4 CASE XXIV. WOOD AND BARK MEASURE.* RULE. Multiply the length of the pile in feet and inches, by the width, and that product again by the height of the pile, the last product is the solidity; which divided by 128 the quotient is cords; if any thing remains, divide it by 16, the quotient is feet of wood; if any thing still remains, divide by 4, the quotient will be quarters of a foot of wood, &c. Examples. 1. What is the quantity of wood in a pile, that is 9 feet 6 inches long, 6 feet wide, and 4 feet 6 inches high? ft. ft. ft. ft. 9 6'x60'X46′256 6'÷÷128-2 cords & solid ft. Ans. 2. What is the solidity of a pile of wood 22 ft. 9 in. long, 5 ft. 8 in. wide, and 2 feet 6 inches high? Ans. 24† cords. 3. What is the solidity of a pile of bark that is 9 feet long, 10 ft. 6 in. high, and 4 ft. 6 in. thick? Ans. 425 sol. ft. or 3 cords 2 ft. CASE XXV. Having the base, or bottom of a pile of wood, or bark given, to find how high to build, that the pile may contain any quantity of wood, or bark required. RULE Find the solid feet contained in the pile of wood you would build; reduce these feet to solid inches, and use them for a dividend; find the superficial area of the base in inches, and use them for a divisor; divide, and the quotient is the inches in height. * Wood and bark are sold by the cord, and 1728 inches make 1 solid foot; 18 solid feet make 1 foot of wood; 8 feet of wood 1 cord; 128 solid feet one cord. Examples. 1. How high must a pile of wood, or bark be to contain 8 ft. or 1 cord; which stands upon a base 48 in. by 48 in. ? 1 cord 128 sd. ft. x1728221184 sd. in. dividend. 2. I demand the height of a pile of wood that will contain 4 feet, the base, or bottom of which is Ans. 437 in. or 3 ft. 7 in. 4 by 5 feet. 3. I demand the height of a pile of wood, that shall contain 9 feet, that stands upon a base, that is 6 by 5 feet. Ans. 572 in. or 4 ft. 93 in. CASE XXVI. To find the solidity of a parallelopipedon. DEFINITION. A parallelopidedon is a figure having six rectangular sides, every opposite pair of which are equal and parallel. RULE.-Multiply the length breadth and thickness together the product is the solidity. Example. 1. A farmer would make a large chest 21 ft. long, 5 ft. 6 in. wide, and 3 ft. 9 in. high, the solidity of which is required. 21 ft. 0 in. × 5 ft. 6 in. x 3 ft. 9 in.433 ft. 1' 6" Ans. 2. How many solid feet in a cart that is 8 ft. long, 4 ft. 4 in. wide, and 2 ft. 4 in. high? CASE XXVII. Ans 80 ft. 10′ 8′′. To find the solidity of any cubical figure, DEFINITION-Any figure having six square, or equal sides is called a cube. વ RULE. Multiply one side into another, and this product by the third, the last product is the solidity. Examples. 1. What is the solidity of a tea chest that is 3 ft. 6 in. every way? 3 ft. 6' x 3 ft. 6′ × 3 ft. 6'42 ft. 10′ 6′′ Ans. 2. How many solid feet will 60 bales of goods occupy in a store; each bale measuring 4 ft. 3 in. every way? Ans. 4605 ft. 11' 3". 3. How many solid feet are in a square room that is 12 feet long, 12 feet wide and 12 feet high? Ans. 1728. 4. How many solid feet in a pillar that is 16 feet square? Ans. 4096. 5. There is a pit dug 8 feet deep, 8 feet long and 8 feet wide; how many solid feet of sand were thrown out of it? Ans. 512. GUAGING. DEFINITION.-Guaging is the art of measuring all kinds of vessels, determining the quantity of liquor contained in them; practitioners in the art, generally make their calculations by means of instruments; the instruments used in guaging, are the calipers, Gunter's sliding rule, Gunter's scale, &c. the guaging rod is used to take, or find the outs. The vessels used for liquor are various in shapes and names, viz. pipes, hogsheads, barrels, runlets, &c. also among brewers, coolers, backs, vats, &c. are used. Solidity of liquid measure, &c. A gallon of wine occupies a space equal to 231 sol. in. A gallon of beer occupies a space equal to 282 sol. in.. A gallon in corn measure is equal to 268.8, sol. in. A bushei in corn measure is equal to 2150-4 sol, in, Generally speaking there are three sorts of casks, which are judged of according to the curvature of their sides, viz. 1. If the sides of the cask are very curving from end to end, it may be said to represent the middle frustum of a spheroid, (see the figure E F G H, case 13, solids.) 2. If the sides of the cask are more straight i more properly represents the middle frustum of an elliptic spindle, (see the figure, case 14, solids.) 3. If the cask is straight from the end to the bung, and of a true taper, (such a cask is rarely found) it represents two frustums of a round cone; the two bases form the middle diameter. (See the frustum of a round cone case 5, solids, figure first,) which represents half of such a cask. GENERAL RULE, Find the solidity of either of the above figures, (or any other figure) in solid inches, and divide the solidity by 231 for wine gallons; by 282 for beer gallon; and by 268.8 for gallons of grain or corn and by 2150·4 for bushels of corn; and the quotients will be the answers respectively. CASE I. To guage a spheroidical cask. RULE 1. To twice the square of the bung diameter, add the square of the head diameter, and multiply the sum by the length of the cask, divide the product by 882 for wine, by 1077 for ale, or beer, and by 1026-3 for gallons of corn or grain; and the quotients will be the answers respectively. RULE 2. Find the solidity of the cask by the following rule, viz. To the square of the diam. at the end, add twice the square of the middle, or bung diameter; multiply the sum by the length of the cask, and again by 2618, the last pro. is the solidity; which divide by 231 for wine; 282 for ale, or beer; and by 268-8 for gallons of corn, or grain: the quotients will be the answers res; pectively. Examples. 1. What is the content of a spheroidical cask, in wine, ale or beer, and corn gallons; whose middle or bung diameter B D (see figure, case 13, solids) is equal to 20 inches, and the end diameter E G or F H is equal to 13 inches, and the length of the cask 22 inches? Solved by rule first. Bung diam. B D 20 × 20 × 2800 twice the square. şum 969 X 2221318 Pro. Pro. 21318÷8822419 gal. of wine, Ans. 213181077 1985 gal. of ale or beer, Ans. 1077 21318-1026'3=20- 7920 10 gal. of corn, &c. Ans. The same question by rule second. Diam. E G or F H 13 × 13-169 square of E G or F H. Bung diam. BD 20 × 20 × 2=800 twice square BD add. 969 sum. Sum 969 × 22 length=21318×·2618=5581·0524 sol. Solidity 5581 0524÷231—24·16† gal. of wine, Ans. 5581·0524-282=19•79† gal. of ale, &c. Ans. 5581·0524-268·8=20·76† gal. of corn, &c. Ans. NOTE.--Dimensions are always taken in inches; due allowance must be made for the thickness of the heads, &c. |