Geoscience Reference
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angle between them over 45°
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, the repeating circle had two independent telescopes
and a scale that was a complete circle. It required two operators and was too big for
one person to hold; it was more accurate than a conventional quadrant but less
convenient to use. Mayer's idea was tried out in Britain by the Royal Navy, but
because it was less practical its use was not adopted - the Navy's push to find a
more compact instrument (easier to hold and operate on a ship in uncertain weather)
caused the development of the sextant (a 60° angle on the scale). On land and in a
scientific or a mapping survey the repeating circle was better.
People
Jean-Charles Borda (1733-99)
Borda declined opportunities to become a Jesuit and started a career as a mathematician in
the army where he studied ballistics and geometry. On the basis of his work he was made
a member of the Academy in 1756. He saw action in the army in the Seven Years War and
moved on to the navy, sailing extensively in the Atlantic Ocean between 1765 and 1782.
At first Borda was on missions of exploration but later as a naval commander helped
orchestrate the French victory over the British navy in support of the American War of
Independence. In 1782 he was captured by the British and returned to France under parole,
retiring to his estate during the early years of the French Revolution but returned to Paris
to chair the Commission on Weights and Measures. Here, Borda proposed the decimaliza-
tion of angles (a right angle of 100 degrees, each divided into 100 minutes, and each minute
into 100 seconds) and calculated trigonometric tables based on decimal degree inputs.
If the repeating circle was used for astronomy, the scale was adjusted to be
parallel to the line between the stars; if the instrument was used for surveying the
scale was horizontal. A surveyor aligned one telescope on the first object,
A
, and
clamped it on to the axis. Another surveyor aligned the other telescope on
B
,
and clamped it accordingly. The scale read the angle, say θ, between the objects,
but this was not the end of the measurement. The second surveyor rotated the two
telescopes, both locked in place, passing his telescope to the first surveyor so that
the second telescope sighted
A
. He unclamped the second telescope and passed it
back to the second surveyor to sight
B
. The angle between the two telescopes was
now 2q and could therefore be more accurately measured. The doubling could be
repeated perhaps ten or twenty times, progressively reducing the sighting error by
repetition and by measuring the angles progressively against different sectors of
the circle, reducing any systematic error in the engraving of the scale. The new
instrument could read angles perhaps five or ten times more accurately than previ-
ously possible.
It is not clear whether the Academy selected Borda's repeating circle to measure
the Paris Meridian because of its accuracy or whether Borda pressed the Academy
to adopt it for the prestigious project in order to reflect well on his invention. Either
way, the Academy commissioned four instruments to Borda's design (one survives
and is housed in the museum of the Marseille Observatory) commissioned from the
instrument maker Étienne Lenoir.
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The maximum angle that a quadrant could measure between two stars was double this because
of the mirror reflection, hence the name “quadrant”, a quarter of a circle being 90°.
