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    Re: How Many Chronometers?
    From: George Huxtable
    Date: 2009 May 11, 12:00 +0100

    Frank Reed wrote-
    
    "This method of getting longitude by lunar altitudes has two problems..."
    
    Yes, those same two problems were discussed in an earlier reply, in
    "[NavList 8189] Longitude by altitudes. was [NavList 8178] Re: How Many
    Chronometers?" but Frank didn't see fit to refer to, or even acknowledge,
    that contribution, made back on 8 May.
    
    "... but they're not necessarily more problematic than standard "lunar
    distance" sights."
    
    That statement minimises the real problems in the proposed method.
    
    He continues- "First, this method only works if the motion of the Moon on
    the celestial sphere (in SHA and Dec). is more or less vertical at the time
    its altitude is observed. Since the Moon's "horns" are nearly perpendicular
    to its motion among the stars, there is a simple observational test. If the
    line through the horns is within thirty degrees of horizontal, then you can
    safely use this method with minimal error."
    
    I agree, that seems a reasonable test. Unfortunately, it rules the method
    out, most of the time, over much of the World, at latitudes such as mine
    (51�). Within, and near the tropics, the method might be acceptable quite a
    lot of the time, if problem 2 could be bypassed. So let's consider problem
    2.
    
    Frank wrote "Second, the horizon at sea probably shouldn't be trusted to
    more than half a minute of arc. " I'm not sure what he is trying to tell us
    here. Is he implying that we CAN trusr the horizon to be no more than half a
    minute out? I would agree that much of the time it might well be within half
    a minute, but sometimes it can be displaced by more; much more. Anyone
    "trusting" that it won't be more is over-optimistic.
    
    He continues "This applies mostly to sights taken at different times. If we
    can observe the Moon's altitude and almost simultaneously observe altitudes
    of other bodies, the lower limit on the horizon error probably can be
    dropped to 0.25 minutes of arc."
    
    Presumably, though he doesn't say so, he is assuming that if the time
    interval is short, the dip of the horizon will be the same for each
    observation, which is indeed reasonable. But it depends on azimuths. If the
    Moon is observed in one direction, and Sun or star is observed in the
    opposite direction, then even if the amount of dip is exactly the same in
    each case, the shift between their plotted position lines will be double the
    deviation of dip from its presumed value. In which case, for each minute of
    arc error in dip, the deduced longitude would be out by a whole degree .
    
    And then, there are all the other problems of observing an indistinct or
    disturbed horizon, from the heaving deck of a ship at sea, in real waves;
    problems which have been dismissed
    
    Frank concludes- "So we have a puzzle: why weren't lunar altitudes for
    longitude ever used or recommended in practice (historically)?"
    
    There's no puzzle. The method is inferior in every respect to direct
    measurement of lunar distance. They were right to dismiss it. Where lies its
    advantage?
    
    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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