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    Re: Lunar altitudes
    From: Jan Kalivoda
    Date: 2003 Apr 13, 14:47 +0200

    Only one remark:
    The errors of dip and refraction in both altitudes of the Moon and a star can 
    be each enormous for finding the GMT by this way - but they could neutralize 
    each other, not double in this method. From these altitudes the local hour 
    angle of Moon and other body is computed. Star's LHA is added to its Right 
    Ascension to obtain the Local Sidereal Time. The Moon's LHA is then 
    subtracted from this LST to obtain the Right Ascension of the Moon in the 
    moment of observation. You can then obtain the GMT by interpolating the time 
    according to the gained Moon's RA in the almanac backwards.
    So if one LHA is added, the other LHA subtracted during the procedure, their 
    errors from the wrong dip and refraction can neutralize each other, if they 
    are roughly the same in the both altitude values, not reinforce, however 
    great they are. The old authors sought the conditions, when these errors can 
    be compared in amount - similar azimuths and altitudes of both bodies 
    observed in the same time, above all.
    Please, send me the Sadler's paper, George. Thank you very much in advance.
    Jan Kalivoda
    ----- Original Message -----
    From: "George Huxtable" 
    Sent: Sunday, April 13, 2003 1:00 PM
    Subject: Re: Lunar altitudes
    > 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-
    > Dan,
    > Here's a link to their publicatins web page, I think you'll find info
    > there...
    > http://www.ion.org/shopping/order_list.cfm
    > ==================
    > 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
    >   http://www.rin.org.uk
    > 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
    > themselves.
    > 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-
    >   editor@rin.org.uk
    > 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
    > avoided.
    > 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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