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    Re: Latitude + Longitude @ Noon
    From: George Huxtable
    Date: 2005 Jun 6, 11:42 +0100

    Henry Halboth wrote-
    >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" 
    >> 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 @ Chro time = 17-09-30 GMT - Sun's LL @ 75-38-20
    >> PM obs @ Chro time = 17-19-00 GMT - Sun's LL @ 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 @ 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
    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
    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!
    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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