In the grid coordinate system, the area is laid out in squares of convenient size, and the elevation of each comer point is determined. While this method lends itself to use on relatively level ground, ridge or valley lines must be located by spot elevations taken along the lines. The locations of the desired contours are then determined on the ridge and valley lines and on the sides of the squares by interpolation. This gives a series of points through which the contour lines may be drawn Figure 8-14 illustrates this method. Assume that the squares here measure 200.0 feet on each side. Points a, b, and c are points on a ridge line, also 200.0 feet apart. You need to locate and draw the 260.0-foot contour line. By inspection, you can see that the 260.0-foot contour must cross AD since the elevation of A is 255.2 feet and the elevation of D is 263.3 feet. However, at what point does the 260.0-foot contour cross AD? This can be determined by using a proportional equation as follows.

Assume that the slope from A to D is uniform. The difference in elevation is 8.1 feet (263.3 255.2) for 200.0 feet. The difference in elevation between 255.2 and 260.0 feet (elevation of the desired contour) is 4.8 feet. The distance from A to the point where the 260.0-foot contour crosses AD is the value of x in the proportional equation: 8.1:200 = 4.8:x or x = 118.5 feet. Lay off 118.5 feet from A on AD and make a mark.

In the same manner, you locate and mark the points where the 260.0-foot contour crosses BE,EF, EH, and GH. The 260.0-foot contour crosses the ridge, obviously, between point b (elevation 266.1 feet) and point c (elevation 258.3 feet). The distance between b and c is again 200.0 feet. Therefore, you obtain the location of the point of crossing by the same procedure just described.

You now have six plotted points: one on the ridge line between b and c and the others on AD, BE, EF, EH, and GH. A line sketched by hand through these points is the 260.0-foot contour line. Note that the line is, in effect, the line that would be formed by a horizontal plane that passed through the ridge at an elevation of 260.0 feet. Note, too, that a contour line changes direction at a ridge summit.

If you locate and plot all the important irregularities in an area (ridges, valleys, and any other points where

Figure 8-16.-Sketching contours by interpolation between control points of known elevations.

elevation changes radically), you can draw a contour map of the area by interpolating the desired contours between the control points.

A very elementary application of the method is shown in figure 8-15. Point A is the summit of a more or less conical hill. A spot elevation is taken here. Spot elevations are also taken at points B, C, D, E, and F,

which are points at the foot of the hill. It is desired to draw the 340.0-foot contour. Point a on the contour line is interpolated on the line from A to B, point b is interpolated on the line from A to C, point c is interpolated on the line from A to D, and soon. Figure 8-16 shows a more complicated example in which contours are interpolated and sketched between controlling spot elevations taken along a stream.