back-sights and fore-sights, taking the difference and adding it algebraically to the elevation of the initial point. The pro

The back-sight and fore-sight readings for one setting of the level are not recorded on the same line, but both sights on one turning-point are on the same line. When turning. points are plotting-points of the profile, an entry is made in both F. S. aud I. S. columns. When a B. M. is set during the work, the sight upon it is entered in I. S. column and not in F. S. column, which is reserved for turning points.

The record. A form of record for profile and grade leveling follows; other forms are used, but this is a very convenient one inasmuch as numbers to be added or subtracted are found in adjacent columns.

RECORD FOR PROFILE LEVELING AND GRADE.

DETERMINATION OF GRADE.-Having constructed the profile, a grade line may be marked upon it and the amount of cut or fill at any and all points may be at once determined by measuring to scale the distance from the grade line to the surface profile line. The distances so found may then be marked upon the stakes, which is all that is necessary to enable the grade being established, if it is a simple ditch or trench, as for sewers, drains, etc. If the grade line is to be a road, however, and the sides of cuts and fills required to be given a certain slope, other stakes, called "slope stakes," must be set on the points marking the extreme lines of cuts or fills. The operation of determining their positions to fulfill the required conditions is called "cross section leveling." (See Chapter XXV.)

Should the required grade be determined upon before any leveling is done, as a grade of 1 on 100, and an elevation assumed for the initial point, then the amount of cut or fill may be determined during the leveling and marked upon the stakes at once, without constructing the profile. Referring to the Profile Record, the elevation of grade would be found. for each profile point by adding to the height of the initial point, if an up-grade, or subtracting from the height of the initial point if a down-grade, the differences of elevation corresponding to the successive distances from the initial point of the profile points-i. e., at 100 feet distance from B. M. the elevation of grade would be 1 foot below that at B. M. (or 89); at 200 feet, 2 feet below, etc.

These differences of elevation may be found by multiplying the tangent of the angle of grade by the horizontal distances from the initial point. The difference between the elevation of grade and surface elevation at any point would be the cut or fill.

CHAPTER XI.

METHODS USED IN "FILLING IN."

The methods and instruments that will most likely be employed in locating points for the control of a map in military topography having been explained, there remains to be considered the "filling in" of the details. For this purpose the same instruments may also be used.

The "filling in" consists principally in representing, by conventional signs and symbols, the undulations and accidents of ground, steepness of slopes, relative heights of commanding points, and all occurring incidents of water. A sufficient number of points for this purpose are located by their three coördinates-viz., direction, distance, and elevation. The representation of details between the determined points completes the survey, and draws upon the artistic skill, perception, and judgment of the topographer.

The method in general use for representing the configuration of the surface of ground is by "contours."

CONTOURS are the horizontal projections to scale, on the map, of the intersections (contour lines) of the surface of the ground by imaginary horizontal planes.*

These imaginary planes are taken at equal vertical intervals, as 1, 5, 10, 25, 50, or 100 feet.

Contours show not only relative heights of points, but also the shape of the ground by their curves, and the steepness of slopes by their distance apart.

*In the survey of large areas, where the curvature of the earth is considered, the imaginary lines projected are the intersections of the ground by imaginary level surfaces.

The usual method of explaining this is to assume a hill surrounded by a body of water, and to suppose the water to rise one foot (or the vertical interval chosen) at a time, until the hill is covered. The contour line defined by the edge of the water at each successive rise may be considered as the intersection of the surface of the ground by the imaginary plane, and the one to be represented by the contour on the map.

FIG. 151.

FIC.152.

FIG. 153.

If it were desired to represent a right cone upon a horizontal surface (Fig. 151), the base would be shown by the largest or outer circle and the apex by the central dot. If the cone be cut by

equidistant horizantal planes, the lines of intersection with the surface are shown upon the plane by the inner circles.

If the cone is oblique (Fig. 152), it will still be represented by circles, but they will not be concentric, but nearest to each other on the steepest side.

If the figure were half egg-shaped, then it would be represented something after the manner in Figure 153. If two intersecting cones of the same size (Fig. 154), the

FIG. 154.

FIC.155.

bases will be shown

by the two outer

circles cutting each other, and the upper parts by the separate

concentric circles. If the two cones are oblique and of different sizes, they will be represented as shown in Figure 155.

By a reference to the figures, which contain all the elements of contours, it will be seen that since the sections are regular the horizontal projections also are regular, but when a figure has an irregular surface like the ground, and is represented by this method, the lines of intersection will also be very irregular.

DEFINITIONS OF FORMS.-Ridges or water-sheds, exemplified by the ridges of roofs, are the highest lines of land separating lower land. In the case of ridges separating large drainage areas, there are usually smaller ridges projecting out, but connected with the main ridges.

Water-courses or thalwegs, exemplified by the valleys of roofs, are the lowest lines or parts of valleys or ravines, whether occupied by water or not. If water be present, the indication is unmistakable as regards the lowest line, and inferences may be drawn as regards the direction of surrounding slopes,

Varieties of ground. The infinite variety of forms and