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FIELD BOOK.

Bearing and Distance. Offsets Bearing and Distance. Offsets

Ch. L. Ch. L.

Ch. L. Ch. L. AB. N. 85° 0' E. 11.20 0.56 EF. S. 67° 50′ W. 8.20 0.40

[blocks in formation]

at 2.36 0.36 FG. S. 27° 40′ E. 7.06 1.20

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Draw the stationary Lines according to the directions in CASE IV. From A make an Offset of 56 Links to 1; 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 Lines, 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, Parallelograms and Triangles 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 H2 to 36 the Offset 13 and multilpy their Sum 176 by half 286 the length of the H

Line HI, and the product 25168 Square Links will be the Area of the Trapezoid HI32. 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.

FIELD BOOK. See PLATE IV. Fig. 69.

Offsets to the Left.

Bearing and Distance.

Offsets
to the

Remarks.

Right.

Ch. L. Ch. L

Ch.LAB. N.SS° 0′ W. 22.12

A Tower bears from
A. N. 48°. W.

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From B the Tower
bears N. 38° 30′ E.

10.25
15.

1.15

C 1. S. 82° 15' E.

1,2. N. 70 2 D. N. 20

5.45

o E. 13.25
0 E. 3.36)

DF. S. 35° 0' E. 15.15

FA. S. 15° 15′ E. 15.10
at 1.20
7.45

From C go into the Field to 1, on account of some impediment on or near the boundary Line. At D, you get into anether Corner of the Field.

E an inaccessible Corner bears from D. S. 65° 30′ E.

E the inaccessible Corner
bears from F
N. 4° W.

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 the object; and the intersection of the Lines, which represent the Bearings, will determine the place of the object; in the same manner that the Tower is drawn in the Figure.

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.

SECTION III.

REGTANGULAR 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.

1. 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 2d and 3d Columns of the following EXAMPLE.

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and Departure,* or by the Table of Natural Sines,† the Northing or Southing, Easting or Westing made on each Course, and set them down against their several Courses, in their proper Columns, marked N. S. E. W.

Note. To determine whether the Latitude and departure for any particular Course and Distance are accurately calculated, square each of them; and if they are right, the Sum of their Squares will equal the Square of the Distance, for the following reason: The Latitude and Departure represent the two Legs of a Right Angled Triangle, and the Distance the Hypothenuse; and it is a Mathematical truth, that the Square of the Hypothenuse of any Right Angled Triangle is equal to the Sum of the Squares of the two Legs.

3. If the Survey has been accurately taken, the Sum of the Northings will equal the Southings; and the Eastings will equal the Westings. If upon adding up the respective Columns, these are found to differ very considerably, the Field should be again surveyed; as some error must have been committed either in taking the Courses or measuring the Sides. If the difference is small, a judicious, experienced Surveyor will judge from the nature of the ground or shape of the Field surveyed, where the mistake was most probably made, and will correct accordingly, Or, the Northings and Southings, and the Eastings and Westings may be equalled by balancing them, as follows: Subtract one half the difference from that Column which is the largest, and add the other half to that Column which is the smallest; and let the difference to be added or subtracted be divided among the several Courses according to their length.

* For an Explanation of this Table, and the manner of using it, see the Remarks preceding the Table.

† See the Remarks preceding the Table of Natural Sines.

A method of determining whether the Courses are right has been already explained. See page 50. The Surveyor, before he leaves the Field, should calculate the Northings, Southings, &c. and if he finds much difference determine whether the Courses are right. This will show him whether a re-survey is necessary, and will enable him to ascertain whether the error lies in the Courses or Distances.

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