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At 18:24 22/05/2008, you wrote:
>
>
>Mike Burkes wrote-
>
>"A mid morning sun line advanced to to the LAN Lat and Long, the latter
>having been determined by equal AM and PM altitude pairs and averaging, can
>yield three LOPS forming a triangle yielding a running fix. I am sure that
>was the procedure back in the days."
>
>Well, yes, but you can get three such LOPs, providing a fix which can give
>latitude and longitude, whether the AM and PM altitudes are equal or not. So
>what is the advantage of making the altitudes exactly equal?
>
>George.


I think what George is driving at is that with the "New Navigation" of
position lines, all position lines are created equal, no matter what their
azimuth.

As it happens, I have just been reading a paper written in 1919 in which an
instrument specifically built to use "equal altitudes" was discussed -
namely the prismatic astrolabe. This was an instrument primarily used for
precision geographic surveying up until the advent of the GPS, but in 1919
was a relatively new innovation. Dr John Ball of the Survey of Egypt and H.
Knox-Shaw, chief astronomer at Helwan observatory near Cairo, were
reporting on a series of  trials done at the observatory to compare a small
precision astrolabe against a good 'modern' theodolite, both of which had a
nominal precision of 1 second of arc (SOA).

The precision astrolabe (or 'equiangulator' as the Americans called their
version) is a comparatively simple instrument, consisting of a telescope, a
prism and a bowl of mercury. The prism combines the direct and reflected
image (off the surface of the mercury) of a star in such a way that the two
images of the star are seen to move in opposite directions in the
telescope. The moment when the images coincide is the moment when the star
is at the fixed altitude for which the instrument was built - usually 45
degrees. The beauty of the instrument is that nothing is critical in its
adjustment, which makes it particularly rugged for field use. Later
versions of the instrument were (said to be) capable of measuring time to
0.004 seconds and latitude to 0.06 SOA. This is equivalent to finding your
position to within two metres, which is somewhat better than a standard
handheld GPS.

Getting back to the paper, John Ball comments that, "Experience during the
last two decades has shown us that when latitude and time are both to be
determined with a theodolite, the most accurate method is that of equal
altitudes of three or more stars..."

The results of their trials showed the standard deviations with the
precision astrolabe were about 3.2 SOA and with the theodolite, about 5.4
SOA. This was "considerably" larger than the authors expected, which would
have been around 1 SOA for both instruments. Both instruments had
telescopes of about 30x power, which was probably limiting the standard
deviation to about 2 SOA, given a resolving power of about one minute of
arc for the human eye. But (the authors concluded) the precision astrolabe
clearly performed better in this limited mode of observation.

I have read of other trials of this sort, where azimuth precisions were
determined for a variety of theodolites after a long series of readings.
The results are always worse than expected, but seem to be a function of
telescope power at the end of the day.

Geoffrey Kolbe



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