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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 shew that a line drawn from the third.station to the farthest end of the fifth stationary line will express the boundary. Thus,
No. Sta. Deg. Ch. L.
3 172) 5.45
Suppose the point p of the boundary to be inaccessible, by means of the lines 6p or p7, being overflowed, or that of 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. f r boundary; and having ineasured 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 bundary: the crossing or intersection of these two bearings will determine the point p, and of course the boundary 6p7 is also determined.
If your view will then reach in the first station,
Close at the first station. If you would lay down a tower, house, or any other remarkable object in its proper place; 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 fieldbook.
A protraction of this will render all plain, on whiclı lay off all your off-sets and intersections, and proceed to find the content by any of the methods in section the 4th.
The foregoing field-book may be otherwise kept,
1, 2-1f=2f-le=fe, le-deed.
Then 1dx da=lda, by prob. 6, page 183, and 1 ed x da+fc=befc, and 2f * } fc=cf9; the sum
of all which will be labc21 ; the area contained between the stationary line 1, 2, and the bound
ary, l abc 2.
In the same männer you may find the area of Lihg2 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. From 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 ; 80 will you have the respective distances from off-set to off-set, but in a retrogade 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 220. 12L. or 11C. 12L. of four pole-chains. See the figure.
Ch. L. id=2.25 X 32L. half the first off-set= 17200 el=1.65* IC.26L. the sum of the stand d 2.0790 ef=2.60* IC. 32L. the sum of 21 and 3d=3.4320 2f=4.62x37L. half the last off-set= 1.7094 Content of left off-sets on the first dist. in square four-pole chains
7.9404 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, 1A. OR. 6P. to be added to the area within the stationary lines.