WITHIN THE FIELD, FROM WHICH THE SEVERAL ANGLES MAY BE SEEN. Take the bearing of the angles, and measure their distance from the station. FIELD BOOK. See Fig. 56. Fig. 56. Draw a meridian line as N. S. From some point in that line as a centre, lay off the bearing and distance to the several angles, and draw lines from one angle to another, as AB, BC, CD, &c. TO FIND THE AREA. The Area may be calculated according to PROB. XII. by measuring diagonals and perpendiculars; or more accurately according to PROB. IX. RULE 4. As the bearing and distance of the lines from the station to the several angles are known, two sides and their contained angle are given in each of the triangles into which the plot is divided; the area may, therefore, be readily calculated the RULE above referred to. Note. As in the operation, the logarithm of radius is to be subtracted from the sum of the other logarithms, it may be done by rejecting the the left hand figure, without the trouble of putting down the cyphers Triangle aAB. Triangle aDE. aA, 8.70 0.939519aD, 10.50 1.021189 aB, 10 1.000000 a E, 12 1.079181 Sine AaB, 800 - 9.993351 line DaE, 750 9.824944 Doub. area, 85.67 1.932870 Doub. area, 121.7 2.085314 Triangle aBC. Triangle a EF. aB, 10 1.000000 a E, 12 1.079181 ac, 11.40 1905 aF, 8.78 0.943495 Sine BaC, 27° 9. 54 Sine EaF, 550 - 9.913365 Doub. area, 51.75 1.713952 Doub. area, 86.31 1.936041 Triangle aCD. Triangle aFA. aC, 11.40 1.056905 aF, 8.78 0.943495 aD, 10.50 1.021189 a A, 8.70 0.939519 Sine CaD, 780 - 9.990404 Sine FaA, 450 - 9.849485 TO SURVEY A FIELD FROM SOME ONE OF THE ANGLES, FROM WHICH THE OTHERS MAY BE SEEN.* From the stationary angle take the bearing and distance to each of the other angles, with a compass and chain. * This method of practice is subject to much error. Draw a meridian line to pass through the stationary angle as at F. From the point F, lay off the bearing and distance to the several angles, and connect them by lines, as FG, FA, FB, &c. The area may be calculated as taught in the preceding CASE. CASE VII. To SURVEY A FIELD FROM TWO STATIONS WITHIN THE FIELD, PROVIDED THE SEVERAL ANGLES CAN BE SEEN FROM EACH STATION. Find the bearing from each station to the respective angles; and also the bearing and distance from one station to FIELD BOOK. See Fig. 58. Fig. 58. N в N First Station. Second Station AC, N. 380 301 E. BC. S. 820 0 E AD. S. 69 0 E. BD. S. 17 O E AE. S. 59 0 W. BE. S. 28 0 W. AF. N. 63 0 W. BF. S. 49 0 W. AG. N. 21 0 W. BG. N. 76 0 W. AH. North. N. 24 0 W. Stationary line AB. N. 140 E. 20 chains. BH. TO PROTRACT THIS FIELD. At the first station A, draw a meridian line and lay off the bearings to the respective angles ; draw the stationary line AB, according to the bearing and distance; at B draw a meridian line parallel to the other, and lay off the bearings to the angles, as taken from this station ; from each station draw lines through the degree which shows the bearing of each angle, as marked by the protractor or line of chords, and the points where those lines intersect each other will be the angles of the field. Connect those angular points together by lines, and those lines will represent the several sides of the field. field, from each of which the several angles may be seen ; from each station take the bearing of the angles; and take the bearing and distance from one station to the other. FIELD BOOK. See Fig. 59. Fig. 59. First Station. Second Station. AE. N. 90 15 E. BE. N. 500 0' W. AF. N. 16 0 E. BF. N. 29 15 W. AG. N. 14 30 E. BD. N. 24 0 W. AD. N. 39 0 E. BG. N. 21 30 W. AH. N. 40 0 E. BH. N. 5 0 E. AC. N. 72 Ο Ε. BC. N. 20 30 E. Ch. L. The directions given in the last case for plotting the field, will apply in this case also ; and the area in this and the preceding case may be calculated in the manner pointed out in CASE IV. by dividing the plot into triangles and measuring diagonals and perpendiculars. Or the sides may be found by trigonometry, and the area calculated arithmetically, as already taught. |