CASE VI. 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 sach of the other angles, with a compass and chain. Fig. 57. 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 Find the bearing from each station to the respective an. gles; and also the bearing and distance from one station to the other. Fig. 58. FIELD BOOK. See Fig. 58. N: S 0 W. First Station. Second Station. AC. N. 38° 30' E. BC. S. 82° 0 E. AD. S. 69 0 E. BD. S.' 17 0 E. AE S. 59 BE. S. 28 0 W. AF. N. 63 0. W. BF. S. 49 0 W. AG. N. 21 BG. N. 76 0 W. AH. North. BH. N. 24 0 W. Stationary line AB. N. 14° E. 20 chains. 0 W. 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. CASE VIII. TO SURVEY AN INACCESSIBLE FIELD. Fix upon two stations at a convenient distance from the 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. Fig. 59. First Station. Second Station. AE. N. 9° 15' E. BE. N. 500 O' W. AF. N. 16 0 E. BF. N. 29. 15 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 0 E. BC. N. 20 309 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 pre. ceding 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 al. ready taught. CASE IX. WITH THE COMPASS VERY IRREGULAR,' WITHOUT NOTICING Begin near one corner of the field, as at A, Fig. 60. and measure to the next large corner, as B, in a straight line ; noticing also the bearing of this line. From the line take offsets to the several bends, at right angles from the line; noticing in the FIELD BOOK at N what part of the line they are taken, as at A1,H2,13, B4. Proceed in the same man: ner round the field. In the figure the dotted lines rep. resent the stationary lines, s 1 and the black lines the boun. daries of the field. I B 4 Draw the stationary lines according to the directions in CASE IV. From A make an offset of 56 links to I ; measure from A to H 540 links, and make the offset, H 2, 140 links ; measure from A to I 826 links, and make the offset I 3, 36 links at B make the offset B 4, 36 links. Proceed in the same manner round the field, and connect the ends of the .offsets TO FIND THE AREA. Find the area within the stationary lines as before taught ; then of the several small trapezoids, rectangles, and trian. gles made by the stationary lines, offsets, and boundary lines, and add the whole together : thus, add 56 links the offset A 1 to 140 links the offset H 2 and multiply their sum 196, by half 540, the length of the line AH, and the product, 52920 square links, will be the area of the trapezoid AH21; again, add 140, the offset H 2 to 36, the offset I 3, and multiply their sum, 176, by half 286, the length of the line HI, and the product, 25168 square links, will be the area of the trapezoid H132. Proceed in the same manner to calculate the area of all the trapezoids, triangles, &c. CASE X. TO SURVEY A FIELD BY TAKING OFFSETS BOTH TO THE RIGHT AND LEFT ; THAT IS, WITHIN AND WITHOUT THE FIELD, AS OCCASION SHALL REQUIRE, IN CONSEQUENCE OF THE STATIONARY LINES CROSSING THE BOUNDARY LINES ; ALSO, BY INTERSECTIONS, THAT IS, TAKING THE BEARING OF AN INACCESSIBLE CORNER FROM TWO STATIONS. The directions given in the preceding case, together with the following FIELD BOOK, will show the learner how to sur. vey a field like the following, and also to protract it when surveyed. |