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    Latitude + Longitude @ Noon
    From: Henry Halboth
    Date: 2004 Jul 31, 22:56 -0400

    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
    2. For the Latitude
    Alt, Sun's LL {at} AM observation = 75-38-20
    GHA Sun by NA {at} AM obs = 75-46-54 West
    Long by equal altitudes {at} LAN = 76-58-12 W
    Therefore Meridan Angle {at} AM observation = 1-11-18 E
    Alt corr to meridian - Bowditch Tabs 29 + 30 =  +2'-12"
    Declination by Nautical Almanac = + 20-30-06
    Corr Alt {at} 17-09-30 = 75-38-20 + 02-12 + 11-24 = 75-51-56
    Lat {at} 17-09-30 = 89-59-60 - 75-51-56 + 20-30-06 = 34-38-10 N
    Position by obs = Lat 34-38-10 N + Long 76-58-12 W
    Certain parameters/limitations must be recognized
    1. Lat by reduction to the meridian is for the time of sight while the
    Long by equal altitude is tor the time of LAN, necessitating correction
    to a common time for a vessel underway.
    2. If ship movement were involved, an adjustment in the second equal
    altitude would be necessary to allow for any N/S component of the
    distance made good between sights. Although this may be easily
    accomplished, the simplicity of the equal altitude solution becomes
    somewhat more complicated. Essentially the Long is determined without a
    knowledge of instrument error or dip. I suppose the refraction could
    change in the short interval involved.
    3. Recognize that a navigator, dependent on celestial navigation, who has
    been without sights for a number of days, as was frequently not unusual
    on the North Atlantic in winter, finds it necessary to use every trick in
    his bag, and must evaluate the results according to his best judgement of
    conditions at the time of observation. Actually, if in dire need of a
    position, the vessel might be hove to for the few minutes necessary so as
    to obviate any concern as to altitude change by ship movement.
    4. What was my position at the time of  observations? It was Lat
    34-40.073 N + Long 77-00.097 W; by a map program, giving an error of
    about 2' each in Latitude + Longitude, assuming the map program to be
    correct. Given the horizon conditions at the time of sights, this margin
    of error is entirely possible, however, successive Latitudes obtained on
    surrounding dates all produced results of 34-38-40 N + Longitude 76-59-00
    5. I used an on line Nautical Almanac to obtain declination + GHA, and
    frankly do not know how these compare with the printed version of the NA.
    Interpolations were made by inspection, with no effort at extreme
    accuracy - the emphasis was in evaluating a method. I hope that I have
    not made some fool mistake in the transcription.
    6. A rigorous analysis will demonstrate the PM meridian angle to actually
    be 1-11-12 W indicating that the true PM equal altitude was probably
    missed by some 6-seconds of meridian angle arc too early - thus placing
    the Longitude found slightly more to the west. Calculating the actual
    meridian angle at the time of each sight provides a check on accuracy.
    7. If you are unsure of your chronometer, and know your Longitude
    accurately, this method may be employed to ascertain chronometer error -
    I also experimented with this methodology and will report subsequently.
    8. For those interested in such as this, it would probably be more
    appropriate if presented in the form of a proper calculation. This
    cannot, however be done unless transmitted as an attachment.

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