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Peter Fogg , has now expanded on his earlier posting to say-


>Assuming morning star sights were taken, followed by a Longitude Sun sight
>when the Sun's azimuth was at 90� (more below), and the boat has been heading
>in a constant direction at a known speed, without too much interference from
>current, assuming all this (phew!) then the DR should be accurate enough for a
>Fix -

Nothing I find to disagree with there, except that the morning star sights
seem a bit superfluous if a morning observation of the Sun at 90� azimuth
will later be followed by a Sun meridian altitude. The morning Sun sight
would provide a position line for longitude, which could be transferred
according to the known motion of the vessel until noon, and then crossed
with a latitude observation to give a position for the vessel. A good
technique.

But then Peter goes on to say-

>with the safeguard that if observations of meridian passage don't
>coincide with the exact, known, time then this is an indication that perhaps
>the DR is out, or something else is awry.

Here Peter and I definitely disagree. This is the point that I have been
trying to emphasise, that observations of altitude at, and near, the time
of meridian passage DO NOT provide any useful information on timing, or on
longitude, because altitude is then changing so slowly with time. The
observations provide a good value for latitude, but THAT IS ALL. So I
challenge Peter to explain exactly how he proposes to check whether his
"observations of meridian passage don't check with the exact, known, time".
If he can...

This is a matter which is often misunderstood, and I make no apologies for
flogging away at it. I hope Peter doesn't mind being treated as a
"whipping-boy" example in this matter, and if he thinks I am being unfair,
or simply wrong, no doubt he will robustly argue back!

He goes on to say-

>What I was trying to say in the
>earlier posting was that one takes observations of the sun over the few
>minutes the Sun appears to hang in the sky, while knowing the exact moment it
>happens, providing the DR is good.

It's quite true that because the Sun appears to hang in the sky around
noon, the altitude becomes easy to measure well, because it is changing
only slowly. If the DR longitude and the time are known, then the observer
knows the predicted moment at which the Sun will be on the meridian, which
is the recommended instant for measuring the Sun's altitude. If the vessel
(or the Sun) has a North-South component of velocity, then that will not be
exactly the same moment as that of maximum altitude. If the maximum
altitude, rather than the meridian altitude, is what is measured, then it
may need correcting slightly to obtain the meridian altitude. However, this
correction is less than 1 arc-minute at vessel-speeds below 10 knots, and
for many navigational purposes it is commonly ignored. This point is
discussed well in Cotter, "History of Nautical Astronomy", pages 162-165.

That was about measuring the altitude. As for "knowing the exact moment it
happens", that's the impossible bit.

Peter says further-

>If the observer finds herself (or himself) at sea during summer in a wide
>range of Latitudes (reasonable enough assumption) then a Sun sight at 90� of
>aximuth will yield a position line (LOP) running north/south - in other words
>a meridian of Longitude. This can then be advanced to cross the Sun's meridian
>passage sight, which gives an east/west LOP, or Latitude line. Then later on
>in the afternoon the Sun's azimuth will be at 270�, leading to another
>Longitude LOP. And so we go on, constantly testing our DR assumption,
>constantly refining our calculated position.

This is indeed good navigational practice. As is his description of using
successively better approximations when the initial position is very
uncertain.

>Still have a query. To what extent could one use a calculated Longitude, such
>as the 90� and 270� azimuths, or perhaps meridian sights made on land, with
>north and south sticks in the ground if necessary, to ultimately set one's
>clock? This is where this is all going, to try to find a reasonably simple
>(sorry, lunatics) way to establish, and regulate, the Longitude/Time question.

Take an observer who knows exactly where he is in longitude, because he is
in sight of an already-charted landmark, such as Sydney Heads. If he makes
there an observation for longitude, such as the altitude of the Sun at 90�
azimuth, then any discrepancy between those longitudes may be due to an
error in his value for GMT, and can be used to reset his clock.

If he has established, on land, a North-South line with a pair of sticks,
at a place with known longitude, he can set his clock after comparing
longitudes from the moment of the Sun passing across that line at noon.

If an observer is confident about the accuracy of his clock, but doesn't
know his longitude, then such a Sun observation will provide a value for
the unknown longitude.

If an observer neither knows his longitude, nor has a good measure of
Greenwich Time (which was the position Cook was in on his first voyage)
then he is stuck. He needs to find an independent way to obtain Greenwich
Time and set his clock, and only then will he be able to determine
longitudes. Nowadays, we would get that from a radio time check. Cook had
to find the Greenwich Time by observing the exact position of the Moon with
respect to the sky background. That's where all this complication about
lunars comes in.

Has that helped?

George Huxtable.


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