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Henry Halboth wrote-

Frank and George are otherwise most correct in inviting attention to the
affect of accumulated errors in sights taken above opposing sea horizons.
Such methodology has often been advocated as providing the most accurate
fix, in that the box-like configuration resulting tends to average out the
errors of both instrument and observation - but that's another tale.

==================

Henry is right to point to what looks like a bit of a paradox here.

In the context he is referring to, which I take to be a round of star-sights
at dusk to obtain a position, it is indeed excellent practice to observe
altitudes of a number of stars, over a wide range of azimuths. Indeed, if
it's possible, each observation of a star in a particular direction
(southeast, say) can be "balanced" with that of another star in a roughly
opposite direction (northwest). And then, to get a decent "angle of cut"
between position lines, to observe another pair of stars, roughly at
right-angles to the first pair. Which ends up with the sort-of box-like
plotted quadrilateral on the chart, just as Henry describes, rather than the
triangular "cocked hat" that's so often spoken-of on this list.

And there are sound reasons for that long-established practice. There could
be common-errors, applying to all such altitude observations, all round the
horizon: these can be a failure of the actual dip to observe textbook
predictions, or an uncorrected index error in the sextant.  These errors
will move all the resulting position-lines, all towards, or all away from,
the direction of the bit-of-horizon above which they were measured. Then,
when the navigator strikes some sort of middle-value for his estimated
position, within that box, most of any bias due to dip or index error will
be averaged out. This is the "another tale" that Henry refers to.

=================

But what we have recently been discussing is another matter altogether:
determining the angle-across-the-sky between the Moon and another body, by
measuring the two altitudes up from different bits of the horizon. And in
that context, if those two horizons are in opposite directions, then the two
dips (or index errors) combine, and add in such a way that the effect on the
resulting angle between the bodies is doubled, not nulled.

George.

contact George Huxtable, at  george@hux.me.uk
or at +44 1865 820222 (from UK, 01865 820222)
or at 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.

   

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