To find the Area.

The Area may be calculated according to PROB. XII. by measuring Diagonals and Perpendiculars; or more accurately according to PROB. IX. Rule 4.

As the Bearing and Distance of the Lines from the Station to the several Angles are known, two Sides and their contained Angle are given in each of the Triangles into which the Plot is divided; the Area may, therefore, be readily calculated by the Rule above referred to.

Note. As in the operation, the Logarithm of Radius is to be subtracted from the Sum of the other Logarithms, may be done by rejecting the Left-hand figure, without the trouble of putting down the Ciphers and subtracting.

To survey a Field from some one of the Angles, from which the others may be seen.

From the stationary Angle take the Bearing and Distance to each of the other Angles, with a Compass and Chain.

Fig. 59.

Z

FE. N. 30 E.

To draw a Plot of this Field.

Draw a Meridian Line to pass through the stationary Angle as at F. From the Point F, lay off the Bearing and Distance to the several Angles, and connect them by Lines, as FG, FA, FB, &c.

CASE VII.

To survey a Field from two Stations within the Field, provided the several Angles can be seen from each Station.

Find the Bearing from each Station to the respective Angles; and also the Bearing and Distance from one Station to the other.

FIELD BOOK. See Fig. 62..

Fig. 62.

Stationary Line AB. N. 140 E. 20 Chains.

To protract this Field.

At the first Station A, draw a Meridian Line and lay off the Bearings to the respective Angles; draw the Stationary Line AB, according to the Bearing and Distance; at B, draw a Meridian Line parallel to the other, and lay of the Bearings to the Angles, as taken from this Station; from each Station draw Lines through the Degree which shows the Bearing of each Angle, as marked by the Protractor or Line of Chords, and the Points where those Lines intersect each other will be the Angles of the Field. Connect those angular Points together by Lines, and those Lines will represent the several Sides of the

CASE VIII.

To Survey an inaccessible Field.

Fix upon two Stations, at a convenient distance from the Field, from each of which the several Angles may be seen; from each Station take the Rearing of the Angles; and take the Bearing and Distance from one Station to the other.

FIELD BOOK. See Fig. 67.

F

Fig. 67.

Stationary Distance AB, S. 88° 30' E. 19.20..

The directions given in the last CASE for plotting the Field, will apply in this CASE also; and the Area in this and the preceding CASE may be calculated in the manner pointed out in CASE IV. by dividing the Plot into Triangles and measuring Diagonals and Perpendiculars. Or the Sides may be found by Trigonometry, and the Area calculated Arithmetically, as already taught.

CASE IX.

To survey a Field where the boundary Lines are very irregular, without noticing with the Compass every small Bend.

Begin near one corner of the Field, as at A, Fig. 68. 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 N the Line they are taken, as at A 1, H2, I 3, 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 the Field.

S