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    Re: Certaine Errors in Navigation Corrected
    From: Gary LaPook
    Date: 2007 Dec 10, 11:44 -0800

    Gary writes:
    It is interesting to compare Wright's almanac with the modern one. The
    sun's declination today, December 7, 2007 at noon in England is 22�
    35.7' south. If we were using Wright's almanac for the same day, which
    would be November 27th in the column for 1607 (found on page 118), we
    get his value of 22� 38' south which is close enough for government
    work. In comparing Wright's almanac with the modern one you must
    subtract 10 days from his tabulation since England did not change to
    the Gregorian calendar until September 25, 1752 while most Catholic
    countries changed on October 5, 1582. (This caused me much confusion
    when I first looked at his almanac almost thirty years ago since I
    assumed that Wright was also using the Gregorian calendar since he
    published 17 years after that calendar went into effect.)
    Also, comparing his value for the declination of the sun at the summer
    solstice of 1597, he gives it as 23� 30' north while a modern almanac
    program gives it as 23� 29.6' north, a difference within the limit of
    precision of Wright's table!
    Remember that the letter "s" was printed in 1599 with a character that
    looks like the modern letter "f" and that the letters "u" and "v" are
    often interchanged.
    On Dec 8, 5:14 am, RS Peterson  wrote:
    > I would like a copy.  Thanks.  -- Bob
    > glap...---.net wrote:
    > >Gary LaPook writes:
    > >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.
    > >gl
    > >On Dec 4, 8:03 pm, "Gary J. LaPook"  wrote:
    > >>Gary LaPook adds:
    > >>What I meant by: " I suspect that the method was just forgotten in the
    > >>mists of time" was that in Wright's time there was no reason to publish
    > >>a method to calculate altitude as that need did not develop until St.
    > >>Hilaire invented the "new navigation" almost 300 years later. After St.
    > >>Hilaire,  many methods were tried in an effort to  reduce the work
    > >>needed to calculate altitude including different mechanical devices such
    > >>as the Bygrave slide rule (and many more),  "short tables" and
    > >>culminating in the precomputed altitude tables such as H.O 214, H.O.
    > >>218, H.O. 229 and H.O 249. I suspect that nobody thought to look back at
    > >>a book that had been published in the dim and distant past, 1599, and
    > >>that didn't even include a method for calculating altitude, only great
    > >>circle distance.
    > >>Gary LaPook wrote:
    > >>>Gary LaPook writes:
    > >>>You can look at his explanation yourself and you will see that is no
    > >>>allowance for an elliptical earth so it uses the round earth
    > >>>assumption used throughout celestial navigation.
    > >>>I would think his method could produce better accuracy with either
    > >>>modern printing of the form to use, larger scale or precision
    > >>>machining of a mechanical device to do the computation. One tenth
    > >>>minute precision is not needed for flight navigation and many methods
    > >>>and devices were used that produced accuracy that was attainable by
    > >>>the Wright method. I suspect that the method was just forgotten in the
    > >>>mists of time.
    > >>>gl
    > >>>Fred Hebard wrote:
    > >>>>Some naive comments/questions:
    > >>>>First, how much of the discrepency between Wright's calculated
    > >>>>distance and the modern digital calculator is due to the elliptical
    > >>>>shape of the earth, or were you using the same assumptions?
    > >>>>Second, one could guess that a graphical method would be good to 3
    > >>>>decimal places (about what you got for question 1).  Five-decimal-
    > >>>>place precision is needed to get 0.1 arcminute accuracy, more or
    > >>>>less, so a graphical method would only be good to 10 arcminutes, more
    > >>>>or less.  Perhaps it's the lack of precision that led to Wright's
    > >>>>method not being adapted to standard sight reduction.  Certainly back
    > >>>>in his time, simple reduction of noon sights for altitude was easy
    > >>>>enough.  By the period when time sights for longitude became
    > >>>>prevalent, and especially by the point when intercept methods took
    > >>>>over, 3 decimal places wasn't close enough anymore.
    > >>>>Fred
    > >>>>On Dec 4, 2007, at 4:18 AM, Gary J. LaPook wrote:
    > >>>>>Gary J. LaPook wrote:
    > >>>>>It is not surprising that nobody ever noticed this before
    > >>>>>(considering that Wright published in 1599 almost 300 years prior
    > >>>>>to Marc St. Hilaire) that Wright's method of calculating the great
    > >>>>>circle distance on the earth using only a strait edge and a compass
    > >>>>>could just as easily be used to calculate the altitude of a
    > >>>>>celestial body. The great circle distance is simply 60 NM times the
    > >>>>>number of degrees of the great circle between two points and this
    > >>>>>is exactly the same as the zenith distance to a body having the
    > >>>>>geographical position represented by the second point.     The
    > >>>>>formula is 90� minus zenith distance equals altitude.
    > >>>>>Wright's example of calculation of the great circle distance
    > >>>>>between London and Jerusalem resulted in his calculated distance of
    > >>>>>2325 NM and a modern digital calculator comes up with 2316.8 NM a
    > >>>>>difference of  only 8.2 NM or minutes of zenith distance or of
    > >>>>>computed altitude for those coordinates! Using his method Wright
    > >>>>>could compute altitudes to a precision of 8.2'. It is surprising in
    > >>>>>light of the many devices invented later in an attempt to find a
    > >>>>>mechanical method for this calculation that none (that I am aware
    > >>>>>of) attempted to use Wright's method, a method that would seem
    > >>>>>easily adapted to a mechanical device and that could provide much
    > >>>>>greater accuracy using a larger scale and precise machining of the
    > >>>>>parts.
    > >>>>>I would really like it if someone could explain why Wright's method
    > >>>>>works since I have not been able to find such an explanation
    > >>>>>anywhere. I am attaching pages 45-52 of "Certaine Errors" in which
    > >>>>>he lays out his method. I am also including the errata sheet
    > >>>>>showing that the corrections of typos I identified in my previous
    > >>>>>posts were correct.
    > >>>>>gl
    > >>>>>
    > >>>>>
    > --
    > Robert S. Peterson
    > Great Lakes Compass
    > 31 N Alfred, Elgin IL  60123  USA
    > 847/697-6491
    > Compass Adjusting & Repair for Lake Michigan Navigators Since 1985
    > e-mail: rspeterson(at)wowway(dot)com
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