VERY IRREGULAR, WITHOUT NOTICING WITH THE COMPASS EVERY SMALL BEND. 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 what part of the line they are N taken, as at A 1, H2, 13, B 4. Proceed in the same manner round the field. In the figure the dotted lines represent the stationary lines, and the black lines the boundaries of S the field. S4 粥 Ch. L. 8.20 at 1.04 5.88 the end Offsets. Ch. L. 0 40 0.36 0.33 1. 0.12 BIB! at 2.36 4.28 the er.d 4.68 at 4.34 0.36 FG. S. 27° 40' E. 0.96 0.30 CD. N. W. 0.30 DE. N. 11° 10' W. 4.20 | 0.30 GA. S. 25° 20′ W. at 2. the end 1.20 7.06 0.24 0.16 at 3.80 the end 0.80 0.40 6.48 TO PROTRACT THIS FIELD. 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 by links, which will represent the boundaries of the field. 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 AH 21; 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 HI 32. 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 survey a field like the following, and also to protract it when surveyed. NOTE.--To draw a tree, house, tower, or any other remarkable object, in its proper place, in the plot of a field-from any.two stations, while surveying the field take the bearing of an object, and the intersection of the lines, which represent the bearings, will determine the place of the ob TO FIND THE AREA OF THE ABOVE FIELD. Find the area within the stationary lines, and then of the several small trapezoids, &c. remembering to distinguish those without the stationary lines from those which are within. Subtract the area of those within the stationary lines from the area of those without, and add the remainder to the area contained within the stationary lines; the sum will be the whole area of the field. [Or, add the areas of those without the stationary lines, to the area contained within those lines, and subtract from the sum, the areas of the several triangles, trapezoids, &c. within the stationary lines.] SECTION III. RECTANGULAR SURVEYING, OR AN ACCURATE METHOD OF CALCULATING THE AREA OF A FIELD ARITHMETICALLY, FROM THE FIELD BOOK, WITHOUT THE NECESSITY OF PROTRACTING IT, AND MEASURING WITH A SCALE AND DIVIDERS, AS IS COMMONLY PRACTISED. I. Survey the field in the usual method, with an accurate compass and chain, and from the field book set down, in a traverse table, the course or bearing of the several sides, and their length in chains and links, or rods and decimal parts of a rod; as in the 2nd and 3d columns of the following Ex AMPLE. |