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 and the line of collimation perpendicular to the axis of the instrument, or parallel to the level-bar.

288. Loosen the clamp-screw and turn the bar until the level comes directly over two of the leveling screws. By means of these screws, make the level truly horizontal. Then, turn ` the level 180° upon its vertical axis; 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 be not horizontal, rectify half the error with the screws at M and R, Fig. 137, and half with the leveling screws. Then place the bar over the other two leveling 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 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, it follows that the line of collimation, the level, and the bar, are parallel to each other.

It is always necessary to examine the adjustments frequently, in order to secure satisfactory results.

LEVELING RODS.

289. The leveling rods 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 distances of such points of intersection from the ground.

There are three kinds of rods used by Engineers, known as the New York, Philadelphia, and Boston or Yankee rods. The Philadelphia Rod is divided to tenths, and reads to two-hundredths of a foot. The New York and Boston rods are divided to hundredths of a foot, and read by verniers to thousandths. They are all sliding rods.

290. New York Rod.-This rod, which is shown in Fig. 138, is cut in two parts so that both ends may be exhibited. It is made of maple or satin-wood, in two pieces, sliding one from the other, always in the same direction, so that the same end is always held on the ground, and the graduations start from that point.

The graduations are made to tenths and hundredths of a foot, the tenth figures being black, and the feet marked with a large red figure.

A target is used to indicate where the horizontal line cuts the rod.

The face of the target is divided into quadrants, by a horizontal and a vertical diameter; and these diameters are the boundaries of alternate colors with which the diagonal quadrants are painted.

The opening in the face of the target is a

FIG. 188.

little more than a tenth of a foot long, so that in any position a tenth, or a foot figure, can be seen on the surface of the rod.

The right edge of the opening is chamfered, and divided into ten equal spaces, corresponding with nine-hundredths on the rod; the divisions start from the horizontal line which separates the colors of the face. The vernier reads to thousandths of a foot.

For heights less than six and a half feet, the target is moved along the sliding part, to which it is slightly attached by springs, and to which it may be permanently attached by a clamp-screw, and the reading is made by the vernier on the target.

When a greater height is required, the horizontal line of the target is fixed at that point, and the upper half of the rod, carrying the target, is moved out of the lower, the reading being now obtained by a vernier on the graduated side, up to an elevation of twelve feet.

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

The level being adjusted, place it at any convenient point, as G (Fig. 139). At equal distances of about 300 feet in opposite

directions from the instrument, drive two pegs firmly into the ground and take readings of the rod upon them. The difference of the readings will be the difference of level of the tops of the pegs, even though the level be out of adjustment. Now set the level at about 50 feet beyond either peg, nearly in line with them, and again take rod-readings upon them; the difference of these new readings, corrected for curvature of the earth, should equal the difference of level of the pegs as found before. If the readings are not what they should be, the adjustment may be perfected thus: Call the further peg a, the nearer peg b,

FIG. 140.

and the position of the instrument c. (Fig. 140). Let R be the first reading at a, and R' that at b; let r be the second reading at a, corrected for curvature, and r' the corresponding reading at b, also corrected; let

then we have

(R — R') — (r — r') = ± D ;

ab (600 ft.): ac (= 650 ft.) :: ±D: ±d.

Add the correction d to r, and having set the target to this reading on a, bring the horizontal wire to coincide with it by the adjusting screws. See also that the bubble is in the middle of the run at the same time.

SECTION III.

LEVELING IN THE FIELD.

292. The operations of leveling may be undertaken.

1st. For the purpose of determining the difference of level between two given points;

2d. For the purpose of obtaining a section or profile along a given line, as in the preliminary surveys for railroads and canals;

And, as will be described hereafter,

3d. For the purpose of determining the contour lines in a topographical survey;

4thly. For the purpose of determining the volume of any given mass of earthwork or masonry; as the measurement of excavations and embankments for canals and railroads ; and,

5thly. For the purpose of determining and indicating boundaries for filling and excavation; such as setting slope stakes, &c.

Difference of Level between Two Points.

293. 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 called, for the sake of distinction merely, 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.