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Geoffrey Kolbe wrote-

|...you can calculate how an altitude will vary
| with time and so you now have a line with the correct slope to fit to your
| data. This is an additional piece of information that simple averaging or
| statistical fitting by method of least squares, say, does not give you.
| Having got your line with the correct slope, you can draw a line parallel
| to this through your data points for a best fit. Yes, no doubt about it,
| this is superior to simple averaging as an extra piece of information is
| being included that was not there before.

I am less easily convinced than is Geoffrey.

Yes, it's better to calculate the slope thanc trying to determine the slope
of the fitted straight line from the data points themselves; no question
about that. And it's better than simply averaging those changing altitudes
over the time period, if the observations were unequally-spaced in time. (If
they were equally spaced, you would arrive at exactly the same answer).

But having done that, all that's been done is to compensate for the known
steady rate of rise or fall. And it's done nothing to reduce the statistical
scatter of the points about that line. You raise or lower that line, with
that slope, until it runs between your points, as centrally as possible. And
the uncertainty in getting that best fit, by eye, is no better (but may not
be significantly worse) than when tackling the same problem at the moment of
a meridian passage, when the altitude is unchanging, and simple averaging of
all sights gives the best answer. There's no magic process of eliminating
the random scatter. It remains the scatter in each single observation,
divided by the square root of the number of observations.

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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