The calculation of longitudes, indispensable for determining a ship’s exact position at sea, was not possible until the octant’s invention in the 18th century, though it lacked sufficient precision. The French mathematician Charles de Borda finally solved this problem by inventing the reflection circle. Graduated to 720°, Borda’s circle enables the measurement of an angle between two celestial bodies. First the instrument’s telescope is aimed at a celestial body, then a second time via a small semi-reflecting mirror in the middle of the circle. This double measurement limits errors and improves the precision of measurements. Borda carried out several tests during expeditions to the Caribbean and perfected the instrument, giving it its definitive form around 1777. This example was formerly in the physics cabinet of Jacques Alexandre César Charles.