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From the two preceding theorems we learn how to find the area of a map, when the first meridian passes through it; that is, when one part of the map lies on the east and the other on the west side of that meridian. Thus,
The merid. S east 2 multiplied S southings
Dist. when west) into the northings } their sum is the area of the map.
The merid. S east multiplied Ş northings
Dist. when westinto 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 ke contrary way, call, the southings northings, and the porthings southings, and the same rule will hold good.
General Rule for finding Meridian Distances.
1. The meridian distance and departure, both east, or both west, their sum is the meridian distance of the
2. The meridian distance and departure of different
rence 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 to 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.
The next meridian distance 1.98 W. At station 11, the meridian distance 0.12 W. The next departure
The next meridian distance
In the 5th and 11th stations, the meridian distances 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 side 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
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 theo
The difference of these two columns will be the area of the map.
the difference of these two columns will be the content of the survey.
1 NE 75 13.70
23.3994 E 6.61 13.22 E 21 NE 20110.30 N 9.65 15.02 E
144.9430 E 1.80 16.82 El
0.00 24.92 E 3 East 16.20
E 8.10 33.02 E. 4 SW 331 35.30 S 29.4423.28 E
685.3632 W 9.74 13.54 E 5. SW 76 16.00 S 3.87 5.78 E
22.3686 W 7.76 1.98 W 6 North
N 9.00 1.98 W 9.00
0.00 1.98 W 7 SW 8+ 11.60. S 1.211 17.75 W
9.3775 W 5.7713.52 W
N 6.94 18.16 W 8NW 534 11.60,
126.0301 W 4.64 22.80 W
N 15.38,17.06 W 262.3828
9 NE 36219.20
E 5.74 11.32 W
N 12.93 8.64 W 10 NE 22; 14.00
111.7152 E 2.68 5.96 W
S 2.75 0.12 W 11 SE 76312.00
0.3300 E 5.84 5.72 E 12 SW 15 10.85 S 10.48 4.32 E
45.2736 W 1.401 2.92 E 13 SW 162 10.12 w 1.46 0.00 S 9.69 1.16 E
14.1474 A R P
1285.1012 110 2 32.8