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INTERSECTION is the bearings of an object from two stations; the bearing and distance of the stations being known, the distance to the object may be found : thence the plan of a field may be taken by intersections, when all the corners thereof can be seen from two stations, and the area of the field determined by calculations: an example of which follows; the bearing and distance between the two stations, and the bearings from them to the several corners of the field, being as in the following table.
The stations H and I, North and South 28 chains.
By Case 1, Oblique Angled Trigonometry, find the distance from either station, as from I, to the several corners of the field, thus:
To find ID. As sine [D 50.45 9.88896 Is to IH 28 1.4+716 So is sine [H 58.4% 9.92960 11.37676 * - I - 9.88896 To HD 30.75 1,48780 To find IE. As sine [E 47. 9.86443 Is to HH 28 - 1.44,716 So is sine [H 35.30 9.7.6395. - 11.21111 9,86413 To IE 22.23 1.34698 To find IF. As sine [F 78. 9,990%0 Is to IH 28 1.44716 So is sine [H 28.30 9.678.66 11.12582 9.99040 To IF 13.66 1,13542
To find IG. As sine [G 80. 9.993.35 Is to IH 28 1.44,716 So is sine [H 40. 9.80807 11.25523 9.99.335 o, To IG. 18.27 .26188 ".
The bearing and distance from the station I, to each corner of the field, being ascertained, find the difference of latitude and departure of each line inclosing the field; and A being the corner of the survey to begin with. Reverse the line from the next succeeding corner to the point I, &c. as follows.
To find the difference of latitude and departure of AB.
To find the difference of latitude and departure of BC.