THEODOLET, or THEODOLITE (the word is found in both forms), is the name generally given to the instrument used for measuring horizontal angles. In its simplest form the theodolet consists of a divided circle, which is to be set parallel with the horizon, and a telescope which has so much motion in a vertical plane as to enable the observer to view any object which he may require above or below the horizon. The derivation of the word is obscure, although the instru ment and its name are comparatively of recent date. The earlier observers did indeed use divided circles, which they called astrolabes, armillas, &c. [ASTROLABE], for the purposes of surveying, but these were, generally speaking, very rude. The quadrant was employed in all accurate surveys up to the latter half of the last century, although Roemer had shown by reason and example the superiority of the entire circle. [CntoLE.] The first instance of a survey conducted with an entire circle, on a considerable scale, was, so far as we recollect, the Survey of Zealand by Bugge, in 1762-8. (See Bugge's Observationes Astronomicx,' p. 54, where he refers to a description of this instrument in Danish, and p. 61, where he states its merits.) The horizontal circle was two feet in diameter, and constructed by the Danish artist AhL Ramsden finished his great theodolite in 1787, the circle of which is three feet in diameter. This was used for a triangulation, to connect the Observatories of Greenwich and Paris. A very full description of it is given in 'An Account of the Operations carried on for accomplishing a Trigonometrical Survey of England and Wales,' London, 1799, pp. 107-180, with four plates; a reprint, in a great measure, from the Phil. Trans.,' voL 80 et seq. The principal triangles of the English, Irish, and Indian surveys have been observed with this instrument or with those nearly identical in size and construction ; and though several minor additions and improvements have been made, the great theodo lite is still considered as a very efficient and almost infallible instru mcnt. We believe that the high reputation of the great theodolite depends in a great degree on the superstitious care with which it has been used and preserved : it Is undoubtedly a very fine, well-divided instrument, but in common hands its want of solidity and firmness would probably have been felt. It would be impossible as well as useless to give an account of the various constructions of different artists at home and abroad ; but the reader who desires to see what had been done up to 1851 is referred to the Jury Report, Clam X., where the surveying and levelling instruments and theodolites of the Great Exhibition are pretty fully noticed, as to their new points and from the personal observations of Mr. Glaisher. The general properties of a theodolite, that it. should be firm, well balanced, fie., will be easily recognised by a person who knows how to make good use of the instrument, and we shall advert in the course of this article to some of the qualities which are, and to others which are not, essential.
We have given on the preceding page a sketch of the theodolite in its simplest form, such as would be proper for the secondary triangulation of a national survey, or for the most accurate private survey. The tripod which carries the instrument rests with three foot-screws in brass notches let into the top of a wooden stand. The legs of the stand are not fully represented, but the two parts of which each is composed end below in a strong and sharply-pointed metal socket. The circle is fixed, and the upper works, telescope, verniers, levels, &c., turn on a centre, which may be seen just under the cross of the telescope. The adjust ments are very simple. The wooden stand is first set down with a good opening of the legs, and the top nearly horizontal. Tho foot-screws are placed in their notches, the hung from its hook, below the centre of the circle, and the telescope turned round till one level is parallel to the lino joining two foot-screws, while the other level is iu a line from the third foot-screw to the centre. Bring the bubble of the
first-mentioned level into the middle by raising one of the two foot screws and depressing the other, and then adjust the cross-level by raising or depressing the third foot-screw alone. Now turn the telescope round 180", and if the bubbles are not in the middle, bring them half way there by touching the foot-screws, and the other half by screws which adjust the levels themselves. When this has been nicely done, the bubbles will remain in the middle in every position of the telescope. If the objects to be observed by all in the horizon, or in a plane parallel to it, the above adjustment would be sufficient; but when the objects are ont of the horizontal plane they must be referred to it by a perpendicular, that is, the plane described by the telescope must be a great circle, and must also pass through the zenith. There are generally two wires at least in the focus of the telescope, one horizontal and the other vertical. Place the eye-piece to give sharp vision of the wires, and turn the milled screw, seen towards the object-glass, until the objects you are going to observe are distinct. Place the vertical wire on any well-defined object, making the bisection near the crossing of the wire ; raise or depress the telescope until the object is nearly at the bottom or top of the field ; if it is still bisected, the wire is rightly placed, but if not, twist the tube carrying the eye-piece so as to effect a bisection. To make the telescope describe a great circle, select some well-defined object near the horizon, and bisect it : now take the telescope very carefully out of its fe, reverse it, and look again at the object. If it is still bisected, there is no error; but if not, the bisec tion is to be effected half by the tangent-screw of the instrument and half by the screws which carry the wire-plate, screwing up one and releasing the other. Restoring the telescope to its first position, it will be seen whether the adjustment is correct, and if not, the process must be repeated until the bisection is the same in both positions of the telescope, the clamp and tangent-screw remaining fixed. For the adjustment of the axis of the telescope a level would be convenient,but in this instrument the axis is supposed to have been correctly placed by the maker, and the only mode of correcting any error is by filing the T's. It may be ascertained whether the axis is tolerably correct as follows :—hlisect an object as far above or below the horizon as the motion of the telescope will allow. Reverse the telescope, and if the object is still bisected, the pivots of the telescope are the same size : if not. the observer must deduce the difference of the pivots from the altitude and the error observed, which is not difficult. When this has been satisfactorily executed, bisect, as in the last instance, an object as far as possible from the horizon, and read off the verniers. Turn the instrument round 180', return the telescope end for end, bisect the object again, and read off the venders. If the mean readings differ exactly 180•, the axis is horizontal ; but if they do not, the observer will have sufficient data from this, and the altitude or depression, for determining the quantity and direction of the error, which lie may correct by the file or by calculation, according to his pleasure. There is a much easier method of examining the position of the axis by observing an object directly and an seen by retlexion from a fluid, as mercury, oil, or water. The axis is truly horizontal when the vertical wire bisects the object and its reflected image without moving the t?ngent-screw. It must be recollected that the adjustments of the horizontal circle already described must be previously and very scrupulously performed before attempting the examination or adjust ment of the cross-axis.