TO DRAW A PLOT OF THIS FIELD, ACCORDING TO THE PRE

CEDING RULES.

Having drawn the side A B, according to the directions before given for laying off the first course and distance, compare the first and second courses together, and they will be found to be both north and both east; consequently, the an. gle between them is found by RULE 4, as follows: 16° 30' the less course, and 98°, the supplement of the greater, being added, the sum is 114° 30', for the angle at B. Compare the second and third courses, and they will be found to be one north and one south, and both east ; consequently, according to RULE 2, 82', the second course, added to 17°, the third course, the sum 999, is the angle at C. The third and fourth courses are both south, and one east and the other west. The angle between them at D is 126°; for 17°, the third course added to 37°, the fourth course, is 54°, which substracted from 180°, leaves 126°, according to Rule 3. The fourth and fifth courses are one south and the other north, and both west. According to RULE 2, 27°, the fourth course, added to 499, the fifth course, the sum 86°, is the angle at E.

A little practice will render this mode of protracting a field familiar and easy, and an attention to the courses will show in what direction the angle is to be made.

Ch. L.
A B. N. 56° 15' E. 21.60
BC. N. 26 30 E. 13.44
CD. S. 71 30 E. 18.96
DE. S. 26 30 E. 13.44
EF. S. 71 30 W. 18.96
F G. S. 45 0 E. 8.47
GH. S. 63 30 E. 13.44
HI.

45 0 E. 8.47
I K. S. 26 30 E. 13.44
KL. S. 45 0 W. 8.47
L M. S. 63 30 W. 13.44
MN. N. 76 0 W. 24.73

N A. N. 36 45 W. 30.
Acres Roods Rods
Area 167-1-30

N.

The above field may be protracted, and its area calculated according to the directions given in the preceding EXAMPLES.

SEVERAL FIELD BOOKS TO EXERCISE THE LEARNER IN PLOT.

TING FIELDS AND CALCULATING THEIR AREA.

W.

Ch. L. No. I. Rods 8. N. 53° 15' W. 11.60 1. N. 15° 0' E. 320 9. N. 36 45 E. 19.20 2. N. 37 30 E. 160 10. N. 22 30 E. 14. 3. East

120 11. S. 76 45 E. 12. 4. S. 11 0 E. 200 | 12. S. 15 0 W. 10.85 5. South

216 18. S. 16 45 W. 10.12 6. West

160

Acres Roods Rods. 7. . S. 36 30 W. 160 Area 110–2-23 8. N. 38 15

136 Acres Roods Rods.

No. III. Rods Area 744-3-28 1. S. 65° 40' W. 49.7

2. S. 67 15 W. 34.5 No. II. Ch. L. | 3, S. 54 0 W. 17.9 1. N. 75° 0' E 13.70 4. S. 20 0

5.8 2. N. 20 30 E. 10.30 5. S. 7

30 E. 29.4 3. East

16.20 16. N. 83 Ο Ε. 107.4 4. S. 33 30

35.307. N. 5 50 W. 5. S. 76 0 W.. 16. 8. N. 18 30

W. 46. 6. North

9.

Acres Roods Rods

22.

N.

12.5

W.
W.

25

No. IV. Rods.

Rods. 1. N. 43° 0' W. 12.44 | 10. 64° 0' E. 2. N. 64 0 W. 8. 11. N. 49 0 E. 14. 3. N. 52 0

14.60 12. N. 26 10 W. 19.3 4. N. 37 5 51.36 13. N. 21 0 W. 18.3 5. N. 15 30 W. 21.76 14. N. 44 10 W. 18. 6. N. 20 40 W. 44.60 | 15. N. 64 40 E. 30.5 7. N. 88 20 E. 167.60 16. N. 18 30 W. 39. 8. S. 34 40 E. 71.20 17. N. 86 5 E. 26.7 9. S. 75 0 W. 69.72

Acres Roods Rods. 10.' S. 55 0 W. 64.60

Area 48 -1- 12 11. S.

0 W. 18.12 Acres Roods Rods.

No. VII. Ch. L. Area 97 - 2 — 29

1. N. 00 45' W. 9. 2.

19 30 W. 5.35 No. V. Rods. 3. N. 23 0 W. 4.09 1. S. 11° 50 W. 34.6 4. N. 41 35 W. 6.15 2. S. 63

20 E.
93.6 .

3 0 W. 36.75 3. N. 4 0 W. 34.9 6. S. 86 50 W. 13.33 4. S. 89 55 E.

40.1
7.

2 15 W. 17.65 5. N. 5 20 W.

35.5 8. N. 85 45 E. 12.56 6. N. 69 40 W. 60. 9. S. 2 10 E. 8. 7.' S. 78

0

W. 30.6 10. N. 86 45 E. 7.38 8. N. 67 20 W. 1.2 11. S. 3 15 E. 13.20 9. s 72 30 W. 10.4 12. N. 87 O E. 29.92 10. S. 66 55 W. 15.2 13.

49 20 E. 4.04 Acres Roods Rods. 14. North Area 41 -1 -34

15. N. 50 35 E. 6.50

16. S. 22 50 E. 17.94 No. VI. Rods.

17. S. 34 0 W. 3.50 1. S. 34° 0' E.

41 0 W. 3. 2. S. 29 0 E.

22

50 W. 9.25 3. S. 64 50 W. 53.

20. S. 3 40 E. 2.64 4. S. 25 0 E. 4.

21. S. 86 0 W. 2.50 5. S. 66 30 W. 39.

22. S. 0 25 W. 14.50 6. N. 25 0 W. 4.

23.

2 0 W. 5.38 7. S. 64 45 W.

10

0 E. 11.75 8. N. 30 30 W.

86 0

W. 34.60 9. N. 56 30 E. 34.5

Acres Roods Rods.
Area 268 — 3-7

N.

N.

42.8. 18. S. 63.4 19. S.

32.2 24. S.
18.3 25.

CASE. V.

WITHIN THE FIELD, FROM WHICH THE SEVERAL ANGLES MAY BE SEEN.

Take the bearing of the angles, and measure their distance from the station. FIELD BOOK. See Fig. 56.

Fig. 56.

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 substract

ed from the sum of the other logarithms, it may be done by rejecting the left hand figure, without the trouble of putting down

Triangle a A B.

Triangle a DE. a A, 8.70 0.939519 a D, 10.50

1.021189 a B, 10 1.000000 a E, 12

. 1.079181 Sine A a B, 800 9.993351 Sine Da E, 75° . 9.984944

Doub. area, 85.67 - 1.932870 Doub. area, 121.7 - 2.085314

Triangle a BC.

Triangle a EF. a B, 10 1.000000 a E, 12

1.079181 a C, 11.40 1.056905 a F, 8.78

. 0.943495 Sine B a C, 27° 9.657047 Sine Ea F. 550 • 9.913365

Doub. area, 51.75 - 1.713952 Doub. area, 86.31

Triangle a C D

Triangle a FA. a C, 11.40 1.056905! a F, 8.78

0.943495 a D, 10.50 1 021189 a A, 8.70

0.939519 Sine Ca D, 78° 9.990404 Sine Fa A, 450 • 9.849485

Doub. area,

117 - 2.068498 Doub. area, 54.01 - 1.732499

Triangle a AB

a BC a CD a DE a EF a FA

85.67

827
51.75

4
117.1
121.7 3)308
86.31

40
54.01

12)320 516.54 Acres Roods Rods.

-Area 25 — 3 — 12.32 25)827

Double area

Area

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 distance to each of the other angles, with a compass and chain.

6