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Greg wrote:
>     A quick google search of TITANIC web sights showed the TITANIC's
> ocean floor position to be in good agreement with the distress call
> latitude but not the longitude where there is a 20 minute discrepancy.
> What would explain this discrepancy best chronometer error or DR speed
> error? The water was very cold at the time so I doubt that the gulf
> stream was a factor.

1. Sights taken "before 8 o'clock", collision "at 11.43, I think"
during which interval the Titanic was steaming full bore to the west.
Sinking quite some time after the collision, during which time the
ship was drifting ... back to the east (it was a calm night), although
at a considerably reduced rate.

2. The sea bottom was deep below the water surface, and that long way
down taken by the ship may not have been vertical ...

As to the elimination of constant error, this was discussed in some
detail, complete with diagrams, some time ago (thus findable in our
archives).

Yes, sights using opposing azimuths will lead (with constant error
only present, ie; assuming no erratic error which could complicate
things) to a 'box' shape.  Since with each pair of intersecting LOPs
the true fix will lie along a line bisecting the angle formed by their
intersection, with such a box shape the fix will be found ... at the
centre of that shape!

How about that.  Who would have thought.  Incidentally, the same also
holds true for a triangle formed by 3 LOPs.  Assuming only a constant
error, and a spread of azimuths of more than 180d, the fix (free of
that constant error) must be found at the centre of that triangle.

It is only when the assumption is made that the sights are somehow
free of any constant error, and thus subject only to erratic error,
that the  fix becomes 3 times more likely to lie outside than inside
the shape.

How can either presumption be made?  It seems to me that, a priori,
any round of sights may contain some extent of both types of error.

Therefore the most useful approach is to eliminate erratic error at
source.  This can be done via the comparison of a number of sights of
the same body taken over a few minutes with the slope caused by the
apparent rise/fall of the body observed over that period.

Then, erratic error eliminated (to a usefully practical extent), any
remaining error, now assumed to be the constant type, can be dealt
with by bisecting those intersecting LOPs and finding the fix ... at
the centre of the shape.

Et voila tout.  That's it.

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