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The difference of latitude and departure being found for the several courses and distances as above, and the columns added up, there will be wanting 5.74 south difference of latitude, and 28.97 west departure, to make the columns balance, as before directed, which are the difference of latitude and departure from L to B; with which, as in the foregoing example, the bearing of LB is found to be S. 78° 48' W. and distance 29.55 chains; then, in the triangle ABL, there are given the side LB, and by the bearings of the lines, the angles ABL 49° 57, ALB 58° 18, BAL 74° 45', to find the other sides; and by Case 1, Oblique Angled trigonometry, AB is found to be 26.47 chains, which set in its proper place, opposite its bearing, and the side LA 23.82 chains, which place opposite to its bearing; find the difference of latitude and departure to these distances, and proceed as before, to find the area of the survey, which is 244A. 3R.
Specimens of the Pennsylvania method of Calculation; which, for simplicity and ease in finding the JMeridian 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 dis
tances, 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 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 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.
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 departure, it is easy to observe, that in the columns of east
o TO FIND THE CONTENT OF LAND. 157
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.