The sketching board is easily made to serve as a slope board in this manner. Hang a plumb bob about an inch below the center of a straight edge of the board while pointing at the horizon, using the back of the board. Mark a point 5.7" directly below and draw a semicircle through it with the same radius. Now mark the point below the center zero and from it divide the arc using chords one tenth of an inch long. This will give a scale reading in degrees. By sighting along the top of the board at some object at the height of the eye from the ground the degree of slope is shown by the plumb bob on the scale below. Care must be exercised to prevent the wind from disturbing the reading. A protractor may be used in the same manner by sighting along the top and using a plumb bob to record the angle. In reading maps it is important to know whether points are visible from each other due to intervening ridges or other topographical features. This can be told by laying off accurately the distance on the map between the points in question and using as datum the lowest of the 3 points, then draw vertical lines, from the 2 higher points, making them in proportion to their elevation with any convenient scale. Draw a line between the first and last points and, if the intervening vertical cuts this line the second point is not visible from the first. Take for example, two points A and B, 1,760 yards apart, by the map, A 500 feet and B 450 feet above sea level, the intervening point C is 475 feet above sea level and 500 yards from B. As B is the lowest we will call its elevation zero or at datum, then elevation of A is 50 feet and C 25 feet. [Illustration: Plate #10] Another method of deciding visibility is by proportion. Measure the distance between the three points A, B, and C, and obtain their elevations above the datum (lowest of the 3) and using similar triangles. Take the same case as above, letting X represent the point above which the view is clear at 1,260 yards from point A, the line of sight passes through this point. 1760 (A--B) : 500 (B--C) : : 50 (elev. A) : X solving, X = 14.2 Now, since the ground at point C is 25 feet above the base and the line of sight passes within 14.2 feet of the base at this place, an observer at A is unable to see B. The matter of profiling is very simple. Merely mark where the contours cut the edge of a piece of co-ordinate paper and extend the proper elevations, then pass a line through these points, remembering that the surface of the ground has a natural curve. LESSON 6. (FIELD WORK--FIVE HOURS.)