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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 wo 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
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
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
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
Rule.—Place 14 opposite 3: then opposite the weight is a product, the cube root of which is the
A ball 8 pounds in weight is 3.34 inches in diameter.
Specific Gravity and Weight of Bodies.
oz. Pure Platina 23000/Clay
2160 Fine Gold 19400 Brick
2000 Standard Gold 17720 Common Earth. 1984 Quicksilver 13600 Nitre
1900 Lead 11325 Ivory
1825 Fine Silver 11091 Brimstone
1810 Common Silver . 10535 Solid Gunpowder 1745 Copper 9000 Sand
1520 Copper Pence 8915 Coal
1250 Gun Metal 8784 Mahogany
1063 .Cast Brass 8000 Boxwood
1030 Steel 7850 Sea Water
7645 Common Water 1000 Cast Iron 7425 Oak
7320 Gunpowd’rshook close937 Crystal Glass 3150 in a loose heap 836 Granite 3000 Ash
800 White Lead 3160 Maple
755 Marble 2700 Beech
700 Hard Stone 2700'Elm
600 Green Glass 2600 Fir .
550 Flint 2570 Cork
240 Common Stone . 25201 Air at a mean state
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 Münces 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 magni. tude, 294 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,