when set off from two tangents, the work is correct to all purposes. For example. Let it be required to range a curve to a radius of 900 feet; the necessary data from the table following are as follows for 50-feet distances along the Referring to the figure, the points marked I., II., III., IV., V., VI., are the points set-out on the tangent or the abscissæ in distances from A given in the set just quoted; from these points the rectangular offsets, given 'as ordinates in the same set, are set-out, giving points in the curve marked 1, 2, 3, 4, 5, 6, which are 50 feet apart. At the third point, marked 3 or D, which is 150 feet from A the normal DC, given as 12.65 feet, is set-out from D, so that the point C falls in the line AB, the original tangent; the direction CEFF is then a new tangent. Recommencing at E six more points are set-out in the same way as before with the same set of figures; and a new tangent JKL obtained in the former manner. check the work, measure from E, the normal EB-52'42 feet, so that B may fall in the line AB; then if the curve has been well set-out, the points F and B will appear in exactly the same direction when viewed from K. Although this method requires more figures than the former polygonal system, it is more accurate on long Το curves, and more convenient in other respects. It will be observed on examining the following table that often the normal and the ordinate at the third point are practically equal; in such cases it becomes unnecessary to setout any normal at the third point, as the third point on the tangent answers all purposes for sighting in a new tangent. This simplifies the work considerably; but the figures for the normal at the sixth point should, however, always be available for use. The tables and the figure are arranged to suit a sixpoint system, but the same principle may be applied to four, eight, or any even number of points, when the offsets used are not long. In this polygonal system no angular measurement is necessary, a cross-head staff is sufficient for the alignment and setting-out right angles; the method is so simple that, after explaining it once or twice in practice, good chainmen can easily apply it by themselves. RANGING TABLE SUITED TO RADII AND DISTANCES IN Length of Curve R=7} R=10 R=12 R=15 Absc. Ord. Absc. Ord. Absc. Ord. Absc. Ord. 0.998 0.050 O'999 0.040 2955 0'447 0999 0033 1994 0133 5.380 2 275 5646 1747 |