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    Re: Real accuracy of the method of lunar distances
    From: George Huxtable
    Date: 2003 Dec 31, 01:07 +0000

    Jan has made an interesting and valuable posting.
    I have a few comments to make.
    In the days of lunars, it's my guess that mariners were not demanding
    absolute certainty about their longitudes. Nor (it's my guess also) were
    they asking for 99.7% probability. If they knew, to within 95% probability,
    that they were within 30' of their calculated longitude, one way or the
    other, that would in general be acceptable, in an age and in a trade that
    wasn't particularly safety-conscious. After all, it would be significantly
    better than their dead-reckoning, after an ocean voyage, if a mariner had
    no chronometer. The errors involved in lunar-distance measurements may
    horrify Jan, but that was the best that could be done.
    In the case of the fortunate mariner who possessed a chronometer, making a
    passage across an ocean, a check of position by lunars would be a useful
    confidence-building measure, to make sure that his new-fangled tick-tock
    hadn't gone seriously wrong. For those on longer expeditions, who may be
    away from civilisation (or from capes of known longitude) for many months
    and sometimes years, it would become essential to check the chronometer,
    somehow. It could not be trusted to keep good time over such long periods,
    as the hardened steel balance-spring aged and the poor oils of those days
    gradually thickened, and the climate changed..
    Well, the best thing was to make a landfall now and again, and with a
    steady platform underfoot, make a long series of lunars with high accuracy,
    averaging many observations.  With a long enough program of lunars from a
    fixed point, perhaps even some of the errors in the Moon's tables might
    have averaged out. These could perhaps be backed up with observations of
    Jupiter satellites, if the season was right.
    This was how Cook managed his one good chronometer. It was valuable to him
    to interpolate for time between island landfalls. On its own, without such
    cross-checking for errors, it would have been pretty useless long before
    the end of the voyage. Not to mention its occasional stoppings. This is an
    aspect of the Cook chronometers that hasn't been properly emphasised,
    except by Derek Howse.
    It's been noticeable that even in these days of highly precise sextants and
    timekeepers, many of the lunar measurements reported to this list have been
    out by a minute-of-arc or two from their expected value, even though many
    of them have had the advantage of measuring from on-land. This would not
    have been very acceptable to our Ancient Mariner. I wonder what causes
    these errors, which are nowhere near as accurate as Gregory was getting in
    Australia in the 1850s? Partly, of course, it's lack of experience. We have
    a shot at a lunar from time to time: they were repeating it again and
    again, and were familiar with just how closely the other-body should
    "brush" the edge of the Moon to give the right answer.
    If stars are measured, and two stars chosen, one East and one West of the
    Moon by about the same amount, then any fixed scale-error in the sextant
    would cancel, together with index-correction errors. That's one problem
    with a Moon-Sun lunar, there's only one Sun.
    I wonder to what extent "irradiation" might play a part? That was a
    correction which the almanac used to ask for, when measuring upper-limb Sun
    altitudes. I was dubious about the reality of irradiation, which makes
    bright objects look bigger than they really are, until it was demonstrated
    to me, in a way you can easily try yourself. You need a bright white
    extended source of light, such as a sunlit cloud outside the window, a
    well-lit lampshade, even a white computer screen. Hold up your hand, say
    six inches from your eye (15cm), doesn't matter much how far. Now bring
    first-finger tip and your thumb slowly together. There's an isthmus of
    bright light between them, and as this narrows, you see a dark shadow
    suddenly jump across the gap as finger and thumb touch.
    That's an effect of irradiation. As long as there's a narrow bridge of
    light between finger and thumb, the eye makes it look significantly wider
    than it really is, because it's so much brighter than its surroundings. But
    once the light bridge shrinks to nothing, there is of course no such
    widening. Hence the sudden jump.
    Perhaps part of the lost lunar art was in knowing just how much to allow
    for irradiation when taking a Sun-lunar, even if the observer didn't know
    what the effect was called, or what caused it.
    When taking a star-lunar, I wonder if the shade that's needed to stop the
    Moon brightness overwhelming the star perhaps cuts down the light level of
    the Moon so that irradiation is no longer such a problem.
    Perhaps some lunar observers on this list have managed to achieve the same
    accuracies that their predecessors were doing 200 years ago. If so, I hope
    they will tell us about it.
    Of course, what we next have to consider is the effect on the accuracy of a
    lunar of a pitching, rolling, deck, finding a patch to lie down where the
    square sails overhead didn't blot out the two objects you needed to see at
    the same time. It's hard to imagine how difficult it would be keeping both
    objects in the narrow field-of-view that sextant-telescopes had in those
    days, when the magnification was as high as the x9.5 quoted by Jan. What a
    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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