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    Re: Measuring Dip in the 18th Century
    From: Alexandre Eremenko
    Date: 2013 Dec 26, 22:01 -0500

    Brad,
    
    > So who did care, first?  Who published the first dip table?
    
    I can only guess that this could be some Purtuguese from the circle
    of Henry the Navigator.  (Infante Dom Henrique de Avis).
    He created the first research facility for naval science, Vila do Infante.
    This was before the
    first Portuguese travels around Africa.
    
    Unfortunately I have never seen any serious discussion of navigation of
    that time, and I suppose all literature must be in Portuguese.
    (Most English books on history of navigation even do not mention those
    Portuguese).
    
    On the other hand, I think Frank is right, and dip was a pure theoretic
    problem before they started to use precision instruments.
    So it is quite possible that dip tables were not published before XVIII
    century.
    
    
    Alex.
    
       It couldn't
    > possibly be Wright in 1599, as he credits Nunes.  As the Portuguese were
    > the earliest European navigators, I expect that the earliest dip tables
    > are
    > theirs.  But this is just a guess.
    >
    > The land based astronomers would not have cared.  Their altitudes were not
    > referenced to the horizon.  It needs a sea based navigator to require a
    > dip
    > table, as they would need to reference the altitude to the horizon.
    >
    > -++++++++-
    >
    > For Bruce
    >
    > Each of the ancient navigation texts had many, many pressings.  To clarify
    > the dates I have gathered so far.
    >
    > Atkinson; Epitome of Navigation 1706
    > Wakely; Mariners Compass Rectified 1694
    > Norwood; Seaman's Practice 1637
    > Wright; Certaine Errors; 1599
    >
    > For example, my pressing of Atkinson was published in 1753.  How many
    > pressings intervened is unknown to me. It is a survivor, with both boards
    > still present and barely attached!
    >
    > Brad
    >
    > ________________________________
    >
    > Frank wrote:
    >
    >> This
    >> is an example of something that mathematicians and other "natural
    >> philosophers" understood from a very early era (try Ptolemy)
    >
    > Certainly Ptolemy would understand everything about dip, but he did not
    > really care. He had more important things to care about (parallax,
    > refraction), and never used natural horizon. The accuracy of observations
    > at that time and instruments used is a hotly discussed question,
    > but I suppose he was happy with 1'.
    > Unfortunately nothing is known about how they divided the arcs of their
    > instruments.
    >
    > Alex.
    >
    >>
    >> The dip table from 1599 that Gary posted is easy enough to
    >> reverse-engineer. You can calculate nearly matching values using the
    >> simple formula dip=1.10*sqrt(h) with dip in minutes and h in feet (with
    >> that constant the dip calculated for 90 feet altitude rounds to 10
    >> instead
    >> of the listed 11 but the difference is only half a minute of arc in any
    >> case). Since the mathematical details of refraction were unknown, we can
    >> safely conclude that this was a geometric dip table for a slightly
    >> over-estimated radius of the Earth.
    >>
    >> -FER
    >>
    >> ----------------------------------------------------------------
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    >>
    >> : http://fer3.com/arc/m2.aspx?i=125928
    >>
    >>
    >>
    >>
    >
    > : http://fer3.com/arc/m2.aspx?i=125931
    >
    >
    > : http://fer3.com/arc/m2.aspx?i=125932
    >
    >
    >
    >
    
    

       
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