THEODOLITE

(Yunanca köken — orijinale bakınız.) A surveying instrument for measuring the angular distances between objects projected on the plane of the horizon. In accurate surveying, when the instrument used for observing the angles is a sextant or reflecting circle, or such that its plane must be brought into the plane of the three objects which form the angular points of the triangle to be measured, the altitudes of the two distant objects above the horizon of the observer must be determined, and a calculation is then nece ary to reduce the observed angles to the plane of the horizon. The object of the theodolite is to measure the horizontal angles at once, and thereby render the previous calculation, and even the observation of the altitudes, unnece ary. It is easy to conceive, in a general way, how this object may be effected. A telescope with cro wires in its focus must be mounted so as to be moveable both about a vertical and horizontal axis, in order that it may be brought to bear upon any object, whether in the horizon, or above or below it; and the proper means applied for measuring, with the utmost accuracy, the angle described about the vertical axis (which is the horizontal angle) in turning the telescope round from one object to another. It is consequently nece ary to fix a graduated circle to the vertical axis, so that its plane may be exactly horizontal, and its centre coincident with the vertical axis; and about the same axis a radial bar, firmly connected with the telescope, must revolve parallel to the plane of the circle, for the purpose of indicating the divisions pa ed over on the limb of the circle when the telescope is turned from the first object to the second. And in order to render the instrument subservient to the purpose of measuring altitudes, a graduated vertical arch is attached to the telescope; but as it seldom happens, in the practice of surveying, that the objects observed are very much elevated above or depre ed below the horizon, or that the vertical angles are required to be taken with the same degree of accuracy as the horizontal angles, the vertical arch is generally only a portion of a circle of smaller radius, and le minutely divided than the horizontal circle. The theodolite, as now generally constructed for the purposes of ordinary surveying, may be described as follows: — The horizontal limb or circle consists of two circular plates, which turn freely on each other. The lower or graduated plate receives the divisions of the circle, and the upper or vernier plate has two vernier divisions diametrically opposite. The vertical axis consists of two conical parts, one working within the other. The external part is attached to the graduated plate, and the internal to the vernier plate. The diameter of the under plate is somewhat larger than that of the vernier plate, and its edge is sloped off to receive the graduation; and portions of the opposite edges of the vernier plate are sloped off in like manner to receive the vernier divisions. The graduation is usually to thirty minutes of a degree, but is subdivided by tlie verniers into single minutes; and in a well-made instrument quarter minutes may be estimated by the eye. For the purpose of adjusting the plane of the circle to the horizon, the external axis is litteil into a ball, which works in a socket between two parallel plates held firmly together by the ball and socket, I he under j)late being connected with the staff-head supporting the instrument. But lliis adjustment may also 122a THEODOLITE, be made (and in larger instruments is usually made) by a tripod support, having a foot screw at each extremity acting against s[ plate of metal supported by the stalK Upon the plane of the vernier plate are placed two spirit levels at right angles to each other, with their proper adjusting screws, by which the circle is brought accurately into the horizontal plane indicated by the levels. The centre of the circle is adjusted over the point which forms the centre of the station from which the observation is to be made by means of a plummet. Instead of the vernier plate described above, the index is sometimes formed by three radial bars connected with the internal vertical axis, each carrying a vernier at its extremity; and a fourth bar carries the clamp, by which the system is secured to the graduated limb. The horizontal axis of the vertical limb (which is usually a semicircle) is supported by a frame firmly imbedded in the vernier plate, and turning along with it about the vertical axis. The telescope has two collars or rings of bell metal, ground truly cylindrical, on which it rests in supports permanently attached to the vertical limb, so that both move together in the vertical plane. The divisions on this limb are read off to single minutes by means of a fixed vernier connected with the frame, and so adjusted that the index points to the zero of the graduated arc when the optical axis of the telescope is truly horizontal. For effecting this adjustment, or determining its index error, a spirit level is attached to the telescope, at one end by a joint, and at the other by a screw, whereby the end is raised or depre ed until the air bubble stands at the middle of the gla tube. The telescope is then reversed; and if the air bubble of the level still stands at zero, the adjustment is perfect; if not, the index error becomes known by bringing the level to the proper position, and may either be corrected or allowed for in the observations. In some theodolites the telescope is supported in the manner of a transit instrument; that is to say, the telescope and the horizontal axis on which it turns form one piece, and the vertical limb is a complete circle. By this construction the instrument becomes better adapted for determining the altitudes of stars, and consequently for finding the direction of the meridian and the azimuths of objects, or for other astronomical purposes. In fact, it becomes an altitude and azimuth instrument. In theodolites for common topographical purposes the horizontal circle is seldom mOre than five inches in diameter; but as the double vertical axis gives the means of carrying round the telescope from the first object to the second without disturbing the graduated circle, and then, by clamping the vernier and graduated plates, of bringing it back, and the graduated circle along with it, to the first object, the measure of the angle may be repeated any number of times, exactly as with the repeating circle, and a very considerable degree of accuracy obtained even with a circle of this small size. {See Repeating Circle.) But the principle of repetition is better carried into effect by means of a particular kind of stand or tripod, called a repeating stand, which turns round concentrically with the vertical axis of the theodolite; and this apparatus is usually had recourse to when the instrument is on a large scale. As the accuracy of the observation must depend on the horizontal circle remaining perfectly fixed while the telescope and verniers are turned round, a second telescope, called a watch telescope, is sometimes attached to the horizontal circle beneath the limb, which, being directed to a fixed object, serves to detect any disturbance of the circle clamp, or accidental shifting of position while the upper telescope with the verniers is turned from the first object to the second. But this can scarcely be applied to the repeating theodolite. The principal adjustments of the theodolite are, first, to rectify the line of coUimation of the telescope; secondly, to make the axis of the horizontal limb truly vertical; and, thirdly, to adjust the zero of altitude. For the practical methods of making these adjustments in the case of the common surveying theodolite, and instructions as to the mode of observing, the reader may be referred to Simms's 2'reatise on Mathematical Instruments, 1834. In geodetical operations, where very great accuracy is indispensable, as, for example, in measuring an arc of the meridian, the instrument is constructed on a much larger scale. The great theodolite by Ramsden, belonging to the Board of Ordnance, which has been used for measuring most of the principal angles of the British Trigonometrical Survey, has a horizontal circle of three feet in diameter, and two telescopes of thirty-six inches focal length. A similar one of equal dimensions had formerly been constructed by the same excellent artist for the Royal Society, and was used by General Roy in his operations for connecting the observations of Green wich and Paris towards the end of tlic last century, and also by Colonel Colby and Captain Kater for the same purpose in 1821. A full description of this superb instruxnent is given in the Fhil. Trans, vol. Ixsix., and in the [s. 1241]