The chimney of the farm-house and the oak-tree in the corner of the wheat-field, are thus employed in this survey. At C, the corner of the field, is in the centre of the brook, and from this point to D, the brook is the boundary. A straight line is run between the stations, and offsets are measured to each bend of the brook. It is necessary, in such a case, for the chainmen to exercise unusual care in keeping in the line between the stations, otherwise the lengths of the offsets cannot be correctly measured. At E, the bearing of the oak-tree is taken (N. 734° E.). On the course between E and F, a marsh is encountered, which the chainmen pass, by an offset course. At F, another bearing is taken of the oak-tree (S. 441° E.). At G, the bearing of the farm-house chimney is noted (S. 26° E.). At G and H the bearings of the division-fences are taken. On the course from H to I, the turnpike is again crossed; the intersection of both sides, together with the bearing, are carefully noted. From I to K, the intersection and bearing of the fence between the potato and the wheat field, are recorded. The course from K to A closes the survey. To locate the buildings about the farm-house, a few measurements would be necessary; but they may begin with the point already located by the bearings taken to the chimney nearest the north end of the house. The dimensions of the buildings, their distances apart, and the direction of one side of each afford sufficient data for locating them, correctly, upon the map. NOTE. The advantage of the compass over other instruments with which angles are measured, lies chiefly in this that the Bearing of a course may be measured at any point on the line. When the angle between adjacent sides is taken with the Transit, the work can only be done at the corners of the field; and when, as frequently happens, a hill intervenes between two consecutive stations, it becomes necessary to locate a point on the hill, in the true line, and then return to the corner to measure the angle; whereas, when the compass is employed, the establishment of the intermediate point on the hill affords the means of taking the proper bearing without going to the angle. Furthermore, the bearings may be measured with the compass, by placing it at the alternate stations only. The disadvantage of these rapid methods is that there is no check upon the needle readings, as there is in back-sighting. 124. To Correct Local Attraction.-Suppose that bearings and reverse-bearings have agreed for several stations, and that then a back-sight differs from the preceding fore-sight; it may be concluded that local attraction affects the needle at the last station only. 26 28 24 S Suppose the fore-sight at P to have been N. 30 E., and the back-sight at S to be S. 28 W.; suppose the fore-sight at S to be N. 26 W.; what is the correct fore-sight at S? From Fig. 67 we see that the needle at S, instead of being parallel to the needle at P (as indicated by the dotted needle) as it should be, has been deflected by local attraction (as shown by the full needle), so that its south end is moved 2° to the W., and its north end 2° to the E. of its proper position. Hence the fore-sight at S, being taken from the needle in a false position, is 2° too large, and should be only N. 24 W. By similar reasoning, aided by a mental picture of the case, any bearing may be corrected. P 30° FIG. 67. If no back-sight and its fore-sight agree, then take the mean of the back-sight and fore-sight which differ least; or seek some ground at a distance, free from local attraction, and then work into the plot to be surveyed, correcting each fore-sight on the way. SECTION IV. AREA OR CONTENTS OF GROUND. Having explained the necessary operations on the field, we shall now proceed to show the manner of computing the contents of ground. 125. The Traverse Table and its Uses.-This table shows the latitude and departure corresponding to bearings that are expressed in degrees and quarters of a degree, from 0 to 90°, and for every course from 1 to 100, computed to two places of decimals. N E The following is the method of deducing the formulas for computing a traverse table; by means of these formulas and a table of natural sines, the latitude and departure of a course may be computed to any desirable. degree of accuracy. Let AD be any course, and NAD its bearing; then AE is the latitude, and ED the departure of the course AD, to the bearing NAD. From Art. 36, we have (using. nat. sines) FIG. 68. Whence, AD AE: 1: cos NAD. lat. course x cosine of bearing. |