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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...@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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