A square is made by taking a sheet of paper, folding the corner down so that the edge of the end coincides with the edge of the side, and then cutting off the superfluous length, each corner of the square is an angle of 90°, i. e., a right angle or a quarter of the compass, say from north to east. The diagonal fold makes at each corner an angle of 45°, or four points of the compass, say from north to north-east; fold this again, and it will give 22½°, or two points of the compass, from north to north-north-east, and this may again be subdivided if needful.
We have often tried the breadth of rivers by firing a rifle ball at some well-defined mark on the other side, with the sight adjusted to 100yds. or more, according to the estimated distance, and noticing whether the ball reached beyond or fell short of the mark. The habit of doing this very greatly corrects and assists the eye in forming estimates of distance. A good stone thrower ought to know the range he can make with pebbles of different sizes. If a native is near buy one of his least valued arrows or spears, and get him to throw it across, and then ask him to throw a similar one on ground where you can recover it and measure the distance, but never ask a savage to throw away weapons of the chase for nothing. In calm weather, we have fired a rifle ball, with its utmost range, on the surface of a lake, and have counted seconds from the time we saw the splash till we heard the sound of its fall. Sound travels 1142ft. in a second, or about a statute mile in 4¾ seconds, or a geographical mile—or rather one minute of latitude, or of longitude on the equator—in 5¾ seconds.
To find, without Instruments, the Height of a Tree or other Object, whose Base is accessible.
Fig. 1. Fold down a square of paper from corner to corner, and you will obtain a triangle, of which two of the sides form a right angle, and the third, or diagonal, forms an angle of 45° with each of them (see next page). Make a mark upon the tree 5ft., or the height of your eye, from the ground, and retire from the tree till, holding the paper steadily with one short side horizontal and the other vertical, you can take sight along its lower edge at the mark, and along the diagonal side at the topmost branches; then pace or measure the distance from the tree, add 5ft. for the height of the eye, and you will have the height of the tree; because, if the two angles of the diagonal be 45°, the base and the perpendicular must be equal. A piece of thin board, with pins set in at each angle to serve as sights, would be better than the paper, but is not so readily extemporised. If you split the end of a wand so as to hold the paper or board quite up to the height of your eye, it will give additional steadiness. The observer in our illustration is unavoidably represented a little too near his work, but he is probably taking the height of the first bifurcation, which is often more important than the height of the tree.
FINDING THE HEIGHT OF A TREE BY RIFLE OR FOLDED PAPER.
Fig. 2. Or, sticking a branch into the ground, select one of its forks, or lash on a cross piece which shall pass through the trigger guard behind the trigger, so that the gun may be about the height of your eye when you aim horizontally at the mark on the tree, the trigger finger grasping the stick for greater steadiness. Take another stick, with a fork or cross rest of equal height with the first, and connect them by a smaller stick of any length, say 18in. or 2ft., and at exactly the same height above the lower rest lash another on the second stick, so that, the base and perpendicular being equal, the gun, when its muzzle is laid on the higher rest, shall form exactly an angle of 45° with its line when previously laid upon the lower one. Now retire until from the lower rest you can sight the mark upon the tree, and from the upper its highest branches; then the distance from your pivot stick, plus 5ft., will be the height of the tree. Our illustration purposely shows this operation in the simplest possible form; but the frame might be steadied by lashing on other cross bars (X fashion), and a friend to help in moving it to a greater or less distance from the tree would greatly assist the observer. It would be inconvenient to make this observation kneeling. A telescope, a long straight reed, a roll of paper, or a straight tube of any material, will answer almost as well as the rifle.
Even a clasp knife (Fig. 3), with a bit of reed stuck into the handle where the point should reach, and resting on the point of the half-opened blade, is better than nothing.