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Frank,

Bolte also referenced an Englishman, Behrens I believe, who did about
80 lunars.  They had a fair amount of data.  Bolte had six observations
per lunar and the Englishman 5, so that's about 600 observations total.
  The great value of these data is that they were taken at sea.

In general, the number of observations needed depends on the amount of
dispersion in the data and how precise you wish to be.  There's no
inherently correct sample size; it depends on the experimental system
and the objectives of the experiment.  I believe these sample sizes are
adequate, but unfortunately we don't have the raw data, only the means,
with no standard deviation about each mean.  Also, Jan has not reported
yet the direction for each of Bolte's lunars.

Bolte and Behrens were reporting the difference between the distance
calculated based on chronometer and the cleared, observed lunar
distance, assuming the chronometer distance was the correct one.  The
average difference for the star observations was less than the
difference for the sun.  This may have been due to the fact that the
sun lunars were mostly taken in the morning when the moon was west of
the sun rather than an equal mix of morning and afternoon, which also
is claimed to be a major factor in the larger standard deviation of the
star differences.  I have yet to understand why the direction of the
observing body would affect the observed value, but at this point, the
effect seems to be real.

I'll poke around in Chauvenet to see whether I can find reference to
the value of taking lunars in both directions.

I still haven't figured out whether these Bolte & Behrens differences
should be treated as deviations or observed values for statistical
analysis.  However, as opposed to the standard deviation of the
differences about their mean, it's clear to me that the mean difference
is the appropriate statistic here, or perhaps the square root of the
mean of the squared differences, which are 30' and 33' for Bolte's star
and sun lunars respectively.  The standard deviations of the
differences would measure the precision of the observations plus any
effects of the body and the direction of measurement, assuming it
should be treated as an observed value rather than a deviation.

I have been taking lunars.  To get 500 would take me about a year.  It
would also help if I had a sextant of known accuracy with a strong
scope.  Since you have done this, I thought perhaps your data might be
of immediate value.

The essence of science is to report claims and along with them the data
on which those claims are based.  You reported a claim about the
relative accuracy of the sun versus stars and planets but no data.  I
referenced these previous data which refuted your claim.

Fred



On Jan 9, 2004, at 2:29 AM, Frank Reed wrote:

> You suggested that 'perhaps I could summarize my data and illustrate
> my claim'. YE GODS, NO!!! Get out your sextant, and TRY IT. Do some
> observations.

> I went back to the original post. It's not quite as you described.
> Here are the errors Jan K posted:
> >>
> 31" for one distance (averaged set of shots) of the Moon and a star
> (18" by Behrens)
> 22" for one distance of the Moon and the Sun (18" by Behrens)
> <<
>
> SHOOT some lunars, gang. Judge for yourselves based on your own
> observations. That's the essence of science.
>

   

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