In 1752, the German astronomer Tobias Mayer had built an experimental model of reflection circle, or repetition circle, based on the double reflection principle, aiming to eliminate the main fault related to octants: the errors of graduation or of a scale. This idea was taken by the French Navy Officer Charles de Borda (1733-1799), and led to the construction of his first circle in 1772. This instrument was tested for the first time aboard the ship “La Baussole”, one of the ships owned by Jean-François de La Pérouse’, the famous French explorer. The outer circle was graduated in half degrees and fractions and counted as double values - exactly like the sextant following the principle of the rotating mirrors - and was graduated from 0° to 720°. The angle, or “angle distance” between two sighted points was obtained by reading the angle difference between the two alidades on the circle. The reading was possible thanks to two verniers. By so doing, it was possible to eliminate the error of a misplaced zero (collimation) and of a wrong graduation. Such defects could occur in any instrument and were caused by faulty graduation of the circle occurred during manufacture. Moreover, by measuring angles between 0° and 180°, it was possible to solve all the problems related to navigation and hydrography. A handle normal to the plane of the circle allowed not only to observe vertical distances but also distances on the horizontal plane, which were more frequently needed when calculating points between lunar distances. The Borda Circle was manufactured in France from 1777 by Lenoir. Its diameter was 26 cm. In England the repetition circle was manufactured by James Throughton, a famous scientific instruments maker. His circle was called “full circle” and had four right-angled radial arms instead of the six arms of the Borda circle built by Lenoir. The circle was widely used during scientific circumnavigation voyages and was kept aboard as hydrography and navigation instrument until World War I. Since then, it’s only been used in hydrography for the measurement of points on nautical charts. The Amici-Magnaghi circle was a similar instrument used until recently by the Italian Navy. This instrument was built by the Italian Hydrographical Navy Institute and was formed by a graduated circle with a handle to hold it horizontally; in the middle of the circle there was a rotating prism, and fixed to circle there was a telescope for land observation. By rotating the prism, a second image was reflected in a was that it coincided with the first image sighted through the telescope. Finally, it was possible to read the angle formed by the two sighted points through two small holes.
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