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These theorems are true, when the surveyor keeps the land he surveys, on his right hand, which we suppose through the whole to be done; but if he goes the contrary way, call the southings northings, and the northings southings, and the same rule will hold good.
General Rule for finding the Meridian distances.
1. The meridian distance and departure, both east, or both west, their sum is the meridian distance of the same name.
2. The meridian distance and departure of different names; that is, one east and the other west, their difference is the meridian distance of the same name with the greater.
Thus in the first method of finding the area, as in the following field-book.
The first departure is put opposite the northing or southing of the first station, and is the first meridian distance of the same name. Thus if the first departure be east, the first meridian distance will be the same as the departure, and east also ; and if west, it will be the same way.
At station 5, the meridian distance
5.78 E. 7.76 W.
The next meridian distance
At station 11, the meridian distance 0.12 W.
The next meridian distance
PL. 10. fig. 3.
In the 5th and íith stations, the meridian distance being less than the departures, and of a contrary name, the map will cross the first meridian, and will pass as in the 5th line, from the east to the west line of the meridian; and in the 11th line it will again cross from the east to the west side, which will evidently appear, if the field-work be protracted, and the meridian line passing through the first station, be drawn through the map.
The field-book cast up by the first method, will be evident from the two foregoing theorems, and therefore requires no further explanation ; but to find the area, by the second method, take this
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 difference of latitude is north; and in north when south: the reason of which is plain, from the two last theorems. The difference of these two columns will be the area of the map.
Il is needless here to insert the coluirns of bearing or distances
in chains, they being the same as before.
No. Lat. and Merid.
N. Area. S. Area
N 0.54 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
0.00 24.92 E 3
E 8.10 33.02 E
S 29.4423.28 E
N 9.00 1.98W
N 6.94 18.16W 8
126.0303 W 4.64 22.80W
N 15.38 17.06W 9
262.3828 E 5.74/11.32W
N 12.93 8.64W 10
111.7 152 E 2.68! 5.96W
S 2.75 0.12W 11
0.3300 E 5.84 5.72 E
S 10.48 4.32 E
9.691 1.46 E
14.1474 IW 1.46 0.00
178.0499 - 284.1012
178 0499 Area in chains, as before, 1107.0513
Construction of the Map 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 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 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 Meridian Dise tances, is supposed to be preferable in Practice to any Thing here
tofore 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