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John Karl has posted a thoughtful message about St Hilaire. I for one, have
no objection to him delving into such matters in serious detail. But I have
difficulties which much of what he has said.

I'm a bit puzzled when he writes-

  In my English translation of his
| 1873 publication...

When he says "my" translation, does that imply that he has translated it? Or
is it John referring to his copy of  a translation, perhaps the one by
Michel Vanvaerenbergh, in the book he wrote with Peter Ifland, "Line of
Position Navigation".

John goes on to say-

| Hilaire's intercept method invites further confusion.  First, we
| observe that the altitude observation and the knowledge of the body's
| GP completely determines the celestial LOP.

No disagreement about that...  But he continues-

| Therefore no sight
| reduction method uses estimations or assumptions.  Again, it's the
| terminology that screws up the concepts.

I don't understand why that follows. There are all sorts of sight reduction
methods making all sorts of estimations and assumptions.
|
| There are several ways to determine the exact LOP by directly
| computing and plotting latitudes and longitudes of as many points as
| we wish (Sumner's being one such method).  But St. Hilaire is
| different -- it doesn't compute Lats and Lons at all.

That's exactly what his 1873 paper, "Note sur la determination du point", IS
doing! In section VI, he assumes a nunber of different lats (or longs), and
deduces the corresponding longs (or lats), using the formulae in section
VII. If there are enough such points, he can draw an exact curve through
them. If there are only two, he can draw a chord between them. And if
there's only one point, obtained by using his estimated lat (or estimated
long) he can work out, using the formulae in section VII, the corresponding
long (or lat) and the azimuth, the position line being taken as the line
through that position at right angles to that azimuth. And the precision of
that approach depends on how good is his initial estimate, for one of those
coordinates.

| Rather, it
| specifies a point's latitude and longitude which I'll call the
| reference point, RP, even though conventionally it's called the
| "assumed" position -- a misnomer.  St. Hilaire calculates the great-
| circle distance and azimuth from this RP to the nearest point on the
| LOP.  This point is exactly on the LOP; let's call it the St. Hilaire
| point (SHP).

It's rather strange: John and I seem to be referring to different papers
here. I just can't find any of that in the 1873 paper I have referred to.
Perhaps John could give section and page numbers. If he is working from the
same translation as I have, it follows the original pagination.

George.

contact George Huxtable at george@huxtable.u-net.com
or at +44 1865 820222 (from UK, 01865 820222)
or at 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.


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