REPEATING CIRCLE. In order to diminish the effect of errors of gradua tion, and to obtain very accurate measure ments by means of comparatively small, and, therefore, portable instruments, a method of observing was invented, or rather brought into use, by Borda, which is now extensively employed, especially in geodetical operations. The method, which consists in moving the telescope successively over portions of the gradua ted limb corresponding to the angle to be measured, and reading only the multiple arc, may be advantageously applied to circular instruments destined for very different purposes: as, for example, to an instrument for the measurement of the zenith distances of stars or terrestrial objects, or the distance of two trigono metrical stations, in which case it is sim ply called called repeating circle ; to a re flecting circle used for observations at sea, when it becomes a repeating reflecting circle; or to a theodolite, when it becomes a repeating theodolite.
When the repeating circle is used for measuring zenith distances, it is con structed so as to be capable of being turned round on a vertical pivot, the di rection of which passes through its cen tre, and to which its plane is parallel, and also of turning in its own plane about a horizontal axis. The instrument being placed in the same vertical plane with the star, the telescope is directed to the star and the bisection made ; the telescope, which carries the verniers with it, is then firmly clamped to the circle, and the circle turned round 180° in azimuth about the vertical pivot. If the circle be
now kept fast, the telescope undamped and carried round till the star is again bisected, it is plain that the arc of the limb passed over by the verniers in conse quence of this motion of the telescope will be double the zenith distance of the star. The same process is repeated as often as may be thought necessary. For the purpose of geodetical measurements the circle is usually furnished with two telescopes, one on the face, and the other on tile back ; and so placed that the opti cal axes of both are exactly in the plane of the circle. The circles used by Me= chain and Delambre in the operations con nected with the measurement of the French arc of meridian, were about 4-10ths of a metre (nearly 16 inches) in diameter, and were divided into arcs equivalent to about 32 sexagesimal se conds, which were subdivided into tenths by the verniers.
The merit of first applying the ingen ious principle of repetition to angular measurements, belongs to Tobias Mayer, I but it was Borda, as above stated, who first brought the instrument into general use. For a description of the repeating circle, its adjustment, and the method of using it, see Blot. Astronomic Physique, tome i.; Delambre Astronomie on Base Metrique, tome i., Puissant traits de Ge odesie ; Roper's Practice of Navigation. The comparative advantages and defects of the instrument are very clearly stated in a paper by Troughton, in the let vol ume of the Memoirs of the Royal Astro nomical Society.