In the second half of the eighteenth century, when the first sextants were built, the art of graduating arcs and circles was not very precise: incorrect divisions often resulted in undetectable errors, or errors that could be corrected only after long and difficult operations.
In sextants, where almost always close by values of angles were read, often the angular distance from the origin of graduations was wrong.
To remedy the defects of the graduations, the astronomer Tobias Mayer invented a method of observation, called "repeating", that required an instrument with a full circle, and proposed, in 1752 in London, a tool that was tested, with good results, but had little success because it was heavy and uncomfortable to use.
The "reflection circle" came into common use only in 1775, amended by G.C.Borda, and took his name.
It essentially consisted of:
- an outer circle, graduated in half degrees and fractions, counted as double values and therefore graduated from 0° to 720°, in ascending order from left to right for an observer standing in the center of the circle;
- an arm carrying the telescope and the small mirror, that could be fixed to the circle and was revolving around the small inner circle, so that the telescope and the small mirror were not fixed as in sextants, but movable with respect to the circle;
- an alidade carrying the large mirror, that was on the opposite side with respect to the telescope and could rotate of an angle twice the one available in sextants, allowing to observe the same angle in two different positions: one on telescope side, the other one on the side of the alidade.
The measurement of an angle could be accomplished in three different ways, called "right reading", "left reading", "cross reading".
Despite the benefits of the tool as compared with the sextant, especially concerning the influence of defects - such as prismatism of mirrors and eccentricity of alidade - and despite the favorable opinions of leading experts, the sextant was preferred by sailors, primarily for the lower cost and greater convenience, owing also to continuing improvements in the art of building graduations.
Despite its merits, already at the end of the nineteenth century the circle was completely abandoned (Capasso ,1994).
Amici's circle and Amici-Magnaghi circle
The difficulties in the fabrication of flat mirrors, especially to get the perfect parallelism of the faces, and the goal of achieving greater clarity in the images with a greater breadth of the measured angles, had suggested, already in the early stages of reflective instrument making, to make use of prisms instead of mirrors.
In England the first attempts to use prisms in the octants were made by Caleb Smith, but the innovation did not show significant advantages over Hadley mirror octants, as other difficulties arose in working with prisms and in achieving a perfect homogeneity of their masses of glass.
The first instrument made of reflective prisms with good properties was built in Modena (Italy) by G.B. Amici (1786-1863); on him Albert Meschiari wrote a thorough essay.
In the instrument the two prisms were placed in front of the telescope's objective and they were both revolving around the center of a graduated circle.
G.B.Magnaghi perfected Amici's circle, while retaining the new arrangement of prisms and the telescope; he made use of two rectangular isosceles prisms arranged with the edges normal to the plane of the instrument. One of them was fixed, with one face normal to telescope's axis, at a height such as to provide free access to direct rays in the upper half of the objective. The other one was led by a rotating alidade on a graduated circle, so that the hypotenuse of the prism was passing through the center of rotation and the faces were perpendicular to the plane of the circle.
The instrument was based on the phenomenon of total reflection in prisms and the property of an isosceles square prism to totally reflect on hypothenuse all rays entering from a catheter and leaving from the other catheter with two mutually cancelling refractions.
The prisms can therefore be used in place of mirrors, as if their hypotenuse faces were flat mirrors, and without changing the optical principle of the device.
Prisms, when used in regular sextants, offered significant advantages in light intensity, in addition to the ability of measuring angles up to over 180° (Capasso , 1994).