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    Re: Latitude + Longitude @ Noon
    From: Henry Halboth
    Date: 2005 Jun 6, 10:36 -0400

    I had taken a series of sights over a 2-week period, including Latitudes
    by Meridian Passage, Longitude by AM time sight, Latitude by equal
    altitudes, and Chronometer error by equal altitudes, all of which I had
    intended to post as examples of practical observation had any interest
    been generated at the time. Accuracy across the board was comparable to
    that demonstrated in the posting made, which I frankly do not consider to
    be that great, based on past performance. It has always been my
    contention that celestial navigation has been de negated by those seeking
    to promote, at least initially, electronic methods. We are prone to
    forget that many of our charts today being utilized in conjunction with
    electronic methods are still based on hydrographic surveys founded on
    astronomical observations, albeit utilizing somewhat more than the sea
    horizon which is the ultimate bugaboo as respects accuracy.
    By-the-by George, I recall making no experience claims publicly on this
    List - although it is quite true that naval navigation can be included in
    my resume, this is but an infinitesimal part of my overall exposure to
    the subject over a rather extended period. I still have sextant +
    chronometer and will travel, although in recent years the chronometer
    rate has not been checked daily.
    On Mon, 6 Jun 2005 11:42:49 +0100 George Huxtable
    > Henry Halboth wrote-
    > >George,
    > >Forwarded for your further comment is the following posting of 31
    > Jul
    > >2004, on the subject. I must say that your failure to respond, and
    > for
    > >that matter the failure of this list to do so in general, was most
    > >dissappointing. I try only to post on practical navigation matters
    > that I
    > >have tried or experimented with at sea and can only say that this
    > list
    > >appears disinterested in such matters.
    > Thanks to Henry for giving us a second chance to examine these
    > observations. I'm sorry their value went unrecognised last time, by
    > me and
    > by others. All I can say, in defence, is that it's only after
    > delving into
    > the numbers that one becomes aware that this is a remarkable example
    > of the
    > ultimate accuracy achievable from sextant observations, taken from
    > on-land.
    > It has given me cause to rethink my view of what's possible.
    > Clearly, that
    > posting called for much more than the hasty scan it was given, and
    > should
    > not have been binned.
    > >On Sat, 31 Jul 2004 22:56:10 -0400 "Henry C. Halboth"
    > >writes:
    > >> I have recently returned from a sojourn at the North Carolina
    > >> Beaches,
    > >> and there had the good fortune of staying literally on the beach,
    > >> with an
    > >> unobstructed view of the sea horizon from almost east to west
    > >> thought
    > >> south. This stay afforded the opportunity for a real "navigation
    > >> holiday"
    > >> - unfortunately, I was plagued with an almost constant "Gulf
    > Stream
    > >> horizon", i.e., hazy to an extent that impacted on the accuracy
    > of
    > >> my
    > >> observed sextant altitudes. Regardless, an effort was made to
    > "try
    > >> out" a
    > >> few of the old favorites sometimes here spoken about. First,
    > let's
    > >> take a
    > >> look at Latitude + Longitude determination at noon by equal
    > >> altitudes -
    > >> actually determination of Longitude by equal altitude + Latitude
    > by
    > >> reduction to the meridian. In this example. a Plath vernier
    > sextant
    > >> was
    > >> used;  IC = 0, and height of eye = 20-Ft.
    > >>
    > >> On Tuesday, July 20, 2004 - Chronometer considered accurate
    > >
    > >> 1. For the Longitude
    > >> AM obs {at} Chro time = 17-09-30 GMT - Sun's LL {at} 75-38-20
    > >> PM obs {at} Chro time = 17-19-00 GMT - Sun's LL {at} 75-38-20
    > >> Mean Chro time of obs = 17-14-15 GMT = time of LAN
    > >> GHA by NA for 17-14-15 GMT = 76-58-12 W = Long {at} LAN
    > ===============
    > Let's pause here. I've no doubt that any competent navigator could
    > get a
    > decent value for latitude, but it's the longitude that's of
    > particular
    > interest in the light of recent discussions. Let's concentrate on
    > longitude. I've checked over Henry's working in a different way, and
    > have
    > no cause to question his deduced long. of 76deg 58' 12" W.
    > We need to compare that with his long., taken from a map, which is
    > quoted
    > later as 77deg 00.097', or 77deg 00' 06". So that observation is
    > within a
    > couple of miles of the true longitude. Good going, indeed,
    > particularly for
    > an observation that spanned only 9 min 30 sec of time, and was taken
    > with a
    > Vernier sextant.
    > It could, of course, have been a fluke. When there's a scatter in
    > observations, now and again, just by chance, the occasional result
    > will be
    > spot-on the true value. So we need to check for consistency. Further
    > down
    > the page, we are told-
    > "successive Latitudes obtained on surrounding dates all produced
    > results of
    > 34-38-40 N + Longitude 76-59-00.W."
    > So, on surrounding dates, he has measured longitudes to be within a
    > mile or
    > so of the expected map value. Consistency was achieved. The
    > observation of
    > 20 July 04 wasn't a fluke, then.
    > Henry provides no detailed observations for those "surrounding
    > dates", and
    > it would be interesting to see those details, though I have no
    > reason to
    > doubt his conclusions.
    > ==============
    > Henry doesn't give details of how he made his observation, but it
    > seems
    > likely to me that he used the following simple trick for
    > equal-altitudes,
    > or something like it. Perhaps he will confirm whether or not my
    > guess is
    > right.
    > Having estimated what the maximum altitude of the Sun is going to be
    > at
    > noon, the sextant is deliberately clamped at a value that's roughly
    > a
    > couple of arc-minutes minutes short of that. From that moment, the
    > sextant
    > adjustments remain untouched.
    > Then chronometer times are carefully noted, for the Sun's lower-limb
    > appearing on the horizon, on the way up, and again, after noon, on
    > the way
    > down. No attempt can be made to measure the Sun's maximum altitude,
    > because
    > it would involve disturbing the sextant adjustment to do so.
    > So, for longitude, the observer's task is simply to assess the two
    > moments
    > when the position of the Sun's limb on the horizon is exactly the
    > same. It
    > doesn't matter whether the image is affected by irradiation, it
    > doesn't
    > matter whether there's a bit of overlap,  or not, between Sun and
    > horizon,
    > as long as the two pictures look EXACTLY THE SAME the result will be
    > correct. The sextant reading doesn't enter into it, so as long as
    > it's
    > firmly locked during the measurement, a Vernier sextant is just as
    > good for
    > this purpose as a micrometer type. It's a matter of judgment and
    > experience
    > to click the watch at the right moments. It requires memorising
    > exactly
    > what the Sun-on-horizon picture was at the first time-click, and
    > clicking
    > again when it looks identical, after noon.
    > From the accuracy of his resulting longitudes, I reckon that Henry
    > must be
    > capable of estimating the equality of those two pictures to within
    > about
    > 0.1 arc-minute, which is only 1 part in 300 of the Sun's diameter.
    > Quite an
    > achievement...
    > Although he has complaned that "I was plagued with an almost
    > constant "Gulf
    > Stream horizon", i.e., hazy to an extent that impacted on the
    > accuracy of
    > my observed sextant altitudes.", I think his horizons, around those
    > noons,
    > must have been pretty sharp to allow such precision.
    > Henry Halboth has told us before that he was a US Navy navigator in
    > World
    > War 2, which must put him into his eighties now, and he must be
    > pleased, as
    > we are, that his right eye is as clear, and his right arm as steady,
    > and
    > his mind as sharp, as ever.
    > The precision he has been able to achieve has caused me to rethink
    > my own
    > estimates of what's possible from an on-land observation. Quite an
    > eye-opener it has been, indeed.
    > Although the accuracy of the sextant reading is irrelevant to the
    > longitude
    > determination, it's important for latitude. Because the peak
    > altitude
    > wasn't measured, latitude had to be calculated using the
    > before-and-after
    > observations, and Henry refers to Bowditch tables 29 and 30,
    > designed for
    > the purpose, for that small adjustment; a valid and accurate
    > procedure.
    > ==============
    > But let's not get too carried away by all this. These measurements
    > were
    > made from on-land.
    > As I wrote, in response to a posting by Lu Abel, "It's quite a lot
    > harder,
    > and less accurate, when you observe a Sun altitude in real-life, at
    > sea,
    > above a real sea-horizon."
    > And I'm sure that Henry Halboth is very aware of that difference. I
    > ask him
    > to estimate, from his own considerable experience, how much his
    > estimate of
    > longitude would be degraded if it was measured from a small craft at
    > sea,
    > wedged against the mast, the vessel heaving up and down on the
    > waves, the
    > horizon-line made up of overlapping wavetops, the sextant needing to
    > be
    > tweaked about to keep the images in view, and perhaps a telescope
    > with less
    > magnification. Not storm conditions, just the ordinary seas that any
    > offshore navigator expects to contend with.
    > As for me, I would expect, under those circumstances, that instead
    > of
    > comparing two altitudes, before and after noon, to an accuracy of
    > say 0.1
    > arc-minutes, I would find it difficult to claim to detect equality
    > to
    > within 2 or 3 arc-minutes from my own small boat. The time-span of
    > the
    > observation would need to be extended accordingly, along the lines
    > suggested by Frank Reed.
    > So, what's realistic, from a small craft at sea rather than from a
    > hotel-room balcony? That's the question I ask of Henry.
    > ===============
    > Finally, a small detail. Henry acknowledges that measurements taken
    > from a
    > moving vessel would require correction for the Northerly component
    > of
    > velocity; a correction that doesn't apply to his observations from a
    > fixed
    > point. But he has neglected another correction, due not to the
    > motion of
    > the observer, but to the change in declination of the Sun, which is
    > moving
    > Southward, away from him, at about 0.4 knots at that date. That
    > motion
    > causes his centre-of-symmetry to be slightly earlier than the true
    > moment
    > of meridian passage, and by my reckoning the required correction
    > would
    > shift the position, calculated from his observations, a couple of
    > miles
    > further West (if I've got it right). See my recent posting "Northing
    > correction to Noon longitudes". This would put his deduced
    > longitudes even
    > closer to the mapped values!
    > George.
    > ================================================================
    > contact George Huxtable by email at george---.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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