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In the military specification for the USN Mark 3 sextant I saw a method
  for checking arc calibration, different from the one Alexandre
observed at Freiberg.

The Mark 3 under test was fastened to a precision horizontal rotary
table, with the index mirror at the table's center. A collimator
attached to the rotary table in front of the sextant simulated the sea
horizon: it was positioned such that you saw its reticle when looking
through the horizon glass in the normal manner. (I can't remember if the
test used a special high power telescope instead of the sextant's scope.)

A second collimator, aimed at the index mirror but fixed to an optical
bench (i.e., it didn't move with the rotary table), simulated the star.

To begin the test, you set the sextant to zero, then rotated the table
and made small adjustments to the collimators until both reticles
coincided as seen through the sextant. From this zero position, rotation
of the precision table would change the angle between the collimators,
thereby simulating any desired star altitude.

The mil-spec had a table of allowable errors. The tolerances were larger
when a filter was in use. I vaguely recall the accuracy was similar to
high grade German and Japanese sextants.

   

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