As 100 links: 66 feet :: 217.6 links: 143.6 feet, the descent B below the level of A. Hence, B bears N. 79° 54′ E from A. Nearest horiz. dist. 3547 links. Sum of obl. dist. 8948 links. Answer. With the angular elevation or depression in the third column, and the oblique distance in the fourth (as course and distance) are found the horizontal distance in the fifth, and the perpendicular ascent or descent on the sixth, for each station (as difference of latitude and departure :) then, with the bearing and horizontal distance we get the difference of latitude and departure in the two last columns. The ascents and descents in the sixth column are distinguished by the letters E and D in the third, signifying elevation or depression; and being added separately, the difference of their sums is set at the bottom of the column with the name of the greater, and shews the perpendicular descent of B below the horizontal level of A. In like manner the northings and southings in the seventh column are distinguished by the letters N. and S. in the second, &c. PROMISCUOUS QUESTIONS. 1. The perambulator, or surveying wheel, is so contrived as to turn just twice in the length of a pole or 16 feet; what then is the diameter? Answ. 2.626 feet. 2. Two sides of a triangle are respectively 20 and 40 perches; required the third so that the content may be just an acre? Answ. either 23.099 or 58.876 perches. 3. I want the length of a line by which my gardener may strike out a round orangery that shall contain just half an acre of ground. Answ. 27 yards. 4. What proportion does the arpent of France, which contains 100 square poles of 18 feet each, bear to the American acre, containing 160 square poles of 16.5 feet each, considering that the length of the French foot is to the American as 16 to 15? Answ. as 512 to 605. 5. The ellipse in Grovesner square measures 840 links the longest way, and 912 the shortest, within the rails now the wall being 14 inches thick, it is required to find what quantity of ground it incloses, and how much it stands upon? Answ. it incloses 4A. 6P. and stands on 1760 square feet. 6. Required the dimensions of an elliptical acre with the greatest and least diameters in the proportion of 3 to 2? Answ. 17.479 by 11. 653 perches. 7. The paving of a triangular court at 18d. per foot, came to 100l. The longest of the three sides was 88 feet; what then was the sum of the other two equal sides? Answ. 106.85 feet. 8. In 110 acres of statute measure, in which the pole is 16 feet, how many Cheshire acres, where the customary pole is 6 yards, and how many of Ireland, where the pole in use is 7 yards. Answ. 92A. 1R. 28P. Cheshire; 67A. 3R. 25P. Irish. 9. The three sides of a triangle containing 6A. 1R. 12P. are in the ratio of the three numbers, 9, 8, 6, respectively; required the sides? Answ. 59.029, 52.47, and 39.353. 10. In a pentangular field, beginning with the south side, and measuring round towards the east, the first or south side is 2735 links, the second 3115, the third 2370, the fourth 2925, and the fifth 2220; also the diagonal from the first angle to the third is 3800 links and that from the third to the fifth 4010: required the area of the field? Answ. 117A. 2R. 28P. 11. Required the dimensions of an oblong garden containing three acres, and bounded by 104 perches of pale fence? Answ. 40 perches by 12. 12. How many acres are contained in a square meadow, the diagonal of which is 20 perches more than either of its sides. Answ. 4A. 2R. 11P. 13. If a man six feet high travel round the earth, how much greater will be the circumference described by the top of his head than by his feet? Answ. 37.69 feet. N. B. The required difference is equal to the circumference of a circle 6 feet radius, let the magnitude of the earth be what it may. 14. Required the dimensions of a parallelogram containing 200 acres, which is 40 perches longer than wide? Answ. 20 perches by 160. 15. What difference is there between a lot 28 perches long by 20 broad, and two others each of half the dimensions? FINIS. Answ. 1A. 3R. |