GAUGING CASKS. To find the Mean Diameter of a Cask. RULE.-Add of the difference between the head and bung diameter to the head diameter. This reduces the cask to a cylinder. Then multiply the square of the mean diameter by the length. Place the product opposite 1: then opposite BG is the number of beer gallons, and under wG is the number of wine gallons. Example.-There is a cask whose head diameter is 25 inches, bung diameter 31 inches, and whose length is 36 inches: how many beer gallons and how many wine gallons does it contain? 6 is the difference between 25 and 31. of 6 is 4. This, added to 25, makes 29 inches, the mean diameter. The square of 29 is 841. Place this opposite 1: then opposite 36 is 302+. Place this last opposite 1: then opposite BG is 85 gallons, and opposite wg is 103 gallons, the answer. To find the Weight of an Iron Ball, from its Diameter. RULE.-Place the cube of the diameter opposite 1: then opposite 14 is the weight. Example.-What is the weight of an iron ball 6.7 inches in diameter ? 6.7X6-7=45, and 45X6.7-301-5. Place 301-5 opposite 1: then opposite 14 is 42.29 pounds, the answer. A ball 5.54 inches diameter ? A ball 32 inches circumference? Place 32 opposite D: then opposite 1 is the diameter. Now cube the diameter, and place that cube opposite 1: then opposite 14 is 148 pounds, the answer. To find the Weight of a Leaden Ball from its Diameter or Circumference. RULE.-Place the cube of the diameter opposite 1: then opposite 21.5 is the weight. A ball is 6.6 inches in diameter: what is its weight? Answer, 61.6 pounds. A ball 5.3 inches in diameter ? Answer, 32 pounds nearly. To find the Diameter of an Iron Ball from its Weight. RULE. Place the weight opposite 1: then opposite 7.11 is a product, the cube root of which is its diameter What is the diameter of a 24 pound ball? To find the Diameter of a Leaden Ball from its Weight. RULE. Place 14 opposite 3: then opposite the weight is a product, the cube root of which is the answer. A ball 8 pounds in weight is 3.34 inches in diameter. NOTE. The several sorts of wood are supposed to be dry. Also, as a cubic foot of water weighs just 1000 ounces, the numbers in this table express, not only the specific gravities of the several bodies, but also the weight of a cubic foot of each, in avoirdupois ounces; and therefore the weight of any other quantity, or the quantity of any other weight, may be found, as in the next two proposi tions. To find the Magnitude of any Body from its Weight. RULE.-Place the weight of the material in ounces under its specific gravity: then opposite 1728 is its magnitude in cubic inches; and opposite 1 is the answer in cubic feet. Example.- How many cubic inches of gunpowder are there in one pound weight, shaken close? Place 16 (the number of ounces in a pound) opposite 937 then opposite 1728 is its content or magnitude, 29 inches. How many cubic inches are there in 3 pounds of cast brass? Place 48 (the number of ounces in 3 pounds) opposite 8000 then opposite 1728 is the answer, 103-5. To find the Weight of a Body from its Magnitude. RULE. Place the contents of the body opposite 1728 then opposite its specific gravity is its weight in ounces. How many ounces avoirdupois in 864 cubic inches of sand? Place 864 opposite 1728: then opposite 1520 (the specific gravity of sand) is 760 ounces, the answer. |