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Let the line, 3, 6, represent the boundary, which by means of water, briers, or any other impediment, cannot be measured. In this case make one or more stations within or without the land, where the distances may be measured, and draw a line from the beginning of the first to the end of the last distance, thus; make stations at 3, 4, and 5, taking the bearings, and measuring the distances as usual, which insert in your field-book, and draw a mark like one side of a parenthesis, from the third to the fifth station, to show that a line drawn from the third station to the farthest end of the fifth stationary line will express the boundary. Thus,
Suppose the point p of the boundary to be inacCessible by means of the lines 6p or p7, being overflowed, or that a quarry, furze, &c, might prevent your taking their lengths: in this case take the bearing of the line 6, 7, which insert opposite to the sixth station in your field-book with the other bearing; then direct the index to the point p, and insert its bearings on the left side of the field-book, opposite to the sixth station, annexing thereto the words Int. for boundary ; and baving measured and inserted the distance 6, 7, set the index in the direction of the line 7p, and insert its bearing on the left of the seventh station of the field-book, annexing thereto the words Int. for boundary: the crossing or intersection of these two bearings will determime the point p, and of course the boundary 6p7 is also determined.
If your view will then reach in the first station,
take its bearing, stationary line, and off-sets as before, and you have the field-book completed. Thus,
St. 318 Int. to a tower 1/358 22.12 At 4C. 25L. L. IC.
12L. at 7C. 40L. L. 3C. 40L. au 13C. L. IC. 25L.
2311 Int. to ditto
22978 | 22.12 At 4C. 10L. R. 1C.
20L, at 10C. 25L. R. 1C. 51L. att 13C. 10L. 0. at 15C. L. 45L.
31721| 5 45
5 250 3.361 155; Int. for bound. 6195 15.15 At 1C. 20L. L. 2C. 274 Int. for ditto. 7/1051 15.10 20L. at 7C. 45L.
L. 2C. 32L. at 11C. 25L. 0. at
12C. 25L. R. 36L. Close at the first station.
you would lay down a tower, house, or any other remarkable object in its properplace; from any two stations, take bearings to the object, and their intersection will determine the place where you are to insert it, in the manner that the tower is set out in the figure, from the intersection taken at the first and second stations of the above field book.
A protraction of this will render all plain, on which lay off all your off-sets and intersections, and proceed to find the content hy any of the methods in section the 4th.
The foregoing field-book may be otherwise kepts
How to cast up off-sets by the pen.
Pl. 11. fig. 2.
1, 2-1f=21, 2f-le=fe, le-deed. Then Id x da=lda, by proh. 6, page 183, and edx}(da+eb)=beda, ;(ebifc) fe=besc, and 2x;fc
09; the sum of all which will be labc21; the area contained between the stationary line, 1, 2; and the boundary, 1 abc 2.
In the same manner you may find the area of aihg2, of ik3i, as well as what is without and withinside of the stationary line 7, 1.
If therefore the left hand off-sets exceed the right hand ones, it is plain, the excess must be added to the area within the stationary lines, but if the right hand off-sets exceed the left hand ones, the difference must be deducted from the said area; if the ground be kept on the right hand, as we have all along supposed; or in words, thus ;
To find the contents of off-sets.
1. Froin the distance line, take the distance to the preceding off-set, and from that the distance of the one preceding it, &c. in four-pole chains ; so will you have the respective distances from offset to off-set, but in a retrograde order.
2. Multiply the last of these remainders by the first off-set, the next by the sum of the first and second, the next by half the sum of the second and third, the next by half the sum of the third and fourth, &c. The sum of these will be the area produced by the off-sets.
Thus, in the foregoing field-book, the first stationary line is 22C. 12L. or 11C. 12L. of four-pole chains. See the figure.
Ch. L. Id=2.25x 324, half the first off-set= .7200 ed=1.65R1C. 26L. the sum of the 1st and 2d 2.0790 ef=2.60 1C. 32L. the sum of 2d and 3d=3.4320 *=4.62x37L. half the last off-set= 1.7094 Content of left off-sets on the first dist. in square four-pole chains
In like manner the rest are performed. The sum of the left hand off-sets will be 14.0856 And the sum of the right hand ones 3.6825
Excess of left hand off-sets in squ: 4 pole C. 10.4031
Excess of left hand off-sets above the right hand ones, TA. OR. 6P. to be added to the area within the stationary lines.