EXAMPLE V.

To Survey a Field by taking Offsets, when the Boundary Lines are very irregular. See Fig. 50.

Offsets are Perpendicular Lines, measured from the Stationary Distances to the Angular Points of the land.

In the Figure, the marked Lines represent the Boundary of the Field, and the dotted Lines, those Stationary Distances, from which Offsets are taken. From A to B, the Field is bounded by a brook. Take the Course and Distance from A to B. From this Line, measure the Offsets to the several Angles, at Right Angles from the Line; noticing, in the Field Book, at what part of the Line they are taken; as at a, c, d, e, &c. Proceed in the same manner round the Field, or at every place, where it is thought most convenient to take Offsets.

D 2

Draw the Stationary Lines according to the Directions in either of the preceding examples. At Right Angles from these Lines, and at the proper places, according to the Field Book, lay off the several Offsets, by Perpendicular Lines, to the Right and Left, as they were taken. Connect the ends of the Perpendiculars by Lines, which will represent the Boundary of the Field.

To find the Area.

Find the Area within the Stationary Lines, as before taught; then of the small Triangles, Trapezoids, &c., between these and the Boundary Lines; add the contents of those without the Stationary Lines, to the Area; and from this sum subtract the Contents of those within; the Remainder will be the Area of the Field. The Area within the Stationary Lines is 2412 Rods. The figure, Aiba, is an Oblique Triangle, the Base, Ab, 20 Rods, 20

Links, and the Perpendicular, ia, 5 Rods 2 Links, known by the Field Book. Its Area is 52,8 Rods. The figure, bhe, is a Right Angled Triangle. By Subtracting Ab from Ac, known by the Field Book, we have the Base bc, 8,6 Rods, and the Perpendicular hc is 4,4 Rods. Its Area is 18,9 Rods. The figure hgdc is a Trapezoid. Subtract Ac from Ad, the Remainder 5,32 Rods is its Perpendicular Height cd, and the half sum of its Parallel Sides (See Problem 6. Sec. 3. Part 2.) hc and gd is 3,2 Rods. Its Area is 17 Rods. The next figure, in Course on the Plan, is a Trapezoid. Its Area is 14,2 Rods; the next figure is a Triangle. Its Area is 14,2 Rods. All the above figures are without the Stationary Line AB. The Sum of the Areas, of the two remaining figures is 131 Rods, within the Stationary Line. Therefore 117,1 Rods, the Sum of the External Areas, being added to 2412 Rods, make 2529,1 Rods, from which Subtract 131, and the Remainder 2398,1 Rods=14 Acres, 3 Roods, 38 Rods is the Area of the Field. The Student will perceive, that some Decimals are omitted in the preceding calculations.

In Practical Surveying it is recommended to adopt the method here presented of taking Offsets, where the Field is bounded by short lines, not only on account of the ease of Surveying, Protraction and Calculation, but the quantity of ground can be ascertained with greater certainty than by the usual method. It must be admitted that the Area of any Field, arithmetically computed, from the measure taken on the ground, will be more accurate than that which is obtained from Geometrical Projection.

EXAMPLE VI.

To Survey a Field from one Station, within the Field, from which all the Angles can be seen. See Fig. 51.

Take the Course and Distance, from the Station, to each Angle of the Field.

Fig. 51.

B

FIELD BOOK.

From Station to A. N. 20° W. 8 Chains 70 Links.

Draw a Meridian Line as N. S. Select any Point in this Line as at d for the Station; from which lay off the several Courses and Distances; connect the ends of these Distances by Lines, as AB, BC, &c., which will represent the Boundary of the Field.

To find the Area.

Find the Area of the several Triangles, into which the Field is divided by the Stationary Lines; their Sum is the Area of the Map, in Square Chains and Links, which reduce to Acres.

Field Books to Exercise the Learner in plotting Fields and finding their Area.