. Forest mensuration. wth of trees. This differenceor loss in diameter at successive distances from the butt, is termed taper of logs gives them their characteristic foims. On accountof this taper, logs are never truly cylindrical no matter how closelythey may approach the cylinder in form. The geometrical forms to which logs can be compared must there-fore be circular in cross section and tapering. The forms suitable forthis purpose are the paraboloid, cone, and neiloid. 1 Exceptions to this practice may be found in some regions, in scaling, when thelog rule in use gives a large ove
. Forest mensuration. wth of trees. This differenceor loss in diameter at successive distances from the butt, is termed taper of logs gives them their characteristic foims. On accountof this taper, logs are never truly cylindrical no matter how closelythey may approach the cylinder in form. The geometrical forms to which logs can be compared must there-fore be circular in cross section and tapering. The forms suitable forthis purpose are the paraboloid, cone, and neiloid. 1 Exceptions to this practice may be found in some regions, in scaling, when thelog rule in use gives a large over-run which is offset by including width of one bark (§83). FOEMUL^ FOR SOLID CONTENTS OF LOGS 19 These three sohds form a series of successively diminishing per-centages of the volume of a cjdinder of equal basal area and tapers to zero at the tip. But logs are cut with two parallelfaces at the two ends. The corresponding solids are the truncatedforms of these bodies, termed frustums, as shown in Fig. Fig. 3.—Forms of the cylinder, paraboloid, cone and neiloid, and truncated formsor frustums of the last three solids. 27. Formulae for Solid Contents of Logs. The comparative vol-umes of these four solids are stated by formulae below; when 5 = Area of base, square feet, 6| = Area of cross-section, at | height, 6 = Area of top, /i = Height or length, in feet. 1 Each of these solids is formed by the revolution of a curve about a central axis. A true Appolonian paraboloid is derived from that form of a conic section (a symmetrical curve formed by the intersection of a plane with a cone) in which the plane is parallel with the side of the cone. For the conoid formed by the revolution of this curve about its axis, the ratio between a cross section taken at right angles with the axis at any point, and the height above this point to the apex, is constant Bhfor all points on the axis. This gives a volume equal to —. Logs which taper regularly will have straight sides
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