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    Re: Measuring Dip in the 18th Century
    From: Gary LaPook
    Date: 2013 Dec 26, 10:27 -0800
    Edward Wright was a mathamatition  of the highest order, he was the one that actually developed the table of meridinial parts which allowed for the drafting of accurate charts on Mercator's (up til that time only theroretical) projection. It is a delightful book, he is fun to read, it feels like you are talking to a modern friend abut navigation. There is lots of other in his book. I've posted about him in the past starting with this one:

    http://fer3.com/arc/m2.aspx/Certaine-Errors-Navigation-Corrected-LaPook-sep-2007-g3247

    with much further discussion continuing for several months, just go back to the archives for the last few months of 2007.

    http://fer3.com/arc/m2.aspx/Certaine-Errors-Navigation-Corrected-LaPook-dec-2007-g4281

    http://fer3.com/arc/m2.aspx/Wrights-1599-Chart-showingScillies-LaPook-nov-2007-g4165

    I now have a complete copy of "Certaine Errors In Navigation" in PDF
    > format and can email it off list to anyone who might want a copy. It
    > is a delightful book to read, Mr. Wright sounds like a thoroughly
    > modern man.

    I recommend it.

    gl






    From: Brad Morris <bradley.r.morris@gmail.com>
    To: garylapook@pacbell.net
    Sent: Thursday, December 26, 2013 8:44 AM
    Subject: [NavList] Re: Measuring Dip in the 18th Century


    Thanks for that Gary.  1599!  Wow.  That's another 100 years on the Mariner's Compass Rectified tables of 1694.
    I suspect that there are navigational dip tables for the earliest of instruments that measure altitude vis the horizon.  So for the cross staff at sea, there must have been a dip table. 
    I wonder, what is the earliest published dip table? 
    Brad

    On Dec 26, 2013 2:53 AM, "Gary LaPook" <garylapook---.net> wrote:

    Edward Wright's book included a dip table  that was accurate up to a 20 foot height of eye. Above that the dip corrections are about one minute to great. See attached.

    gl



    From: Brad Morris <bradley.r.morris---.com>
    To: garylapook---.net
    Sent: Monday, December 23, 2013 1:44 PM
    Subject: [NavList] Re: Measuring Dip in the 18th Century


    Hi Frank
    Dip tables didn't just spring into being, 100% accurate.  There had to be precursors. 
    I agree with you that the earlier dip tables were dependent on geometric dip and further that it depended upon an accurate assessment of the size of the sphere.  Inaccuracies in size would indeed mask refraction. 
    In checking my copy of Atkinson "Epitome of Navigation" 1753 edition, I find references to how to observe and reduce an observation to a latitude.  There is no dip table nor reference to one.
    My 1753 edition is a reprint of the 1706 first edition.  It directs that an altitude be taken with a quadrant, Hadley's quadrant, a cross-staff, a fore-staff or Davis quadrant.  Atkinson directs the reader to "The Mariner's Compass, Rectified", for details of those instruments. 
    Wakely wrote the "Mariners Compass Rectified" in 1694.  In it, he admonishes the navigator to correct observations by dip and refraction and does offer both tables, attached.  It is unclear which year is offered by Google.
    In practice, the navigator is to subtract both dip and refraction from the observed altitude.  http://books.google.com/books?id=lYfS6E_3JrEC&pg=PA21&lpg=PA21&dq=mariners+compass+rectified+dip&source=bl&ots=JCoOhrRjJz&sig=3tQL8yL61Ma7KizVIMhRst1aElo&hl=en&sa=X&ei=j6i4UoaPJKa_sQSj4IK4CQ&ved=0CCsQ6AEwAQ
    Brad

    On Dec 23, 2013 3:13 PM, "Brad Morris" <bradley.r.morris---.com> wrote:

    Hi Bruce
    I found an interesting reference to the dip table
    http://books.google.com/books?id=nPw_AAAAYAAJ&pg=PA236&lpg=PA236&ots=yEL5ZIF20C&focus=viewport&dq=historical+%22dip+of+the+horizon%22&output=html_text
    Synopsis:  Before 1635, Wright thinks that altitudes should be corrected for the dip of the horizon, but cannot do so without an accurate measure of the earth.  In 1635, Mr Norwood finds an accurate measure and in 1637, publishes the "Seaman's Practice". 
    I could not find the "Seaman's Practice" online, but reprints are available.  Perhaps, therefore, some NavList'r might have a copy and check to see if it contains a dip table.
    This would push back the dip table origin at least 100 years from your assessment. 
    Brad
    On Dec 22, 2013 10:15 AM, "Bruce J. Pennino" <bpennino.ce---.net> wrote:

    Alexandre:
     
    I'm going to try to simply answer your comment  without causing  any more "brain ache" on this topic. Surveyors, navigators, astronomers especially, and even mathematicians.....ouch....(just kidding and trying to add a little levity to a weary topic)  realized there are two major issues to dip.  First, the relatively simple geometric issue due to a person viewing the horizon created by a so-called round ball , earth.  A  true tangent  was needed at the person's location to do the CN triangle math. There are second-order issues such as the  earth is an oblate spheroid, etc, but forget about those. Once a radius has been selected, with a relatively simple trigonometric right triangle geometry setup, one (even I could do it) will calculate that the dip coefficient due to geometry only is about 1.06-1.07.  REPEAT  geometric dip only:  dip (minutes of arc) = 1.07 sqrt HoE ft.  
     
    It has been known  "almost forever"  that this value 1.07 is too large due to the second issue, the bending (refraction)of light from the horizon . Early surveyors who did a lot of celestial measurements to determine true north etc estimated that the 1.07  value for the dip coefficient was about  5-10 % too large because of light refraction. I've found this in my oldest surveying book which goes back to the 1880s, and can also be found in books dated the 1950s-60s.Corrections are given in the textbooks, but usually without any "backup".
     
    I've done some research and in the very earliest almanacs there is a dip table which includes the total dip.  I've not been able to find the exact British astronomer who did it, but it was about or just before Maskelyne. He (they) developed the modern dip table that has not been changed significantly since the mid to late 1700s. In the present nautical almanac, dip (which includes geometry and light bending) is given as 0.97 sqrt Height of Eye(ft).  The refraction of light to the celestial body is in the other NA tables.   
     
    The coefficient 0.97 has worked marvelously well for over 200 years and is certainly good enough for all practical purposes, even if there is some "funny business" going on at the horizon. From shore, I've made dip measurements with my theodolite and concluded that using  0.97 as an average value may be slightly  too high, but I have only about 40 data points. I'm in the process of tabulating all of my data and writing notes. I'll eventually  let NavList have my data and notes.  I tend to agree with the work done by  Peters (he took over 3000 measurements offshore) that a better average total dip coefficient might be about 0.89. But the practical difference of a couple of minutes is so small that it is only of interest to those aiming for the highest average accuracy over a number of observations. And unfortunately, of interest to  those of us who have chosen to investigate (gotten hooked) onto  this oddity?!  
     
    A good day to all,  Merry Christmas and Happy ,Healthy New Year.

    Bruce
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
    ----- Original Message -----
    Sent: Saturday, December 21, 2013 9:48 PM
    Subject: [NavList] Re: Measuring Dip in the 18th Century


    For the dip,
    you don't have to take any measurements,
    Dip (under normal conditions)
    it is a simple geometric problem.
    Such dip tables could (in principle)
    be made by any mathematician in 2-nd century BC.
    
    Refraction is another matter...
    
    Alex.
    
    > I'm not so sure how tricky it was to make those measurements because they
    > sure got accurate results. I am absolutely blown away by the accuracy of
    > the refraction and the dip tables in the 1799 edition of the New Practical
    > Navigator, edited by Bowditch. I compared a sample of the values in the
    > 1799 tables with the modern tables and only rarely did the discrepancy
    > exceed six seconds of arc, 0.1'. See attachments.
    >
    > gl
    >
    >
    >
    >
    > ________________________________
    >  From: Marcel Tschudin 
    > To: garylapook---.net
    > Sent: Friday, December 20, 2013 1:24 AM
    > Subject: [NavList] Measuring Dip in the 18th Century
    >
    >
    >
    >
    > ________________________________
    > Andy Young draw my attention to the following publication:
    >
    > Huddart Joseph (1797): Observations on Horizontal Refractions Which Affect
    > the Appearance of Terrestrial Objects, and the Dip, or Depression of the
    > Horizon of the Sea. Philosophical Transactions of the Royal Society of
    > London, Vol. 87, (1797), pp. 29-42
    >
    > a pdf copy of it can be obtained from JSTOR
    > http://www.jstor..org/betasearch?Query=Huddart+joseph&fq=py:[1796+TO+1798]
    >
    > Andy wrote: "Huddart managed to measure the altitudes of the Sun's limbs
    > above both the northern and southern horizons around noon, interpolating
    > to find the apparent altitudes exactly at culmination. This was evidently
    > a difficult and tricky measurement to carry out, especially with the
    > rather primitive instrumentation available to him; he comments that the
    > instrumental limitations prevent it from being done except in a restricted
    > zone of latitude, and that it can't be done near the equator because of
    > the rapid change in azimuth as the Sun passes near the zenith.
    > Nevertheless, he apparently was able to get useful information from this
    > work."
    >
    > He thought that this publication may eventually also be of interest to
    > some members of NavList.
    >
    > Marcel
    >
    > : http://fer3.com/arc/m2.aspx?i=125858
    > Attached File: http://fer3.com/arc/img/125869.1799 refraction and dip
    > tables.jpg
    >
    > Attached File: http://fer3.com/arc/img/125869.img_0002.jpg
    >
    > Attached File: http://fer3.com/arc/img/125869.img_0001.jpg
    >
    >
    > : http://fer3.com/arc/m2.aspx?i=125869
    >
    >
    >
    >
    
    
    Attached File:

    (img/125898.mcr-refraction.jpg: Open and save)

    Attached File:

    (img/125898.mcr-dip.jpg: Open and save)



    Attached File:

    (img/125922.certaine_page_01.jpg: Open and save)

    Attached File:

    (img/125922.dip table.jpg: Open and save)

    : http://fer3.com/arc/m2.aspx?i=125925


       
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