3. Find the area of five lands, from the following dimensions. 2436 205 2000 210 1700 214 1400 218 1000 220 700 215 400 209 000 205 Area 5a. Or. 29p. 4. Required the area of six lands, from the following notes. 3365 199 3000 2500 214 2000 1800 236 1000 800 201 000 175 Area 7a. Or. 8p. Note. The sum of the breadths in the last example is 1025, which being divided by 5, their number, we obtain 205 for the mean breadth; then 3965 multiplied by 205, is equal to 639825 square links, which are equal to 6 acres, 3 rouds, 24 perches, the area, which is too little by 24 perches, proving the inaccuracy of the common method. If a piece of ground be narrowest about the middle, the common method will give the area too much. PROBLEM V. To measure a mere or wood. By the help of your cross, fix four station-staves on the outside of the mere or wood, so as to form a rectangle; then measure each of its sides, taking insets to the boundaries, which must be treated as before directed. It is, however, a more expeditious method than the former, to measure the four sides of a quadrilateral figure, having one right angle; then construct the figure, and measure the diagonal and perpendiculars by the scale. Note 1. If a mere or wood be of a triangular shape, its area may be found y measuring the three sides of a circumscribing triangle; and proceeding as before. 2. By this problem you may survey fields into which you are not permitted to enter, or which contain obstructions. EXAMPLE. Let the following figure represent a wood, the area of which is required. B Set up your cross at station A, and let your assistant fix the marks B and D, so that the angle at A may be a right angle; and measure the line AB, taking insets to the fence, as you proceed. Then fix the mark C, as most convenient; measure the other three lines, and you will find in your field-book the following dimensions. ANSWER. Having constructed the figure, you will find the diagonal BD to measure 1930, the perpendicular Aa 923, and Ca 605 links; hence the area of the wood is 12a. 3r. 20p. PROBLEM VI. To measure and plan roads, rivers, canals, &c. In measuring roads, rivers, or canals, angles or tielines must be taken at the different turns, in order to lay down the chain-lines; and offsets must be taken to the boundaries, as you proceed, to enable you to draw the plan. Note 1. The length of a road is generally returned either in miles, furlongs, and poles, or else in miles and yards. 2. A machine called a "Perambulator" is sometimes used to ascertain the lengths of roads. It has a wheel of 8 feet 3 inches, or half a pole, in circumference, which being made to pass over the ground, puts in motion the clockwork within; and the distance measured is pointed out by an index on the outside. This instrument is much more expeditious for measuring the length of a road, than the chain; but it is certainly less correct; for by the wheel passing over stones, sinking into holes, &c. the distance is made to appear more than it is in reality. EXAMPLES. 1. Let the following figure represent a serpentine road, a plan of which is required. |