legs, and place them firmly. Then loosen the clamp-screw S, and direct the telescope to a small, well-defined, and distant object. Then slide the eye-glass till the spider's lines are seen distinctly; after which, with the screw X, adjust the object-glass to its proper focus, when the object and the spider's lines will be distinctly seen. Note now the precise point covered by the intersection of the spider's lines.

Having done this, revolve the telescope in the Y's, half round, when the attached level CD will come to the upper side. See if, in this position, the horizontal hair appears above or below the point, and in either case, loosen the one, and tighten the other, of the two screws which work the horizontal hair, until it has been carried over half the space between its last position and the observed point. Carry the telescope back to its place; direct again, by the screws at M and R, the intersection of the spider's lines to the point, and repeat the operation, till the horizontal hair neither ascends nor descends while the telescope is revolved. similar process will arrange the vertical hair, and the line of collimation is then adjusted.

SECOND ADJUSTMENT.

A

To make the axis of the attached

level CD parallel to the line of collimation.

Turn the screw N, or the screws M and R, until the bubble of the level DC stands at the middle of the tube. Then open the loops, and reverse the telescope. If the bubble still stands at the middle of the tube, the axis of the level is horizontal; but if not, it is inclined, the bubble being at the elevated end. In such case, raise the depressed, or depress the elevated end, by means of the screw h, half the inclination; and then with the screw N, bring the level to a horizontal position. Reverse the telescope in the Y's, and make the same correction again; and proceed thus, until the bubble stands in the middle of the tube, in both positions of the telescope; the axis of the level is then horizontal.

Let the telescope be now revolved in the Y's. If the bubble continue in the middle of the tube, the axis of the level is not only horizontal, but also parallel to the line of collimation. If, however, the bubble recedes from the centre, the

must be made parallel to it, by means of two small screws, which work horizontally; one of these screws is seen at q. By loosening one of them, and tightening the other, the level is soon brought parallel to the line of collimation; and then, if the telescope be revolved in the Y's, the bubble will continuc at the middle point of the tube. It is, however, difficult to make the first part of this adjustment, while the axis of the level is considerably inclined to the line of collimation : for, allowing the level to be truly horizontal in one position of the telescope, after it is reversed, there will be but one corresponding position in which the bubble will stand at the middle of the tube. This suggests the necessity of making the first part of the adjustment with tolerable accuracy; then, having made the second with care, re-examine the first, and proceed thus till the adjustment is completed.

THIRD ADJUSTMENT. To make the level CD and the line of collimation perpendicular to the axis of the instrument, or parallel to the horizontal bar EE.

Loosen the clamp-screw S, and turn the bar EE, until the level DC comes directly over two of the levelling screws. By means of these screws, make the level CD truly horizontal. Then, turn the level quite round; if, during the revolution, it continue horizontal, it must be at right angles to the axis of the instrument about which it has been revolved. But if, after the revolution, the level CD be not horizontal, rectify half the error with the screws at M and R, and half with the levelling screws. Then place the bar EE over the other two levelling screws, and make the same examinations and corrections as before; and proceed thus, until the level can be turned entirely around without displacing the bubble at the centre. When this can be done, it is obvious that the level DC and the line of collimation, are at right angles to the axis of the instrument about which they revolve; and since the axis is carefully adjusted by the maker, at right angles to the bar EE, it follows, that the line of collimation, the level DC, and the bar EE, are parallel to each other.

The level is now adjusted. When used, however, it is best to re-examine it every day or two, as the work will be

Of Levelling Staves.

173. The levelling staves are used to determine the points at which a given horizontal line intersects lines that are perpendicular to the surface of the earth, and to show the distance of such points of intersection from the ground.

They are thus constructed. AB (Pl. 4, Fig. 3) is a rectangular piece of wood, in the middle of which is a groove abcd. Into this groove a slide Inst enters, and is moved freely along the groove. At the upper end of the slide is a rectangular board fhow, called a vane, six inches, in the direction hi. The vane is divided into four equal parts, by the lines fg, hi the two rectangles fh, ig, are usually painted black, and the other two, if, hg, white; so that the lines fg and hi may be distinguished with great accuracy. The slide from fg to In, is of the same length with the body of the staff AB: hence, when the line fg coincides with bc, the lower end of the slide In, will coincide with ad. The pins p and q, which work in grooves, and are largest at the ends Ρ and 9, are pressed in to hold the slide in any position at which it may be placed. The length of the staff is generally six feet, and it is usually divided into eighths or tenths of an inch. The slide is divided in the same way. The longer lines show the feet, the shorter, the inches. The object to be attained by these divisions, is, to ascertain the distance of the line fg from the ground.

When the line fg is brought to the top of the staff, to coincide with bc, the lower line wio of the vane, coincides with the line marked 6, on the left of the staff: which shows, the staff standing upright, that the line fg is six feet above the ground. From the line marked 6, to the lower end of the staff, is, indeed, but 5 feet 9 inches; but the line fg is three inches above the line wio, so that fg is six feet from the ground.

If, from the last position, the slide be run up until the line wio coincides with the division marked 1, on the left of the staff, the line fg will be six feet and one inch from the ground: if, till it coincides with bc, it will be six feet and three inches, the inches being marked on the staff. If the slide be still run up, until 7 on the slide coincides with bc, the line fg will be

seven feet from the bottom of the staff. The count above 6 feet 3 inches is always made on the slide. The manner of counting off, for the parts of an inch, is too plain to require particular explanation.

Having run down the slide till the upper line h, of the vane, coincides with bc, place bB on the ground, and the staff vertical. It is now plain, that the line fg is three inches above the ground. These three inches are marked on the right of the staff. If the slide be run up till the lower line h coincides with 1, on the right of the staff, the line fg will be one foot from the ground, and similarly, until six feet be shown at the other end of the staff.

The feet are marked 1, 2, 3, &c., from the upper end, and are reversed in the present position of the staff; but are upright when the staff is placed for use. In the last position of the staff, the count is made at the lower line of the vane.

174. There is a method of testing the adjustments of the level, which ought not to be neglected, since all the results depend on the accuracy of the instrument. The method is this:

The level being adjusted, place it at any convenient point, as G (Fig. 4). At equal distances of about 100 yards, on either side, and in the same line with the level, place the levelling staves CE, BF. Make the level horizontal with the levelling screws. Then, turn it towards either staff, as BF, and run the vane up or down, as required, until the intersection of the hairs strikes the centre: then make the slide fast, and note carefully the height of the vane. Turn the level half round, and do the same in respect of the staff CE. Let the telescope be now reversed in the Y's. Sight again to the staff BF, and note the exact height of the vane. Let the telescope be now turned half round, and the same be done for the staff CE. If the two heights last observed, are equal to those first noted, each to each, the line of collimation will be perpendicular to the axis of the instrument, and if the bubble has, at the same time, preserved its place at the middle point of the tube, the instrument is truly adjusted.

For, had the line of collimation been inclined to the axis of the level, it would, in the first instance, have taken the direction AF or Ad; and when turned half round, it would

reversed in the Y's, and again directed to the staff BF, the line of collimation would take the direction Ad or AF, and when turned to the staff CE, it would take the direction AE or Ab and the two distances BF, Bd, or Cb, CE, can only be equal to each other when the line of collimation falls on the horizontal line gf.

175. Having described the instruments used in levelling, we will explain the practical operations on the field.

When it is proposed to find the difference of level of any two objects, or stations, all levels made in the direction of the station at which the work is begun, are, for the sake of distinction merely, called back-sights; and levels taken in the direction of the other station, fore-sights.

Before going on the field with the level, rule three columns, as below, and head them, stations, back-sights, fore-sights.

176. To find the difference of level between any two points, as A and G (Pl. 4, Fig. 5).

The level being adjusted, place it at any point as B, as nearly in the line joining A and G as may be convenient. Place a levelling staff at A, and another at N, a point lying as near as may be in the direction of G. Make the level laorizontal, by means of the levelling screws; turn the telescope to the staff at A, and direct the person at the staff to slide up the vane until the horizontal line ab cuts its centre; then note the distance Ab (equal to 10 feet in the present example), and enter it in the column of back-sights, opposite station 1. Sight also to the staff at N, and enter the distance