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    Re: Tides by bearing of the moon
    From: George Huxtable
    Date: 2009 Apr 7, 15:07 +0100

    Thanks to D Walden for pointing us toward Archibald Patoun, author of a
    treatise in navigation which was published in Glasgow in 1730 and remained
    in print, in several editions, over the next half-century. I must admit to
    never even having heard of his name before. Perhaps he was better known
    North of the border.
    
    His book has been fully digitised and available at-
    http://books.google.com/books?id=8yEB2eQCxg0C&printsec=titlepage&source=gbs_summary_r&cad=0#PPA87,M1
    
    The passage that was brought to our attention was the way of stating tide
    predictions according to the compass bearing of the Moon. I hadn#t realised
    that it had survived so late as the mid-18th century.
    
    This curious procedure had by than a long history of a couple of centuries,
    documented first in tide-maps by the Breton, Brouscon. As a VERY  rough
    approximation, high water at a particular port precedes or follows the
    meridian passage of the Moon by a fixed interval, and that is the assumption
    that it's based on. In the days when mariners carried no timepiece, and were
    lucky to have even a sandglass, it was easier to think of the tide as
    relating to the passage of the Moon in terms of the Moon's bearing rather
    than a time interval. After all, in mediaeval times, they had been
    accustomed to the day, dawn to dusk, being divided into 12 hours, which
    could differ greatly from the 12 hours of the night, and which changed with
    the seasons. So allowing for passage of time in absolute-hours wasn't an
    easy concept.
    
    But the whole business is rather a fiction. It assumes that the direction of
    the Moon changes by 15 degrees per hour, and this was supposedly confirmed
    by look-up tables. That would be roughly true if the Moon was viewed from
    the North Pole, but much less so when viewed from lower latitudes. Patoun's
    list relates to ports in Northwest Europe, but if viewed from the tropics
    (as an extreme example), the Moon would be nearly East all morning, quickly
    changing to nearly West, around noon.
    
    Because there are two tides each day, Patoun always lists two opposite
    bearings on which the two high-tides occur. From the coast of Flanders, for
    example, he gives the Moon's bearing as South, and North. The Moon's bearing
    being South is clear enough, when meridian transit occurs, but of course the
    Moon can never have a bearing of North. Indeed, the whole concept of "Moon's
    bearing" is a nonsense when the Moon is below the horizon. Nor is the
    concept particularly useful when the Moon is invisible because it's nearly
    new. Nor, indeed, when it's overcast, even.
    
    Anyway, the time-shift, between Moon meridian passage and high water, alters
    considerably as the phase of the Moon changes, because of the changing phase
    differences of the gravity-pulls, from Moon and Sun. So the whole business
    could only be rough-and-ready, at its best.
    
    Rather more logical in concept was the definition of "tidal establishment"
    of a port, which applied only to times of full Moon and new Moon, and
    referred then to the clock-time of high water.
    
    As for Patoun's book as a whole, it seems very long-winded, making heavy
    weather of concepts that appear trivial to us today, such as noon latitude
    observations, and with much irrelevant material about ancient calendar
    systems. It carries useful traverse tables and five-figure log trig tables.
    Anyway, it's been interesting to see it for the first time.
    
    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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