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    Re: Lunars for dummies like me
    From: George Huxtable
    Date: 2004 Sep 24, 00:00 +0100

    Jim Thompson wrote-
    >I am still crawling up the lunar distance learning curve.
    >I understand most of the issues around how navigators estimated their
    >longitude using GMT from a lunar distance sight, and latitude from a noon
    >sun sight.  But I am stupidly stuck on step 5.  Did navigators of the day
    >set a ship's clock to GAT obtained from the lunar distance, and then
    >therefore know the difference in time between when they took their lunar
    >observation of GAT, and when they took their morning or afternoon time sight
    >of the sun?  Or did they do this without any ship's timepiece at all?
    Jim seems to be getting up that curve rather well.
    To be honest, I don't know the answer to Jim's reasonable question. I think
    it might have changed somewhat as the years went by.
    Once a clock that could be used at sea (but not yet any sort of
    chronometer) had evolved, it would be useful for establishing the local
    apparent time (for setting the sequence of the four-hour watches, for
    example). No great accuracy was called for. It would bridge the intervals
    between sunny days, when a time-sight would be used to set it right. In
    those cloudy periods, clock adjustments might be made, perhaps each day, to
    allow for estimated DR Easting or Westing. If the ship's navigator didn't
    concern himself with longitude by lunar distances (and many vessels still
    relied on latitude sailing well into the 1800s) then the ship's clock
    didn't matter much.
    Jim asks whether they could have assessed their longitudes from lunars
    without any timepiece at all, and the answer is (in certain circumstances)
    yes. The special cirumstances were a Sun-Moon lunar, taken in the morning
    or afternoon at a time when the Sun's altitude would provide a useful
    time-sight. Then, because Local apparent Time was determined from the Sun
    time-sight, at the same moment that Greenwich Apparent Time was determined
    from the lunar distance, there was no need for an on-board clock or
    deck-watch to determine the time-interval between them.
    In general, however, (and especially using star lunars at night) the
    measurements of Local Apparent Time and Greenwich Apparent Time were
    separate events, measured at different times. To determine longitude from
    the difference between them, first they have to be put on the same
    time-scale. To do this, it's necessary to know the time-interval between
    them, and use it to advance or retard the Local Apparent Time from the
    time-sight, to become the LAT at the moment of the lunar. That's where the
    ship's timepiece comes in.
    And because it's only a time INTERVAL that's required, it doesn't matter a
    damn whether the clock that's used is following local time or Greenwich
    Time. All that's needed is (ideally) some knowledge of its rate (of gaining
    or losing, in seconds per day, with respect to GMT), and to be sure no
    adjustment has been made to it in the interval.
    No great accuracy is called for here. If the interval could be relied on to
    say half-a-minute of time, that would contribute no more than 7.5
    arc-minutes to the resulting longitude: acceptable in a lunar context,
    which has low accuracy anyway. That half-minute error should be maintained
    over the interval between the two observations, which will normally be less
    than 12 hours or so, unless a long period of cloudy weather intervenes. So
    it's not a demanding requirement. Of course, if a proper chronometer was on
    board, that would be used in preference.
    I have omitted a small complication above. A clock can follow Mean Time,
    but not Apparent Time, which is irregular. To follow Apparent Time requires
    regular resetting to allow for the changing Equation of Time. So a clock's
    rate of gaining/losing on Apparent Time is deduced from its known rate on
    Mean Time after adjusting by a small correction that varies in a known way
    over the year.
    >For example, is this correct?:
    >1. Navigator took a lunar distance observation on the evening of day 1,
    >yielding GAT for that point in time and space.
    >2. Navigator continued careful dead reckoning.
    >3. Navigator determined latitude at LAN from a noon sun sight on day 2.
    >4. Navigator took a time sight of the sun late in the afternoon of day 2,
    >when the sun was nearly due west, yielding LHA of the sun based on careful
    >dead reckoning for latitude, and therefore obtained LAT.
    >5. Navigator advanced his estimate of GAT from the lunar sight to the
    >afternoon sight, using a local timepiece set to GAT at the time of the lunar
    >sight the day before, and then determined longtiude using the formula GAT =
    >LAT +WLo or -ELo.
    I think this is fine until you get to 5. You can advance/retard either
    observation, by the time difference between them shown by the clock, to put
    it into step with the other, and then the resulting longitude will be the
    position at the moment of the "other". And there's no requirement for the
    local timepiece to have been "set to GAT", as long as its difference from
    GAT was established, the day before.
    I hope I've got that right. I still find that time is very slithery stuff;
    hard to get a firm grip on.
    contact George Huxtable by email at george---.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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