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7. S. 27 E. 6.60 Ans. Area 182 A. O R. 21.7 P. and the bearing and distance of the 3d side S. 66° 23' W. 28.06 ch.
5. Being furnished with the field-notes of a tract of land, and requested to calculate the area, I found, on examining them, that the figures expressing the angles of bearing of the 4th and 5th sides were so defaced as to be illegible; but as the remaining data are sufficient, the area is required. The field-notes are as follow.
Ch. 1. S. 60°: W. 10.34 2. N. 271 W. 17.88 3. N. 51 E. 15.85 4. N. E.
9.61 5. S. - E. 19.18 6. S. 16. E. 22.21 7. S. 711 W. 16.66 8. N. 711 W. 5.76
Ans. 81 A. 2 R. 27 P.
Containing Off-sets and Intersections.
Off-sets are lines drawn or measured, perpendicularly from a stationary line, to the angular points of the land In taking surveys, bounded on some of their sides by streams of water, it is unnecessary to make a station at every bend in the stream, because the field-work can be taken, and the calculations made with more facility, and with equal accuracy, by making use of off-sets.
Directions for taking Of sets. Take as many stations in the irregular boundary as may be most convenient. Then take the bearing from the first station to the second; and in measuring the distance stop against each bend in the stream and measure the perpendicular distance from it* to the stationary line. Note the distance in the field-book as a right-hand, or left-hand off-set, according as the boundary lies on the right, or left of the stationary line; also note against each off-set, its distance from the beginning of the stationary line. If there be more than two stations, proceed in the same manner with the others.
Note. In calculating by off-sets, the irregular boun.
. dary is considered as straight between the ends of each two adjacent off-sets ; there should therefore be so many taken that this supposition may be made without any material error in the survey.
To find the area contained between a stationary line and
an irregular boundary by means of offsets.
Subtract the stationary distance of each off-set, from that of the one immediately following ; the remainders
• When the boundary is a brook or rivulet, it is customary to measure to the middle of the channel ; but when it is a river in which the tide flows, the measure must be taken no farther than to low-water mark.
will be the distances, intercepted on the stationary line, between each two adjacent off-sets respectively.
Multiply the sum of each two adjacent off.sets by their intercepted distance on the stationary line; half the sum of the products will be the area required*.
Note. The area of the off-sets must be added to, or subtracted from, the area within the stationary lines, according as the stationary lines on which the off-sets are taken are within, or without, the boundary of the survey.
EXAMPLE 1. Fig. 82. Required the area of a piece of meadow, bounded on one side by a brook, the field-notes being as follow.
Ch. 1. N. 16°į E. 14.35 2. East 7.82 3. S. 3; W. 14.45 4. N. 86W. 11.07
Left-hand off-sets on the 3d side.
Sta. Dist. Off-sets. No. Ch.
Ch. 1. 0.00 0.30 2. 0.95 0.84 3. 2.03 0.86 4. 3.28 0.50 5. 5.20 1.80
7.43 2.35 7. 8.98 1.45 8. 10.46 1.08 9. 11.71 1.85 10. 14.45 0.35
The area of the part ABCD within the stationary lines will be found, by either of the rules in the preceding section, to be 18 A. 1 R. 11 P.
* DEMONSTRATION. Considering the boundary as straight between the ends of each two adjacent off-sets, it is plain that the area contained between the stationary line and boundary will be divided by the off-sets into trapezoids
EXAMPLE 2. Fig. 83. Required the area of a survey from the following fieldnotes.
Left-hand off'sets. 2nd Stationary Line. 4 Stat. Line.
Sta. Dist. Offsets. Sta. Dist. Offsets.
Ch. No. Ch. Ch. No. Ch. Ch. 1. N. 36° W. 30.00 1. 0.00 0.50 1. 0.00 0.55 2. N. 561 E. 21.60 2. 6.10 3.40 2. 4.20 2.50 3. N. 26; E. 13.44 3. 10.15 3.10 3. 8.05 3.20 4. S. 71, E. 18.96 4. 14.08 3.96 4. 15.15 2.45 5. S. 26; E. 13.46 5. 19.20 2.70 5. 18.96 0.50 6. S. 45 W. 42.41 6. 21.60 0.55 5th Stat. Line,
3rd Stat. Line. 1. 0.00 0.50 1. 0.00 0.00 0.55 2.
0.55 2. 5.12 2.75 2. 13.44 0.55 3. 10.00 1.90
4. 13.46 0.70
The area within the stationary lines, found by either of the rules in the preceding section, is 1152.5381 square chains.
To find the area of the off-sets.