perfectly horizontal. Movable about the centre of this plane is another plane, or a movable arm, carrying a pair of sights or a telescope, which can be placed so that the line of sight may pass through the object. If then this line be directed to one object, and the position of the two plates or of the arm on the plate be noted by an index properly situated, and then be turned so as to point to another object, the angle through which the plate or the arm has turned will be the horizontal angle contained by two planes drawn from the centre of the instrument to the two objects.

155. Vertical angles are measured by having a pair of sights or a telescope so adjusted as to move on a horizontal axis, the horizontal position of the sights or the telescope being indicated either by a plumb-line or a level.

156. The transit with a vertical arc, or the theodolite, are so arranged as to perform both these offices. As a full understanding of the use of the different parts of these instruments is necessary to their proper management, we shall enter, considerably in detail, into a description of them.

THE TRANSIT AND THE THEODOLITE.*

157. General Description. The Transit or the Theodolite (Figs. 51 and 52) consists of a circular plate, divided at its circumference into degrees and parts, and so supported that it can be placed in a perfectly horizontal position. This divided circle is called the limb. An axis exactly perpendicular to this plate, bearing another circular plate, passes through its centre. This plate is so adjusted as to move very nearly in contact with the former without touching it. By this arrangement the upper plate can be turned freely about their common centre. This plate carries a telescope Q, resting on two upright supports KK, upon which it is movable in a vertical plane. The telescope, having thus a horizontal and a vertical motion,

*The author is indebted to Professor Gillespie's "Treatise on Land Surveying" for many of the features in his mode of presenting the subjects of the Transit and Theodolite, their verniers and their adjustments.

can readily be pointed to any object. The second described plate has an index of some kind, moving in close proximity to the divided arc, so that the relative position of the plates may be determined. If then the telescope be directed to one object, and afterwards be turned to another, the index will travel over the arc which measures the horizontal angle between the objects.

In order to place the plates in a perfectly horizontal position, levelling screws and levels are required: these, as well as the other parts of the instrument, will be fully described in their proper place.

158. The above description applies to both instruments. The transit, however, is so arranged that the telescope can turn completely over; it can, therefore, be directed backwards and forwards in the same line. If the same thing is to be done by the theodolite, the telescope must be taken from its supports and have its position reversed. This operation is troublesome, and is, besides, very apt to derange the position of the instrument.

For surveying purposes, therefore, the transit is much to be preferred; and when the axis on which the telescope moves is provided with a vertical arc it serves all the purposes of a theodolite.

The theodolite has a level attached to the telescope. This is not generally found in the transit.

159. The accuracy of these instruments depends on several particulars :

1. By means of the telescope the object can be distinctly seen at distances at which it would be invisible by the unassisted eye.

2. The circle, with its vernier index, enables the observer to record the position of the telescope with the same degree of precision with which it can be pointed.

3. There are arrangements for giving slow and regular motion to the parts, so as to place the telescope precisely in the position required.

4. There are other arrangements for making the plates of the instrument truly horizontal.

5. Imperfections in the relative position of the different parts of the instruments may be corrected by screws, the heads of some of which are shown in the drawings.

However complicated the arrangements for performing these various operations may make the instruments appear, that complication disappears when they are viewed in detail and properly understood.

160. In the figures of these instruments, V is the vernier, covered with a glass plate. In some theodolites the whole divided limb is seen. In others (and in the transit) but a small portion is exposed,—it being completely covered by the other plate, except the small portions near the vernier. Transits have generally but one vernier, though in some instruments there are two. The theodolite has generally two, and sometimes three or four. B is the compass box, containing the magnetic needle N. A, A, are the levels. C and D are screws; the former of which is designed to clamp the lower plate, and the latter to clamp the plates together. T and U are tangent screws, to give slow and regular motion when the plates are clamped: by the former the whole instrument is turned on its axis, and by the latter the upper plate is moved over the other. P, Pare the levelling plates; and S, S, S, are three of the four levelling screws. E is the vertical circle, with its vernier F. G is a level attached to the telescope. H is a screw to clamp the horizontal axis, (not visible in the figure of the theodolite,) and I a tangent screw, to give it regular motion.

161. The Telescope. A telescope is a combination of lenses so adjusted in a tube as to give a distinct view of a distant object. It consists, essentially, of an object-glass, placed at the far end of the tube, and an eye-piece at the near end.

By the principles of optics, the rays of light proceeding from the different points of the object are brought to a