The reflecting circle was invented by the German geometer and astronomer Tobias Mayer in 1752, with details published in 1767. His development preceded the sextant and was motivated by the need to create a superior surveying instrument.
The reflecting circle is a complete circular instrument graduated to 720° (To measure distances between heavenly bodies, there is no need to read an angle greater than 180°, since the minimum distance will always be less than 180°.). Mayer presented a detailed description of this instrument to the Board of Longitude and John Bird used the information to construct one sixteen inches in diameter for evaluation by the Royal Navy, This instrument was one of those used by Admiral John Campbell during his evaluation of the lunar distance method. It differed in that it was graduated to 360° and was so heavy that it was fitted with a support that attached to a belt.It was not considered better than the Hadley octant and was less convenient to use.As a result, Campbell recommended the construction of the sextant. Jean Jean-Charles de Borda further developed the reflecting circle. He modified the position of the telescopic sight in such a way that the mirror could be used to receive an image from either side relative to the telescope. This eliminated the need to ascertain that the mirrors were precisely parallel when reading zero. This simplified the use of the instrument. Further refinements were performed with the help of Etienne Lenoir. The two of them refined the instrument to its definitive form in 1777. This instrument was so distinctive it was given the name Borda circle.