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

focus within the tube, (Fig. 53,) there forming an inverted image. Crossing at this focus, they proceed on to the eye-piece, by the lenses of which they are again refracted, and made to issue in parallel pencils, thus giving a distinct magnified image of the object.

162. The Object-glass. Whenever a beam of light passes through a lens, it is not merely refracted, but it is likewise separated into the different colored rays of the solar spectrum. This separation of the colored rays, or the chromatic aberration, causes the edges of all bodies viewed with such a glass to be fringed with prismatic colors, instead of being sharply defined. It has been found, however, that the chromatic aberration may be nearly Fig. 54.

removed, by making a compound lens of flint and crown glass, as represented of in Fig. 54, in which A is a concavoв convex lens of flint glass, and B a double convex lens of crown glass,-the convexity of one surface being made to agree with the concavity of the other lens. The two are pressed together by a screw in the rim of the brass box which contains them, thus forming a single compound lens. When the surfaces are properly curved, this arrangement is nearly achromatic.

A

The object-glass is placed in a short tube, movable by a pinion attached to the milled head W. (Figs. 51, 52.) By this means it may be moved backwards and forwards, so as to adjust it to dis- B tinct vision.

C

163. The Eye-piece. The eye-piece used in the telescopes employed for surveying purposes consists of two plano-convex lenses, fixed in a short tube, the convex surfaces of the lenses being A

Fig. 53.

D