Fig. 2. If you have not a compass, choose A as before, set in a stake at B, and prolong the line to C; then on this line erect a perpendicular by looping a cord on the stake at C, and with a sharpened peg held at the other end of it drawing the arc, D E; then, making D and E equidistant from B, draw through these three points the line D B E F; on this line retire toward F till A and B form an angle of 45°, which may be measured either by folding a square of paper diagonally, or by pegging out a piece of string divided into two lengths of 24in. and one of 32in. See that the longest or diagonal side bears truly upon A, and one of the shorter sides on B, which will take place at the point F, then F B will be equal to B A, or the breadth of the river. Repeat this also if the ground allows, on the opposite side G, and take the mean of the two observations.
The correctness of all these observations may be greatly increased by resting your rifle on each successive point, and carefully sighting all the lines with it.
Fig. 3. Another excellent and simple plan is—choose A; set in B; from B erect the perpendicular B C, C D, divided equally at C; from D erect the perpendicular D E; retire along it till the stake C bears truly upon A, which will be at F, then F D will equal B A.
Fig. 4. If the river bank is so curved that you cannot draw B C D at right angles, you have two alternatives. If there is plenty of room retire as far as you please from the bank before planting the stake B, and deduct from the result the distance you retire from the bank. Or, if there is not room, you may draw B C D, as in Fig. 4, diagonally, and contrive to keep D E as nearly parallel to A B as you can; but any defect in parallelism will greatly affect the correctness of your measurement, as will be evident from the dotted line G.
Fig. 5. If the river is wide, choose A as before; set in B, and retire any measured distance, say 6yds., to C; then from B and C erect perpendiculars of equal length, and draw the square B C, D E; test it by stretching a cord from corner to corner; then, prolonging the line C E, bring the stake D in one with A, and produce the line A D till it intersects C E at F; then divide F E into six parts, measure as many of them as you can on the line E D, and you will find as many of them as there are yards on the line B A; therefore, in the present instance, 11yds. will be the breadth of the river, and one may be deducted because the marks are not close to the edge of the banks; or say, as E F is to E D so is B D to B A.
Fig. 6. To erect a perpendicular on a given point on any line, measure equal distances on either side; set in pegs, loop a cord on them alternately, and strike two arcs, their intersection will be perpendicular to the given point. To cross the end of a line by another at right angles, set a peg some distance back, loop a cord on it, and strike an arc. Measure equal distances from the end of your given line to the arc, then a line drawn through the three points will be at right angles to the first.
A scale of equal parts may be made by folding a slip of paper in half, then folding each part in half, and so subdividing it as much as you wish, but do not fold it in half, and then double the two parts to get the quarters at one operation, and then double the four parts to get the eighths, or you will find them come out very unequally.
A measuring tape may be made by taking a narrow white tape, say ¼in., and winding it on a slip of card barely an inch wide, just so little spirally that each turn may not half cover the preceding one, then carefully blacken the edges, and, when you unwind the tape, mark every twelfth inch with figures to denote feet, and every sixth with an extra line.