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I forgot to mention in my previous message that
the angle measured in the numerical example was assumed 120d,
about the largest angle available on modern sextants.
(Larger angles produce larger errors).
A simple consequence of this formula is that
the "tolerance" in this angle is about 15'
for "practical purposes", even for the Lunars.

This partially explains why sextant is such a good
and robust instrument: the errors in the final result mostly
depend quadratically on the errors in adjustment.
And a square of a small number is a VERY small number.
This applies to the "side error" as well (perpendiculatiry
of the horizon glass). Some experts even recommend not to adjust
the side error completely, leaving some 0.5'. This simplifies
bringing two star images together when measuring IC or
star distances.

An exception is the INDEX error which is simply added to
the result. That's why one has to determine the index error
very carefuly and precisely.

Alex

On Mon, 17 Apr 2006, Alexandre E Eremenko wrote:

> Dear Robert,
> The only book I know that contains a COMPLETE
> theory of sextant is Chauvenet. (I am sure that there
> are others, but this is really complete, very concise,
> and written in good English:-)
>
> In particular, on p. 115 (vol. 2) the following formula
> is derived:
> Err=-2 L^2 sin1" tan(h/4),
> where Err is the resulting error, in seconds
> L is the deviation of your mirror from
> perpendicularity (in seconds) and h the angle you measure.
>
> In more modern notation this becomes:
> Err=-0.00057 L^2 tan(h/4)
> where both Err and L are in minutes now.
>
> For example, if L=5'
> Then Err=0.008 or 05", which is completely negligible.

   

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