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It seems to me that the problem of measuring azimuth at sea is two
fold. First is that even a corrected magnetic compass is only accurate
to about one degree. Second is devising a sufficiently accurate
instrument to measure the difference in azimuth between stars.

If you can solve the second problem you could  devise a least squares
solution to the problem of fitting the difference in azimuths, and
indeed of one star was Polaris this would be more or less the same as
having the absolute azimuth. But to measure the azimuth one still
needs a horizontal reference of some kind. The question then is if you
can get away with a less accurate horizontal reference than needed to
measure altitudes to one minute.

There is a lot more to this problem that just solving the equations
with Newton's method on a computer!

On 20 October 2017 at 15:28, Herman Dekker  wrote:
> Hello Francis,
>
> How does your "specially adapted Az compass " looks like? I have found a
> compass that is usable till about H=60°. Above that height it is a guess
> every time.
>
> Regards,
>
> HermanD
>
> 



-- 
Professor of Applied Mathematics
University of Manchester
http://www.maths.manchester.ac.uk/bl

   

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