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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@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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