Fr.: cercle à réflexion
An instrument for measuring angular distances, based on the same principle as the → octant, but with a full circular limb divided into 720°. It was invented in 1752 by the German astronomer Johann Tobias Mayer (1723-1762) to improve on the octant which often gave wrong results because of incorrect graduations. The instrument consisted of an index arm and a small telescope, both pivoted centrally. In practice, the index arm is first set to zero, and the telescope rotated until the two images of a star are seen in coincidence (the one directly, the other by double reflection). Then the index arm is freed, and rotated until the other object is seen in coincidence after double reflection. The angle has now been measured, but the double operation is repeated several times, and the final angle divided by the number of repetitions to find a mean value. Hence, the instrument was sometimes called a "repeating circle." The reflecting circle had little success because it was heavy and uncomfortable to use. Its improved form is called → Borda circle.