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    Re: Lunar altitudes
    From: George Huxtable
    Date: 2003 Apr 13, 12:00 +0100

    Dan Allen asked-
    >> On Saturday, April 12, 2003, at 02:54 AM, Wolfgang Koeberer wrote:
    >> > Chichester,F., Longitude without time, in: Journal of the Institute of
    >> > Navigation, Vol. 19 (1966), 106 -107 (with comments by D.H. Sadler, one
    >> > time superintendent of HM Nautical Almanac Office, p. 107 - 109).
    >> Does anyone know how to get reprints of articles like this?
    >> I've always wanted to read Sir Francis' article, but I've never known
    >> how to get ahold of it.
    and Phil Guerra replied-
    Here's a link to their publicatins web page, I think you'll find info
    Comment from George Huxtable-
    I think there is a bit of confusion here. There are separate institutes of
    navigation, issuing journals with rather similar names, on either side of
    the Atlantic.
    In Washington there's the Institute of Navigation, producing a journal
    "Navigation", and I think the website referred to by Phil Guerra pointed
    there. Wolfgang carefully distinguished publications in that journal by
    appending "(Washington)" in his list. However, the Chichester publication
    was not in that journal.
    In London there is what's now named the "Royal Institute of Navigation",
    though once it was the plain unvarnished Institute of Navigation, and this
    produces a quarterly "Journal of Navigation". At some time in its history
    this journal may have been named "Journal of the Institute of Navigation,
    or later "Journal of the Royal Institute of Navigation" (JRIN), and it may
    conceivably have been filed in some maritime libraries under these
    headings, perhaps only for some part of its print run.
    The RIN has a website at
    and as I recall, if you poke around in there you can find a complete index
    to publications in the Journal. But only an index: not access to the papers
    The RIN is usually friendly and helpful to non-members, and Heather Leary
    may be prepared to help with copies or scans of older papers: you might ask
    her anyway, at-
    or by phone at +44 207591 3133.
    The correspondence Wolfgang refers to predates (by a long way) my own
    membership of the RIN, so I don't have my own copies of these papers to
    send around.
    However, thanks to list member Clive Sutherland, I do have a copy of the
    1978 Sadler paper which put rather an authoritative conclusion to the
    argument, which Wolfgang referred to as-
    Sadler, D.H., Lunar Methods For "Longitude Without Time", in: Journal of
    the Institute of Navigation, Vol.31 (1978), 244 - 249 (with a historical
    note pointing out that the Board of Longitude in 1802 resolved  that it
    "will not in future take into their consideration  any methods of
    ascertaining the Longitude founded on the Moon`s Altitude...).
    I have made a scan of a photocopy of this paper on my own rather primitive
    equipment: it is everywhere legible (but not much more than that). This
    could be sent out as an attachment, in TIFF encoding. The paper has 6 pages
    and each scanned image covers two of those pages.
    Because of the Nav-L list's request (which I understand, but regret) for
    "no attachments, please", this won't be available on-list, but I will
    happily send a copy off-list to any list member who asks for it in the next
    few days.
    Intending to illuminate his readers, Sadler included a diagram of such
    devilish complexity that I can't understand it, so if you enjoy a puzzle
    you will find an interesting one there. If you do work it out, please
    explain it to the rest of us...
    In addition to Wolfgang's list of references, Sadler includes two more,
    which I have not followed up-
    Ortlepp, B (1969), Longitude without time, Nautical Magazine, vol 210, 276.
    Ortlepp, B. (1977) Improved plotting solution to longitude without time,
    Nautical Magazine, vol 218, 334.
    I am not familiar with all the arguments in all that correspondence, but my
    own simplistic view is this-
    Measuring altitudes up from the horizon was a familiar task to a navigator.
    Howeve, any measurements of altitude, measured up from the horizon, are
    degraded by the unknown errors in the angle between the observed horizon
    and the true horizontal; particularly variation in the dip from its assumed
    value. Determining time from the relative altitudes of two bodies would
    involve those horizon uncertaincies, twice over.
    Measuring the lunar distance, the angle between the Moon and another body
    up in the sky, though a tricky oparation which required much skill, avoided
    involvement of the horizon. It allowed a precision of a fraction of a
    minute to be achieved in the lunar distance. As each minute of error in the
    lunar distance gives rise (in low latitudes) to a 30-mile error in
    position, it was crucial that any avoidable errors should indeed be
    This matter was well understood back in the mid-1700s, and was the reason
    why the lunar distance method was settled on. This judgment of a our
    navigational ancestors stood the test of time, until the whole method
    superseded by the chronometer. It's only right for their reasoning to be
    re-examined from time to time, however.
    John S Letcher, jr, in "Self-contained celestial navigation with H.O. 208"
    (1977), devotes a whole 10-page chapter (chap 17, "Time by lunar lines of
    position") to this matter. He concludes-
    "Although it is fundamentally slightly inferior to lunar distances in
    accuracy, the lunar altitude method is far easier to work out, and it can
    be applied easily by anyone who knows how to work ordinary sights...."
    I have two comments about this.
    1. In my opinion, Letcher makes light of the inferiority, which is more
    serious than he allows.
    2. Letcher was writing before on-board computers or calculators were
    generally available. For those who are prepared to use them, the mathematic
    difficulties in clearing the lunar distance have largely disappeared,
    though the difficulties in the observation remain.
    George Huxtable.
    contact George Huxtable by email at george@huxtable.u-net.com, by phone at
    01865 820222 (from outside UK, +44 1865 820222), or by mail at 1 Sandy
    Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.

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