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CASE V. To survey a Field from one Station, at any place within the Field, from which the several Angles may be seen,
Take the Bearing of the Angles, and measure their
B. N. 60 E. 10.
F. N. 65 W. 8,78
To protract this Field. Draw a Meridian line as N. S. From some point in that Line as a Centre lay off the Bearing and Distance to the several Angles, and draw Lines from one Angle to another, as AB, BC, CD, &c.
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, it may done by rejecting the Left hand figure, without the trouble
of putting down the Cyphers and subtracting. Triangle aAB.
Triangle aCD. aA, 8.70 0.93952 aC, 11.40
1.05690 aB, 10 1.00000 aD, 10.50
1.02119 Sine AaB, 80°
Sine CaD, 78°
CASE VI. 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
ing and Distance to the several Angles, and connect them by Lines, as FG; FA, FB, &c.
The Area may be calculated as taught in the preceding CASE.
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 respect. ive Angles ; and also the Bearing and Distance from one Station to the other. FIELD BOOK. See Plate III. Fig. 62. First Station.
BH. N. 24 O W.
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 off 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 Field.
survey an inaccessible Field. Fix upon two Stations, at a convenient distance from
be seen ; from each Station take the Bearing of the Angles; and take the Bearing and Distance from one Station to the other.
FIELD BOOK. Şee Plate IV. Fig. 67.
Ch. L. 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. 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, Plate IV. 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 the Line they are taken, as A 1, H2, I3, 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
Bearing and Distance.
Offsets) Bearing and Distance.
Ch. L.]Ch L.
Ch. L. Ch. L AB. N. 850 O' E. 11.20 0.56 EF. S. 67° 50' W. 8.20 0.40 at 5.401 1.40
at 1.34 0.36 8.26 0.36
2.96 0.33 the end 0.36
the end) 0.12 BC. N. 7° 20' E. 7.961 0.20
at 2.36 0.36 FG. S. 27° 40' E. 7.06 1.20 4.28 0.96
0.24 the end 0.30
the end) 0.16 CD. N. 62° 0' W. 4.68
IGA. S. 250 20' W. 6.48 at 4.34 0.30
at 3.80 0.80 DE. N, 11° 10' W.4.201 0.30
the end) 0.40
To protract this Field. Draw the stationary Lines according to the directions in CASE IV. From A make an Offset of 56 Links to l; measure from A to H 540 Links and make the Offset H 2, 140 Links; measure from A to 1 826 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 thu Offset H2 to 36 the Offset 13 and