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15C. from 2, take the off-set nk 45L. and still opposite to the second station say at 15C. L. 45L.

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 fieldbook, and draw a mark like one side of a parentheses, from the third to the fifth station, to show that a line drawn from the third station to the furthest end of the fifth stationary line will express the boundary, Thus,

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Suppose the point p of the boundary to be inaccessible, by means of the lines 6p or p7, being overflowed, or that of a quary, 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 bearings; then direct the index to the point p, and insert its bearing on the left side of the field-book, opposite to the sixth station, annexing thereto the words, Int. for boundary; and having 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 fieldbook, annexing thereto the words Int. for boundary;

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the crossing or intersection of these two bearings will determine the point p, and of course the boundary 6 p7 is also determined.

If your view will then reach to the first station, take its bearing, stationary line, and off-sets, as before, and you have the field-book completed. Thus,

The FIELD-BOOK.

Remarks and Intersect.

Deg. C. L.

St.

OFF-SETS.

318 Int. to a tower 1358 22.12 At 4C. 25L. L. 1C.

12L. at 7C. 40L.

L. 3C4. OL. at 13

C. L. 1C. 25 L.

231 Int. to ditto 22973 21.12 At 4C. 10L. R. 1C.

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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,

from the intersections taken at the first and second stations of the above field-book.

A protraction of this will render all plain, on which lay off 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, thus,

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How to cast up off-sets by the pen.

1, 2—1ƒ,=2ƒ, 1f,-1e-fe, 1e-1d=ed.

Then idx da=1da, by prob. 6. page 183, and ed xda+eb=adeb by the doctrine of trapezia ; also fex eb+fc-befc, and 2fx fc-cf2; the sum of all which will be 1 abc, 21; 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 2ihg2 of ik3i as well as what is without and with-inside 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; so will you have the respective distances from off-set 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

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.

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1d=2.25x32L. half the first off-set,=

.7200

ed=1.65x1C. 26L. the sum of the 1st & 2d 2.0790

ef=2.60x1C. 32L. the sum of 2d and 3d

2f-4.62x37L. half the last off-set,=

3.4320

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

Acres 1.04031

.16124

4

Perches 6.4496

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