     or
                     last
                     in
                     Orions
                     Belt
                  
                   
                      
                  
                
                 
                   
                     1
                  
                   
                     α
                  
                   
                     2
                  
                   
                     Lucida
                     in
                     Humero
                     sinistro
                     Orionis
                  
                   
                     05.
                     38.
                     07
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     The
                     latter
                     or
                     right
                     Shoulder
                     of
                     Orion
                  
                   
                      
                  
                
                 
                   
                     3
                  
                   
                     ●
                  
                   
                     15
                  
                   
                     Calx
                     Castoris
                  
                   
                     05.
                     56.
                     05
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     The
                     Heel
                     of
                     Gemini
                  
                   
                      
                  
                
                 
                 
                   
                     2
                  
                   
                     β
                  
                   
                     9
                  
                   
                     In
                     Collario
                     Canis
                     Majoris
                  
                   
                     06.
                     09.
                     13
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     The
                     fore-foot
                     of
                     the
                     Great
                     Dog
                  
                   
                      
                  
                
                 
                   
                     2
                  
                   
                     γ
                  
                   
                     17
                  
                   
                     In
                     summo
                     Pede
                     sinistro
                     sequentis
                     ♊
                  
                   
                     06.
                     19.
                     25
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     Bright
                     Star
                     on
                     the
                     Foot
                     of
                     ♊
                  
                   
                      
                  
                
                 
                   
                     1
                  
                   
                     α
                  
                   
                     1
                  
                   
                     Syrius
                     seu
                     Canis
                     Major
                  
                   
                     06.
                     31.
                     11
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     The
                     Great
                     Dog
                     Star
                  
                   
                      
                  
                
                 
                   
                     3
                  
                   
                     ζ
                  
                   
                     11
                  
                   
                     In
                     Dextro
                     Genu
                     Herculis
                     ♊
                  
                   
                     06.
                     45.
                     38
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     Left
                     Knee
                     of
                     Gemini
                  
                   
                      
                  
                
                 
                   
                     3
                  
                   
                     γ
                  
                   
                     4
                  
                   
                     Ad
                     Aurem
                     Dextram
                     Canis
                     Majoris
                  
                   
                     07.
                     11.
                     00
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     On
                     the
                     Neck
                     of
                     Canis
                     Major
                  
                   
                      
                  
                
                 
                   
                     1
                  
                   
                     α
                  
                   
                     2
                  
                   
                     Procyon
                     seu
                     Canis
                     Minor
                  
                   
                     07.
                     22.
                     53
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     The
                     Little
                     Dog
                  
                   
                      
                  
                
                 
                   
                     2
                  
                   
                     α
                  
                   
                     12
                  
                   
                     Cor
                     Hydrae
                     ,
                     Alphard
                  
                   
                     09.
                     12.
                     07
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     Hydra's
                     Heart
                  
                   
                      
                  
                
                 
                   
                     3
                  
                   
                     κ
                  
                   
                     7
                  
                   
                     Trium
                     in
                     Cervice
                     Leonis
                     Australio●
                  
                   
                     09.
                     50.
                     22
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     Southern
                     in
                     the
                     Neck
                     of
                     Leo
                  
                   
                      
                  
                
                 
                   
                     1
                  
                   
                     ●
                  
                   
                     8
                  
                   
                     Lor
                     Leonis
                  
                   
                     09.
                     51.
                     31
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     Lions
                     Heart
                  
                   
                      
                  
                
                 
                   
                     3
                  
                   
                     ζ
                  
                   
                     5
                  
                   
                     Trium
                     in
                     Cervice
                     Leonis
                     Borealior
                  
                   
                     09.
                     59.
                     06
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     Northern
                     in
                     the
                     Neck
                     of
                     Leo
                  
                   
                      
                  
                
                 
                   
                     2
                  
                   
                     γ
                  
                   
                     6
                  
                   
                     Trium
                     in
                     Cervice
                     Leonis
                     Media
                     .
                     Juba
                  
                   
                     10.
                     02.
                     27
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     Lions
                     Crest
                  
                   
                      
                  
                
                 
                   
                     2
                  
                   
                     δ
                  
                   
                     20
                  
                   
                     In
                     Lumbis
                     Leonis
                     Duarum
                     quae
                     Sequitur
                  
                   
                     10.
                     57.
                     21
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     In
                     the
                     Loyn
                     of
                     Leo
                  
                   
                      
                  
                
                 
                   
                     3
                  
                   
                     θ
                  
                   
                     21
                  
                   
                     In
                     Vertebra
                     Femoris
                     Dextri
                     Leonis
                  
                   
                     10.
                     57.
                     50
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     On
                     the
                     Buttock
                     of
                     Leo
                  
                   
                      
                  
                
                 
                   
                     1
                  
                   
                     β
                  
                   
                     27
                  
                   
                     Cauda
                     Leonis
                  
                   
                     11.
                     32.
                     58
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     Lions
                     Tail
                  
                   
                      
                  
                
                 
                   
                     3
                  
                   
                     ι
                  
                   
                     23
                  
                   
                     In
                     Femore
                     Dextro
                     Leonis
                  
                   
                     11.
                     07.
                     44
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     On
                     the
                     Thigh
                     of
                     Leo
                  
                   
                      
                  
                
                 
                 
                   
                     3
                  
                   
                     β
                  
                   
                     5
                  
                   
                     In
                     Extremo
                     Alae
                     sinistra
                     Virginis
                  
                   
                     11.
                     34.
                     31
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     Above
                     the
                     left
                     wing
                     of
                     Virgo
                  
                   
                      
                  
                
                 
                   
                     3
                  
                   
                     γ
                  
                   
                     7
                  
                   
                     Sub
                     strophio
                     seu
                     Castula
                     Virginis
                  
                   
                     12.
                     25.
                     43
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     On
                     the
                     left
                     wing
                     of
                     Virgo
                  
                   
                      
                  
                
                 
                   
                     3
                  
                   
                     δ
                  
                   
                     10
                  
                   
                     Ad
                     Cingulum
                     Virginis
                  
                   
                     12.
                     39.
                     58
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     In
                     the
                     Girdle
                     of
                     Virgo
                  
                   
                      
                  
                
                 
                   
                     3
                  
                   
                     ι
                  
                   
                     13
                  
                   
                     Alae
                     Dextra
                     ♍
                     precedens
                     .
                     Vindemiatrix
                  
                   
                     12.
                     46.
                     46
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     Virgo's
                     right
                     wing
                     .
                     Vindemiatrix
                  
                   
                      
                  
                
                 
                   
                     1
                  
                   
                     α
                  
                   
                     14
                  
                   
                     Spica
                     Virginis
                  
                   
                     13.
                     08.
                     46
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     Virgins
                     Spike
                  
                   
                      
                  
                
                 
                   
                     3
                  
                   
                     ζ
                  
                   
                     15
                  
                   
                     Sub
                     Perizomate
                     ad
                     pedem
                     dextrum
                     ♏
                  
                   
                     13.
                     13.
                     38
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     On
                     the
                     Buttock
                     of
                     Virgo
                  
                   
                      
                  
                
                 
                   
                     3
                  
                   
                     κ
                  
                   
                     20
                  
                   
                     In
                     sinistra
                     Tibia
                     Bootis
                     trium
                     Borealior
                  
                   
                     13.
                     32.
                     33
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     Most
                     Northern
                     on
                     the
                     left
                     knee
                     of
                     Bootes
                  
                   
                      
                  
                
                 
                   
                     1
                  
                   
                     α
                  
                   
                     23
                  
                   
                     Arcturus
                  
                   
                     14.
                     01.
                     24
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     Arcturus
                  
                   
                      
                  
                
                 
                   
                     3
                  
                   
                     ζ
                  
                   
                     19
                  
                   
                     In
                     Dextra
                     Tibia
                     Bootis
                  
                   
                     14.
                     26.
                     20
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     Bend
                     of
                     Bootes
                     right
                     knee
                  
                   
                      
                  
                
                 
                   
                     2
                  
                   
                     α
                  
                   
                     1
                  
                   
                     Lanx
                     A●stralis
                  
                   
                     14.
                     33.
                     46
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     Southern
                     Ballance
                  
                   
                      
                  
                
                 
                   
                     2
                  
                   
                     β
                  
                   
                     3
                  
                   
                     Lanx
                     Borealis
                  
                   
                     15.
                     00.
                     15
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     Northern
                     Ballance
                  
                   
                      
                  
                
                 
                   
                     3
                  
                   
                     γ
                  
                   
                     7
                  
                   
                     In
                     media
                     lance
                     Boreali
                     Prima
                     &
                     Superior
                  
                   
                     15.
                     18.
                     13
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     Middle
                     of
                     the
                     Northern
                     Ballance
                  
                   
                      
                  
                
                 
                   
                     2
                  
                   
                     α
                  
                   
                     9
                  
                   
                     Precedens
                     trium
                     in
                     medio
                     neru
                     colli
                     serpentis
                  
                   
                     15.
                     28.
                     54
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     Bright
                     Star
                     in
                     the
                     Serpents
                     neck
                  
                   
                      
                  
                
                 
                   
                     2
                  
                   
                     β
                  
                   
                     1
                  
                   
                     In
                     fronte
                     ♏
                     ad
                     Boream
                     prima
                     fulgens
                  
                   
                     15.
                     46.
                     04
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     Highest
                     in
                     Scorpio's
                     forehead
                  
                   
                      
                  
                
                 
                   
                     3
                  
                   
                     δ
                  
                   
                     2
                  
                   
                     In
                     dextra
                     manu
                     serpentarii
                     Borealior
                  
                   
                     15.
                     58.
                     23
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     Northern
                     in
                     the
                     left
                     hand
                     of
                     Serpentarius
                  
                   
                      
                  
                
                 
                 
                   
                     3
                  
                   
                     γ
                  
                   
                     5
                  
                   
                     Ad
                     Originem
                     Alae
                     Dextrae
                     Aquilae
                  
                   
                     19.
                     31.
                     38
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     Pinion
                     of
                     Aquila's
                     Right
                     Wing
                  
                   
                      
                  
                
                 
                   
                     2
                  
                   
                     α
                  
                   
                     3
                  
                   
                     Lucida
                     in
                     Eductione
                     Colli
                     Aquila
                  
                   
                     19.
                     35.
                     51
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     Aquila's
                     Bright
                     Star
                  
                   
                      
                  
                
                 
                   
                     3
                  
                   
                     β
                  
                   
                     2
                  
                   
                     In
                     Collo
                     Aquilae
                  
                   
                     19.
                     39.
                     57
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     Neck
                     of
                     Aquila
                  
                   
                      
                  
                
                 
                   
                     3
                  
                   
                     α
                  
                   
                     1
                  
                   
                     Septentrionalis
                     duplex
                     in
                     Cornu
                     Capricorn
                  
                   
                     20.
                     00.
                     50
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     Northern
                     in
                     the
                     Horn
                     of
                     Capricorn
                  
                   
                      
                  
                
                 
                   
                     3
                  
                   
                     ι
                  
                   
                     1
                  
                   
                     Luoida
                     Cauda
                     Delphini
                     trium
                     Antecedens
                     .
                  
                   
                     20.
                     18.
                     23
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     Dolphins
                     Tail
                  
                   
                      
                  
                
                 
                   
                     3
                  
                   
                     β
                  
                   
                     4
                  
                   
                     In
                     Humero
                     Dextro
                     Aquarii
                  
                   
                     21.
                     14.
                     58
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     Left
                     Shoulder
                     of
                     Aquary
                  
                   
                      
                  
                
                 
                   
                     3
                  
                   
                     γ
                  
                   
                     23
                  
                   
                     In
                     Eductione
                     Caudae
                     Capricorni
                     Antecedens
                  
                   
                     21.
                     22.
                     57
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     First
                     in
                     the
                     Tail
                     of
                     Capricorn
                  
                   
                      
                  
                
                 
                   
                     3
                  
                   
                     ι
                  
                   
                     1
                  
                   
                     In
                     Rictu
                     Pegasi
                     Enif
                     .
                  
                   
                     21.
                     28.
                     44
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     Mouth
                     of
                     Pegasus
                  
                   
                      
                  
                
                 
                   
                     3
                  
                   
                     δ
                  
                   
                     24
                  
                   
                     In
                     Eductione
                     Caudae
                     Capricorni
                     succedens
                  
                   
                     21.
                     30.
                     07
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     Last
                     in
                     the
                     Tail
                     of
                     Capricorn
                  
                   
                      
                  
                
                 
                   
                     3
                  
                   
                     α
                  
                   
                     2
                  
                   
                     Humerus
                     sinister
                     Aquarii
                  
                   
                     21.
                     49.
                     43
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     Right
                     Shoulder
                     of
                     Aquary
                  
                   
                      
                  
                
                 
                   
                     3
                  
                   
                     γ
                  
                   
                     9
                  
                   
                     In
                     Lavo
                     Cubito
                     Aquarii
                  
                   
                     22.
                     05.
                     37
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     Right
                     Elbow
                     of
                     Aquary
                  
                   
                      
                  
                
                 
                   
                     3
                  
                   
                     δ
                  
                   
                     18
                  
                   
                     In
                     sinistra
                     Tibia
                     Aquarii
                  
                   
                     22.
                     38.
                     15
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     Right
                     shin
                     or
                     knee
                     of
                     Aquary
                  
                   
                      
                  
                
                 
                   
                     2
                  
                   
                     β
                  
                   
                     18
                  
                   
                     In
                     Eductione
                     Cruris
                     Pegasi
                     .
                     Scheat
                  
                   
                     22.
                     48.
                     43
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     Pegasus
                     Thigh
                  
                   
                      
                  
                
                 
                   
                     2
                  
                   
                     α
                  
                   
                     17
                  
                   
                     Ala
                     Pegasi
                     .
                     Marchab
                  
                   
                     22.
                     49.
                     05
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     Pegasus
                     Wing
                  
                   
                      
                  
                
                 
                   
                     2
                  
                   
                     γ
                  
                   
                     19
                  
                   
                     In
                     Exteema
                     Ala
                     Pegasi
                  
                   
                     23.
                     57.
                     03
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     End
                     of
                     Pegasus
                     Wing
                  
                   
                      
                  
                
                 
                 
                   
                     3
                  
                   
                     ι
                  
                   
                     8
                  
                   
                     Australior
                     in
                     Dextra
                     manu
                     Serpentarii
                  
                   
                     16.
                     01.
                     57
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     Southern
                     in
                     the
                     left
                     hand
                     of
                     Serpentarius
                  
                   
                      
                  
                
                 
                   
                     3
                  
                   
                     γ
                  
                   
                     3
                  
                   
                     In
                     sinist
                     .
                     Humero
                     Herculis
                     trium
                     Australior
                  
                   
                     16.
                     08.
                     07
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     Hercules
                     Right
                     Shoulder
                  
                   
                      
                  
                
                 
                   
                     1
                  
                   
                     α
                  
                   
                     8
                  
                   
                     Cor
                     Scorpii
                  
                   
                     16.
                     10.
                     18
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     Scorpius
                     Heart
                  
                   
                      
                  
                
                 
                   
                     3
                  
                   
                     β
                  
                   
                     2
                  
                   
                     In
                     sinist
                     .
                     Humero
                     Herculis
                     trium
                     Borealior
                  
                   
                     16.
                     16.
                     41
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     Northern
                     in
                     Hercules
                     Right
                     Shoulder
                  
                   
                      
                  
                
                 
                   
                     3
                  
                   
                     ζ
                  
                   
                     19
                  
                   
                     In
                     Femore
                     Dextro
                     Serpentarii
                  
                   
                     16.
                     19.
                     59
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     Serpentarius
                     left
                     knee
                  
                   
                      
                  
                
                 
                   
                     3
                  
                   
                     θ
                  
                   
                     13
                  
                   
                     In
                     Femore
                     sinistro
                     Serpentarii
                     
                       3
                       um
                    
                     Borealior
                  
                   
                     16.
                     52.
                     02
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     Right
                     Ham
                     of
                     Serpentarius
                  
                   
                      
                  
                
                 
                   
                     3
                  
                   
                     α
                  
                   
                     1
                  
                   
                     Caput
                     Herculis
                  
                   
                     17.
                     00.
                     23
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     Hercules
                     Head
                  
                   
                      
                  
                
                 
                   
                     3
                  
                   
                     δ
                  
                   
                     5
                  
                   
                     Herculis
                     Humerus
                     Dexter
                  
                   
                     17.
                     01.
                     57
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     Left
                     Shoulder
                     of
                     Hercules
                  
                   
                      
                  
                
                 
                   
                     2
                  
                   
                     α
                  
                   
                     1
                  
                   
                     Caput
                     Serpentarii
                  
                   
                     17.
                     20.
                     22
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     Serpentarius
                     Head
                  
                   
                      
                  
                
                 
                   
                     3
                  
                   
                     β
                  
                   
                     5
                  
                   
                     In
                     sinist
                     .
                     Humero
                     Serpentarii
                     
                       2
                       rum
                    
                     Superior
                  
                   
                     17.
                     27.
                     55
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     Northern
                     in
                     Serpentarius
                     right
                     Shoulder
                  
                   
                      
                  
                
                 
                   
                     3
                  
                   
                     γ
                  
                   
                     3
                  
                   
                     In
                     eodem
                     duarum
                     Inferior
                  
                   
                     17.
                     32.
                     23
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     Southern
                     in
                     Serpentarius
                     Right
                     Shoulder
                  
                   
                      
                  
                
                 
                   
                     3
                  
                   
                     ζ
                  
                   
                     16
                  
                   
                     Prima
                     post
                     Serpentarium
                     in
                     Cauda
                     Serpentis
                  
                   
                     17.
                     44.
                     09
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     Last
                     but
                     two
                     in
                     the
                     Serpents
                     Tail
                  
                   
                      
                  
                
                 
                   
                     3
                  
                   
                     κ
                  
                   
                     17
                  
                   
                     In
                     Penultima
                     Flexione
                     Caudae
                     Serpentis
                  
                   
                     18.
                     05.
                     20
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     Last
                     but
                     one
                     in
                     the
                     Serpents
                     Tail
                  
                   
                      
                  
                
                 
                   
                     3
                  
                   
                     θ
                  
                   
                     18
                  
                   
                     Extrema
                     Caudae
                     Serpentis
                  
                   
                     18.
                     40
                     37
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     Last
                     in
                     the
                     Serpents
                     Tail
                  
                   
                      
                  
                
                 
                   
                     3
                  
                   
                     ι
                  
                   
                     11
                  
                   
                     Extrema
                     Caudae
                     Aquilae
                  
                   
                     18.
                     51.
                     06
                  
                
                 
                   
                      
                  
                   
                      
                  
                   
                      
                  
                   
                     Last
                     in
                     the
                     Eagles
                     Tail
                  
                   
                      
                  
                
              
            
          
        
         
           
           
             TABLES
             OF
             AEQUATION
             OF
             Natural
             Days
             .
          
           
           
           
             
               
                 A
                 Table
                 of
                 Aequation
                 of
                 Natural
                 Days
                 .
              
               
                 
                   Day
                
                 
                   Jan
                
                 
                   Dif
                   .
                
                 
                   Feb.
                   
                
                 
                   X
                
                 
                   March
                
                 
                   X
                
                 
                   Apr.
                   
                
                 
                   X
                
                 
                   May
                
                 
                   X
                
                 
                   June
                
                 
                   X
                
              
               
                 
                    
                
                 
                   ′
                   ″
                
                 
                   ″
                
                 
                   ′
                   ″
                
                 
                   ″
                
                 
                   ′
                   ″
                
                 
                   ″
                
                 
                   ′
                   ″
                
                 
                   ″
                
                 
                   ′
                   ″
                
                 
                   ″
                
                 
                   ′
                   ″
                
                 
                   ″
                
              
               
                 
                   1
                
                 
                   8.55
                
                 
                    
                
                 
                   14.54
                
                 
                    
                
                 
                   10.16
                
                 
                    
                
                 
                   0.51
                
                 
                    
                
                 
                   4.12
                
                 
                    
                
                 
                   1.10
                
                 
                    
                
              
               
                 
                    
                
                 
                    
                
                 
                   22
                
                 
                    
                
                 
                   1
                
                 
                    
                
                 
                   18
                
                 
                    
                
                 
                   16
                
                 
                    
                
                 
                   2
                
                 
                    
                
                 
                   13
                
              
               
                 
                   2
                
                 
                   9.17
                
                 
                    
                
                 
                   14.53
                
                 
                    
                
                 
                   9.58
                
                 
                    
                
                 
                   0.35
                
                 
                    
                
                 
                   4.14
                
                 
                    
                
                 
                   0.57
                
                 
                    
                
              
               
                 
                    
                
                 
                    
                
                 
                   23
                
                 
                    
                
                 
                   2
                
                 
                    
                
                 
                   18
                
                 
                    
                
                 
                   17
                
                 
                    
                
                 
                   2
                
                 
                    
                
                 
                   12
                
              
               
                 
                   3
                
                 
                   9.40
                
                 
                    
                
                 
                   14.51
                
                 
                    
                
                 
                   9.41
                
                 
                    
                
                 
                   0.18
                
                 
                    
                
                 
                   4.16
                
                 
                    
                
                 
                   0.45
                
                 
                    
                
              
               
                 
                    
                
                 
                    
                
                 
                   22
                
                 
                    
                
                 
                   3
                
                 
                    
                
                 
                   17
                
                 
                    
                
                 
                   17
                
                 
                    
                
                 
                   1
                
                 
                    
                
                 
                   12
                
              
               
                 
                   4
                
                 
                   10.02
                
                 
                    
                
                 
                   14.48
                
                 
                    
                
                 
                   9.24
                
                 
                    
                
                 
                   0.01
                
                 
                    
                
                 
                   4.17
                
                 
                    
                
                 
                   0.33
                
                 
                    
                
              
               
                 
                    
                
                 
                    
                
                 
                   21
                
                 
                    
                
                 
                   3
                
                 
                    
                
                 
                   15
                
                 
                    
                
                 
                   1
                
                 
                    
                
                 
                   14
                
              
               
                 
                   5
                
                 
                   10.23
                
                 
                    
                
                 
                   14.45
                
                 
                    
                
                 
                   9.06
                
                 
                    
                
                 
                   0.14
                
                 
                    
                
                 
                   4.16
                
                 
                    
                
                 
                   0.19
                
                 
                    
                
              
               
                 
                    
                
                 
                    
                
                 
                   21
                
                 
                    
                
                 
                   5
                
                 
                    
                
                 
                   17
                
                 
                    
                
                 
                   15
                
                 
                    
                
                 
                   1
                
                 
                    
                
                 
                   12
                
              
               
                 
                   6
                
                 
                   10.44
                
                 
                   14.40
                
                 
                   8.49
                
                 
                   9.29
                
                 
                   4.15
                
                 
                    
                
                 
                   0.07
                
                 
                    
                
              
               
                 
                    
                
                 
                    
                
                 
                   18
                
                 
                    
                
                 
                   5
                
                 
                    
                
                 
                   17
                
                 
                    
                
                 
                   14
                
                 
                    
                
                 
                   1
                
                 
                    
                
                 
                   13
                
              
               
                 
                   7
                
                 
                   11.02
                
                 
                    
                
                 
                   14.35
                
                 
                    
                
                 
                   8.32
                
                 
                    
                
                 
                   0.43
                
                 
                    
                
                 
                   4.14
                
                 
                    
                
                 
                   0.06
                
                 
                    
                
              
               
                 
                    
                
                 
                    
                
                 
                   18
                
                 
                    
                
                 
                   6
                
                 
                    
                
                 
                   18
                
                 
                    
                
                 
                   15
                
                 
                    
                
                 
                   2
                
                 
                    
                
                 
                   13
                
              
               
                 
                   8
                
                 
                   11.20
                
                 
                    
                
                 
                   14.29
                
                 
                    
                
                 
                   8.14
                
                 
                    
                
                 
                   9.58
                
                 
                    
                
                 
                   4.12
                
                 
                    
                
                 
                   0.19
                
                 
                    
                
              
               
                 
                    
                
                 
                    
                
                 
                   18
                
                 
                    
                
                 
                   6
                
                 
                    
                
                 
                   19
                
                 
                    
                
                 
                   14
                
                 
                    
                
                 
                   2
                
                 
                    
                
                 
                   13
                
              
               
                 
                   9
                
                 
                   11.38
                
                 
                    
                
                 
                   14.23
                
                 
                    
                
                 
                   7.55
                
                 
                    
                
                 
                   1.12
                
                 
                    
                
                 
                   4.10
                
                 
                    
                
                 
                   0.32
                
                 
                    
                
              
               
                 
                    
                
                 
                    
                
                 
                   17
                
                 
                    
                
                 
                   7
                
                 
                    
                
                 
                   18
                
                 
                    
                
                 
                   14
                
                 
                    
                
                 
                   2
                
                 
                    
                
                 
                   12
                
              
               
                 
                   10
                
                 
                   11.55
                
                 
                    
                
                 
                   14.16
                
                 
                    
                
                 
                   7.37
                
                 
                    
                
                 
                   1.26
                
                 
                    
                
                 
                   4.08
                
                 
                    
                
                 
                   0.44
                
                 
                    
                
              
               
                 
                    
                
                 
                    
                
                 
                   17
                
                 
                    
                
                 
                   9
                
                 
                    
                
                 
                   19
                
                 
                    
                
                 
                   14
                
                 
                    
                
                 
                   3
                
                 
                    
                
                 
                   13
                
              
               
                 
                   11
                
                 
                   12.12
                
                 
                    
                
                 
                   14.07
                
                 
                    
                
                 
                   7.18
                
                 
                    
                
                 
                   1.40
                
                 
                    
                
                 
                   4.05
                
                 
                    
                
                 
                   0.57
                
                 
                    
                
              
               
                 
                    
                
                 
                    
                
                 
                   16
                
                 
                    
                
                 
                   8
                
                 
                    
                
                 
                   20
                
                 
                    
                
                 
                   12
                
                 
                    
                
                 
                   4
                
                 
                    
                
                 
                   13
                
              
               
                 
                   12
                
                 
                   12.28
                
                 
                    
                
                 
                   13.59
                
                 
                    
                
                 
                   6.58
                
                 
                    
                
                 
                   1.52
                
                 
                    
                
                 
                   4.01
                
                 
                    
                
                 
                   1.01
                
                 
                    
                
              
               
                 
                    
                
                 
                    
                
                 
                   15
                
                 
                    
                
                 
                   9
                
                 
                    
                
                 
                   19
                
                 
                    
                
                 
                   11
                
                 
                    
                
                 
                   4
                
                 
                    
                
                 
                   13
                
              
               
                 
                   13
                
                 
                   12.43
                
                 
                    
                
                 
                   13.50
                
                 
                    
                
                 
                   6.39
                
                 
                    
                
                 
                   2.03
                
                 
                    
                
                 
                   3.57
                
                 
                    
                
                 
                   1.23
                
                 
                    
                
              
               
                 
                    
                
                 
                    
                
                 
                   15
                
                 
                    
                
                 
                   9
                
                 
                    
                
                 
                   19
                
                 
                    
                
                 
                   12
                
                 
                    
                
                 
                   5
                
                 
                    
                
                 
                   13
                
              
               
                 
                   14
                
                 
                   12.58
                
                 
                    
                
                 
                   13.41
                
                 
                    
                
                 
                   6.20
                
                 
                    
                
                 
                   2.15
                
                 
                    
                
                 
                   3.52
                
                 
                    
                
                 
                   1.36
                
                 
                    
                
              
               
                 
                    
                
                 
                    
                
                 
                   13
                
                 
                    
                
                 
                   10
                
                 
                    
                
                 
                   19
                
                 
                    
                
                 
                   11
                
                 
                    
                
                 
                   5
                
                 
                    
                
                 
                   14
                
              
               
                 
                   15
                
                 
                   13.11
                
                 
                    
                
                 
                   13.31
                
                 
                    
                
                 
                   6.01
                
                 
                    
                
                 
                   2.26
                
                 
                    
                
                 
                   3.47
                
                 
                    
                
                 
                   1.50
                
                 
                    
                
              
               
                 
                    
                
                 
                   Add
                
                 
                   12
                
                 
                   Add
                
                 
                   11
                
                 
                   Add
                
                 
                   19
                
                 
                   Substract
                
                 
                   11
                
                 
                   Substract
                
                 
                   5
                
                 
                   Add
                
                 
                   12
                
              
               
                 
                   16
                
                 
                   13.23
                
                 
                   13.20
                
                 
                   5.42
                
                 
                   2.37
                
                 
                   3.42
                
                 
                   2.02
                
                 
                    
                
              
               
                 
                    
                
                 
                    
                
                 
                   12
                
                 
                    
                
                 
                   11
                
                 
                    
                
                 
                   15
                
                 
                    
                
                 
                   11
                
                 
                    
                
                 
                   7
                
                 
                    
                
                 
                   12
                
              
               
                 
                   17
                
                 
                   13.35
                
                 
                    
                
                 
                   13.09
                
                 
                    
                
                 
                   5.23
                
                 
                    
                
                 
                   2.48
                
                 
                    
                
                 
                   3.35
                
                 
                    
                
                 
                   2.14
                
                 
                    
                
              
               
                 
                    
                
                 
                    
                
                 
                   11
                
                 
                    
                
                 
                   12
                
                 
                    
                
                 
                   19
                
                 
                    
                
                 
                   9
                
                 
                    
                
                 
                   7
                
                 
                    
                
                 
                   12
                
              
               
                 
                   18
                
                 
                   13.46
                
                 
                    
                
                 
                   12.57
                
                 
                    
                
                 
                   5.04
                
                 
                    
                
                 
                   2.57
                
                 
                    
                
                 
                   3.28
                
                 
                    
                
                 
                   2.26
                
                 
                    
                
              
               
                 
                    
                
                 
                    
                
                 
                   11
                
                 
                    
                
                 
                   12
                
                 
                    
                
                 
                   19
                
                 
                    
                
                 
                   9
                
                 
                    
                
                 
                   7
                
                 
                    
                
                 
                   12
                
              
               
                 
                   19
                
                 
                   13.57
                
                 
                    
                
                 
                   12.45
                
                 
                    
                
                 
                   4.46
                
                 
                    
                
                 
                   3.06
                
                 
                    
                
                 
                   3.21
                
                 
                    
                
                 
                   2.38
                
                 
                    
                
              
               
                 
                    
                
                 
                    
                
                 
                   9
                
                 
                    
                
                 
                   14
                
                 
                    
                
                 
                   19
                
                 
                    
                
                 
                   9
                
                 
                    
                
                 
                   8
                
                 
                    
                
                 
                   12
                
                 
                    
                
              
               
                 
                   20
                
                 
                   14.06
                
                 
                    
                
                 
                   12.31
                
                 
                    
                
                 
                   4.27
                
                 
                    
                
                 
                   3.15
                
                 
                    
                
                 
                   3.13
                
                 
                    
                
                 
                   2.50
                
                 
                    
                
              
               
                 
                    
                
                 
                    
                
                 
                   9
                
                 
                    
                
                 
                   14
                
                 
                    
                
                 
                   19
                
                 
                    
                
                 
                   8
                
                 
                    
                
                 
                   9
                
                 
                    
                
                 
                   12
                
              
               
                 
                   21
                
                 
                   14.15
                
                 
                    
                
                 
                   12.17
                
                 
                    
                
                 
                   4.08
                
                 
                    
                
                 
                   3.23
                
                 
                    
                
                 
                   3.04
                
                 
                    
                
                 
                   3.02
                
                 
                    
                
              
               
                 
                    
                
                 
                    
                
                 
                   8
                
                 
                    
                
                 
                   13
                
                 
                    
                
                 
                   18
                
                 
                    
                
                 
                   7
                
                 
                    
                
                 
                   8
                
                 
                    
                
                 
                   12
                
              
               
                 
                   22
                
                 
                   14.23
                
                 
                    
                
                 
                   12.04
                
                 
                    
                
                 
                   3.50
                
                 
                    
                
                 
                   3.30
                
                 
                    
                
                 
                   2.56
                
                 
                    
                
                 
                   3.14
                
                 
                    
                
              
               
                 
                    
                
                 
                    
                
                 
                   6
                
                 
                    
                
                 
                   14
                
                 
                    
                
                 
                   19
                
                 
                    
                
                 
                   7
                
                 
                    
                
                 
                   9
                
                 
                    
                
                 
                   11
                
              
               
                 
                   23
                
                 
                   14.29
                
                 
                    
                
                 
                   11.56
                
                 
                    
                
                 
                   3.31
                
                 
                    
                
                 
                   3.37
                
                 
                    
                
                 
                   2.47
                
                 
                    
                
                 
                   3.25
                
                 
                    
                
              
               
                 
                    
                
                 
                    
                
                 
                   6
                
                 
                    
                
                 
                   13
                
                 
                    
                
                 
                   19
                
                 
                    
                
                 
                   7
                
                 
                    
                
                 
                   10
                
                 
                    
                
                 
                   10
                
              
               
                 
                   24
                
                 
                   14.35
                
                 
                    
                
                 
                   11.37
                
                 
                    
                
                 
                   3.12
                
                 
                    
                
                 
                   3.44
                
                 
                    
                
                 
                   2.37
                
                 
                    
                
                 
                   3.35
                
                 
                    
                
              
               
                 
                    
                
                 
                    
                
                 
                   5
                
                 
                    
                
                 
                   15
                
                 
                    
                
                 
                   19
                
                 
                    
                
                 
                   6
                
                 
                    
                
                 
                   9
                
                 
                    
                
                 
                   10
                
              
               
                 
                   25
                
                 
                   14.40
                
                 
                    
                
                 
                   11.22
                
                 
                    
                
                 
                   2.53
                
                 
                    
                
                 
                   3.50
                
                 
                    
                
                 
                   2.28
                
                 
                    
                
                 
                   3.45
                
                 
                    
                
              
               
                 
                    
                
                 
                    
                
                 
                   4
                
                 
                    
                
                 
                   16
                
                 
                    
                
                 
                   18
                
                 
                    
                
                 
                   5
                
                 
                    
                
                 
                   10
                
                 
                    
                
                 
                   12
                
              
               
                 
                   26
                
                 
                   14.44
                
                 
                    
                
                 
                   11.06
                
                 
                    
                
                 
                   2.35
                
                 
                    
                
                 
                   3.55
                
                 
                    
                
                 
                   2.18
                
                 
                    
                
                 
                   3.57
                
                 
                    
                
              
               
                 
                    
                
                 
                    
                
                 
                   4
                
                 
                    
                
                 
                   16
                
                 
                    
                
                 
                   19
                
                 
                    
                
                 
                   4
                
                 
                    
                
                 
                   11
                
                 
                    
                
                 
                   10
                
              
               
                 
                   27
                
                 
                   14.48
                
                 
                    
                
                 
                   10.50
                
                 
                    
                
                 
                   2.16
                
                 
                    
                
                 
                   3.59
                
                 
                    
                
                 
                   2.07
                
                 
                    
                
                 
                   4.07
                
                 
                    
                
              
               
                 
                    
                
                 
                    
                
                 
                   2
                
                 
                    
                
                 
                   16
                
                 
                    
                
                 
                   18
                
                 
                    
                
                 
                   4
                
                 
                    
                
                 
                   11
                
                 
                    
                
                 
                   10
                
              
               
                 
                   28
                
                 
                   14.50
                
                 
                    
                
                 
                   10.34
                
                 
                    
                
                 
                   1.58
                
                 
                    
                
                 
                   4.03
                
                 
                    
                
                 
                   1.56
                
                 
                    
                
                 
                   4.17
                
                 
                    
                
              
               
                 
                    
                
                 
                    
                
                 
                   1
                
                 
                    
                
                 
                    
                
                 
                    
                
                 
                   17
                
                 
                    
                
                 
                   3
                
                 
                    
                
                 
                   11
                
                 
                    
                
                 
                   8
                
              
               
                 
                   29
                
                 
                   14.51
                
                 
                    
                
                 
                    
                
                 
                    
                
                 
                   1.41
                
                 
                    
                
                 
                   4.07
                
                 
                    
                
                 
                   1.45
                
                 
                    
                
                 
                   4.25
                
              
               
                 
                    
                
                 
                    
                
                 
                   1
                
                 
                    
                
                 
                    
                
                 
                    
                
                 
                   17
                
                 
                    
                
                 
                   3
                
                 
                   11
                
                 
                    
                
                 
                   8
                
              
               
                 
                   30
                
                 
                   14.52
                
                 
                    
                
                 
                    
                
                 
                    
                
                 
                   1.24
                
                 
                    
                
                 
                   4.10
                
                 
                    
                
                 
                    
                
                 
                   1.34
                
                 
                    
                
                 
                   4.33
                
                 
                    
                
              
               
                 
                    
                
                 
                    
                
                 
                   1
                
                 
                    
                
                 
                    
                
                 
                    
                
                 
                   17
                
                 
                    
                
                 
                    
                
                 
                    
                
                 
                   12
                
                 
                    
                
                 
                    
                
              
               
                 
                   31
                
                 
                   14.53
                
                 
                    
                
                 
                    
                
                 
                    
                
                 
                   1.07
                
                 
                    
                
                 
                    
                
                 
                    
                
                 
                   1.22
                
                 
                    
                
                 
                    
                
              
               
               
                 
                   Day
                
                 
                   July
                
                 
                   X
                
                 
                   August
                
                 
                   X
                
                 
                   Sept.
                   
                
                 
                   X
                
                 
                   Octob.
                   
                
                 
                   X
                
                 
                   Novemb
                
                 
                   X
                
                 
                   Decemb
                
                 
                   X
                
              
               
                 
                    
                
                 
                   ′
                   ″
                
                 
                   ″
                
                 
                   ′
                   ″
                
                 
                   ″
                
                 
                   ′
                   ″
                
                 
                   ″
                
                 
                   ′
                   ″
                
                 
                   ″
                
                 
                   ′
                   ″
                
                 
                   ″
                
                 
                   ′
                   ″
                
                 
                   ″
                
              
               
                 
                   1
                
                 
                   4.43
                
                 
                    
                
                 
                   4.36
                
                 
                    
                
                 
                   3.41
                
                 
                    
                
                 
                   13.13
                
                 
                    
                
                 
                   15.28
                
                 
                    
                
                 
                   5.51
                
                 
                    
                
              
               
                 
                    
                
                 
                    
                
                 
                   8
                
                 
                    
                
                 
                   9
                
                 
                    
                
                 
                   21
                
                 
                    
                
                 
                   13
                
                 
                    
                
                 
                   8
                
                 
                    
                
                 
                   28
                
              
               
                 
                   2
                
                 
                   4.51
                
                 
                    
                
                 
                   4.27
                
                 
                    
                
                 
                   4.02
                
                 
                    
                
                 
                   13.26
                
                 
                    
                
                 
                   15.20
                
                 
                    
                
                 
                   5.23
                
                 
                    
                
              
               
                 
                    
                
                 
                    
                
                 
                   7
                
                 
                    
                
                 
                   9
                
                 
                    
                
                 
                   21
                
                 
                    
                
                 
                   14
                
                 
                    
                
                 
                   9
                
                 
                    
                
                 
                   28
                
              
               
                 
                   3
                
                 
                   4.58
                
                 
                    
                
                 
                   4.18
                
                 
                    
                
                 
                   4.23
                
                 
                    
                
                 
                   13.40
                
                 
                    
                
                 
                   15.11
                
                 
                    
                
                 
                   4.55
                
                 
                    
                
              
               
                 
                    
                
                 
                    
                
                 
                   7
                
                 
                    
                
                 
                   12
                
                 
                   21
                
                 
                    
                
                 
                   13
                
                 
                    
                
                 
                   10
                
                 
                    
                
                 
                   29
                
              
               
                 
                   4
                
                 
                   5.5
                
                 
                    
                
                 
                   4.06
                
                 
                    
                
                 
                   4.44
                
                 
                    
                
                 
                   13.53
                
                 
                    
                
                 
                   15.01
                
                 
                    
                
                 
                   4.2
                
                 
                    
                
              
               
                 
                    
                
                 
                    
                
                 
                   7
                
                 
                    
                
                 
                   11
                
                 
                    
                
                 
                   20
                
                 
                    
                
                 
                   13
                
                 
                    
                
                 
                   10
                
                 
                    
                
                 
                   30
                
              
               
                 
                   5
                
                 
                   5.12
                
                 
                    
                
                 
                   3.55
                
                 
                    
                
                 
                   5.04
                
                 
                    
                
                 
                   14.06
                
                 
                    
                
                 
                   14.51
                
                 
                    
                
                 
                   3.56
                
                 
                    
                
              
               
                 
                    
                
                 
                    
                
                 
                   6
                
                 
                    
                
                 
                   11
                
                 
                    
                
                 
                   20
                
                 
                    
                
                 
                   13
                
                 
                    
                
                 
                   12
                
                 
                   Substract
                
                 
                   29
                
              
               
                 
                   6
                
                 
                   5.18
                
                 
                    
                
                 
                   3.44
                
                 
                    
                
                 
                   5.24
                
                 
                    
                
                 
                   14.19
                
                 
                    
                
                 
                   14.39
                
                 
                    
                
                 
                   3.27
                
                 
                    
                
              
               
                 
                    
                
                 
                    
                
                 
                   6
                
                 
                    
                
                 
                   13
                
                 
                    
                
                 
                   21
                
                 
                    
                
                 
                   12
                
                 
                   13
                
                 
                    
                
                 
                   29
                
              
               
                 
                   7
                
                 
                   5.24
                
                 
                    
                
                 
                   3.31
                
                 
                    
                
                 
                   5.45
                
                 
                    
                
                 
                   14.31
                
                 
                    
                
                 
                   14.26
                
                 
                    
                
                 
                   3.58
                
                 
                    
                
              
               
                 
                    
                
                 
                    
                
                 
                   5
                
                 
                    
                
                 
                   13
                
                 
                    
                
                 
                   20
                
                 
                    
                
                 
                   11
                
                 
                    
                
                 
                   13
                
                 
                    
                
                 
                   30
                
              
               
                 
                   8
                
                 
                   5.29
                
                 
                    
                
                 
                   3.18
                
                 
                    
                
                 
                   6.05
                
                 
                    
                
                 
                   14.42
                
                 
                    
                
                 
                   14.13
                
                 
                    
                
                 
                   2.28
                
                 
                    
                
              
               
                 
                    
                
                 
                    
                
                 
                   4
                
                 
                    
                
                 
                   13
                
                 
                    
                
                 
                   21
                
                 
                    
                
                 
                   10
                
                 
                    
                
                 
                   13
                
                 
                    
                
                 
                   30
                
              
               
                 
                   9
                
                 
                   5.33
                
                 
                    
                
                 
                   3.05
                
                 
                    
                
                 
                   6.26
                
                 
                    
                
                 
                   14.52
                
                 
                    
                
                 
                   14.00
                
                 
                    
                
                 
                   2.58
                
                 
                    
                
              
               
                 
                    
                
                 
                    
                
                 
                   4
                
                 
                    
                
                 
                   13
                
                 
                    
                
                 
                   20
                
                 
                    
                
                 
                   09
                
                 
                    
                
                 
                   15
                
                 
                    
                
                 
                   30
                
              
               
                 
                   10
                
                 
                   5.37
                
                 
                    
                
                 
                   2.52
                
                 
                    
                
                 
                   6.46
                
                 
                    
                
                 
                   15.01
                
                 
                    
                
                 
                   13.45
                
                 
                    
                
                 
                   1.28
                
                 
                    
                
              
               
                 
                    
                
                 
                    
                
                 
                   4
                
                 
                   Add
                
                 
                   14
                
                 
                    
                
                 
                   21
                
                 
                    
                
                 
                   9
                
                 
                    
                
                 
                   1●
                
                 
                    
                
                 
                   30
                
              
               
                 
                   11
                
                 
                   5.41
                
                 
                    
                
                 
                   2.38
                
                 
                    
                
                 
                   7.07
                
                 
                    
                
                 
                   15.10
                
                 
                    
                
                 
                   13.29
                
                 
                    
                
                 
                   0.58
                
                 
                    
                
              
               
                 
                    
                
                 
                    
                
                 
                   3
                
                 
                    
                
                 
                   14
                
                 
                    
                
                 
                   21
                
                 
                    
                
                 
                   8
                
                 
                    
                
                 
                   10
                
                 
                    
                
                 
                   31
                
              
               
                 
                   12
                
                 
                   5.44
                
                 
                    
                
                 
                   2.24
                
                 
                    
                
                 
                   7.28
                
                 
                    
                
                 
                   15.18
                
                 
                    
                
                 
                   13.13
                
                 
                    
                
                 
                   0.28
                
                 
                    
                
              
               
                 
                    
                
                 
                    
                
                 
                   2
                
                 
                    
                
                 
                   16
                
                 
                    
                
                 
                   21
                
                 
                   8
                
                 
                    
                
                 
                   1●
                
                 
                    
                
                 
                   30
                
              
               
                 
                   13
                
                 
                   5.46
                
                 
                    
                
                 
                   2.08
                
                 
                    
                
                 
                   7.49
                
                 
                    
                
                 
                   15.26
                
                 
                    
                
                 
                   12.56
                
                 
                    
                
                 
                   0.03
                
                 
                    
                
              
               
                 
                    
                
                 
                    
                
                 
                   2
                
                 
                    
                
                 
                   16
                
                 
                    
                
                 
                   20
                
                 
                    
                
                 
                   8
                
                 
                    
                
                 
                   18
                
                 
                    
                
                 
                   30
                
              
               
                 
                   14
                
                 
                   5.48
                
                 
                    
                
                 
                   1.52
                
                 
                    
                
                 
                   8.09
                
                 
                    
                
                 
                   15.34
                
                 
                    
                
                 
                   12.38
                
                 
                    
                
                 
                   0.33
                
                 
                    
                
              
               
                 
                    
                
                 
                    
                
                 
                   1
                
                 
                    
                
                 
                   16
                
                 
                    
                
                 
                   22
                
                 
                    
                
                 
                   6
                
                 
                    
                
                 
                   19
                
                 
                    
                
                 
                   30
                
              
               
                 
                   15
                
                 
                   5.49
                
                 
                    
                
                 
                   1.36
                
                 
                    
                
                 
                   8.30
                
                 
                    
                
                 
                   15.40
                
                 
                    
                
                 
                   12.19
                
                 
                    
                
                 
                   1.03
                
                 
                    
                
              
               
                 
                   Add
                
                 
                   ●
                
                 
                    
                
                 
                   16
                
                 
                   Substract
                
                 
                   20
                
                 
                   Substract
                
                 
                   6
                
                 
                   Substract
                
                 
                   19
                
                 
                    
                
                 
                   30
                
              
               
                 
                   16
                
                 
                   5.49
                
                 
                    
                
                 
                   1.20
                
                 
                    
                
                 
                   8.50
                
                 
                    
                
                 
                   15.46
                
                 
                    
                
                 
                   12.00
                
                 
                    
                
                 
                   1.33
                
                 
                    
                
              
               
                 
                    
                
                 
                    
                
                 
                   0
                
                 
                    
                
                 
                   16
                
                 
                    
                
                 
                   19
                
                 
                    
                
                 
                   5
                
                 
                    
                
                 
                   21
                
                 
                    
                
                 
                   29
                
              
               
                 
                   17
                
                 
                   5.49
                
                 
                    
                
                 
                   1.04
                
                 
                    
                
                 
                   9.09
                
                 
                    
                
                 
                   15.51
                
                 
                    
                
                 
                   11.39
                
                 
                    
                
                 
                   2.02
                
                 
                    
                
              
               
                 
                    
                
                 
                    
                
                 
                   1
                
                 
                    
                
                 
                   17
                
                 
                    
                
                 
                   20
                
                 
                    
                
                 
                   4
                
                 
                    
                
                 
                   21
                
                 
                    
                
                 
                   30
                
              
               
                 
                   18
                
                 
                   5.48
                
                 
                    
                
                 
                   0.47
                
                 
                    
                
                 
                   9.29
                
                 
                    
                
                 
                   15.55
                
                 
                    
                
                 
                   11.18
                
                 
                    
                
                 
                   2.32
                
                 
                    
                
              
               
                 
                    
                
                 
                    
                
                 
                   1
                
                 
                    
                
                 
                   17
                
                 
                    
                
                 
                   19
                
                 
                    
                
                 
                   3
                
                 
                    
                
                 
                   22
                
                 
                    
                
                 
                   29
                
              
               
                 
                   19
                
                 
                   5.47
                
                 
                    
                
                 
                   0.30
                
                 
                    
                
                 
                   9.48
                
                 
                    
                
                 
                   15.58
                
                 
                    
                
                 
                   10.56
                
                 
                    
                
                 
                   3.01
                
                 
                    
                
              
               
                 
                    
                
                 
                    
                
                 
                   2
                
                 
                    
                
                 
                   18
                
                 
                    
                
                 
                   18
                
                 
                    
                
                 
                   2
                
                 
                    
                
                 
                   22
                
                 
                    
                
                 
                   30
                
              
               
                 
                   20
                
                 
                   5.45
                
                 
                    
                
                 
                   0.12
                
                 
                    
                
                 
                   10.6
                
                 
                    
                
                 
                   16.00
                
                 
                    
                
                 
                   10.34
                
                 
                    
                
                 
                   3.31
                
                 
                    
                
              
               
                 
                    
                
                 
                    
                
                 
                   2
                
                 
                    
                
                 
                   17
                
                 
                    
                
                 
                   19
                
                 
                    
                
                 
                   2
                
                 
                    
                
                 
                   23
                
                 
                    
                
                 
                   29
                
              
               
                 
                   21
                
                 
                   5.43
                
                 
                    
                
                 
                   0.05
                
                 
                    
                
                 
                   10.25
                
                 
                    
                
                 
                   16.02
                
                 
                    
                
                 
                   10.11
                
                 
                    
                
                 
                   1.00
                
                 
                    
                
              
               
                 
                    
                
                 
                    
                
                 
                   3
                
                 
                    
                
                 
                   19
                
                 
                    
                
                 
                   19
                
                 
                    
                
                 
                   1
                
                 
                    
                
                 
                   2●
                
                 
                    
                
                 
                   28
                
              
               
                 
                   22
                
                 
                   5.40
                
                 
                    
                
                 
                   0.24
                
                 
                    
                
                 
                   10.44
                
                 
                    
                
                 
                   16.03
                
                 
                    
                
                 
                   9.47
                
                 
                    
                
                 
                   1.28
                
                 
                    
                
              
               
                 
                    
                
                 
                    
                
                 
                   4
                
                 
                    
                
                 
                   19
                
                 
                    
                
                 
                   19
                
                 
                    
                
                 
                   1
                
                 
                    
                
                 
                   24
                
                 
                    
                
                 
                   28
                
              
               
                 
                   23
                
                 
                   5.36
                
                 
                    
                
                 
                   0.43
                
                 
                    
                
                 
                   11.03
                
                 
                    
                
                 
                   1●
                   .
                   04
                
                 
                    
                
                 
                   9.23
                
                 
                    
                
                 
                   4.56
                
                 
                    
                
              
               
                 
                    
                
                 
                    
                
                 
                   4
                
                 
                    
                
                 
                   20
                
                 
                    
                
                 
                   17
                
                 
                    
                
                 
                   0
                
                 
                    
                
                 
                   24
                
                 
                    
                
                 
                   27
                
              
               
                 
                   24
                
                 
                   5
                   .
                   3●
                
                 
                    
                
                 
                   1.03
                
                 
                    
                
                 
                   11.20
                
                 
                   16.04
                
                 
                   8.59
                
                 
                   5.23
                
                 
                    
                
              
               
                 
                    
                
                 
                    
                
                 
                   4
                
                 
                    
                
                 
                   19
                
                 
                    
                
                 
                   17
                
                 
                    
                
                 
                   2
                
                 
                   25
                
                 
                    
                
                 
                   27
                
              
               
                 
                   25
                
                 
                   5.28
                
                 
                    
                
                 
                   1.22
                
                 
                    
                
                 
                   11.37
                
                 
                    
                
                 
                   16.02
                
                 
                    
                
                 
                   8.34
                
                 
                    
                
                 
                   5.50
                
                 
                    
                
              
               
                 
                    
                
                 
                    
                
                 
                   6
                
                 
                   Substract
                
                 
                   19
                
                 
                    
                
                 
                   17
                
                 
                    
                
                 
                   3
                
                 
                    
                
                 
                   26
                
                 
                    
                
                 
                   27
                
              
               
                 
                   26
                
                 
                   5.22
                
                 
                    
                
                 
                   1.41
                
                 
                    
                
                 
                   11.54
                
                 
                    
                
                 
                   15.59
                
                 
                    
                
                 
                   8.08
                
                 
                    
                
                 
                   6.17
                
                 
                    
                
              
               
                 
                    
                
                 
                    
                
                 
                   7
                
                 
                    
                
                 
                   19
                
                 
                    
                
                 
                   17
                
                 
                   3
                
                 
                    
                
                 
                   27
                
                 
                    
                
                 
                   27
                
              
               
                 
                   27
                
                 
                   5.15
                
                 
                    
                
                 
                   2.00
                
                 
                    
                
                 
                   12.11
                
                 
                    
                
                 
                   15.56
                
                 
                    
                
                 
                   7.41
                
                 
                    
                
                 
                   6.44
                
                 
                    
                
              
               
                 
                    
                
                 
                    
                
                 
                   7
                
                 
                    
                
                 
                   20
                
                 
                    
                
                 
                   16
                
                 
                    
                
                 
                   4
                
                 
                    
                
                 
                   26
                
                 
                    
                
                 
                   26
                
              
               
                 
                   28
                
                 
                   5.08
                
                 
                    
                
                 
                   2.20
                
                 
                    
                
                 
                   12.27
                
                 
                   15.52
                
                 
                    
                
                 
                   7.15
                
                 
                   7.10
                
                 
                    
                
              
               
                 
                    
                
                 
                    
                
                 
                   8
                
                 
                    
                
                 
                   20
                
                 
                    
                
                 
                   16
                
                 
                    
                
                 
                   5
                
                 
                    
                
                 
                   27
                
                 
                    
                
                 
                   26
                
              
               
                 
                   29
                
                 
                   5.00
                
                 
                    
                
                 
                   2.40
                
                 
                    
                
                 
                   12.43
                
                 
                    
                
                 
                   15
                   .
                   4●
                
                 
                    
                
                 
                   6.48
                
                 
                    
                
                 
                   7.36
                
                 
                    
                
              
               
                 
                    
                
                 
                    
                
                 
                   7
                
                 
                   20
                
                 
                    
                
                 
                   16
                
                 
                    
                
                 
                   6
                
                 
                    
                
                 
                   29
                
                 
                    
                
                 
                   24
                
              
               
                 
                   30
                
                 
                   4.53
                
                 
                    
                
                 
                   3.00
                
                 
                    
                
                 
                   12.59
                
                 
                    
                
                 
                   15.41
                
                 
                    
                
                 
                   6.19
                
                 
                    
                
                 
                   8.00
                
                 
                    
                
              
               
                 
                    
                
                 
                    
                
                 
                   8
                
                 
                    
                
                 
                   20
                
                 
                    
                
                 
                    
                
                 
                    
                
                 
                   7
                
                 
                    
                
                 
                    
                
                 
                    
                
                 
                    
                
                 
                   24
                
              
               
                 
                   31
                
                 
                   4.45
                
                 
                    
                
                 
                   3.20
                
                 
                    
                
                 
                    
                
                 
                    
                
                 
                    
                
                 
                   15.34
                
                 
                    
                
                 
                    
                
                 
                    
                
                 
                   8.24
                
                 
                    
                
              
            
          
        
         
           
           
             CALCULATION
             OF
             Hours
             and
             Minutes
             for
             an
             HORIZONTAL-DIAL
             .
             DUBLIN
             Lat.
             53°
             .
             20′
             .
          
           
           
           
             
               
                 Calculation
                 of
                 Hours
                 and
                 Minutes
                 for
                 an
                 Horizontal
                 Dial
                 :
                 
                   Dublin
                   Lat
                   :
                   53°
                   20°
                
                 .
              
               
                 
                   Time
                   from
                   Noon
                
                 
                   Hour
                   dist
                   .
                   on
                   the
                   Plain
                
              
               
                 
                   h
                   ′
                
                 
                   0
                   ′
                
              
               
                 
                   XIi
                   .
                   00
                
                 
                   00.00
                
              
               
                 
                   1
                
                 
                   0.12
                
              
               
                 
                   2
                
                 
                   0.24
                
              
               
                 
                   3
                
                 
                   0.36
                
              
               
                 
                   4
                
                 
                   0.48
                
              
               
                 
                   5
                
                 
                   1.0
                
              
               
                 
                   6
                
                 
                   1.12
                
              
               
                 
                   7
                
                 
                   1.24
                
              
               
                 
                   8
                
                 
                   1.36
                
              
               
                 
                   9
                
                 
                   1.48
                
              
               
                 
                   10
                
                 
                   2.0
                
              
               
                 
                   11
                
                 
                   2.12
                
              
               
                 
                   12
                
                 
                   2.25
                
              
               
                 
                   13
                
                 
                   2.37
                
              
               
                 
                   14
                
                 
                   2.49
                
              
               
                 
                   15
                
                 
                   3.1
                
              
               
                 
                   16
                
                 
                   3.13
                
              
               
                 
                   17
                
                 
                   3.25
                
              
               
                 
                   18
                
                 
                   3.37
                
              
               
                 
                   19
                
                 
                   3.49
                
              
               
                 
                   20
                
                 
                   4.1
                
              
               
                 
                   21
                
                 
                   4.13
                
              
               
                 
                   22
                
                 
                   4.25
                
              
               
                 
                   23
                
                 
                   4.37
                
              
               
                 
                   24
                
                 
                   4.49
                
              
               
                 
                   25
                
                 
                   5.1
                
              
               
                 
                   26
                
                 
                   5.13
                
              
               
                 
                   27
                
                 
                   5.25
                
              
               
                 
                   28
                
                 
                   5.37
                
              
               
                 
                   29
                
                 
                   5.49
                
              
               
                 
                   30
                
                 
                   6.1
                
              
               
                 
                   XII
                   .
                   30
                
                 
                   6.1
                
              
               
                 
                   31
                
                 
                   6.14
                
              
               
                 
                   32
                
                 
                   6.26
                
              
               
                 
                   33
                
                 
                   6.38
                
              
               
                 
                   34
                
                 
                   6.50
                
              
               
                 
                   35
                
                 
                   7.2
                
              
               
                 
                   36
                
                 
                   7.14
                
              
               
                 
                   37
                
                 
                   7.27
                
              
               
                 
                   38
                
                 
                   7.39
                
              
               
                 
                   39
                
                 
                   7.51
                
              
               
                 
                   40
                
                 
                   8.3
                
              
               
                 
                   41
                
                 
                   8.15
                
              
               
                 
                   42
                
                 
                   8.28
                
              
               
                 
                   43
                
                 
                   8.39
                
              
               
                 
                   44
                
                 
                   8.51
                
              
               
                 
                   45
                
                 
                   9.4
                
              
               
                 
                   46
                
                 
                   9.16
                
              
               
                 
                   47
                
                 
                   9.28
                
              
               
                 
                   48
                
                 
                   9.40
                
              
               
                 
                   49
                
                 
                   9.52
                
              
               
                 
                   50
                
                 
                   10.5
                
              
               
                 
                   51
                
                 
                   10.17
                
              
               
                 
                   52
                
                 
                   10.29
                
              
               
                 
                   53
                
                 
                   10.42
                
              
               
                 
                   54
                
                 
                   10.54
                
              
               
                 
                   55
                
                 
                   11.6
                
              
               
                 
                   56
                
                 
                   11.18
                
              
               
                 
                   57
                
                 
                   11.31
                
              
               
                 
                   58
                
                 
                   11.43
                
              
               
                 
                   59
                
                 
                   11.55
                
              
               
                 
                   60
                
                 
                   12.8
                
              
               
                 
                   I.
                   00
                
                 
                   12.8
                
              
               
                 
                   1
                
                 
                   12.20
                
              
               
                 
                   2
                
                 
                   12.33
                
              
               
                 
                   3
                
                 
                   12.45
                
              
               
                 
                   4
                
                 
                   12.57
                
              
               
                 
                   5
                
                 
                   13.9
                
              
               
                 
                   6
                
                 
                   13.22
                
              
               
                 
                   7
                
                 
                   13.34
                
              
               
                 
                   8
                
                 
                   13.47
                
              
               
                 
                   9
                
                 
                   13.59
                
              
               
                 
                   10
                
                 
                   14.11
                
              
               
                 
                   11
                
                 
                   14.24
                
              
               
                 
                   12
                
                 
                   14.37
                
              
               
                 
                   13
                
                 
                   14.49
                
              
               
                 
                   14
                
                 
                   14.1
                
              
               
                 
                   15
                
                 
                   15.14
                
              
               
                 
                   16
                
                 
                   15.26
                
              
               
                 
                   17
                
                 
                   15.39
                
              
               
                 
                   18
                
                 
                   15.51
                
              
               
                 
                   19
                
                 
                   16.4
                
              
               
                 
                   20
                
                 
                   16.17
                
              
               
                 
                   21
                
                 
                   16.29
                
              
               
                 
                   22
                
                 
                   16.41
                
              
               
                 
                   23
                
                 
                   16.54
                
              
               
                 
                   24
                
                 
                   17.7
                
              
               
                 
                   25
                
                 
                   17.20
                
              
               
                 
                   26
                
                 
                   17.32
                
              
               
                 
                   27
                
                 
                   17.45
                
              
               
                 
                   28
                
                 
                   17.57
                
              
               
                 
                   29
                
                 
                   18.10
                
              
               
                 
                   30
                
                 
                   18.23
                
              
               
                 
                   I.
                   30
                
                 
                   18.23
                
              
               
                 
                   31
                
                 
                   18.35
                
              
               
                 
                   32
                
                 
                   18.48
                
              
               
                 
                   33
                
                 
                   19.1
                
              
               
                 
                   34
                
                 
                   19.14
                
              
               
                 
                   35
                
                 
                   19.27
                
              
               
                 
                   36
                
                 
                   19.39
                
              
               
                 
                   37
                
                 
                   19.52
                
              
               
                 
                   38
                
                 
                   20.4
                
              
               
                 
                   39
                
                 
                   20.17
                
              
               
                 
                   40
                
                 
                   20.30
                
              
               
                 
                   41
                
                 
                   20.43
                
              
               
                 
                   42
                
                 
                   20.56
                
              
               
                 
                   43
                
                 
                   21.9
                
              
               
                 
                   44
                
                 
                   21.22
                
              
               
                 
                   45
                
                 
                   21.35
                
              
               
                 
                   46
                
                 
                   21.48
                
              
               
                 
                   47
                
                 
                   22.1
                
              
               
                 
                   48
                
                 
                   22.14
                
              
               
                 
                   49
                
                 
                   22.27
                
              
               
                 
                   50
                
                 
                   22.40
                
              
               
                 
                   41
                
                 
                   22.53
                
              
               
                 
                   52
                
                 
                   23.6
                
              
               
                 
                   53
                
                 
                   23.19
                
              
               
                 
                   54
                
                 
                   23.32
                
              
               
                 
                   55
                
                 
                   23.45
                
              
               
                 
                   56
                
                 
                   23.58
                
              
               
                 
                   57
                
                 
                   24.11
                
              
               
                 
                   58
                
                 
                   24.24
                
              
               
                 
                   59
                
                 
                   24.38
                
              
               
                 
                   60
                
                 
                   24.51
                
              
               
               
                 
                   II.
                   00
                
                 
                   24.51
                
              
               
                 
                   1
                
                 
                   25.5
                
              
               
                 
                   2
                
                 
                   25.18
                
              
               
                 
                   3
                
                 
                   25.31
                
              
               
                 
                   4
                
                 
                   25.44
                
              
               
                 
                   5
                
                 
                   25.57
                
              
               
                 
                   6
                
                 
                   26.10
                
              
               
                 
                   7
                
                 
                   26.24
                
              
               
                 
                   8
                
                 
                   26.38
                
              
               
                 
                   9
                
                 
                   26.51
                
              
               
                 
                   10
                
                 
                   27.4
                
              
               
                 
                   11
                
                 
                   27.18
                
              
               
                 
                   12
                
                 
                   27.31
                
              
               
                 
                   13
                
                 
                   27.44
                
              
               
                 
                   14
                
                 
                   27.58
                
              
               
                 
                   15
                
                 
                   28.11
                
              
               
                 
                   16
                
                 
                   28.25
                
              
               
                 
                   17
                
                 
                   28.39
                
              
               
                 
                   18
                
                 
                   28.52
                
              
               
                 
                   19
                
                 
                   29.6
                
              
               
                 
                   20
                
                 
                   29.19
                
              
               
                 
                   21
                
                 
                   29.33
                
              
               
                 
                   22
                
                 
                   29.47
                
              
               
                 
                   23
                
                 
                   30.0
                
              
               
                 
                   24
                
                 
                   30.14
                
              
               
                 
                   25
                
                 
                   30.28
                
              
               
                 
                   26
                
                 
                   30.41
                
              
               
                 
                   27
                
                 
                   30.55
                
              
               
                 
                   28
                
                 
                   31.9
                
              
               
                 
                   29
                
                 
                   31.23
                
              
               
                 
                   30
                
                 
                   31.37
                
              
               
                 
                   II.
                   30
                
                 
                   31.37
                
              
               
                 
                   31
                
                 
                   31.51
                
              
               
                 
                   32
                
                 
                   32.4
                
              
               
                 
                   33
                
                 
                   32.18
                
              
               
                 
                   34
                
                 
                   32.32
                
              
               
                 
                   35
                
                 
                   32.46
                
              
               
                 
                   36
                
                 
                   33.0
                
              
               
                 
                   37
                
                 
                   33.
                   ●●
                
              
               
                 
                   38
                
                 
                   33.28
                
              
               
                 
                   39
                
                 
                   33.43
                
              
               
                 
                   40
                
                 
                   33.57
                
              
               
                 
                   41
                
                 
                   34.11
                
              
               
                 
                   42
                
                 
                   34.25
                
              
               
                 
                   43
                
                 
                   34.39
                
              
               
                 
                   44
                
                 
                   34.53
                
              
               
                 
                   45
                
                 
                   35.8
                
              
               
                 
                   46
                
                 
                   35.22
                
              
               
                 
                   47
                
                 
                   35.36
                
              
               
                 
                   48
                
                 
                   35.50
                
              
               
                 
                   49
                
                 
                   36.5
                
              
               
                 
                   50
                
                 
                   36.19
                
              
               
                 
                   51
                
                 
                   36.34
                
              
               
                 
                   52
                
                 
                   36.48
                
              
               
                 
                   53
                
                 
                   37.2
                
              
               
                 
                   54
                
                 
                   37.17
                
              
               
                 
                   55
                
                 
                   37.31
                
              
               
                 
                   56
                
                 
                   37.46
                
              
               
                 
                   57
                
                 
                   38.0
                
              
               
                 
                   58
                
                 
                   38.15
                
              
               
                 
                   59
                
                 
                   38.29
                
              
               
                 
                   60
                
                 
                   38.44
                
              
               
                 
                   III.
                   00
                
                 
                   38.44
                
              
               
                 
                   1
                
                 
                   38.59
                
              
               
                 
                   2
                
                 
                   39.14
                
              
               
                 
                   3
                
                 
                   39.28
                
              
               
                 
                   4
                
                 
                   39.43
                
              
               
                 
                   5
                
                 
                   39.57
                
              
               
                 
                   6
                
                 
                   40.12
                
              
               
                 
                   7
                
                 
                   40.27
                
              
               
                 
                   8
                
                 
                   40.42
                
              
               
                 
                   9
                
                 
                   40.57
                
              
               
                 
                   10
                
                 
                   41.12
                
              
               
                 
                   11
                
                 
                   41.27
                
              
               
                 
                   12
                
                 
                   41.42
                
              
               
                 
                   13
                
                 
                   41.57
                
              
               
                 
                   14
                
                 
                   42.12
                
              
               
                 
                   15
                
                 
                   42.27
                
              
               
                 
                   16
                
                 
                   42.42
                
              
               
                 
                   17
                
                 
                   42.57
                
              
               
                 
                   18
                
                 
                   43.12
                
              
               
                 
                   19
                
                 
                   43.27
                
              
               
                 
                   20
                
                 
                   43.42
                
              
               
                 
                   21
                
                 
                   43.57
                
              
               
                 
                   22
                
                 
                   44.13
                
              
               
                 
                   23
                
                 
                   44.29
                
              
               
                 
                   24
                
                 
                   44.44
                
              
               
                 
                   25
                
                 
                   44.59
                
              
               
                 
                   26
                
                 
                   45.15
                
              
               
                 
                   27
                
                 
                   45.30
                
              
               
                 
                   28
                
                 
                   45.45
                
              
               
                 
                   29
                
                 
                   46.1
                
              
               
                 
                   30
                
                 
                   46.16
                
              
               
                 
                   III.
                   30
                
                 
                   46.16
                
              
               
                 
                   31
                
                 
                   46.32
                
              
               
                 
                   32
                
                 
                   46.47
                
              
               
                 
                   33
                
                 
                   47.3
                
              
               
                 
                   34
                
                 
                   47.19
                
              
               
                 
                   35
                
                 
                   47.35
                
              
               
                 
                   36
                
                 
                   47.50
                
              
               
                 
                   37
                
                 
                   48.5
                
              
               
                 
                   38
                
                 
                   48.21
                
              
               
                 
                   39
                
                 
                   48.37
                
              
               
                 
                   40
                
                 
                   48.53
                
              
               
                 
                   41
                
                 
                   49.9
                
              
               
                 
                   42
                
                 
                   49.25
                
              
               
                 
                   43
                
                 
                   49.40
                
              
               
                 
                   44
                
                 
                   49.56
                
              
               
                 
                   45
                
                 
                   50.12
                
              
               
                 
                   46
                
                 
                   50.28
                
              
               
                 
                   47
                
                 
                   50.44
                
              
               
                 
                   48
                
                 
                   51.0
                
              
               
                 
                   49
                
                 
                   51.16
                
              
               
                 
                   50
                
                 
                   51.33
                
              
               
                 
                   51
                
                 
                   51.49
                
              
               
                 
                   52
                
                 
                   52.5
                
              
               
                 
                   53
                
                 
                   52.21
                
              
               
                 
                   54
                
                 
                   52.37
                
              
               
                 
                   55
                
                 
                   52.54
                
              
               
                 
                   56
                
                 
                   53.10
                
              
               
                 
                   57
                
                 
                   53.26
                
              
               
                 
                   58
                
                 
                   53.43
                
              
               
                 
                   59
                
                 
                   53.59
                
              
               
                 
                   60
                
                 
                   54.15
                
              
               
               
                 
                   IIII.
                   00
                
                 
                   54.15
                
              
               
                 
                   1
                
                 
                   54.32
                
              
               
                 
                   2
                
                 
                   54.48
                
              
               
                 
                   3
                
                 
                   55.5
                
              
               
                 
                   4
                
                 
                   55.21
                
              
               
                 
                   5
                
                 
                   55.37
                
              
               
                 
                   6
                
                 
                   55.54
                
              
               
                 
                   7
                
                 
                   56.11
                
              
               
                 
                   8
                
                 
                   56.28
                
              
               
                 
                   9
                
                 
                   56.45
                
              
               
                 
                   10
                
                 
                   57.1
                
              
               
                 
                   11
                
                 
                   57.18
                
              
               
                 
                   12
                
                 
                   57.35
                
              
               
                 
                   13
                
                 
                   57.51
                
              
               
                 
                   14
                
                 
                   58.8
                
              
               
                 
                   15
                
                 
                   58.25
                
              
               
                 
                   16
                
                 
                   58.42
                
              
               
                 
                   17
                
                 
                   58.59
                
              
               
                 
                   18
                
                 
                   59.16
                
              
               
                 
                   19
                
                 
                   59.32
                
              
               
                 
                   20
                
                 
                   59.49
                
              
               
                 
                   21
                
                 
                   60.7
                
              
               
                 
                   22
                
                 
                   60.24
                
              
               
                 
                   23
                
                 
                   60.41
                
              
               
                 
                   24
                
                 
                   60.58
                
              
               
                 
                   25
                
                 
                   61.15
                
              
               
                 
                   26
                
                 
                   61.32
                
              
               
                 
                   27
                
                 
                   61.50
                
              
               
                 
                   28
                
                 
                   62.7
                
              
               
                 
                   29
                
                 
                   62.24
                
              
               
                 
                   30
                
                 
                   62.42
                
              
               
                 
                   IIII.
                   30
                
                 
                   62.42
                
              
               
                 
                   31
                
                 
                   62.
                   ●●
                
              
               
                 
                   32
                
                 
                   63.
                   ●6
                
              
               
                 
                   33
                
                 
                   63.33
                
              
               
                 
                   34
                
                 
                   63.51
                
              
               
                 
                   35
                
                 
                   64.8
                
              
               
                 
                   36
                
                 
                   64.26
                
              
               
                 
                   37
                
                 
                   64.43
                
              
               
                 
                   38
                
                 
                   65.1
                
              
               
                 
                   39
                
                 
                   65.18
                
              
               
                 
                   40
                
                 
                   65.36
                
              
               
                 
                   41
                
                 
                   65.53
                
              
               
                 
                   42
                
                 
                   66.11
                
              
               
                 
                   43
                
                 
                   66.28
                
              
               
                 
                   44
                
                 
                   66.46
                
              
               
                 
                   45
                
                 
                   67.4
                
              
               
                 
                   46
                
                 
                   67.22
                
              
               
                 
                   47
                
                 
                   67.39
                
              
               
                 
                   48
                
                 
                   67.57
                
              
               
                 
                   49
                
                 
                   68.14
                
              
               
                 
                   50
                
                 
                   68.32
                
              
               
                 
                   51
                
                 
                   68.50
                
              
               
                 
                   52
                
                 
                   69.8
                
              
               
                 
                   53
                
                 
                   69.26
                
              
               
                 
                   54
                
                 
                   69.44
                
              
               
                 
                   55
                
                 
                   70.2
                
              
               
                 
                   56
                
                 
                   70.20
                
              
               
                 
                   57
                
                 
                   70.38
                
              
               
                 
                   58
                
                 
                   70.56
                
              
               
                 
                   59
                
                 
                   71.14
                
              
               
                 
                   60
                
                 
                   71.32
                
              
               
                 
                   V.
                   00
                
                 
                   71.32
                
              
               
                 
                   1
                
                 
                   71.50
                
              
               
                 
                   2
                
                 
                   72.8
                
              
               
                 
                   3
                
                 
                   72.26
                
              
               
                 
                   4
                
                 
                   72.44
                
              
               
                 
                   5
                
                 
                   73.2
                
              
               
                 
                   6
                
                 
                   73.20
                
              
               
                 
                   7
                
                 
                   73.38
                
              
               
                 
                   8
                
                 
                   73.56
                
              
               
                 
                   9
                
                 
                   74.14
                
              
               
                 
                   10
                
                 
                   74.33
                
              
               
                 
                   11
                
                 
                   74.51
                
              
               
                 
                   12
                
                 
                   75.9
                
              
               
                 
                   13
                
                 
                   75.28
                
              
               
                 
                   14
                
                 
                   75.46
                
              
               
                 
                   15
                
                 
                   76.4
                
              
               
                 
                   16
                
                 
                   76.23
                
              
               
                 
                   17
                
                 
                   76.41
                
              
               
                 
                   18
                
                 
                   76.59
                
              
               
                 
                   19
                
                 
                   77.17
                
              
               
                 
                   20
                
                 
                   77.36
                
              
               
                 
                   21
                
                 
                   77.55
                
              
               
                 
                   22
                
                 
                   78.13
                
              
               
                 
                   23
                
                 
                   78.31
                
              
               
                 
                   24
                
                 
                   78.50
                
              
               
                 
                   25
                
                 
                   79.8
                
              
               
                 
                   26
                
                 
                   79.27
                
              
               
                 
                   27
                
                 
                   79.45
                
              
               
                 
                   28
                
                 
                   80.4
                
              
               
                 
                   29
                
                 
                   80.22
                
              
               
                 
                   30
                
                 
                   80.40
                
              
               
                 
                   V.
                   30
                
                 
                   80.40
                
              
               
                 
                   31
                
                 
                   80.59
                
              
               
                 
                   32
                
                 
                   81.18
                
              
               
                 
                   33
                
                 
                   81.37
                
              
               
                 
                   34
                
                 
                   81.55
                
              
               
                 
                   35
                
                 
                   82.14
                
              
               
                 
                   36
                
                 
                   82.32
                
              
               
                 
                   37
                
                 
                   82.51
                
              
               
                 
                   38
                
                 
                   83.9
                
              
               
                 
                   39
                
                 
                   83.28
                
              
               
                 
                   40
                
                 
                   83.47
                
              
               
                 
                   41
                
                 
                   84.5
                
              
               
                 
                   42
                
                 
                   84.24
                
              
               
                 
                   43
                
                 
                   84.43
                
              
               
                 
                   44
                
                 
                   85.2
                
              
               
                 
                   45
                
                 
                   85.20
                
              
               
                 
                   46
                
                 
                   85.38
                
              
               
                 
                   47
                
                 
                   85.57
                
              
               
                 
                   48
                
                 
                   86.16
                
              
               
                 
                   49
                
                 
                   86.34
                
              
               
                 
                   50
                
                 
                   86.53
                
              
               
                 
                   51
                
                 
                   87.11
                
              
               
                 
                   52
                
                 
                   87.31
                
              
               
                 
                   53
                
                 
                   87.50
                
              
               
                 
                   54
                
                 
                   88.9
                
              
               
                 
                   55
                
                 
                   88.28
                
              
               
                 
                   56
                
                 
                   88.47
                
              
               
                 
                   57
                
                 
                   89.6
                
              
               
                 
                   58
                
                 
                   89.25
                
              
               
                 
                   59
                
                 
                   89.44
                
              
               
                 
                   60
                
                 
                   90.00
                
              
            
             
             
               
                 A
                 Table
                 of
                 the
                 most
                 noted
                 Circumpolar-Stars
                 ,
                 or
                 those
                 that
                 set
                 not
                 in
                 the
                 Lat.
                 53°
                 .
                 20′
                 .
                 for
                 shewing
                 the
                 time
                 of
                 Night
                 by
                 a
                 Line
                 and
                 Plummet
                 ,
                 to
                 the
                 year
                 1680
                 ,
                 and
                 serves
                 for
                 20
                 years
                 to
                 come
                 .
              
               
                 
                   Mag
                
                 
                   Stars
                   Names
                   .
                
                 
                   Rt.
                   Ascension
                   in
                   Time
                   under
                   the
                   Pole-star
                
                 
                   Diff.
                   in
                   Time
                   betwixt
                   the
                   polestar
                   &
                   pole
                
                 
                   Azimuth
                   under
                   the
                   Pole-star
                
                 
                   Coast
                
              
               
                 
                    
                
                 
                   H
                
                 
                   H
                   ′
                   ″
                
                 
                   H
                   ′
                   ″
                
                 
                   °
                   ′
                   ″
                
                 
                    
                
              
               
                 
                   Ursa
                   Major
                
                 
                    
                
                 
                    
                
                 
                    
                
                 
                    
                
              
               
                 
                   2
                
                 
                   On
                   his
                   Back
                
                 
                   00.
                   03.
                   53
                
                 
                   0.
                   04.
                   26
                
                 
                   0.
                   37.
                   12
                
                 
                   E
                
              
               
                 
                   3
                
                 
                   Penult
                   in
                   Dracos
                   Tail
                
                 
                   00.
                   20.
                   17
                
                 
                   0.
                   03.
                   19
                
                 
                   0.
                   19.
                   12
                
                 
                   E
                
              
               
                 
                   2
                
                 
                   Cor
                   Caroli
                
                 
                   00.
                   36.
                   44
                
                 
                   0.
                   0.
                   05
                
                 
                   0.
                   00.
                   54
                
                 
                   E
                
              
               
                 
                   2
                
                 
                   His
                   Rump
                   Aliot
                
                 
                   00.
                   39.
                   25
                
                 
                   0.
                   0.
                   14
                
                 
                   0.
                   02.
                   06
                
                 
                   W
                
              
               
                 
                   2
                
                 
                   Middle
                   of
                   its
                   Tail
                
                 
                   01.
                   07.
                   02
                
                 
                   0.
                   03.
                   44
                
                 
                   0.
                   33.
                   00
                
                 
                   W
                
              
               
                 
                   2
                
                 
                   End
                   of
                   the
                   Tail
                
                 
                   01.
                   28.
                   56
                
                 
                   0.
                   05.
                   49
                
                 
                   0.
                   57.
                   00
                
                 
                   W
                
              
               
                 
                   2
                
                 
                   Last
                   but
                   two
                   in
                   Dracos
                   Tail
                
                 
                   01.
                   47.
                   40
                
                 
                   0.
                   10.
                   58
                
                 
                   1.
                   16.
                   48
                
                 
                   W
                
              
               
                 
                    
                
                 
                   Ursa
                   Minor
                
                 
                    
                
                 
                    
                
                 
                    
                
                 
                    
                
              
               
                 
                   2
                
                 
                   Higher
                   Guard
                
                 
                   02.
                   26.
                   05
                
                 
                   0.
                   24.
                   10
                
                 
                   1.
                   55.
                   48
                
                 
                   W
                
              
               
                 
                   3
                
                 
                   Lower
                   Guard
                
                 
                   02.
                   57.
                   15
                
                 
                   0.
                   26.
                   50
                
                 
                   2.
                   24.
                   36
                
                 
                   W
                
              
               
                 
                   Draco
                
                 
                    
                
                 
                    
                
                 
                    
                
              
               
                 
                   3
                
                 
                   27
                   in
                   Ticho's
                   Cat.
                   
                
                 
                   02.
                   59.
                   49
                
                 
                   0.
                   18.
                   01
                
                 
                   2.
                   27.
                   00
                
                 
                   W
                
              
               
                 
                   3
                
                 
                   26
                
                 
                   03.
                   35.
                   17
                
                 
                   0.
                   21.
                   04
                
                 
                   2.
                   55.
                   48
                
                 
                   W
                
              
               
                 
                   3
                
                 
                   25
                
                 
                   03.
                   54.
                   54
                
                 
                   0.
                   24.
                   39
                
                 
                   3.
                   10.
                   12
                
                 
                   W
                
              
               
                 
                   3
                
                 
                   20
                
                 
                   03.
                   58.
                   34
                
                 
                   0.
                   30.
                   43
                
                 
                   3.
                   12.
                   36
                
                 
                   W
                
              
               
                 
                   3
                
                 
                   24
                
                 
                   04.
                   36.
                   43
                
                 
                   0.
                   30.
                   49
                
                 
                   3.
                   34.
                   48
                
                 
                   W
                
              
               
                 
                   3
                
                 
                   First
                   in
                   the
                   Head
                
                 
                   04.
                   59.
                   30
                
                 
                   0.
                   23.
                   42
                
                 
                   3.
                   45.
                   00
                
                 
                   W
                
              
               
                 
                   2
                
                 
                   Bright
                   in
                   the
                   Head
                
                 
                   05.
                   25.
                   01
                
                 
                   0.
                   24.
                   11
                
                 
                   3.
                   53.
                   24
                
                 
                   W
                
              
               
                 
                   1
                
                 
                   Lucida
                   Lyrae
                
                 
                   06.
                   05.
                   34
                
                 
                   0.
                   20.
                   30
                
                 
                   4.
                   00.
                   36
                
                 
                   W
                
              
               
               
                 
                   3
                
                 
                   N.
                   in
                   the
                   upper
                   turn
                
                 
                   06.
                   37.
                   04
                
                 
                   0.
                   35.
                   44
                
                 
                   4.
                   01.
                   12
                
                 
                   W
                
              
               
                 
                   3
                
                 
                   S.
                   in
                   the
                   upper
                   turn
                
                 
                   07.
                   11.
                   22
                
                 
                   0.
                   37.
                   56
                
                 
                   3.
                   56.
                   24
                
                 
                   W
                
              
               
                 
                    
                
                 
                   Cygnus
                
                 
                    
                
                 
                    
                
                 
                    
                
                 
                    
                
              
               
                 
                   3
                
                 
                   Vpper
                   Wing
                
                 
                   07.
                   13.
                   26
                
                 
                   0.
                   21.
                   49
                
                 
                   3.
                   56.
                   24
                
                 
                   W
                
              
               
                 
                   3
                
                 
                   Her
                   Brest
                
                 
                   07.
                   51.
                   26
                
                 
                   0.
                   19.
                   20
                
                 
                   3.
                   45.
                   00
                
                 
                   W
                
              
               
                 
                   4
                
                 
                   N.
                   Cepheus
                   R.
                   Arm
                
                 
                   07.
                   55.
                   07
                
                 
                   0.
                   28.
                   46
                
                 
                   3.
                   44.
                   00
                
                 
                   W
                
              
               
                 
                   2
                
                 
                   Swans
                   Tail
                
                 
                   08.
                   10.
                   30
                
                 
                   0.
                   19.
                   59
                
                 
                   3.
                   37.
                   12
                
                 
                   W
                
              
               
                 
                    
                
                 
                   Cephus
                
                 
                    
                
                 
                    
                
                 
                    
                
              
               
                 
                   4
                
                 
                   S.
                   on
                   his
                   R.
                   Arm
                
                 
                   08.
                   11.
                   32
                
                 
                   0.
                   26.
                   57
                
                 
                   3.
                   36.
                   36
                
                 
                   W
                
              
               
                 
                   2
                
                 
                   Right
                   shoulder
                
                 
                   08.
                   45.
                   35
                
                 
                   0.
                   25.
                   02
                
                 
                   3.
                   18.
                   36
                
                 
                   W
                
              
               
                 
                   3
                
                 
                   His
                   Girdle
                
                 
                   08.
                   53.
                   30
                
                 
                   0.
                   30.
                   44
                
                 
                   3.
                   13.
                   48
                
                 
                   W
                
              
               
                 
                   4
                
                 
                   N.
                   in
                   his
                   Cap
                
                 
                   09.
                   41.
                   52
                
                 
                   0.
                   18.
                   16
                
                 
                   2.
                   40.
                   48
                
                 
                   W
                
              
               
                 
                   4
                
                 
                   Before
                   his
                   Head
                
                 
                   10.
                   09.
                   17
                
                 
                   0.
                   15.
                   56
                
                 
                   2.
                   19.
                   12
                
                 
                   W
                
              
               
                 
                   4
                
                 
                   Left
                   shoulder
                
                 
                   10.
                   20.
                   44
                
                 
                   0.
                   17.
                   48
                
                 
                   2.
                   09.
                   36
                
                 
                   W
                
              
               
                 
                   3
                
                 
                   His
                   Knee
                
                 
                   11.
                   10.
                   00
                
                 
                   0.
                   17.
                   59
                
                 
                   1.
                   25.
                   48
                
                 
                   W
                
              
               
                 
                    
                
                 
                   Cassiopea
                
                 
                    
                
                 
                    
                
                 
                    
                
              
               
                 
                   3
                
                 
                   Her
                   Chair
                
                 
                   11.
                   46.
                   07
                
                 
                   0.
                   05.
                   54
                
                 
                   0.
                   51.
                   00
                
                 
                   W
                
              
               
                 
                   4
                
                 
                   Seat
                   of
                   the
                   Chair
                
                 
                   12.
                   11.
                   48
                
                 
                   0.
                   03.
                   14
                
                 
                   0.
                   25.
                   48
                
                 
                   W
                
              
               
                 
                   4
                
                 
                   Head
                
                 
                   12.
                   17.
                   20
                
                 
                   0.
                   02.
                   07
                
                 
                   0.
                   20.
                   24
                
                 
                   W
                
              
               
                 
                   3
                
                 
                   Brest
                
                 
                   12.
                   20.
                   48
                
                 
                   0.
                   01.
                   50
                
                 
                   0.
                   16.
                   48
                
                 
                   W
                
              
               
                 
                   4
                
                 
                   Girdle
                
                 
                   12.
                   28.
                   46
                
                 
                   0.
                   00.
                   59
                
                 
                   0.
                   09.
                   00
                
                 
                   W
                
              
               
                 
                   3
                
                 
                   H●pp
                
                 
                   12.
                   37.
                   50
                
                 
                   0.
                   00.
                   02
                
                 
                   0.
                   00.
                   10
                
                 
                   W
                
              
               
                 
                   3
                
                 
                   Knee
                
                 
                   13.
                   08.
                   45
                
                 
                   0.
                   03.
                   41
                
                 
                   0.
                   31.
                   12
                
                 
                   E
                
              
               
                 
                   3
                
                 
                   Legg
                
                 
                   13.
                   39.
                   38
                
                 
                   0.
                   07.
                   53
                
                 
                   1.
                   01.
                   12
                
                 
                   E
                
              
               
                 
                   2
                
                 
                   Foot
                   of
                   Androm
                   .
                
                 
                   13.
                   50.
                   37
                
                 
                   0.
                   06.
                   19
                
                 
                   1.
                   12.
                   00
                
                 
                   E
                
              
               
               
                 
                    
                
                 
                   Perseus
                
                 
                   H
                   ′
                   ″
                
                 
                   H
                   ′
                   ″
                
                 
                   °
                   ′
                   ″
                
                 
                    
                
              
               
                 
                   4
                
                 
                   Left
                   shoulder
                
                 
                   14.
                   33.
                   32
                
                 
                   0.
                   10.
                   52
                
                 
                   1.
                   51.
                   36
                
                 
                   E
                
              
               
                 
                   3
                
                 
                   Bend
                   of
                   his
                   side
                
                 
                   14.
                   43.
                   40
                
                 
                   0.
                   11.
                   03
                
                 
                   2.
                   00.
                   36
                
                 
                   E
                
              
               
                 
                   3
                
                 
                   Right
                   shoulder
                
                 
                   14.
                   55.
                   31
                
                 
                   0.
                   13.
                   42
                
                 
                   2.
                   10.
                   48
                
                 
                   E
                
              
               
                 
                   3
                
                 
                   Medusa's
                   Head
                
                 
                   14.
                   59.
                   14
                
                 
                   0.
                   11.
                   45
                
                 
                   2.
                   13.
                   48
                
                 
                   E
                
              
               
                 
                    
                
                 
                    
                
                 
                    
                
                 
                    
                
                 
                    
                
                 
                   E
                
              
               
                 
                   2
                
                 
                   Bright
                   *
                   in
                   his
                   side
                
                 
                   15.
                   14.
                   59
                
                 
                   0.
                   14.
                   29
                
                 
                   2.
                   26.
                   24
                
                 
                   E
                
              
               
                 
                   4
                
                 
                   Left
                   Thigh
                
                 
                   15.
                   37.
                   56
                
                 
                   0.
                   14.
                   35
                
                 
                   2.
                   44.
                   24
                
                 
                   E
                
              
               
                 
                   3
                
                 
                   Left
                   Knee
                
                 
                   15.
                   51.
                   39
                
                 
                   0.
                   14.
                   57
                
                 
                   2.
                   54.
                   36
                
                 
                   E
                
              
               
                 
                   4
                
                 
                   Before
                   his
                   Right
                   Knee
                
                 
                   16.
                   01.
                   08
                
                 
                   0.
                   18.
                   05
                
                 
                   3.
                   00.
                   36
                
                 
                   E
                
              
               
                 
                   4
                
                 
                   Middle
                   of
                   his
                   Right
                   Knee
                
                 
                   16.
                   09.
                   47
                
                 
                   0.
                   18.
                   06
                
                 
                   3.
                   06.
                   36
                
                 
                   E
                
              
               
                 
                    
                
                 
                   Auriga
                
                 
                    
                
                 
                    
                
                 
                    
                
                 
                    
                
              
               
                 
                   4
                
                 
                   Left
                   Elbow
                
                 
                   16.
                   58.
                   15
                
                 
                   0.
                   19.
                   27
                
                 
                   3.
                   33.
                   36
                
                 
                   E
                
              
               
                 
                   1
                
                 
                   Capella
                
                 
                   17.
                   13.
                   55
                
                 
                   0.
                   20.
                   49
                
                 
                   3.
                   40.
                   48
                
                 
                   E
                
              
               
                 
                   2
                
                 
                   Right
                   shoulder
                
                 
                   17.
                   58.
                   07
                
                 
                   0.
                   21.
                   55
                
                 
                   3.
                   55.
                   12
                
                 
                   E
                
              
               
                 
                    
                
                 
                   Ursa
                   Major
                
                 
                    
                
                 
                    
                
                 
                    
                
                 
                    
                
              
               
                 
                   4
                
                 
                   His
                   Lipp
                
                 
                   20.
                   31.
                   52
                
                 
                   0.
                   27.
                   38
                
                 
                   3.
                   37.
                   48
                
                 
                   E
                
              
               
                 
                   3
                
                 
                   N.
                   in
                   his
                   Right
                   Foot
                
                 
                   20.
                   50.
                   49
                
                 
                   0.
                   20.
                   53
                
                 
                   3.
                   28.
                   12
                
                 
                   E
                
              
               
                 
                   3
                
                 
                   S.
                   in
                   the
                   same
                
                 
                   20.
                   55.
                   23
                
                 
                   0.
                   20.
                   13
                
                 
                   3.
                   21.
                   00
                
                 
                   E
                
              
               
                 
                   3
                
                 
                   Left
                   Knee
                
                 
                   21.
                   24.
                   15
                
                 
                   0.
                   19.
                   57
                
                 
                   3.
                   07.
                   12
                
                 
                   E
                
              
               
                 
                   4
                
                 
                   Higher
                   in
                   his
                   hind
                   Foot
                
                 
                   22.
                   11.
                   32
                
                 
                   0.
                   13.
                   56
                
                 
                   2.
                   30.
                   36
                
                 
                   E
                
              
               
                 
                   2
                
                 
                   Lower
                   Leader
                   in
                   □
                
                 
                   22.
                   54.
                   50
                
                 
                   0.
                   12.
                   57
                
                 
                   1.
                   50.
                   24
                
                 
                   E
                
              
               
                 
                   2
                
                 
                   Higher
                   Leader
                
                 
                   22.
                   57.
                   59
                
                 
                   0.
                   14.
                   20
                
                 
                   1.
                   47.
                   24
                
                 
                   E
                
              
               
                 
                   3
                
                 
                   Last
                   in
                   Draco's
                   Tail
                
                 
                   23.
                   24.
                   13
                
                 
                   0.
                   13.
                   36
                
                 
                   1.
                   20.
                   24
                
                 
                   E
                
              
               
                 
                   2
                
                 
                   Bears
                   Left
                   Thigh
                
                 
                   23.
                   43.
                   36
                
                 
                   0.
                   06.
                   38
                
                 
                   0.
                   59.
                   24
                
                 
                   E
                
              
            
          
           
             FINIS
             .