Of all these measures of solidity the three principal integers used in Gaging are the Wine-gallon, the Alegallon, and the Malt-bushel, The square roots of these numbers are called the Square Gage-points of the respective measures. Thus, The 231 15.19) square is 16-79 gage Wine-gallons. square 282 Ale-gallons. root of 2150-42 46-37) point for Malt-bushels. The numbers themselves are called simply Gagepoints, and are used on the lines A and B, but their square roots, that is, the square gage-points, are used on the lines C and D. PROBLEM I. To determine the Content of a Square Area an Inch in Depth. RULE. By the Pen. Multiply the side by itself, and divide the product by the number of cubic inches in the proposed integer. By the Sliding Rule. Set the square gage-point, for the proposed integer, on D, to 1 on C, and opposite to the given side on D, will be found the content on C. EXAMPLE 1. Let FGHI be a square, whereof the side is 90 inches; the area, for an inch in depth, is required in wine gallons, ale-gallons, and malt-bushels. W.G. divisor 231) 8100 (35-06 wine gallons. A. G. divisor 282) 8100 (28-72 ale gallons. M.B. divisor 2150) 8100 (3.76 malt bushels. NOTE. The decimal in the malt-bushel divisor is generally omitted, as comparatively of little value. 46.37 Sq. G.P. 16.79 to 1 against 90 are 28-72 A. G. {20}, on C. [35.06 W.G.) 3.76 M.B. EXAMPLE 2. The side of a square being 76-4 inches, what is the area, at an inch deep, in wine-gallons, ale-gallons, and malt-bushels? SOLUTION BY THE PEN. 76.4 side of the square 76.4 side 3056 4584 5348 W.G. divisor 231) 5836.96 (25.26 wine gallons. A. G. divisor 282) 5836-96 (20-69 ale gallons. M.B. divisor 2150) 5836.96 (2.71 malt bushels. BY THE SLIDING RULE. on D. on C. .on D. on C. (25.26 W.G.) Sq. G.P. 16.79 to 1 against 76-4 are 20-69 A. G. 46.37 2-71 M. B.J PROBLEM II. To determine the Content of a Rectangular Area an Inch in Depth. RULE. By the Pen. Multiply the length by the breadth, and divide the product 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 the breadth on B, and opposite to the length on A, will be the content on B. EXAMPLE. Let DEFG be a rectangle, whereof the length FG is 80 inches, and the breadth FD, 35 inches; the area for an inch in depth is required in wine-gallons, alegallons, and malt-bushels. SOLUTION BY THE PEN. 35 breadth of the rectangle W.G. divisor 231) 2800 (12-12 wine gallons. A. G. divisor 282) 2800 (9.93 ale gallons. M.B. divisor 2150) 2800 (1.30 malt bushels. To determine the Content of an Inch-deep Area in Form of a Parallelogram not Rectangular. RULE. By the Pen. Upon one of the longest sides demit a perpendicular from the opposite side, and multiply the length of the base, on which the perpendicular falls, by the perpen. dicular. Then the product divided by the number of cubic inches in the proposed integer will be the content. By the Sliding Rule. Set the gage-point, for the proposed integer, on A, to the perpendicular breadth on B, and opposite to the length on A, will stand the content on B. EXAMPLE. Let ABCD be a rhomboid, whereof the base is 69.5 inches, and the perpendicular breadth EF, 40 inches; the number of wine gallons, ale gallons, and malt bushels the figure will contain, the depth being an inch, is required. |