leaves 14.6=0P, the height of the point 0 above the datum plane. Next take sights at 1, 2, 3, 3.40, and 4 equal respectively to 3.7, 3.0, 5.1, 4.8, and 8.3, and subtract the same from 19.832; the remainders 16.1, 16.8, 14.7, 15.0, and 11.5 will be the respective heights of the points 1, 2, 3, 3.40, and 4. Then, as it will be necessary to change the position of the instrument, select a point in the neighborhood of 4 suitable as a turning point (t.p. in the figure), and take a careful reading on it=8.480; subtract this from 19.832, and the remainder, 11.352, will be the height of the turning point. Now carry the instrument forward to a new position, as between 5 and 6, shown in the figure, while the rodman remains at t.p.; take a second reading on t.p.4.102, and add it to 11.352, the height of t.p. above PP'; the sum 15.454 will be the height of the instrument CD in its new position. Now take sight upon 5, 6, and 7, equal respectively to 4.9, 2.8, and 0.904; subtract these sights from 15.454, and the results 10.6, 12.7, and 14.550 will be the heights of the points 5, 6, and 7 respectively. The point 7, being suitable, is made a turning point, and the instrument is moved forward to a point between 9 and 10. The sight at 76.870 added to the height of 7 gives 21.420 as the height of the instrument EF in its new position. The readings at 8, 9, 10, and 11, which are respectively 5.4, 3.6, 5.8, and 9.0, subtracted from 21.420, will give the heights of these points, namely, 16.0, 17.8, 15.6, and 12.4.

Proceed in like manner until the entire section is levelled, establishing bench marks at intervals along the line to serve as reference points for future operations.

As wind and bright sunshine affect the accuracy of levelling, for careful work a calm and cloudy day should be chosen; and great pains be taken to hold the rod vertical and to manipulate the level properly.

A record of the work described above is kept as follows:

The first column contains the numbers or names of all the points on which sights are taken. The second column contains the sight taken on the first bench mark, and the sight on each turning point taken immediately after the instrument has been moved to a new position. These are called Plus Sights (S.) because they are added to the heights of the points on which they are taken to obtain the height of the instrument given in the third column (H.I.). The fourth column contains all the readings except those recorded in the second column. These are called Minus Sights (— S.) because they are subtracted from the numbers in the third column to obtain all the numbers in the fifth column except the first, which is the assumed depth of the datum plane below the bench. The fifth column (H. S., height of surface) contains the required heights of all the points of the section named in the first column. together with the heights of all benches and turning points.

To find the difference of level between any two points of the section, we have only to take the difference between the numbers in the fifth column opposite these points.

The real field notes are contained in the first, second, fourth, and last columns; the other columns may be filled after the field operations are completed. The field book may contain other columns; one for height of grade (H.G.), another for depth of cut (C.) and another for height of embankment or fill (F.).

To plot the section. Draw a line PP' (Fig. 45), to represent the datum plane, and beginning at some point as P, lay off the distances 100, 200, 300, 340, 400 feet, etc., to the right, using some convenient scale, say 200 feet to the inch. At these points of division erect perpendiculars equal in length to the height of the points 0, 1, 2, 3.40, 4, etc., given in the fifth column of the above field notes, using in this case a larger scale, say 20 feet to the inch. Through the extremities of these perpendiculars draw the irregular line. 0, 1, 2, 3 ..... 11, and the result, with some explanatory figures, will be the required plot or profile.

The making of a profile is much simplified by the use of profile paper, which may be had by the yard or roll.

If a horizontal plot is required, the bearings of the different portions of the section must be taken.

A plot should be made, if it will assist in properly understanding the field work, or if it is desirable for future reference in connection with the field notes.

§ 35. SUBSTITUTES FOR THE Y LEVEL.

For many purposes not requiring accuracy, the following simple instruments in connection with a graduated rod will be found sufficient.

The Plumb Level (Fig. 46) consists of two pieces of wood joined at right angles. A straight line is drawn on the

upright perpendicular to the upper edge of the crosshead.

The instrument is fastened to a support by a screw through the centre of the cross-head. The upper edge of the crosshead is brought to a level by making the line on the upright coincide with a plumb-line.

FIG. 46.

FIG. 47.

FIG. 48.

A modified form is shown in Fig. 47. A carpenter's square is supported by a post, the top of which is split or sawed so as to receive the longer arm. The shorter arm is made vertical by a plumb-line which brings the longer arm to a level.

The Water Level is shown in Fig. 48. The upright tubes are of glass, cemented into a connecting tube of any suitable material. The whole is nearly filled with water, and supported at a convenient height. The surface of the water in the uprights determines the level.

By sighting along the upper surface of the block in which the Spirit Level is mounted for the use of mechanics, a level line may be obtained.

EXERCISE V.

1. Find the difference of level of two places from the following field notes: back-sights, 5.2, 6.8, and 4.0; fore-sights, 8.1, 9.5, and 7.9.

2. Write the proper numbers in the third and fifth columns of the following table of field notes, and make a profile of the section:

3. Stake 0 of the following notes stands at the lowest point of a pond to be drained into a creek; stake 10 stands at the edge of the bank, and 10.25 at the bottom of the creek. Make a profile, draw the grade line through 0 and 10.25, and fill out the columns H. G. and C., the former to show the height of grade line above the datum, and the latter, the depth of cut at the several stakes necessary to construct the drain.