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    Re: Navigation Weekend: summary and thanks
    From: Frank Reed
    Date: 2008 Jun 20, 00:09 -0400

    Hi Jim.
    
    You wrote:
    "You mentioned Joel Silverberg's talk about determining latitudes by the
    double altitude method, when I think you meant longitudes."
    
    No, latitude. This was a very popular mathematical problem in the late 18th
    and early 19th centuries. By the end of the 19th century, it was understood
    as a partial solution of an ordinary two-sight running fix. Imagine you're
    in a middle latitude, like 42 North (that's about where I am right now). You
    shoot the Sun's altitude at 9am and then again at 10am. By modern methods,
    this gives you two LOPs which you can cross to get a fix in latitude and
    longitude. By early 19th century methods, you could use one altitude as a
    time sight for longitude (using that altitude to generate local time which
    is then compared with a chronometer to yield longitude) and the two
    altitudes together plus the time interval as a "double altitude" to get
    latitude (essentially using the rate of change of altitude to determine
    latitude). There was a related "double altitude" problem which gave latitude
    from simultaneous altitudes of two stars. In fact, when Sumner's paper first
    appeared, some commentators decided that it was just a graphical solution to
    the double altitude problem. In a limited sense, they were right, but of
    course they missed out on the fact that it was much more than that.
    
    That said, I gather that you're referring to determining longitude by equal
    altitudes, a topic which was also under discussion on NavList recently.
    
    You wrote:
    "I hope that he mentioned the sometimes significant effect of relative
    motion between the body and the observer, as Bowditch did."
    
    We've discussed that recently, too.
    
    And:
    "This was the subject of my 1985 paper in Navigation, where I derived an
    equation for compensating. Alas, I was later informed that the same equation
    was in the Admiralty Manual of Navigation volume III, out of print for some
    years. I was later able to confirm this from a 1938 copy."
    
    Back in 1985, it was so much harder than it is today to find out what's "out
    there" in the science of navigation. You may be interested to know that
    there was an entire navigation manual printed which was devoted to finding
    latitude AND longitude by sights around noon. It was Hewitt Schlereth's
    "Latitude & Longitude by the Noon Sight" published in 1982. His "Table 4"
    gave the Shift in Longitude due to the motion of the observer. This is
    nothing more than a tabulation of that equation that you (presumably) also
    derived.
    
    And you wrote:
    "There has been much published misconception about the method by ignoring
    this effect."
    
    Yes, there sure has! Less than a month ago, the email newsletter from "Ocean
    Navigator" described this method and made no mention at all of the motion of
    the observer. Shame on them. :-) But while the motion of the observer is
    certainly something we have to worry about, there has also been a
    misconception which has developed suggesting that this is a "terminal"
    problem for determining longitude around noon. And that's not the case at
    all. One can calculate the offset (either directly from the offset equation
    or from a little table like Schlereth's) or we can correct the raw sights in
    advance. Personally, I prefer the latter approach since it requires no
    special tables or calculations, and it's very easy to explain and therefore
    remember. But this is mostly a question of personal preference.
    
    Another issue often glossed over in accounts of drawing that noon curve is
    the problem of finding the axis of symmetry "by eyeball" which is not
    especially accurate with noisy data. There are a few ways of dealing with
    this. Bowditch has one. I've got my own technique which I think works quite
    well (fold the graph in half and hold it up to a light --details in other
    posts).
    
    
    Of the Navigation Weekend, you wrote:
    "Again, thanks for a most enjoyable account."
    
    You're welcome. Sorry you couldn't join us. :-)
    
     -FER
    
    
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