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I have been following in a desultory way the current discussion
between George Huxtable and Frank Reed about errors in lunars. My
interest is perhaps more in the instruments of navigation than in its
practice. I did once do a lunar about thirty years ago, under the
tutelage of a retired surveyor who spent his holidays as �fifth mate
for navigation� aboard a South Pacific islands steamer. We used seven
figure log tables, so you will understand that I was not necessarily
keen to repeat the experience.

In a previous posting about sextant calibration, I gave the re-setting
error of my ex-USSR SNO-T sextant as about 4 seconds, its micrometer
error as about 2 seconds and its backlash error as up to 12 seconds.

On the occasions when I have directed a sextant at the sky rather than
at an autocollimator instrument, I have noticed that my determination
of index error is seldom the same twice running. At first I put all of
it down to my inexperience  and shaky right arm, but I have quite a
lot of experience with making and using optical instruments and am a
careful observer. George�s requests for �Error budgets� led me to try
to find out what sort of spread of results I(and possibly others)
might expect when finding the index error of their sextants.

I made three sets of thirty careful observations for each method:
using a sharply defined land horizon about 6 km away; using the sun�s
limbs; and using a 2nd magnitude star. To make things easier and to
avoid fatigue, I clamped the sextant atop a theodolite sextant so I
could make each observation a leisurely one. I also glued a simple but
effective paper vernier over the micrometer index to reduce to some
extent a tendency to bias the results in a more or less favourable
direction when estimating tenths. Here are my results for the standard
deviations:

        Method                    S.D.      95% range
Horizon, reflected image up to direct image     0.142        0.56
Horizon, direct image up to reflected image     0.157        0.62
Sun�s limbs                         0.155        0.61
Star                                0.174        0.68

For those who might think that statistics is a new form of contact
adhesive, I should point out that the standard deviation is a measure
of the dispersion of the results about the mean value; and 1.96
standard deviations each way will �capture� 19 out of 20 or 95% of
results. 1 S.D. each way will include about 64% of results. So, my
sextant-eye-brain system will give an index error of more than 0.3
minutes away from the best estimate, the mean, one time in twenty.
About 45% of the time it will be more than about a minute and a half
away from the mean.

Physicists are supposed to be good at error estimation and my
education was in the biological sciences, so I leave the rest to
George and others...

Bill Morris
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