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    Re: Double Altitudes: Prelude to Sumner's line?
    From: Fred Hebard
    Date: 2005 Feb 28, 07:34 -0500

    On Feb 28, 2005, at 6:34 AM, Jim Thompson wrote:
    >> -----Original Message-----
    >>> on 2/11/05 7:22 AM, Jim Thompson at jim2@JIMTHOMPSON.NET wrote:
    >>> Sumner opens his Introduction with this glorious single-sentence
    > paragraph:
    >>> "It is not so much the object of this work to present the navigator
    >>> with
    > a new method of 'Double Latitudes', as to afford him an accurate
    > method of
    > finding, by one Altitude of the Sun taken at any hour of the day, with
    > the
    > Chronometer time, the True Bearing of the Land, the Latitude, &c.,
    > being,
    > from any cause, uncertain; and to place him on his guard, when near a
    > dangerous coast..."
    > On re-reading this paragraph, I think that I need to understand the
    > significance of his phrase, "Double Latitudes".  If calculating a
    > second
    > solution for a sight based on an assumed latitude was well known
    > practice by
    > 1837 for other purposes, then that would have been the building block
    > that
    > allowed Sumner to creatively apply the technique to his problem, and
    > thus
    > allow him to stumble on the celestial line of position concept when he
    > found
    > himself off Small's Light.  I do not understand the concept of "Double
    > Latitudes", however, so I might have that all wrong.  I tried a google
    > search, but turned up nothing on that technique.  I found lots on
    > "double
    > altitude", but not "double latitude".  Does anyone wish to explain the
    > concept?
    > Jim Thompson
    Sumner didn't use St. Hilaire's method, assuming one location and then
    finding a line of position based on azimuth and distance from that
    position.  Rather, he assumed two latitudes and found the longitudes
    corresponding to those latitudes.  Then fitted a line of position
    through those two locations.
    Having the assumed latitude plus the sight, he determined longitude.
    Assuming a second latitude gave him a second longitude, with the same
    sight data.

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