The Construction of the Map from either the 1st or the 2d Table. Plate X. fig. 3. Draw the line NS. for a north and south line, which call the first meridian; in this line assume any point, as 1, for the first station. Set the northing of that stationary line, which is 3.54, from 1 to 2, on the said meridian line. Upon the point 2 raise a perpendicular to the eastward, the meridian distance being easterly, and upon it set 13.22, the second number in the column of meridian distance, from 2 to 2, and draw the line 12, for the first distance line: from 2 upon the first meridian, set the northing of the second stationary line, that is, 9.65 to 3, and on the point 3 erect a perpendicular eastward, upon which let the meridian distance of the second station 16.82, from 3 to 3, and draw the line 2 3, for the distance line of the second station. And since the third station has neither northing nor southing, set the meridian distance of it 33.02, from 3 to 4, for the distance line of the third station. To the fourth station there is 29.44, southing, which set from 3 to 5; upon the point 5, erect the perpendicular 55; on which lay 13.54, and draw the line 4 5. In the like manner proceed to set the northings and southings on the first meridian, and the meridian distances upon the perpendiculars raised to the east or west; the extremities of which connected by right lines, will complete the map. A SPECIMEN OF THE PENNSYLVANIA METHOD OF CALCULATION; WHICH, FOR ITS SIMPLICITY AND EASE, IN FINDING THE MERIDIAN DISTANCES, IS SUPPOSED TO BE PREFERABLE IN PRACTICE TO ANY THING HERETOFORE PUBLISHED ON THE SUBJECT. IND in the first place, by the following ta FIN bles, 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 avoid the inconvenience of changing the denomination of either of the departures. we The learner must not expect that in real practice the columns of lat. and those of dep. will exactly balance when they are 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 lat. and dep. 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 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 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 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, 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 diffèrence 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. |