« PreviousContinue »
When the meridian distances are east, put the products of north and south areas in their proper columns; but when west, in their contrary columns ; that is, in the column of south area, when the dif. ference of latitude is north; and in north when south : the reason of which is plain, from the two last tlieorems. The difference of these two columns will be the area of the map,
It is needless here to insert the columns of bearing or distances
in chains, they being the same as before.
No. Lat. and Merid.
N. Area. S. Area
N 3.54! 6.61 E
23.3994 E 6.61 |13.22 E
N 9.65 15.02 E 2
144.9430 E 1.80 16.82 E
E 8.10 33.02 E
178.0499 Area in chains, as before, 1107.0513
Construction of the Man from either the 1st or the 2d Table.
PL. 10. 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 I 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 1 2, 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 23, 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 to 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 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,