PROBLEM XIV. ***. To Lauout an Oblong Piece of Ground, so that the Length -shall exceed the Breadth, by a given difference. To the given area, add the square of half the difference ; and to the square root of their sum, add half the difference, for the length; and from that square root, take half the difference, for the breadth. ExAMPLE. Required to lay out an oblong piece of ground, to contain 47A. 2R. 16P. and to be 80 perches longer than wide. A - s In laying out new lands, it is customary to allow 6 acres to every 100, for roads. *The land, with this al lowance, may be called Gross ; and with this allowance, deducted it may be called JWeat. RULE. The gross, divided 6 quotes the neat; The neat, multiplied produces the gross. ExAMPLEs. 1. How much land must be inclosed, to have 850A. 2R. 20P. meat. 2. How much neatmeasure is there in a tract of 901A. 2R. 26P. gross Any quantity of land may be laid out, or inclosed, in the form of rSquare By Problem II.) Page 103 | Oblong, 1 side given IV. 105 A.< proportion given, XIII. 117 diff of Lat. & Bear. given, XIV. 118 Triangle, the base given, VII. 108 lcircle, XII. 116 PROBLEM XVI. To JMap a Survey, from the Field Motes, and find the RULE. Draw a line on the paper, to represent the first meridian; put JN" at the top, for North; S at the bottom, for South; E at the right hand, for East; and W at the left hand, for West; (for in making, or viewing maps, we always suppose to face the North) then, in a convenient place, make a point in the line, for the first station lay the straight edge of the Protractor to the line, with the contre mark to the point; turn the arch of the Protractor East or West, as the bearing is; and from the North or South end of the Protractor, as indicated by the bearing, prick off the degrees mentioned; then, through this point, draw a line from the first, on which lay the first distance, and through this last point, draw a line parallel to the first meridian: to this second meridian, and at the end of the first distance, lay the Protractor as above said, and so proceed from station to station, and close at the place of be* * ginning. Then dispose the map into triangles and trapeziums; measure the several bases and perpendiculars, on the same scale that the map was laid down from ; find the content of each triangle and trapezium, by the preceding problems, and their sum will be the area of the map. ExAMPLE 1. Required to lay down a Map of 20 Perches to an inch, from the following Notes, and find the Content. Beginning at a stone, corner of AB’s land; from thence, N. 43° # E. 10.51 chains, to a stake; thence, S. 54° 4 E. 14.20 chains, to a sapling, corner of CD's land; thence, S. 49° 4 W. 13.45 chains, to an oak tree ; thence, N. 42° 4 W. 12.75 chains, to the place of beginning. |