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A Specimen of the Pennsylvania Method of CALCULATION; which, for its Simplicity and Ease, in finding the Meridion Distances, is supposed to be preferable in Practice to any Thing heretofore published on the Subject.
FIND in the first place, by the Traverse Table,
the lat. and dep. for the several courses and distances, as already taught; and if the survey be truly taken, the sums of the northings and southings will be equal, and also those of the eastings and westings. Then in the next place, find the meridian distances, by choosing such a place in the column of eastings or westings, as will admit of a continual addition of one, and subtraction of the other; by which means we avoid the inconvenience of changing the denomination of either of the departures.
The learner must not expect that in real practice the columns of lat. and those of dep. will exactly balance when they are at first added up, for little inaccuracies will arise, both from the observations taken in the field, and in chaining; which to adjust, previous to finding the meridian distances, we may observe, That if, in small sur
' veys, the difference amount to two tenths of a perch for every station, there must have been some error committed in the field; and the best way in this case, will be to rectify it on the ground by a resurvey, or at least as much as will discover the error. But when the differences are within those limits, the work may be balanced in the following manner : on a slate, or separate piece of paper, find the lat. and dep. to each course and distance,
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 shals 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 respective 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.