Specimens of the Pennsylvania method of Calculation ; which, for simplicity and ease in finding the Meridian 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 latitude and departure 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 castings 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 latitude, and those of departure will exactly balance, when they are at first added up; for little inac curacies 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 surveys, 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 re-survey, 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 latitude and departure to each course and distance, 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 a manner, as that the numbers may be altered nearly in proportion to their corresponding distances. A. R. P. 218.0 218.4 257.2 257.0 218.2 218.2 257.1 (257.1 207 3. 22.69 218.0 257.0 The latitudes and departures being thus balanced, proceed to insert the meridian distances by the above method, where we will 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 depar ing, 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 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, 110 aeres, 2 quarters, 23 perches. |