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I wrote:

> George says the old almanacs used apparent
> time, and I see no way to get HORIZONS to calculate with that time
> scale, or give the equation of time. However, it can give the local
> apparent solar time at Greenwich with this command:

Note that the value includes the effect of geocentric parallax and
dinural aberration at the Greenwich Observatory. I.e., the equation of
time obtained thereby is specifically for that location. For the
geocentric value, you could get values for observers on the equator at 0
and 180 degrees longitude, add 12 h to the latter, and mean the pairs.


Alexandre E Eremenko wrote:
>
> Interestingly, many mid XX century sextants have quite large
> corrections in their certificates (30" to 45").
> Which means of course that the manufactures simply DO NOT CARE
> to make a perfect arc. There is no doubt that in XX century there
> is such a technical possibility: the arcs of theodolites, for
> example are divided to much greater precision than sextant arcs
> (good theodolites measure to 1" and some to 0.1")

Jesse Ramsden built a 1-second theodolite in the 1780s for the first
triangulation to connect Greenwich and Paris. It was a masterpiece, the
most accurate ever made up to that time. The instrument still exists. It
weighs about 200 pounds, and the horizontal circle is three feet in
diameter.

http://content.cdlib.org/xtf/view?docId=ft6d5nb455&doc.view=content&chunk.id=d0e7853&toc.depth=1&anchor.id=0&brand=eschol

Theodolites in the 20th century were much smaller. For example, the U.S.
Coast & Geodetic Survey's principal triangulation instrument in the
1930s and 40s weighed about 30 pounds. It had a metal circle 9 inches in
diameter, with readings to one second (tenths estimated) via micrometers
180 degrees apart. Its accuracy could be tested by measuring the same
angles using different parts of the circle, and comparing results.

"If the micrometers have been carefully adjusted for run, the mean curve
for the variations of graduations for a first-order circle, as
determined from field observations, should not have a range greater than
3.5 seconds. This test can be made with better results in a laboratory,
employing collimators as sighting targets. Under these conditions the
range of the variations should not exceed 2.4 seconds for the best circles."

In the 1950s they started using the Wild T3. It had a 5.5 inch
horizontal circle etched on glass. The micrometer graduations were .2
second. Opposite sides of the circle were read simultaneously in a
single micrometer operation, through an eyepiece right beside the
telescope eyepiece. No longer did you put the telescope on the mark,
then step around to the side of the theodolite to read the micrometer
while your assistant read the opposite micrometer.

Reading the circle at points 180 degrees apart is standard practice. The
circle's eccentricity with respect to the instrument's axis of rotation
is cancelled by taking the mean of both readings. A sextant doesn't have
that capability. In addition, it always uses the same spot on the arc to
measure a given angle. On the other hand, a theodolite's horizontal
circle can rotate to any desired position so you can average out
graduation errors. That is, you set the circle to a certain position,
sight the targets and record the angles, move the circle to a different
position, re-observe all the targets, etc.

During the golden age of U.S. triangulation, each point was observed
with 16 different circle positions. These were arranged so the repeated
measurements of a given point would be well distributed around the
circle and throughout the range of the micrometer too. So, though the
instruments read out to single seconds, it took elaborate procedures to
actually get that accuracy.

Nowadays theodolites such as the Wild T3000 give an immediate digital
output to a tenth second. But that still doesn't mean the angle is
measured that accurately in the real world. Even the National Institute
of Standards and Technology doesn't claim .1 second in its calibration
service. And that's in a laboratory.
http://ts.nist.gov/MeasurementServices/Calibrations/Angular.cfm

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