If there be a fmall Piece above or below, that won't reach a Parallel, or if there be any long irregular Excrefcences on either Side, let thefe be caft up by Triangles, and their Content be added to the Sum of the Oblongs, for the Content of the Map. If your Map be laid down by a Scale of forty Perches to an Inch, it is best to have Quarter Inch Parallels, and then every Acre will be 4 Tenths of an Inch in Length, which may be laid on the other Edge of the Scale. Let your Map be laid down by what Scale foever, if you caft it up by the large Scale of Acres, or by that of 20 Perches to an Inch, the true Content may be cafily obtained, as will hereafter be fhewn. The The larger your Scale is by which your Map is laid down, the more certain the Content will be by any Method whatsoever. When a Perfon is fome Time accuftomed to this Method, he will prefer it to any of the foregoing for its Expedition and Certainty. If you be unprovided with a Scale of Acres, you may measure the Lengths of the Oblongs by the Divifions on the Edge of the Protractor; and if the Map be ruled with half Inch Parallels, the Sum of the Lengths of the Oblongs being divided by 16, will give the Content in Acres, if the Map was laid down by 20 Perches to an Inch but if by 40, divide the Sum by 4, and you the Content required, have Fifth Method to determine the Area of Ground. To determine the Area of a Piece of Ground, having the Map given, by Weight, Let the Map, Plate VIII. Fig. 6. be that whofe Area is required. Let Parallels be drawn at half an Inch afunder, and others at Right-Angles to thofe at a like Distance; fo will each Square be a Quarter of a Square Inch in Area, With With a Pair of fine Sciffars, or a Penknife, cut away all the Squares marked a, which the Bounds of the Map do not reach, as unneceffary and uselefs; then will remain all the whole Squares contained within the Body of the Map, and the Squares which the Bounds pafs through, which are marked z, z, z, &c. Count the Number of whole Squares in the Body of the Map, and those marked z, together, which Number note down; then find with Grains and Tenths of a Grain, the Weight of all that Paper. Call the Number of Squares, firft Area, and their Weight in Grains and Parts, call their first Weight. Cut the Map then clofe by the Bounds, fo will the Pieces of Squares without the Bounds, marked z, be cut away, and the Map only remain, which weigh in Grains and Decimals of a Grain, as before. Then fay, as the first Weight is to the first Area, fo is the second Weight to the fecond Area, which gives the Area of the Map in Squares, and Decimals of a Square. Then by knowing by what Scale it was laid down, the Area of each Square is known, and confequently the Area of the whole Map. The Area of each Square by the different Scales moft ufed, will be thus: The following was an Experiment made a few Years fince upon the Map, Plate X. Fig. 3, which when caft up by the following univerfal Methods, gives 110A. 2R. 32P. The Map was laid down by a Scale of 20 Perches to an Inch. Number of Squares in the Map, and those mark ed, z, 223. Weight of the Paper Grains. 74.6 59.2 Then 74.6 223: 59.2: 176.96 Squares in the Map, and each Square being 100 Perches, makes 17696 Perches, or 110A. 2R. 16P. differing only 16 Perches from the true Content. This may also be performed by drawing a Trapezium about the Map, and finding its Content as before, cutting it out and weighing it, and afterwards the Map: by faying, as the Weight of the Trapezium is to the Content of the Trapezium, fo is the Weight of the Map to the Content of the Map. But this Method will not be fo exact as the foregoing one, for there will be a much greater Space, or Area comprehended between the Trapezium and the Map, than that contained in the Parts of Squares thro' which the Lines of the Map run, and the Map; therefore as there are fonie Inequalities in all Paper, the greater the Error will be. |