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    Re: Luni-Solar Distance
    From: George Huxtable
    Date: 2010 Oct 19, 22:03 +0100

    Ken Muldrew wrote-
    On 19 Oct 2010 at 16:23, George Huxtable wrote:
    > We've discussed this matter on the list before, but I can't put my finger
    > on the postings. As I remember, Frank expressed the view that reiteration
    > would seldom if ever be necessary. If I have it right, that view seems to
    > be in some doubt..
    One of the topics that has come up on this subject before is the apparent
    agreement among the lunar cognescenti of the late 18th and early 19th
    centuries that calculated altitudes was the preferred tecnique for land-
    based navigation (with a hand-held sextant). William Wales and Philip
    Turnor both taught this method (both of whom were well aquainted with
    Maskelyne, though I'm not sure if I have ever seen any direct evidence
    that Maskelyne also advocated for this method). Patterson instructed
    Merriwether Lewis not to bother with altitudes on the Voyage of Discovery.
    I don't know if this was because of the non-tropical nature of these land-
    based voyages or because land-travel is inherently more amenable to
    calculated altitudes (better longitude by account, better latitude
    knowledge (you can always use a star if you miss the sun), or just because
    you have to take 3 sights anyway (time, latitude, & lunar distance) so you
    may as well get time and latitude in the bargain). Even when land-based
    navigators used the sun for their time sight, immediately before taking a
    lunar, they would still calculate the altitude of the sun when working
    their lunar.
    Ken is correct. Land explorers (in America anyway, where we have good
    documentation), such as Thompson, would calculate his altitudes, rather
    than measure them. Perhaps Ken can tell us whether Thompson just accepted
    the first resulting value, or whether he ever did any reiteration.
    Of course, land explorers travelled much less far, in the course of a day,
    15 miles or so, than ships did, which could travel 10 times as far. So, on
    land, if a lunar was correct a day or two before, an estimate of assumed
    longitude could be made that wouldn't be very far out. And then, in the
    worst-case geometry that I discussed in the previous posting, any error in
    that estimate would be roughly halved by such a once-round lunar
    calculation, without iteration. A bit unsatisfactory, that, after all the
    effort of taking a lunar.
    In most cases, however, that worst-case (which calls for the Moon to be
    passing near the observer's zenith) would not apply, as that happens more
    in tropical latitudes, and less-so in Canada, for example. In higher
    latitudes, the resulting longitude would be somewhat less affected by a bad
    assumption of initial longitude, and a single rould of calculation may be
    more acceptable. It's more likely to have troubled David Livingstone, who
    was using lunar distances in the Congo.
    I don't know of any texts which have considered this question of a need for
    reiteration when altitudes have been calculated, and wonder whether
    travellers were even aware of its potential for causing error. Can anyone
    point to such a publication? Can Ken tell us whether Wales or Turnor
    addressed it? More to the point, it would be nice to have access to such a
    text to confirm whether or not I have analysed the problem correctly.
    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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