EXAMPLES. I. Find the solidity of a paraboloid whose diameter is 17 feet, and height 27 feet. Ans. 3248 feet. 2. Find the number of gallons in a parabolic boiler whose diameter is 5 feet, and depth 4 feet. TAPERING TIMBER. Ans. 333 278. XLIV. To find the solidity of a tapering treė. Multiply the square of the quarter girt by the length. Ex. Find the content of a tapering tree whose length is 33 ft. 3 in., and girt 56 inches. The girt is the circumference of the tree in the middle, and is conveniently taken with a piece of string, or a common measuring tape. The content is best found by the Sliding Rule. This rule contains a line called the "girt-line," which with the slide will furnish the solidity in feet with great rapidity. The rule is :-Set the length on C to 12 on D, then opposite the quarter girt on D is the content on C. THE ANCHOR RING. XLV. To find the surface of an anchor ring. Multiply the mean diameter of the ring by the thickness; then multiply twice by 22 and divide by 49. Ex. Find the surface of an anchor ring whose inner diameter is 14 inches, and thickness 4 inches. To find the solidity of an anchor ring. Multiply the square of the thickness by the mean diameter of the ring; then multiply twice by II and divide by 49. Ex. Find the solidity of an anchor ring whose thickness is 3 inches, and inner diameter 9 inches. EXAMPLES. I. Find the surface of an anchor ring whose inner diameter is 8 ft. 5 in., and thickness 15 inches. 2. Find the cost of painting a fly-wheel whose inner diameter is 18 feet, and thickness 20 inches, at id. per foot. Ans. 1. 6s. 113d. 3. Find the solidity of an anchor ring whose thickness is 24 inches, and inner diameter 63 inches. Ans. 112 4. Find the weight of a fly-wheel whose thickness is 9 inches, and outer diameter 12 feet. Ans. 3 tons. I qr. 2 lbs. THE WEDGE. XLVII. To find the solidity of a wedge. To twice the length of the thick end of the wedge add the length of the thin end; then multiply by the breadth of the thick end, and by the perpendicular from the thin end upon the base, and divide by 6. Ex. The length and breadth of the thick end of a wedge are 15 and 6 inches, the breadth at the thin end |