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    Re: I couldn't resist!
    From: John Huth
    Date: 2012 Oct 20, 08:06 -0400
    No, it's possible to factor in the leap days in a declination table.   I think that Regiomontanus' ephemerides predicted out 50 years or so.   

    The Julian calendar had leap years, the Gregorian calendar requires a correction after 400 years.   

    The earth's orbit is quite stable, and as long as you have the leap days, you can do a decent job to a fraction of a degree (say 1/3 of a degree).

    The day/year disagreement is so close to 1/4th of a day, it's pretty reliable at the accuracy you'd need for a quadrant or astrolabe, certainly - probably even a cross staff for solar declinations.   

    The breakdown appears when you look at planets, where Mars, for example, was a big problem, as Kepler and Brahe found out.

    On Sat, Oct 20, 2012 at 12:58 AM, Lu Abel <luabel@ymail.com> wrote:
    That's realignment from Julian calendar (which had a leap year every four years) to the Gregorian calendar that has a leap year every four years except on centennial (xx00) years except when the latter are multiples of four hundred (which is why we had a leap year in 2000).  

    As another post suggested one can construct fairly accurate declination tables for the next year or three, it's over longer terms that one needs increasingly precise knowledge of all the forces at work in order to construct declination tables years in the future.  So I would suggest that if one can construct a reasonably accurate projection 400 days from now it's irrelevant if next February has 28 or 29 days, as long as my math and my calendar agree.

    From: Brad Morris <bradley.r.morris@gmail.com>
    To: NavList@fer3.com
    Sent: Friday, October 19, 2012 9:19 PM

    Subject: [NavList] Re: I couldn't resist!

    Okay, I accept that. 
    Does the declination table of of the sun, as published, show the leap year?  Columbus' journey predates the re-alignment of the calendar.
    On Oct 19, 2012 11:48 PM, "Luther Abel" <luabel@ymail.com> wrote:


    I always thought leap years were well known from Roman (or even Greek) times onwards. 

    On Oct 19, 2012, at 2:00 PM, Brad Morris <bradley.r.morris@gmail.com> wrote:

    Hi Lu
    Next we must consider the measurement as Columbus may have taken it at sea.  An astrolabe depends upon a pendulus mass to define the vertical.  A pendulum at sea would be horrible (for time keeping or altitude measurements).  The deck is pitching, rolling and yawing.  The instrument is held manually, depending on the pendulum for vertical.  Consequently, the navigator would be forced to say "Its between this and that minima and maxima, so I think the observational measurement is X"
    Of course, stiction and friction of the members come in to play.  What if your pendulum is just off vertical, but the friction keeps it in place?  That results in a non-reproducible measurement.
    Mind, this is on an instrument whose scale may not be accurate in the first place.
    So Columbus (or Dias) takes his "guesstimate" of the altitude and compares that to his declination table.  But to which date?  The table was created without leap years!  So as time goes by, the table entry slowly shifts away from true result.  It took years to generate the table, and its in error right from the very start! (See my comments about the table generation issues).
    Best Regards

    On Oct 19, 2012 4:48 PM, "Brad Morris" <bradley.r.morris@gmail.com> wrote:
    In my current employment, I use a device known as an Ultradex for metrology and calibration.  The device is mechanically accurate to 1/20th of 1 arc-second and reproducibly is 1/5th of one arc second.  An arc second is 1/3600 of a degree.  The one I use is no longer state of the art, there are better.  The type I use is so accurate, it was used for bomb sight calibration by the US military.
    Discussion of angular construction and claims of estimated accuracy need be taken with a degree of skepticism.  To what known standard can you trace that?  What methodology did you use in that determination?
    I use NMTBA standard methods of the determination of accuracy and repeatability, three sigma, using NIST trace-able tools that are within calibration and with recent certifications.  I think I may know a little about angular measurement!  
    Why bring this up?  There is a perception that angular construction in Columbus' day can use methods that we know today.  Just as I assumed that he sailed latitude lines (error), assumptions about the accuracy and repeatability of the meridian measurement used to create the declination table and the astrolabe's scale are just that, broad assumptions.
    On Oct 19, 2012 4:24 PM, "Lu Abel" <luabel@ymail.com> wrote:
    And let's not forget all the "knowledge" handed down by the Church, like the mythical kingdom in Africa of Presbyter John.  I'm not surprised that some of that "knowledge" included the earthly paradise he describes.

    From: Apache Runner <apacherunner@gmail.com>
    To: NavList@fer3.com
    Sent: Friday, October 19, 2012 12:37 PM
    Subject: [NavList] Re: I couldn't resist!

    Pretty, amazing huh?   One bad shot of Polaris and he thinks the world is shaped like a pear. 

    To be fair, there are other pieces of evidence that he was slowly losing his mind around that time.   

    On the other hand, there's the amazing forecast of a hurricane hitting Hispanola.   It's like he drifted between  some high functioning state and insanity. 

    On Fri, Oct 19, 2012 at 2:58 PM, G Becker <george@gwbeckerpls.com> wrote:
    I was hesitant to post this, but here is it. The following is a quote from a paper on the theory of a Roman World Survey in 44BC. ;/
    "A letter written by Columbus to the Spanish Royal Family during his third voyage in the Caribbean revealed his surprising belief: "I have always maintained that the world-land and water-was a sphere, but now I have seen so many irregularities that I am induced to form another idea of the World. Land that Their Majesties have discovered (America) are part of a sphere, but on the other hand, the earth is shaped like a pear to whose summit is the Earthly Paradise from which descend the four rivers, as written in the holy scriptures..."" (4) Columbus had come to this conclusion after having arrived at the mouth of the Rio Orinoco River
    (4) L. Lavonto "Los primeros italianos en America" Caracas. 2001
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