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Henry Halboth responded to Kieran Kelly's request included this comment-

If observed with Sun's center on the
>visible horizon as at sea, a correction for refraction + parallax + dip
>(if applicable) would technically be necessary; it was, however,
>customary for seagoing navigators to observe the Sun when a diameter
>above the horizon and to ignore this correction - certainly not "precise"
>but good enough in ascertaining compass error at sea. One may also refer
>to Tables 27 + 28 in Bowditch and achieve the same result by
>interpolation.

That's interesting. When Henry says that navigators "observe the Sun when a
diameter above the horizon", what part of the Sun disc does that refer to?
If it's the Sun's centre, that would correspond reasonably closely with the
statement in the Admiralty Navigation Manual, vol II, that at the moment of
Theoretical Sunset, when the true altitude of the Sun's centre was at 0deg
0', the altitude of the Sun's lower limb would be 16 arc-minutes.

Presumably, if a closer approximation to theoretical sunset was wanted, an
observer could also allow for his height of eye, adding say 4 minutes to
the altitude of the observed Sun (perhaps just by estimation) if his height
above sea level was 16 feet.

However, there's never going to be any great precision in estimating the
moment of theoretical sunset that way, because the refraction near the
horizon is so great, and so variable.

It seems, then, that we have two very different "moments of sunset".
There's the dictionary definition, the instant when the last rays twinkle
at the horizon, which is what the sunset predictions at 3-day intervals in
the Nautical Almanac refer to (though perforce they omit any correction for
height of eye, not knowing what that will be). And there's Theoretical
Sunset, when the true altitude of the Sun's centre is zero, and the Sun's
centre actually appears to be a diameter (or more, depending on dip) above
the horizon. It's this latter moment, of theoretical sunset, that's been
used for tables of sunset times and amplitudes in several epitomes, such as
Raper and Norie, without stating that important distinction clearly, or at
all.

Henry says that the method of estimation he describes was customary for
navigators, and I believe him. But I haven't seen it referred to in
textbooks, and I wonder whether it was ever advocated in formal advice to
mariners.

=========================================
=========================================

This may be relevant to my earlier question of April 6th, "Request for help
re sunset predictions." to which Henry, and Dan Allen, have responded.

Here it is, again.

===============
"I'm following some whaling journals of William Scoresby the younger, who
visited the Greenland Sea (West of Spitzbergen) each year from 1811.

Some of his time-sights, to determine LAT, were taken by observing the
moment of sunset. I take that to be defined by the last glimpse of the
Sun's upper limb above the horizon. Does anyone think differently?

To my mind, it's a poor choice of moment to determine time, when the Sun's
centre appears to be actually below the horizon, and refraction corrections
are large, and rather variable. However, that was what he did, on occasion.
It saved the trouble of getting his sextant out, no doubt.

He appears to have obtained his local time, at the moment of sunset, from
tables into which he entered lat and dec, quoting a resulting time of
sunset to the second, e.g. "6h 13m 28s pm".

Does anyone know where such tables were to be found, by a navigator in 1811?

My earliest such compendium is Raper's "Practice of Navigation", 1864, in
which table 26 is "apparent time of the Sun's rising and setting",
tabulating lat at intervals of 1deg, but dec at intervals of 2deg, and
giving a time to the nearest minute. Not nearly good enough for
interpolating a result to the nearest second. Not only that, the time of
sunset, for all lats, when the dec is exactly zero, is given as exactly
6pm. That would only be true for a star (with no semidiameter) and if the
refraction and dip were exactly zero: or if all three quantities cancelled
out to zero. It seems that Raper's table 26 is intended to give no more
than a rough notion of time of sunset, good enough for many purposes, but
not for a time-sight.

I also have an edition of Norie's, tables dating from 1914, which gives
table XLIII (43), "semidiurnal and seminocturnal arcs" , giving times from
noon to sunset to the nearest minute, and in this case the decs are
tabulated in intervals of 1 degree. But this is claimed to handle "any
celestial object", and there's no provision to insert a Sun semidiameter,
so presumably this table also isn't intended to give any precise timing for
the moment of sunset.

So I ask any Nav-L members, who own or have access to navigation tables for
the early 19th century, whether they can identify any table, anywhere, of
sunrises/sunsets, that Scoresby might have used to get his LHA, in 1811 and
following years."
=================

If Scoresby chose to time for sunset, not the moment of the last twinkle,
but the moment at which the Sun's centre was, say, a diameter above the
horizon (perhaps estimated by eye, and perhaps including an extra allowance
for dip depending on his height of eye), then the Sunset tables in Raper
and Norie would give him the right answer. Or would, if refraction at the
horizon was actually at its predicted "mean value".

So, I ask, would a navigater of the day (1811) be familiar with the "dodge"
that Henry describes above, and accustomed to estimating, by eye, at just
what moment the Sun passes through that particular altitude?

As I noted earlier, it's not, in any way, the ideal moment to take a time-sight.

George.

================================================================
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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