what Scale it was laid down by; and thence you may know what the Content of every fmall Square is, and of course the Content of them all, or the Content of the Map. Thus If your Map be laid down by a Scale of 8 Perches to an Inch, the Side of the Square Inch will be 8, and its Content 8 Times 8, or 64 Perches; and because there are 100 fmall Squares in a large one, the Content of every fmall Square will be 64 of a Perch; wherefore the Number of fmall Squares being multiplied by .64 will give their Content in Perches, and thofe divided by 160, give the Content in Acres. If your Map be laid down by a Scale of 10 Perches to an Inch, the Content of every Square Inch will be ten Times 10, or 100 Perches; and fince every Square Inch contains 100 fmall Squares, therefore every fmall Square will be 1 Perch; confequently the Number of fmall Squares contained in your Map, will be the Content of it in Perches. If your Map be laid down by 15 Perches to an Inch, a Square Inch will contain 15 Times 15, or 225 Perches; and a fmall Square being the hundredth Part of a large one, will contain 2.25 Perches; wherefore the Number of fmall Squares being multiplied by 2.25 will give the Content in Perches; or to the double of the Number of fmall Squares add of them, the Sum is the Content in Perches. If your Map be laid down by 20 Perches to an Inch, the Square Inch will then contain 20. Times 20, or 100 Perches; and 1 fmall Square will con I tain tain 4 Perches; wherefore the Number of small Squares being multiplied by 4, gives the Content in Perches. Or divide the Sum of the fmall Squares, having cut off the laft Figure, by 4; the Quotient is Acres, and what remains, if any, is a Rood or Roods: Then multiply your laft Figure by 4, adding 1 for a Quarter, 2 for Half, or 3 for of a Square, (if you have any fuch in the Sum of your fmall Squares) and you will have the Perches. Thus the Number of fmall Squares in the foregoing Map being 31922, I demand the Content in Acres. 4+ 319/2 Content 79: 3:19 Cut off the laft Figure 2, and divide 319 by the Quotient is 79 Acres, and the Remainder 3, is 3 Roods. Multiply the laft Figure 2 by 4, and add in 2 for the half Square, and you have 10 Perches. The Reafon hereof is plain, when we confider that any Number multiplied by 4, and divided by 160, will give in the Quotient the fame, as if that Number was only divided by 40; or which is the fame thing, cut off the laft Figure for the o, and divide by 4. If your Map be laid down by 25 Perches to an Inch, every Square Inch will be 25 Times 25, or 625 Peiches; wherefore every fmall Square will be. 6.25 Perches. The Number of fmall Squares there fore fore being multiplied by 6, adding of their Number to the Product, will give the Content in Perches. If your Map be laid down by a Scale of 30 Perches to an Inch, every Square Inch will contain 900 Perches, and every fmall Square 9 Perches; the Number of fmall Squares therefore being multiplied by 9, will give the Content in Perches, If your Map be laid down by a Scale of 35 Perches to an Inch, every Square Inch will contain 1225 Perches, and every fmall Square 12.85 Perches; wherefore to 12 times the Number of fmall Squares, add of their Number, and you have the Content in Perches. If your Map be laid down by 40 Perches to an Inch, every Square Inch will contain 1600 Perches, and every fmall Square 16 Perches; the Number of fmall Squares therefore being multiplied by 16, gives the Content in Perches. Or cut off the laft Figure from the Sum of the fmall Squares, and the other Figures are Acres ; multiply that laft Figure by 4, adding in 1, 2, or 3, for 4,2, or 4, as before, and cut off 1 Figure to the Right from the Product, and the other, if any, are Roods: Multiply the laft Figure by 4, and the Product is Perches. For if any Number be divided by 10, which is done by cutting off the laft Figure, it will quote the fame as if that Number were multiplied by 16, and divided by 160. Suppofe ai Suppose the Number of fmall Squares in a Map be 3994, required the Content in Acres. Acres 3994 After the like Manner you may find the Content of any Map, by knowing the Scale by which it was laid down; for the Square of the Scale gives the Content of a Square Inch in Perches, the hundredth Part of which will be the Content of a small Square. I am confident I fhall be judged to be too prolix on this Head; but as this Method has ftood the Teft of many Ages, and is still used by many, I have for the Benefit of those of the floweft Capacity, explained it as fully as I was able. i Third Third Method to determine the Area of Ground. To determine the Area of a Piece of Ground, having the Map given, by reducing it to one Triangle equal thereto, and then finding it's Content. Plate VIII. Fig. 5: Let ABCDEFGH be a Map of Ground, which you would reduce to one Triangle equal thereto. Produce any Line of the Map, as AH, both Ways: Lay the Edge of a parallel Ruler from A to C, having B above it: Hold the other Side of the Ruler, or that next you faft; open till the fame Edge touches B, and by it, with a protracting Pin, mark the Point b on the produced Line: Lay the Edge of the Ruler from 6 to D, having Cabove it: Hold the other Side faft, open till the fame Edge touches C, and by it mark the Point c, on the produced Line. A Line drawn from c to D will take in as much as it leaves out of the Map. Again, lay the Edge of the Ruler from H to F, having G above it, keep the other Side fast, open till the fame Edge touches G, and by it mark the Point g, on the produced Line; Lay the Edge of the Ruler from g to E, having F above it, keep the other Side faft, open till the fame Edge touches F, and by it mark the Point f, on the pro duced |