The reflecting circle–essentially an octant extended to a full circle–was
designed for the purpose of determining longitude by measuring the distance
between the moon and a nearby star (the so-called lunar distance method). Johann
Tobias Mayer, the German astronomer who introduced the form, also developed the
tables of the moon’s motions that were needed for longitude determinations.
Tests of Mayer’s instrument in England in the 1750s led to the invention of
the sextant. The French physicist Jean-Charles Borda described an improved
reflecting circle in 1787, and instruments of this type remained in use into the
nineteenth century. They were used for latitude as well as longitude, and on
land as well as at sea.
Ref: J. A. Bennett, The Divided Circle. A History of Instruments for
Astronomy, Navigation and Surveying (Oxford, 1987), pp.134-136.
Jean-Charles Borda, Description et Usage du Cercle de Réflexion