or Wefting, from the firft Station: For fhould the first Station be at the Eaftermoft Point of the Land, the first Meridian will then pass thro' the Weftermoft, and the Map will be entirely on the Eaft of the firft Meridian: But were the Meridian Distance less than whole Eafting or Wefting, and the first Station at the Eaftermoft Point of the Land, then it is plain, that the firft Meridian will pass through the Map, and Part thereof will lie on the Eaft, and the reft on the Weft of the faid firft Meridian. In this Cafe therefore no Number lefs than the whole Eafting or Wefting will be fufficient for the Meridian Distance, in order that the Map should lie entirely on the Eaft thereof. But if the first Station be not the Eaftermoft Point of the Land, a lefs Number might be fufficient for the Meridian Diftance, but how much less would be troublesome and needless to determine; fince the Meridian Diftance being made equal to the entire Easting or Westing will answer in all Cafes, let the first Station be where it will, as it leaves the Map entirely to the Eaft of the firft Meridian. The fame Reafoning will hold good, if you would have the Map to lie entirely on the Weft of the first Meridian. In the following Table or Field-Book the Eafting of the first stationary Line is marked + 6.61, must be added to 6.54, and placed in a Line with N 3.54, and 68.15+6.61=74.76 must be placed in a Line with E+6.61. Again, 74.76+1.80=76.56, which place in a Line with 9.65; and 76.56+1.80=78.36, which place in a Line with E-+1.80. Proceed in the like. Manner to add the Eaftings, and fubftract the Weft ings, ings, till you have compleated the Column of Meridian Distance; the laft Number of which will be equal to the firft, if the Work be right, because there was just as much added as fubftracted, fince the Sum of the Eaftings is equal to that of the Weftings. The Numbers in the Column of Meridian Diftance which are in the fame Line with the Northings or Southings, in the Column of Latitude and Half Departure, are the Meridian Distances in the Middle of each Line; and those in the fame Column which are in the Line with the Eaftings or Weftings, are the Meridian Distances at every Station, or at the Beginning of every Line: And fince it has been demonftrated in Theo. 3. of this Sect. that if the Meridian Distances taken in the Middle of every Line, be multiplied into the particular Northing or Southing of that Line, that the Difference of the Sums of the North and South Products, will be the Area of the Map; it follows, that the upper Number of every two which ftand in the Column of Meridian Distance, must be multiplied by the Northing or Southing adjoining it. These several Products must be put in the Columns of N. Area, or S. Area, according as the Difference of Latitude is North or South. This if 68.15, the Meridian Distance to the Middle of the first Line, be multiplied by 3.54, the Northing adjoining it, the Product 241.2510, must be put in the Column of North Area; but in the 4th Sationary Line, when 84.82 is multiplied by 29.44, the Southing of that Line, the Product 2497.1008 must be placed in the Column of S. Area, and fo of the reft. Laftly, if you add up the Columns of N. and S. Area; the Difference of thefe will be the Area of the Survey in fquare Four-Pole Chains, which may be easily reduced into Acres as before. Thus the Content of the following Field-Book is 1107.0513 fquare Four-Pole Chains, or 110.70513 Acres. N N 8 NW 5311.69 W-4.64 38.74 6.94 43.38 301.0572 9 NE 36 19.20 E+5.74 50.22 N 15.38 44-48 684-1024 NE 22 14.00 E+2.68 55.58 Area in fquare Four-Pole Chains.1107.0513 Area in Acres and Decimal Parts. 110.70513 The foregoing FIELD-BOOK by a fecond Method. The Content of the foregoing Field-Book may as well be found by putting + to the Weftings, and to the Eaftings; that is, by adding the Weftings and fubtracting the Eaftings, which is plain, if you conceive the firft Meridian to be on the East Side of the Map. Thus, FIELD |