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Here are some further thoughts, following Joel's interesting question,
[NavList 2545] determination of longitude and the prime vertical, and my
reply in 2547

There are significant differences between what a surveyor can discover, from
observing a celestial body, and what a mariner can do, that are worth
thinking about..

Take a surveyor, firmly planted on land with a theodolite or some
equivalent. First, he establishes the direction of his North-South line (and
with a theodolite, and a starry night, that's fairly easy to do). Then he
can measure, at a certain time, both the altitude and the azimuth of a body,
very precisely. From that single observation, that pair of values gives him
a position on the Earth's surface. Not a position line, a position; the
unique position that results in that pair of values.

Not so for the mariner; he can measure the altitude of a body, with some
precision, but that's all. The best he could do, for azimuth, is to take a
compass bearing, and correct it; a procedure that's only good to a degree ot
two. What a mariner ends up with is a position line, not a position, for
each body, which he is why he has to take two such postion lines and cross
them, to arrive at his position.

That applies, in just the same way, to making observations on the prime
vertical, when the azimuth is exactly 90 degrees. A surveyor, knowing true
North, can set his theodolite to exactly 90 degrees azimuth, and wait for
the rising Sun to cross it, noting the time and the altitude when it does
so. From those two pieces of evidence he can derive two quantities, his lat
and his long, both precisely.

However, all the mariner can do is to make a rough guess at the Sun's
azimuth from his compass. At his best estimate of the moment when the Sun is
on the prime vertical (due East) he measures its altitude at that time,
whenever it happens to be, and that is sufficient to put him on a position
line that's oriented very nearly North-South. But he can't state the exact
azimuth at that moment, nor the time when the Sun is exactly East.

Using the prime meridian is really no different from determining a position
line from any celestial body. It makes the trig slightly simpler than the
general case, but in these days of calculators and computers that's a minor
virtue. And instead of an oblique position line, it provides a position line
that runs (almost) exactly North-South, providing a unique value for the
resulting longitude, if that's regarded as an important matter. It can then
be crossed with an East-West position line, at noon, to give latitude, if
that's regarded as an important matter.

But Sumner's lesson to us, and more so that of St Hilaire who followed him,
was that knowing your position in terms of latitude and longitude separately
was, in the days of the chronometer, no longer such an important matter. Any
pair of position lines, however oblique, provided they crossed with a good
"cut", was equally valuable in establishing where you were on a chart. And
that lesson still needs heeding, today.

George.

contact George Huxtable at george@huxtable.u-net.com
or at +44 1865 820222 (from UK, 01865 820222)
or at 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.


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