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    Re: Poor St. Hilaire
    From: Henry Halboth
    Date: 2007 Oct 25, 11:08 -0700

    Hi all,
    Gary is absolutely correct - as far as he goes.
    As the Sumner method was refined, it became
    unnecessary to calculate two (2) positions and to draw
    the LOP between the two.
    With the realization that the Latitude employed with
    and the Longitude determined by the Time Sight
    calculation demonstrated a point on a LOP, and that
    the LOP ran in a direction 90 degrees to the
    right/left of the azimuth of the body employed, it
    became customary to simply plot the LOP through the
    demonstrated point. This obviated the need for the
    second Time Sight calculation and significantly
    simplified the work - this method beame one of the
    standard LOP methods through the 1930s and was popular
    in the MM.
    There is little difference in computational time
    between the Time Sight and Marc St. Hillare founded
    LOP methods and both provide an integrated logarithmic
    computation for the azimuth. Aside from use for
    compass error determination, one reason for the
    proliferation of Azimuth Tables was that many
    navigators preferred their use in combination with
    these LOP methods, as opposed to use of the integrated
    logarithmic solutions.
    --- glapook{at}PACBELL.NET wrote:
    > Gary LaPook writes:
    > I don't get all the fuss about what is or is not the
    > St. Hilaire
    > method. Sumner discovered the "Sumner Line" by doing
    > two "time sight"
    > computations using two different "assumed latitudes"
    > to determine the
    > corresponding longitudes based on ONE observation.
    > His discovery was
    > his coming to the realization that if he did
    > additional such
    > computations using a series of "assumed latitudes"
    > that he would
    > arrive at all the possible positions for his vessel,
    > the first "line
    > of position". He also realized that for short
    > distances and within the
    > reasonable estimates of the accuracy of the sight
    > that this series of
    > points looked a lot like a straight line. This led
    > to his realization
    > that he only had to use two "assumed latitudes" to
    > calculate two
    > points, plot those points on the chart and draw a
    > straight line
    > between them thus the "Line of Position" was born.
    > My understanding of St Hilaire's contribution was
    > his method of
    > calculation of where to draw the LOP. In the days
    > before modern tables
    > and calculators, the computation of a "time sight"
    > was time consuming,
    > burdensome and open to the possibility of a
    > mathematical error. Using
    > Sumner's method of calculation a navigator had to do
    > this difficult
    > computation twice thus doubling the work and chance
    > of error. St.
    > Hilaire's method created the exact same LOP as
    > Sumner's method but
    > only required doing the computation one time, saving
    > work and reducing
    > the chance for an error.
    > Today, with programmable calculators, it is trivial
    > to go back to
    > Sumner's method and plot the LOP after determining
    > two points using
    > the "time sight" computation. I programed a
    > calculator at least twenty
    > five years ago to do just this. I put in the
    > declination and GHA of
    > the body, the observed altitude, and two assumed
    > latitudes, bracketing
    > my D.R. latitude. The calculator turned out the
    > longitudes to go along
    > with the two assumed latitudes and I just plotted
    > these positions on
    > the chart and drew a straight line between them thus
    > drawing the LOP
    > using Sumner's method. It is simpler to prick the
    > two positions on the
    > chart and lay a straight edge across them than it is
    > to have to plot
    > one position and measure an azimuth  and intercept,
    > plot that point
    > and then draw the LOP perpendicular to the azimuth
    > and I recommend
    > this method to you.
    > gl
    > On Oct 23, 7:54 pm, frankr...{at}HistoricalAtlas.net
    > wrote:
    > > Hi John, I've been slowing working through your
    > posts and various replies in
    > > this thread. I'll try to reply in more detail
    > later. For now, at one point
    > > you wrote, "terminology... screws up the
    > concepts." In a later message, you
    > > wrote, "the terminology traps George (and many
    > others) into thinking that
    > > the estimated latitude generates an
    > approximation."
    > >
    > > I do think that you've got a good point here, but
    > it's going to be a hard
    > > sell. First of all, I can guarantee you that the
    > terminology has not
    > > 'trapped' George Huxtable. He understands this
    > material inside and out at a
    > > very deep level (and although George is
    > temporarily lurking, I will add that
    > > he is a tremendous asset to this group). The catch
    > is that experts often
    > > have a hard time remembering what it's like to be
    > a beginner and unless
    > > they've done some recent teaching at the beginner
    > level, any concerns about
    > > terminology are almost incomprehensible. I agree
    > with you that many people
    > > hear the expression "assumed position" and find it
    > very confusing --for a
    > > variety of reasons. I also agree that the
    > approximations or lack of
    > > approximations in many celestial navigation
    > techniques are misunderstood
    > > partly because of strange terminology.
    > >
    > > Something else to consider in this St. Hilaire
    > business. The use of
    > > "plotting" on a little chart to get a positional
    > fix caused a lot of worry
    > > for late 19th century navigators. It seems as if
    > many felt that it was
    > > automatically less accurate than a trigonometric
    > solution with log tables.
    > > Very often, for example, Sumner's method was
    > muddied up with logarithmic
    > > equivalents which added no accuracy but seemed to
    > do so because of the
    > > computational biases of that era.
    > >
    > >  -FER
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