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. a back-sight. Then take the readings of the staff, at as many stakes as can be reached from the position a of the level, entering them as fore-sights. Endeavoring to make the last reading as small as possible. At this last stake drive a small peg for a bench-mark. 4 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 difference, 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 negative 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 distances 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 horizontal hair of the telescope will cut the vane, and drive there another stake, marked 6; and so on, until a sufficient number of stakes have been driven to determine the curve (6). Then, let the line of stakes, marked 6, be surveyed with the compass and chain, and plotted. Other contour lines may be found in a similar manner. 31. We will add another example for determining the contour of an undulating piece of ground (Pl. 4, Fig. 7,) by means of horizontal sections. Let rows of stakes DA, HE, IF, &c., be driven at intervals, depending upon the required accuracy of the survey, and let f, g, h, &c., be stakes driven along the lines, at such points as will best show the accidents of ground. Determine as before the difference of level between each stake, and some fixed point, and then determine where the contour lines cut the lines AD, EH, &c., by the rules already laid down. After the stakes are all placed, and the distances measured, let the differences of level of all the points so designated be found. In the present example, the results of the measurements are, d above D 4 h below H 3 below I 3 p below L 4t below C5 The heights of the points are here compared with each clearly their relative heights, we must assume some one point, and compare all the others with it. Let the point A be taken. The height of This being done, a mere inspection shows us the highest and lowest points, as also the relative heights of the others, reckoning upwards or downwards. Let them be now written in the order of their heights above the lowest point, which is D. The difference of level between A and D being 20 feet, if the difference of level of each of the points below A, be taken from 20 feet, the remainder will be the height above D. Arranging them in their order, we have c above D 2 Habove D 7 p above D 9 Ft. Babove D 12 In this example, the plane of reference is assumed through D, the lowest point of the ground; and the secant planes are taken 3 feet apart. 32. The manner of shading the map, so as to indicate the hills and slopes, consists in drawing the lines of shading perpendicular to the horizontal curves, as already explained. These shading lines are drawn close together, when the slope is abrupt, and further apart, as it grows |