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as in the following example, observing to add an half of the differences to the numbers in the lesser column, and to subtract it from those of the greater, in such manner, as that the numbers may be altered nearly in proportion to their corresponding distances.
N. S. E. W.
53.6 45.0 5.36
45.0 2 N. 45 W. 89 62.9
62.9 3 N. 36 E. 125 101.1
19.2 7 West. 130
130.0 A. R. P.
218.4 257 21 257.0 218.2 1 218.2257.1 | 257.1 20.7 3. 22.69
The latitudes and departures being thus balanced, proceed to insert the meridian distances by the above method, where we still make use of the same field notes, only changing chains and links into perches and tenths of a perch. Then by looking along the column of departare, it is easy to observe, that in the columns of easting, opposite station 9, all the eastings may be added, and the westings subtracted without altering the denomination of either. Therefore by placing 46.0, the east departure belonging to this station in the column of meridian distances, and proceeding to add the eastings and subtract the westings, according to the rule already mentioned, we shall find that at station 8, these distances will end in 0, 0, or a cypher, if the additions and subtractions be rightly made. Then multiplying the upper meridian distance of each station by its respective northing or southing, the product will give the north or south area, as in the examples already insisted on, and which is fully exemplified in the annexed specimen. When these products are all made out, and placed in their respec. tive columns, their difference will give double the area of the plot, or twice the number of acres contained in the survey. Divide this remainder by 2, and the quotient thence arising by 160 (the number of perches in an acre) then will this last quotient exhibit the number of acres and perches contained in the whole survey; which in this example may be called 110 acres, 103 perches, or 110 acres, 2 quarters, 23 perches.
FIELD-NOTES, of the two foregoing Methods, as Practised in Penn.
Cast up by perches and tenths of a perch.
In taking surveys it is unnecessary and unusual
to make a station at every angular point, because the field-work can be taken with much greater expedition, by using off-sets and intersections, and with equal certainty; especially where creeks, &c. bound the survey.
Off-sets are perpendicular lines drawn or measured from the angular points of the land, that lie on the right or left hand to the stationary distance, thus,
PL. 11. fig. 2.
Let the black lines represent the boundaries of a farm or township: and let 1 be the first station; then if you have a good view to 2, omit the angular points between 1 and 2, and take the bearing and length of the stationary line 1, 2, and insert them in your field-book : but in chaining from 1 to 2, stop at d opposite the angular point a, and in your field-book insert the distance from 1 to d, which admit to be 4C. 25L. as well as the measure of the off-set ad, which admit to be IC. 12L. thus : by the side of your field-book in a line with the first station, say at 4C. 25L. L. IC. 12L, that is, at 4C. 25L. there is an off-set to the left hand of IC. 12L.
This done, proceed on your distance line to e opposite to the angle b, and measure eb, supposing then l e to be 7C. 40L. and eb 3C. 40L. say (still in a line with the first station in
field-book) “ at 7C. 40L. L. 3C. 40L.” that is, at 7C. 40L. there is an off-set to the left of 3C. 40L. proceed then with your distance line to f opposite to the angle c, and measure fc; suppose then I f to be 13C. and fc 1C. 25L. say in the same line as before, at 13C. L. IC. 25L. Then proceed from f to 2, and you will have the measure of the entire stationary line 1, 2, which insert in its proper column by the bearing.
In taking off-sets, it is necessary to have a perch chain, or a staff of half a perch, divided into links for measuring them; for by these means the chain in the stationary line is undisturbed, and the number of chains and links in that line from whence, or to which, the off-sets are taken, may be readily known.
Having arrived at the second station, if you find your view will carry you to 3, take the bearing from 2 to 3, and in measuring the distance line, stop at lopposite g ; admit 21 to be 40. IOL. and the off-set lg IC. 20L. then in a line with the second station in your field-book, say at 4C. 1OL. R. IC. 20L. that is, the off-set is a right hand one of IC.2OL. Again at m, which suppose to be 10C. 25L, from 2; take the off-set mh of ic. 15L. and in a line with the second station, say at 10C. 25L. R. IC. 15L. In the same line when you come to the boundary at i, insert the distance 21, 13C. 10L. thus, at 13C. 1OL.0; that is, at 13C. 10L. there is no off-set. At n, which is 15C. from 2, take the offset nk 45L. and still opposite to the second station say at 15C, L. 45. L.