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The merid. east (multiplied southings
Dist. when / west into the northings their sum is the area of the map.
The merid. Seast multiplied (northings
Dist. when west $ into the southings } the sum of these products taken from the former, gives the area of the map..
These theorems are true, when the surveyor keeps the land he surveys, on his right hand, which we suppose thro' 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 MERI
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.
The first meridian distance
The second meridian distance 13.22 E.
The third meridian distance
At station 5, the meridian distance 5.78 E. the next departure
The next meridian distance
At station 11, the meridian distance 0.12 W.
The next meridian distance
Plate X. fig. 3.
In the 5th and 11th 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.
The foregoing Field-Book, Method II. 227
It is needless here to insert the columns of bearing or distances in Chains, being the same as before.
No. La t. and Meridian N. Area.
0.00 24.92 E
S 29.44 23.28 E
N 12.93 8.64 W 10
111.7152 E 2.68 5.96 W
S 2.75 0.12 W
Area in Chains, as before, 1107.0513