BY THE SLIDING RULE. on C. Tab. num. 01288 to 1 against 80 are 82.4 A. G ·00169 10.8 M.B. PROBLEM XII. To determine the Content of a Parabola an Inch in Depth. RULE. By the Pen. Divide two-thirds of the product of the base and perpendicular altitude, by the number of cubic inches in the proposed integer. By the Sliding Rule. Set the gage-point, for the proposed integer, on A, to two-thirds of the altitude on B, then against the base on A, will be found the content of the parabola on B. The Rule for determining the content of a parabola, as has been already stated, is founded on this fact, that every parabola is equal to two-thirds of its circumscribing parallelogram. EXAMPLE. Let ABCD be a parabola, whereof the base BD, is 40.5 inches, and the altitude AC, 34 inches; the content is required for an inch in depth. SOLUTION BY THE PEN. 27 two-thirds of the base 34 altitude or axis AC. 108 W.G. divisor 231) 918 (3.97 wine gallons. A. G. divisor 282) 918 (3.25 ale gallons. 8 M. B. divisor 2150) 918 (0.42 malt busbels. BY THE SLIDING RULE. on A. on B. 2311 on A. on B. G. P. 282 to 22.6 against 40-5 are 3.25 A. G. 2150 BY THE FACTORS. 0.42 M. B. For Wine Gallons. 918 cubic inches in the parabola 0043 W.G. factor for squares 2754 3672 Product 3.9474 content in wine gallons. For Ale Gallons. 918 cubic inches in the parabola 0035 A.G. factor for squares 4590 2754 Product 3.2130 content in ale gallons. For Malt Bushels. 918 cubic inches in the parabola 00046 M.B. factor for squares 5508 3672 Product 0.42228 content in malt bushels. PROBLEM XIII. To determine the Content of a Sector an Inch in Depth. RULE. By the Pen. Multiply the radius by half the length of the arc, and divide the product by the number of cubic inches in the proposed integer, for the content. By the Sliding Rule. Set the gage-point for the proposed integer, on A, to the radius on B, and against half the length of the arc on A, will be the content on B. EXAMPLE. Let DEFG be a sector, whereof the radius DG is 50 inches, and the arc EFG, 74 inches; the content for an inch deep is required in wine gallons, ale gallons, and malt bushels. 2) 74 length of the arc Quotient 37 half the arc W.G. divisor 231) 1850 (8.00 wine gallons. A. G. divisor 282) 1850 (6-56 ale gallons. M. B. divisor 2150) 1850 (0-86 malt bushels. G. P. 282 to 50 against 37 are 6.56 A. G. 2150 0.86 M.B.. |