The advantage of three readings over two for the limb of a theodolite, the telescope of which will turn quite round, is great, and was perhaps first noticed by Mr Pond. In two reverse positions of the circle, made by turning the telescope half round in azimuth, and also half round its own axis, three verniers will give the position of an object upon six different and distant portions of the circle ; hut where two opposite verniers are used, no more than two places of the circle are employed ; fur on reversion the venders only exchange positions. A screw apparatus, as at c, attached to one of the branches of the tripod, clamps the azimuth circle, or allows it a quick or slow motion at pleasure.
The repeating circle of Borda has an azimuth circle of about four inches diameter, the single Vernier of which subdivides it to 3' or 5' : the edge is indented, and acted on by a for the purpose or turning it round, in the same manner that similar means arc employed in the com mon theodolite.
To the top of the pillar is horizontally fixed a strong brass bar d, upon which a similar bar is laid, and secured there by two ringer screws, the head of one of which is represented at e : this is the part where the instrument may be taken asunder for packing, or for more convc Mewly moving it from place to place. At right angles to the bars, and fastened to the upper one, arc erected two supporters, in the tops of which are centered the ends of a horizontal axis, round which the whole of the upper part of the instrument may be turned. A semicir. clef is fastened at its centre, to one end of this axis, and having its position parallel and contiguous to the interior side of one of the supporters, is occasionally laid hold of by a clamp attached to the latter, and thus affords the means of securing the principal circle and telescopes in any position that obscu vations can require.
The centre-work of the upper circle is made fast to the middle of the horizontal axis, which it crosses at right an gles; at its remote end, upon the socket of the centre, is placed a cylindrical counterpoise, which balancing the circle and telescopes, keeps them, respecting motion round the. cross axis, at rest in every position. The coun terpoise, in order to give it a maximum effect, is fixed at the greatest distance from the cross axis, which will al low it to pass the bar on the top of the pillar, when the face of the circle is put horizontal, or in changing its posi tion from one side of the pillar to the other.
The principal circle is 18 inches in diameter, compo sed of an octagonal centre piece, into which are inserted eight conical radii ; these being strong- and tubtilar, arc united at their extremities by a circular limb ; strength ened in its place by a rim or hoop, which being screwed fast to its back, forms what is termed an edge-bar : the division of the circle is by lines, the distance between which is W.
To the back of the octagonal centre piece is screwed the axis whereon the circle and telescopes arc turned round in the plane of the circle : it is nearly eight inches long, but only about two thirds of its length is employed for that purpose, working in the socket of the counter poise ; the rest a bearing round which the socket of the back telescope revolves.
An index with four branches, the verniers of which subdivide the circle to l(P, has an axis of steel attached to its centre, wnich passes through the whole length of the axis of the circle, the latter being a socket wherein it turns round, in the same manner that the axis of the cir cle turns ire the socket of the counterpoise. This index is furnished with the usual apparatus for quick and slow motion, which attaches to, and forms a part of, its chief branch, as at g. There is another index, the position of which is behind the circle, having but one branch, and which carries no vernier ; it is furnished with the means of being clamped, and put in gradual motion like the :o.her in clamping it attaches to the edge-bar of the cir cle ; it is united to a socket, which embraces the part of the axis of the circle not occupied by the socket of the counterpoise.
The instrument has two telescopes similar to each other in almost every respect. The one in front or the circle is fixed to the index at half right-angles between two of its four branches ; the one behind has a position forming the same angle with the only branch of the other index. The connection between the telescopes and indices is formed near the centres, so that the former may take the unbiassed direction which is produced by the axis alone, without being at all influenced by the irregularities of the limb. In the circles of Borda, the telescopes are made to take the direction of the circle, and the accuracy of their :notions depends upon the truth of its plane. These tele scopes are about two feet in length ; the aperture of the objcct-glasses nearly an inch and three quarters, and they are provided with powers of from 30 to 60, according to their different eye-pieces. The telescope behind the cir cle has, in its form, only two cross lines : the plate in which they arc fixed is adjustable respecting the verti cal and horizontal position of the lines, and is also acted on by two drawing screws for placing the line of collima tion parallel to the plane of the circle two others at right angles draw also, and are intended for placing the collima tion parallel to a level, which is to be described. In the front telescope there arc three lines crossing other three ; these are adjustable exactly like the former, only the ad justment last mentioned is not necessary. As the tcles ....Ives of the repeating circle are designed to view objects very differently situated respecting distance, the eye-tubes of both have a motion given them, by teeth and pinions, they may be brought outwards, in order to pro cure distinct vision of near objects.