Beginning at A, the first line measured is the diagonal AB; the course N. 45° E. is set down at the right. The first point requiring notice is the intersection of the diagonals at 1170 links from A. The diagonal is represented by the dotted line crossing the columns, a continuous line being employed to designate a fence or side, and a dotted line a sight-line. At 1445 the fence EF is crossed. The whole length to B is 2492 links.

Turning to the left along BC, at 950 we come to the fence bearing to the left: 950 is surrounded by a line, thus, 950 because it is to be used as a starting-point for another measurement. Having arrived at C, 1760 links from B, again turn to the left towards A: the distance CA is 1135 links. AD is next measured. At 1395 the fence EF is found: the point is marked 1395 : at 2020 the brook is crossed, and

at 2440 links we find the corner D. Turning to the left along DB, at 515 the brook is again crossed. This line is 1760 links long.

Passing now to E, 950 in BC, along the cross fence, the diagonal AB is passed at 425; at 770 CD is passed; 1440 links brings us to 1395 in AD. Passing to D: along DC, at 395 the brook is crossed; at 1390 the fence is found; at 1550 we cross the diagonal AB: 2425 brings us to C, which finishes the work.

245. Test-lines. In the above survey more lines have been measured than are absolutely necessary. It is always better to measure too many than too few. If the redundant lines are not needed in the calculation, they serve as tests by which to prove the work. For the mere purpose of calculation, one of the diagonals and the line EF might have been omitted: the other lines afford sufficient data for making a plat and calculating the area. An error in one of the others will not prevent the notes from being platted, and hence they do not in any way afford a criterion by which we can judge of the accuracy of the measurements; but when to these are added the length of the other diagonal we have a series of values, all of which must be correct or the map cannot be made.

246. General Directions. When about to survey a tract by this method, the surveyor should first examine the tract carefully and erect poles at the prominent points, corners, and false stations, along the boundary lines. He should stake out all diagonals and subsidiary lines which he may wish to measure, setting a stake at the points in

which such lines intersect each other or cross the former lines, in fact, at every point the position of which it may be desirable to fix on the plat.

Having made these preparations, he may, if the tract is at all complicated, make an eye-sketch. This will serve to guïde him in regard to the best course to take in his measurements.

Commencing then at some convenient point of the tract, he should measure carefully the diagonals and sides in succession, passing from one line to such other as will make the least unnecessary walking, and setting down in his notebook the distance to every stake, fence, brook, or other important object met with.

When the tract is large, the work may last through several days. In such cases, each day's work should, if possible, be made complete in itself,-that it may be platted in the evening. This will prevent the accumulation of errors which might occur from a mismeasurement of one of the earlier lines.

247. Platting the Survey. To plat a survey from the notes, select three sides of a triangle and construct it. Then, on the sides of this construct other triangles, until the whole of the lines are laid down. Measure test-lines to see whether the work is correct.

In all cases commence with large triangles, and fill up the details as the work proceeds.

SECTION V.

ON THE METHOD OF SURVEYING FIELDS OF PARTICULAR FORMS.

248. Rectangles. MEASURE two adjacent sides: their product will give the area.

EXAMPLES.

Ex. 1. Let the adjacent sides of a rectangular field be 756 and 1082 links respectively, to plat the field and calculate the content.

Calculation.

=

Content = 1082 × 756 817992 square links = 8 A., 0R., 28.7 P.

Ex. 2. The adjacent sides of a rectangular tract are 578 and 924 links: required the area.

Ans. 5 A., 1 R., 14.51 P.

Ex. 3. Required the area of a tract the sides of which are 9.75 and 11.47 chains respectively.

Ans. 11 A., 0 R., 29 P.

249. Parallelograms. Measure one side and the perpendicular distance to the opposite side. Their product will be the area.

If a plat is required, a diagonal or the distance from one angle to the foot of the perpendicular let fall from the adjacent angle may be measured.

EXAMPLES.

Ex. 1. Given one side of a parallelogram 10.37 chains, and the perpendicular distance from the opposite side 7.63 chains, the distance from one end of the first side to the perpendicular thereon from the adjacent angle being 2.75 chains. Required the area and plat.

Ans. 7 A., 3 R., 25.97 P.

Ex. 2. Desiring to find the area of a field in the form of a parallelogram, I measured one side 763 links, and the perpendicular from the other end of the adjacent side 647 links, said perpendicular intersecting the first side 137 links from the beginning. Required the content and plat.

Ans. 4 A., 3 R., 29.86 P.

250. Triangles. First Method.-Measure one side, and the perpendicular thereon from the opposite angle; noting, if the plat is required, the distance of the foot of the perpendicular from one end of the base.

Multiply the base by the perpendicular, and half the product will be the area.

EXAMPLES.

Ex. 1. Required the area and plat of a triangular tract, the base being 7.85 chains and the perpendicular 5.47 chains, the foot of the perpendicular being 3.25 chains from one end of the base.

Ex. 2. Required the area and plat of a triangle, the base being 10.47 chains, and the perpendicular to a point 4.57 chains from the end, being 7.93 chains.

Ex. 3. Required the area of a triangle, the base being 1575 links, and the perpendicular 894 links.

251. Second Method.-Measure the three sides, and calculate by the following rule:—

From half the sum of the sides take each side severally; multiply the half-sum and the three remainders continually together, and the square root of the product will be the area.