The perspective view of the repeating circle shews all that is provided by the maker, and in the observatory is all that can be required ; but in the field, as no one would think of placing it upon the ground, a stand is wanting ; hut this may be so simple in its construction, as to be made by any one accustomed to work in wood. It should consist of three spreading well braced legs, in serted at top into the under side of a round table, and united below by three crosses, reaching from leg to leg. The diameter of the table should be at least two inches greater than is required by the feet-screws of the tripod. It may be about three feet high, more or less, according to the stature of the observe' : and if a circular groove in the surface of the table receives the fect-screws, the three studs may be dispensed with, and the whole in strument turned rol,nd in order to lay it in the plane of every pair of objects, the angular distance of which is to he taken at the same station ; and that without losing the angular point, as indicated by a plummet suspended below the centre of the instrument.
There will seldom be found ground sufficiently firm •o suppc:t the ‘‘,.cigut of the observer, without deranging the position of an instrument as he walks round it; dud on this account, in the most accurate operations, it i3 usual to level the ground, and to secure steadiness by driving three piles of wood to a sufficient depth for the legs of the stand to rest on.
As perhaps the feet-screws of every instrument are the most unsteady parts, for the purpose of lessening this evil, these are made as short as possible. An ob server, therefore, should provide himself with a number of wedges for propping the tripod, in adjusting the cir cle into the proper plane, agreeable to a rule hereafter to be given.
The repeating circle, as above described, may be con sidered either as a geodetical or as an astronomical in strument; and it owes much of its celebrity to its having been employed in this double capacity by the French as tronomers, in the great trigonometrical operations lately carried on in that kingdom.
Of the manner in which the repeating circle was used on this occasion, a most ample account has been given by the National Institute, in two quarto volumes, enti tled L'arc du Meridien. Much useful information may likewise be found in Puissant's Geodosie, and in a single quarto volume, published separately by Delamhre, enti tled, Methodes analytigues pour /a Determination d'un arc du Meridien.
In all these treatises, a great portion is allotted to cal culations which become necessary, both from the mecha nical construction of the repeating circle, and from the circumstances under which it must frequently be unavoid ably used. Many of these considerations, being common to all instruments, will be given under SURVEYING. And
of those which are peculiar to this instrument, our limits oblige us to omit a great many, and to confine ourselves to those which seem to its most likely to be of general utility.
The repeating circle will not measure the horizontal angle between two objects of different elevations, but it will measure the direct angular distance between two ob jects, and the zenith distance of each of them, from which data, the horizontal angle may be inferred by spherical trigonometry ; and as, in each of these mea surements, the repeating property of the instrument may advantageously be employed; the horizontal angle may no doubt be obtained to a very great degree of preci sion.
Let it h be an arc of the zon, IF h', two terrestrial objects. Z the zenith, and ZII, Zh great circles or the sphere passing- from the zenith to the horizon through the points II' h'. Then in the angle ZI l'h', the three sides ZH', Z//, IVY, being determined by actual measurement with the strument ; the angle Z, equal to the arc II h, may be computed by spherical trigonometry. The problem is very nearly, indeed, similar to the well known case in nautical astronomy, in which it is recittired to determine the true distance of a star from the 11)0011, having given its apparent distance, and the altitude of each by vation ; and for each process, Tables have been devised to facilitate the calculation, which, without such aid, would be very tedious and laborious. The zenith dis tance of a terrestrial object being determined with this Instrument, precisely in the same manner as the zenith distance of a star or other celestial body, nothing here need be said on that part of the process. \Ve however, subjoin an example actually taken by an in istrument of Mr Troughton's construction, to shcw with what extreme accuracy a result may be obtained by an experienced observer.
Zenith distances of a fixed ?nark, taken Sent. 4, 1812, with a repeating circle of 211r Troughton's construction.
until it by the eye to occupy the proper position, then a second time bring the telescope to the object, by the foot screw and turning in azimuth ; lastly, complete the operation by bringing the upper telescope to the other object, by its own proper motion, in conjunction with that of turning round the cross axis. Th- princi ple of the above rule is this ; the cross axis of the stand and the lower telescope being made parallel, and pointed to the object, the circle may be turned round that axis without changing the angular position of tile telescope. When this verification is rightly performed, the intersec tion of the wires of the micrometer of the moveable tele scope should pass over each object in its revolution round its centre. To effect this readily requires sonic little dexterity and practice.