EXAMPLE 3.

In a survey, represented Fig. 81, the corner at A was inaccessible, occasioned by the overflowing of water, but being a tree, it can be seen from the adjacent corners B and L. I therefore set my instrument at B and took the bearing to A, which I reversed, and set in my

field-book as the first bearing. I then proceeded to take the bear. ings and distances of the several sides to L; and at L, I took the bearing of the side LA. The field-notes being as follow, the length of the sides AB and LA, and the area are required.

Ch.
AB, N. 51°4 W.
BC, S. 45; W. 15.16
CD, N. 50 W.22.10
DE, North 18.83
EF, N. 48 E. 22.60
FG, N. 25; W.20.17

East 26.57
HI, S. 30; E. 22.86
IK, S. 44 W. 15.04
KL, S. 47 E. 28,55
LA, S. 203 W.

GH,

By taking the difference of latitude and departure for each of the sides BC, CD, DE, EF, FG, GH, HI, IK, and KL, and balancing, we shall have the difference of latitude and departure of LB, with which its bearing and distance may be found as in the last example.

To tang. of the bearing of LB, S. 78° 49' W.

As rad.
Is to sec. of the bearing of LB 78° 49
So is diff. of lat.

do. 5. 73

10.00000
10.71231
0.75815

11.47046

To length of LB 29.54

1.47046

Now, having the bearings of the lines AB, LB, and AL, the angles contained by them may be found by the rules given page 34. Then in the triangle ALB, all the angles and one side LB will be given to find the other sides AB and LA.

AB, N 51° 15' W BA, S 51° 15' E LB, S 78° 49' W
AL, N 20 30 E BL, N 7849 E LA, S 20 30 W

Sta.

Courses.

Dist.

N.

S.

E.

W.

M. Dist.

N. Area.

S. Area.

BY RULE 2.

AB N 51° W 26.47 16.56

20.65 76.13 E

1260,7 128

55.48 E BCS 451 W 15.16 10.62

10.81 44.67 E

474.3954

33.86 E
CD N 50 W 22.10) 14.20

16.93
16.93 E

240.4060

0.00 DE North, 18.83 18.83

000

0.00 EF N 48 E 22.60 15.12)

16.80

16.80 E

254.01601

33.60 E
FG N 251 W 20.17) 18.20

8.68
24.92 E

453.54401

16.24 E
GH East,
26.57

26.57

42.81 E

69.38 E HIS 301 E 22.86 19.70 11.61

80 99 E

1595,50301

92.60 E IK S 44 W| 15.04

10.82 10.45/ 82.15 E

888.86301

71.70 E
KL S 47 E 28.55

19.48) 20.88
92.58 E

1803.4584

1113.46 E LAS 201 W23.80 22.29

8.341 105.12 E

2343.1248)

96.78 E 82.91182.9 11 75.86175.86)

12208.678817 105.3446

2208.6788

2)4896.6658 Area 244 A. 3 R. 13 P.

2448.3329 Ch.

집

PRACTICAL EXAMPLES.

To be calculated by either of the preceding Rules.

1. Given the boundaries of a tract of land as follow, viz. Ist, S 3501 W, 11.20 ch. 2nd. N 450 W, 24.36 ch. 3rd. N 1501 E, 10.80 ch. 4th. S 77o E, 16 ch. 5th. N 87°; E, 21.50 ch. 6th S 60° E, 14.80 ch. South 10.91 ch. 8th N 850 W, 29.28 ch. to the place of beginning; required the area. Ans. 85 A. 3 R. '17 P.

2. Given the boundaries of a tract of land as follow, viz. Ist. N 19o E, 27 ch. 2nd. S 770 E, 22.75 ch. 3rd. S 27° E, 28.75 ch. 4th. S 52° W. 14.50 ch. 5th. S 15°; E. 19 ch. 6th. West, 17.72 ch. 7th N. 36° W, 11.75 ch. 8th North, 16.07 ch. 9th N 620 W, 14.88 ch. to the place of beginning; required the area.

Ans. 152 A. 2 R. 6 P.

3. Required the area of a tract of land bounded as follows: 1st. S 62° W. 7.57 ch. 2nd. N. 43°1 W, 5.89 ch. 3rd. North, 5.82 ch. 4th. N 3301 W, 8.83 ch. 5th N

N 48° E, 4.81 ch. 6th. N 12° E, 4.66 ch.. 7th. N 62° 1 E, 5.27 ch.8th S 6°E, 5.60 ch. 9th S 40°4 E, 5.87 ch. 10th. East, 6.54 ch. 11th. North, 5.52 ch. 12th. N 68°1 E, 3.10 ch. 13th. S 30° E, 7.90 ch. 14th. S 23° W, 8.80 ch. 15th. S 31°1 E, 6.42 ch. 16th. S 50° W, 8.40 ch. 17th. N 440 W, 6.85 ch. to the place of beginning.

Ans. 44 A. 2 R. 18 P.

4. Given the following field-notes to find the area of the survey ; also the bearing and distance of the 3rd side, which were omitted to be taken on account of obstacles

in the way.

S