and O a tangent-screw. The bar EE is firmly attached at right angles to an axis, which terminates in a ball, enclosed in the socket R. In some instruments this bar is enlarged at the middle so as to form a compass box, in which a magnetic needle is placed. The telescope AB is supported on two wyes, Y1 and Y2, one of which, Y1, is firmly connected with the bar EE, and the other, Y2, is moveable a small distance up or down by the screw N, or in some instruments by two screws, M and P. The eye-tube L is moveable in or out by hand, so as to render the spider's lines distinctly visible, and the tube which contains the object-glass is moved by turning the milled head d, and may thus be so adjusted as to give distinct vision of an object to which the telescope is directed. One end, C, of the ŝpirit-level CD is moveable up or down by the screw m, and the other end is moveable laterally by two opposite screws p and of which only p appears in the figure.

The following adjustments of the level should be examined, and corrected if necessary, before using it in practical operations.

FIRST ADJUSTMENT.

To make the line of collimation coincide with the axis of the telescope.

Having screwed the level to the tripod and set up the instrument so as to stand firmly, loosen the clampscrew, turn the telescope towards some distant welldefined object, and fasten the screw.

By means of

line of collimation is directed exactly to some distinct point in the object, and then proceed according to the instructions in the second paragraph of the first adjustment of the theodolite.

SECOND ADJUSTMENT.

To make the axis of the level CD parallel to the line of collimation.

By turning the screw N, bring the bubble of the level to stand at the middle of the tube. Reverse the telescope in its wyes, and, if the bubble does not then stand in the middle, correct one half of the deviation by the screw m, and the other half by the screw N. Again reverse the telescope in its wyes, and repeat the correction if necessary.

Now by revolving the telescope in its wyes, bring the level to some distance on one side of its lowest or proper position, and if the bubble then deviates from the middle, the deviation must be corrected by means of the screws Ρ and gr which move one end of the level laterally, the correction being continued till the bubble will remain at the middle while the telescope is revolved so as to bring the level to a considerable distance on either side of its lowest position. When this has been done, the first part of the adjustment should again be examined and corrected if neces

sary.

A method by which the second adjustment may be made for an instru ment in which the telescope is not reversible, will be found in the first of the following problems.

THIRD ADJUSTMENT.

To make the line of collimation parallel to the bar EE, or which is the same, at right angles to its axis.

Turn the telescope till it stands directly over two of the levelling-screws, and by means of them bring the bubble to stand at the middle of the tube. Then turn the telescope half round, that is, till it stands over the same screws, but pointing in the opposite direction, and if the bubble does not remain in the middle, correct one half of the deviation by the levelling-screws and the other half by the screw N. Now place the telescope over the other levelling-screws, and proceed in a similar manner. Continue the corrections till the bubble will remain in the middle of the tube during an entire revolution.

These adjustments having been carefully made, the instrument is ready for use. When on the ground it must, in each new position in which it is placed, be levelled. This is done by placing the telescope over two of the levelling-screws and by their means bringing the bubble of the level to the middle of the tube, then doing the same with the telescope over the other two, and again over the first two. Then, if the third adjustment has been accurately made, the bubble will stand in the middle of the tube in any position of the telescope.

OF THE LEVELLING STAFF.

A Levelling Staff consists of a square or rectangu

called a Vane, which is so attached to the staff as to be moveable along it from end to end. It is used for measuring the height of the line of apparent level passing through the telescope of the levelling instrument, above the place where the staff is placed.

The face of the vane, represented in Fig. 111, is divided into four equal parts by two straight lines intersecting each other at right angles; one line being horizontal, and consequently the other vertical. Two opposite parts of the face are painted white and the other two black; thus the lines and their intersection, are easily distinguished even at a considerable distance. A screw, the head of which is shown at m, serves to clamp the vane to the staff in any required position.

The staff is composed of two rectangular bars of wood, between five and six feet long, placed side by side, and forming together a square staff, the breadth of each side of which is about an inch and a quarter. The bars are so connected that one, which is two or three inches the shorter of the two, may be made to slide along the other or principal bar, and thus, when necessary, increase the length of the staff. In order to this, he front or sliding bar has throughout its length, on the side next the other, a projection which is terminated by a brass plate a little wider than the projection and firmly attached to it; and the principal bar has a groove in it to receive the projection and plate of the former. The forms of the projection and groove are exhibited in Fig. 112, which represents a section of the bars, at right angles to their length.

The staff is represented in Fig. 113, in which beefd is the principal bar, which is capped at the bottom with a brass plate; bd is the sliding bar, A is the vane, seen edgewise, and n is a screw which serves to clamp the bars together in any given position. One side of each bar is divided, from bg upwards, into feet and hundredths of a foot; the feet being numbered as in the figure. The subdivisions of the feet are omitted as they could not well be all exhibited. On the chamfered edge of a brass plate connected with the vane, a fine line a is drawn, directly opposite to the horizontal line of the vane. The line a serves therefore to denote on the side of the principal bar, the height that the vane is above the line bg, when that height does not exceed 5 feet.

The height of the vane above the line bg is usually called the height of the vane, although it is less than its true height above the ground or place on which the staff stands, by the length of the part bc. This however produces no error in the use of the staff in levelling, as the difference in level of two places is found from the difference in the heights at the places, of a line of apparent level passing through the levelling instrument, and this difference will evidently be the same whether both heights are measured from the ground, or both from the line bg.

When it is required to raise the vane to a greater height than 5 feet, it must be slid up to a pin at p, which checks it at that height, and be fastened there by the screw m, Fig. 111. Then loosening the screw n, Fig. 114, the front bar, which carries the vane, may