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    Re: Transcription of Worsley's Log
    From: Brad Morris
    Date: 2009 Mar 20, 15:26 -0400

    Hi Henry

     

    Thank you very much for your independent confirmation of George’s original assessment of the issue.   The methodology is now un-disputed!   There are some very minor discrepancies in values which attract my attention. 

     

    When Worsley writes down his polar distance, he gets 102 degrees 51 ½ minutes.  We can subtract the 90 degrees for the South Pole, leaving a North Declination of 12 degrees 51 ½ minutes.    This is marginally different from the value you used to determine his GAT in part one of your equations of 12 degrees 51 minutes 17 seconds (for a difference of 13 seconds).  I wonder why Worsley would have disregarded the more accurate answer you have provided?

     

    In part two of your explanation, we have exact agreement across the board.  We all get precisely the same logarithmic values.  The sum of the four logarithmic values is also the same.  However, when Worsley looks up (and I calculate) the arc-Haversine of 9.14437, we both get time values of 21-4-36, while you obtain 9-4-35.4.   This is due to rounding on my part, if the resolution is extended I obtain 35.51.  I think this just noise at the truncation point of the logarithmic values (5 places, 6 places, etc).   My question is more basic.  Worsley writes down 21-4-36, rounding off to a whole second.  Would that be prudent for the purposes of determination of chronometer error in his day?  Didn’t the arc-Haversine tables show only  the nearest second?

     

    George and I now concur that Worsley must have taken his observation from Point Wild, which on modern charts is South 61 degrees 5 minutes 22 seconds West 54 degrees 53 minutes 45 seconds.  Worsley used the location of Cape Belsham.  I think he did this because it is so very close by  to Point Wild and because Cape Belsham is listed in some tables as the northernmost point of Elephant Island.    Of course, his tables or charts may have suffered from the difficulty of ascertaining lat lon, in his day, in the polar regions.

     

    Best Regards

    Brad

     

     

     

    From: NavList@fer3.com [mailto:NavList@fer3.com] On Behalf Of hch
    Sent: Friday, March 20, 2009 2:28 PM
    To: NavList@fer3.com
    Subject: [Possible SPAM] [NavList 7705] Re: Transcription of Worsley's Log
    Importance: Low

     

    George,

     

    I hadn't intended posting my recap of Worsley's Time Sight quite so soon, as I am still working on the CE portion. However, as you have broached the subject, I post the attachment as a work in progress. Please note that, based on the figures and assumptions available, his calculation is correct, From here forward much, if not all, depends on the Longitude of Cape Belsham that he used.

     

    I hope that the formating is no destroyed in transmission. More to follow.

     

    Henry

    --- On Wed, 3/18/09, George Huxtable <george{at}hux.me.uk> wrote:


    From: George Huxtable <george{at}hux.me.uk>
    Subject: [NavList 7677] Re: Transcription of Worsley's Log
    To: NavList@fer3.com
    Date: Wednesday, March 18, 2009, 8:51 PM

    I was just getting round to replying to Henry Halboth's posting about
    Worsley's navigation, when a second posting appeared, stating-

    "I believe that I have deciphered Worsley's numbers for April 25th. He is
    using the old style format for a Longitude time sight at Latitude 61.4 S,
    which I presume to mean 61-04 S. The numbers in the right hand column,
    although separated by decimal points are actually the logarithmic values
    applicable to the formula employed. I will recalculate and let you know the
    results asap. Depending on the sun's azimith at the time of observation, the
    Latitude used may not be that important to the correctness of the Longitude
    determined.

    By the way, until quiet recently at least, there appears to be an
    international difference of opinion as respects positions on Elephant
    Island."

    ======================

    That's interesting, on several counts.

    Worsley is turning his back on "New Navigation", and instead, just as Henry
    says, deriving longitude from an old-style time-sight of the Sun, away from
    Noon.

    Brad and I, between us, have worked out how he implemented this calculation,
    following exactly Norie's "first method" for time-at-place. This appeared in
    posting [7468], with the relevant section from Norie's Navigator (1900)
    attached. I attach it again, and ask Henry if this corresponds with the
    method he was familiar with, in his days on the bridge. There were many such
    methods in use, and navigators had their own favourites. Brad has put
    together an Excel spreadsheet that reproduces Worsley's method, logs and
    all.

    We're able to follow every detail of many of these calculations of local
    hour angle of the Sun. This could  provide either a measure of chronometer
    error if longitude was known (as for Elephant Island) or a measure of of
    longitude, assuming the chronometer had been corrected. But these
    calculations required a good knowlege of latitude, because at that latitude
    and time-of-year, the Sun didn't appear anywhere near the prime vertical.

    Worsley had serious problems in establishing his latitudes. He only had
    occasional glimpses of the Sun, and an accurate latitude could be deduced
    only when the Sun could be seen at or near noon, which happened rarely.. On
    the day of departure, 24 April, the Sun made its first appearance since
    their arrival on Elephant Island, allowing a morning Sun altitude for a
    time-sight to be observed, but a noon observation for latitude was
    impossible, as the Caird was loading-up and setting-off at around that time.
    So the calculation depended on assumed values for lat and long of Cape Wild,
    Elephant Island.. Because the time-sight was less than 3 hours before local
    noon, it was very sensitive to the accuracy of that latitude.

    ===================

    It interests me that in the era when radio time checks were widely available
    for a chronometer, navigators in Henry Halboth's days were still using
    time-sights of the Sun. Was this just a matter of going through a ritual
    that was by-then already ancient, I wonder, or were those results taken
    seriously? I'm sure Henry has many insights of how things were done in days
    before the War up his sleeve, if we could persuade him to tell us about
    them.

    George.

    contact George Huxtable, at  george{at}hux.me.uk
    or at +44 1865 820222 (from UK, 01865 820222)
    or at 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.








     



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