so on.

q, determined as above, is a point of the third curve, and After having determined the points in which each contour line cuts the lines diverging from A, let the contour lines be drawn through them, so as to indicate the surface of the hill. The numbers (8), (16), &c., show the vertical distances of the respective planes below the point A.

27. Having drawn the horizontal curves, the next thing to be done is so to shade the drawing that it may represent accurately the surface of the ground. This is done by drawing a system of small broken lines, as in the figure, perpendicular in direction to the horizontal curves already described. In all topographical representations of undulating ground, the lines of shading are drawn perpendicular to the horizontal curves.

A profile along either of the diverging lines may be plotted by the rules already given (Art. 20.) The diagram shows the profile along the line AB.

28. The following example will illustrate the methods employed in making a topographical survey, where great accuracy is required.

By means of a theodolite or level, range a line of stakes A, B, C, D, E, &c., along one side, or through the middle of the ground to be surveyed, at equal and convenient distances from each other, say 50 feet apart. Mark, with a piece of red chalk, on each stake in this row, one of the letters of the alphabet, A, B, C, D, E, &c., in their order. At A, range a line of stakes, perpendicular to AE, planting the stakes at intervals of 50 feet; and mark them with the letters 4, 4, 4, &c, which are read A first, A second,

2, 3

1, 2 3,

E2

E3

E4

E5

At B, range a line of stakes also perpendicular to AE, and at distances of 50 feet from each other, and designate them B, B, B, &c. Do the same at C, D, E, &c., until all the stakes are placed, dividing the area to be surveyed into squares of 50 feet on a side. The letters and figures should be plainly marked on a smooth face of each stake, for facility of reference. If this system of notation be followed, the stakes may be recorded without danger of confusion.

The next operation is to determine the difference of level between each stake, and some fixed horizontal plane, which is called a plane of reference. If the sea is near, the plane of mean low water, may be taken as the plane of reference. If not, assume the horizontal plane, passing through the lowest point of the ground to be surveyed, and make a permanent bench-mark at the point of beginning. If the lowest point cannot be easily determined, assume such a plane of reference as shall pass quite below the lowest point of the ground.

In the example, which we have taken for illustration, the stake is at the lowest point, and let us assume the

3

3

Set up the level at some convenient point, as a, take the reading of a levelling staff, set up at E and enter this reading as a back-sight. Then Then take the readings of the staff, at as many stakes as can be reached from the posi tion a of the level, entering them as fore-sights. Endeavor ing to make the last reading as small as possible. At this last stake drive a small peg for a bench-mark.

Move the level to a second point b, and take a backsight to the bench-mark (C4), and fore-sights, to as many stakes as possible. The following is the form of a fieldbook, used in topographical levelling.

If we subtract the first fore-sight (D3), from the backsight (E3), the difference, entered in the column headed diference, is evidently the height of (D3), above the plane of reference through (E3); and we accordingly enter it under the column headed total diff. of level, as well as in the column of differences. If we subtract the fore-sight (C4) from the fore-sight (D3), the difference, entered in the column of difference, is evidently the height of (C4) above (D3); if we now add this difference to the previous total, we shall find the height of (C4) above (E3). Subtracting the fore-sight (E2) from the back-sight (C4), we get the dif ference of level between (E2) and (C4) which, added to the previous total, gives the height of (E2), above the stake. (E3). In subtracting the fore-sight (E4) from the fore-sight (E2), we find a negative result which shows that (E4) is below (E2). We enter, then, this difference with its neg ative sign, and to get the total, we subtract this difference from the previous total, and so on.

As a check on the accuracy of our computation, subtract the fore-sight (C4) from the back-sight (E3), and the difference will give the height of (C4), above the plane of reference.

:

Again, subtract the fore-sight (B4) from the back-sight (C4), and add the remainder to the height of (C4,) and we shall find the height of (B4), which should agree with the height found under the heading, total diff. of level; and so on for each time the level is moved.

PLOTTING THE WORK.

29. Draw, on a piece of paper, a straight line AE From a scale of equal parts, set off distances AB, BC, &c., each to represent 50 feet. Erect perpendiculars at each of the points A, B, C, &c., and then set off the distan ces from A to 2, from 2 to 3, &c., each to represent 50 feet; and through the points 2, 3, 4 and 5, draw parallels to AE. These, by their intersections with the lines drawn through A, B, C, &c., will determine the position of the stakes, A, A, &c.; and write in red ink on the plot, the

height above the plane of reference of each stake, taken from the column of total differences in the field-book. Let us suppose that the horizontal planes are to be taken at distances of 6 feet We may find the points in which the contour

lines intersect the lines at right angles, by the previous method, or perhaps still better, let the Surveyor take the plot thus commenced into the field, and by the eye trace the contour lines on the map. If we note where the lines at right angles cut fences, roads, streams, &c., we can, by joining the points, obtain a plot of the ground.

30. The contour lines may be found as follows: Set up the level at a, and observe that the back-sight, to the stake, placed at (E3), gave a reading of 11.432. Depress the vane equal to the distance between the horizontal secant planes, that is, 6 feet, which is done by placing it at the reading 5.432. Then direct the rodman, by signals up or down the hill, till the horizontal hair of the telescope coincides with the horizontal line of the vane. The foot of the staff is then 6 feet above the first point. Let a stake, marked 6, be driven here, and direct the rodman around