In the examples of interpolation previously given, a single contour line was interpolated between two points of known elevation, a known horizontal distance apart, and by mathematical computation. In actual practice, usual] y more than one line must be interpolated between a pair of points; and large numbers of lines must be interpolated between many pairs of points.

Mathematical computation for the location of each line would be time-consuming and would be used only in a situation where contour lines had to be located with an unusually high degree of accuracy.

For most ordinary contour-line drawings, one of several rapid methods of interpolation is used. In each case it is assumed that the slope between the two points of known elevation is uniform.

Figure 8-32 shows the use of an engineers scale to interpolate the contours at 2-foot intervals between A and B. The difference in elevation between A and B is

between 11 and 12 feet. Select the scale on the engineers scale that has 12 graduations for a distance and comes close to matching the distance between A and B on the map. In figure 8-32, this is the 20 scale. Let the 0 mark on the 20 scale represent 530.0 feet. Then the 0.2 mark on the scale will represent 530.2 feet, the elevation of A. Place this mark on A, as shown.

If the 0 mark on the scale represents 530.0 feet, then the 11.7 mark represents

the elevation of B. Place the scale at a convenient angle to the line from A to B, as shown, and draw a line from the 11.7 mark to B. You can now project the desired contour line locations from the scale to the line from A to B by drawing lines from the appropriate scale graduations (2, 4, 6, and so on) parallel to the line from the 11.7 mark to B.

Figure 8-33 shows a graphic method of interpolating contour lines. On a transparent sheet, draw a succession of equidistant parallel lines. Number the lines as shown in the left margin. The 10th line is number 1; the 20th, number 2, and so on. Then the interval between each pair of adjacent lines represents 0.1 feet. Figure 8-33 shows how you can use this sheet to interpolate contour lines at a 1-foot interval between point A and point B. Place the sheet on the map so that the line representing 1.7 feet (elevation of A is 500.0 + 1.7, or 501.7 feet) is on A, and the line representing 6.2 feet (elevation of B is 500.0 + 1.7, or 506.2 feet) is on B. You can see how you can then locate the l-foot contours between A and B.

For a steeper slope, the contour lines would be closer together. If the contour lines were too close, you might find it advisable to give the numbers on the graphic sheet different values, as indicated by the numerals in the right-hand margin. Here the space between each pair of lines represents not 0.1 foot, but 0.2 foot. Points A and B have the same elevations as points A and B, but the fact that the horizontal distance between them is much shorter shows that the slope between them is much steeper. You can see how the 1-foot contours between A and B can be located, using the line values shown in the right margin.

A third method of rapid interpolation involves the use of a rubber band, marked with the correct, equal decimal intervals. The band is stretched to correct bring the graduations on the points.