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CUBIC OR SOLID MEASURE. 137. Cubic or Solid Measure is used in measuring such bodies or things as have length, breadth, and thickness; as timber, stone, &c.
Note 1. — A pile of wood 8ft. in length, 4ft. in breadth, and 4ft. in height, contains a cord.
Also, one ton of timber, as usually surveyed, contains 502 cubic or solid feet.
Sawed timber, joists, plank, and scantlings are now generally bought and sold by what is called board measure.
NOTE 2. — A cube is a solid bounded by six square and equal sides.
If the cube is 1 foot long, 1 foot wide, and 1 foot high, it is called a cubic or solid foot. If the cube is 5 feet long, 3 feet wide, and 3 feet thick, it is called a cubic or solid yard.
Now, since each side of a cubic yard, as represented in the diagram, contains 9 sq ft. of surface (Art. 135), it is plain, if a block be cut off from one side, one foot thick, it can be divided into 9 solid blocks, with sides 1 foot in length, breadth, and thickness, and therefore will contain 9 solid feet; and since the
whole block or cube is three feet thick, 3 ft. = 1 yd.
it must contain 3 solid feet X 9 = 27
solid feet; for 3 solid feet X 3 X 3 = 27 solid feet. Hence,
To find the contents of a cubic body, multiply the numbers denoting its length, breadth, and thickness together.
NOTE 3. – A cubic foot of distilled water at the maximum density, at the level of the sea, and the barometer at 30 inches, is equal in weight to 624lb. or 1000oz. avoirdupois.
NOTE 4. - A cubic foot of lead weighs 7083lb.; of brass, 5343lb.; of copper, 555lb.; of wronght-iron, 4863lb.; of cast-iron, 450f1b.; of marble, 1711b.; of granite, 165lb.; of clay, 130lb.; of common soil, 1241b.; of bricks, 124lb.; of sand, 951b.; of sea-water, 64ilb.; of oak wood, 55lb.; of Anthracite coal, 541b.; of Bituminous coal, 50lb.; of red-pine wood, 421b.; and of white-pine wood, 301b.
EXAMPLES. 1. In 29 cords of wood how many solid inches ? 2. In 6414336 cubic inches how many cords? 3. In 19 tons of timber how many solid inches ? 4. How many tons of timber in 1313280 cubic inches ? 5. How many cubic feet of wood in 128 cords? 6. How many cords of wood in 16384 cubic feet?
7. How many cubic feet in a pile of wood, 40 feet long, 4 feet wide, and 7 feet high ? 8. How many cords of wood in 8650 cubic feet?
Ans. 67 cords, 74 cubic feet. 9. How many cubic feet in a granite block, 17 feet long, 11 feet wide, and 9 feet high ?
Ans. 1683 cubic feet.
LIQUID OR WINE MEASURE
138. Liquid or Wine Measure is used in measuring all kinds of liquids, except, in some places, beer, ale, porter, and milk.
Note 1. – By laws of Massachusetts, 32 gallons make 1 barrel. In some States 313 gallons, and in others from 28 to 32 gallons, make 1 barrel. 42 gallons make 1 tierce, and 2 tierces make 1 puncheon.
NOTE 2. — The term hogshead is often applied to any large cask that may contain from 50 to 120 gallons, or more.
NOTE 3. – The Standard Unit of Liquid Measure adopted by the government of the United States is the Winchester Wine Gallon, which contains 231 cubic inches, and is of a capacity to hold 810.00lb. Avoirdupois of distilled water, at its maximum density, weighed in air, the barometer being at 30 inches. It has the name Winchester, from its standard having been formerly kept at Winchester, England. The Imperial Gallon, now adopted in Great Britain, contains 277100 cubic inches; so that 6 Winchester gallons make about 5 Imperial gallons.
NOTE 4. – 1 gallon of alcohol weighs 7lb.; of camphene, 7žlb.; of proof spirits, 71;lb.; of spirits of turpentine, clb.; of sperm oil, 7 lb.; of olive oil, 7lb.; of linseed oil, 781b.; and of molasses, 113lb.
NOTE 5. — The fluid measure of apothecaries, used by them in measuring liquids of medical prescriptions, divides the gallon (marked Cong.) into 8 pints (0.); the pints into 16 fluid ounces (f3 ); the fluid ounces into 8 fluid drams (f3 ); and the fluid drams into 60 minims (m) or drops. The abbreviation Cong. stands for congiarium, the Latin for gallon, and the 0. is the initial of octans, the Latin for an eighth, the pint being an eighth of a gallon.
EXAMPLES. 1. In 57T. 3hhd. 50gal. 3qt. how many pints ? 2. In 116830 pints how many tuns ? 3. Reduce 96hhd. 47gal. 2qt. to gills. 4. How many hogsheads in 195056 gills ? 5. What cost 40 hogsheads of wine at $ 0.374 per pint ?
6. How much may be gained by buying 2 hogsheads of molasses, at 40 cents a gallon, and selling it at 12 cents a
Ans. $ 10.08.
139. Beer Measure is used in measuring beer, ale, porter, and milk.
TABLE. 2 Pints (pt.)
make 1 Quart, 4 Quarts
1 Gallon, 54 Gallons
hhd. pt. 2
Note 1. — The gallon of beer measure contains 282 cubic inches; and has been usually reckoned, 36 gallons equal 1 barrel; 2 hogsheads, or !08 gallons, 1 butt; 2 butts, or 216 gallons, 1 tun.
NOTE 2. - Beer Measure is becoming obsolete. Milk and malt liquors, at the present time, are bought and sold, very generally, by wine or liquid
1. How many pints in 46hhd. 49gal.? 2. In 20264 pints how many hogsheads ? 3. In 368hhd. how many pints ? 4. In 158976 pints how many hogsheads ? 5. At 29 cents per gallon, what cost 76 hogsheads of ale?
Ans. $ 1190.16. 6. How much may be obtained by selling 47hhd. 36gal. of lager-beer at 5 cents a quart ?
Ans. $ 514.80.
140. This measure is used in me
measuring grain, fruit, salt, &c.
TABLE. 2 Pints (pt.)
make 1 Quart, 8 Quarts
pk. 4 Pecks
1 NOTE 1. – · The Standard Unit of Dry Measure adopted by the United States government is the Winchester bushel, which is in form a cylinder, 185 inches in diameter, and 8 inches deep, containing 2150 cubic inches. The Standard Imperial bushel of Great Britain contains 22187000 cubic inches, so that 32 Imperial bushels equal about 33 Winchester bushels. The gallon in Dry Measure contains 2681 cubic inches.
NOTE 2. — Of wheat a standard bushel is 60lb.; of shelled corn, 561b.; of corn on the cob, 70lb.; of rye, 561b.; of barley, 481b.; of buckwheat in Pa., 501b.; in Kentucky, 521b.; in Mass., 481b.; of oats in Ohio, II., Mass., &c., 321b.; of oats in Ky., 33f1b.; of oats in Me., 30lb.; of oats in Pa., 30]b.; of clover-seed, 60lb.; of flax-seed, 561b.; of Timothy-seed, 45lb.; of bran, 2015.; of beans, 60lb.; of onions, in Pa., Ky., &c., 57lb.; of onions in Mass., 521b.; of salt in Kv., 561b.; of salt in II., 50lb.; of dried apples in Pa., 221b.; of dried apples in III., 241b.; of dried peaches in Pa., 331b.; of dried peaches in III., 321b.; of stove coal in Ill., 80lb.; of bituminous coal in the Western States, 761b.; and of hard-wood charcoal, 3012. The weight by law, of a fow
of the articles named, to a bushel, is not uniform in all the States, and therefore may vary slightly from the above, in a few States not mentioned.
NOTE 3. — In some places it is customary, in measuring coal, potatoes, and like articles, to “heap" the bushel, as it is called, and in that case 5 even pecks are about equal to 1 “ heaped bushel.” The “coal bushel,” as established by laws of Massachusetts, Ohio, and some other States, is of greater capacity than the Winchester bushel. In some parts of the United States a chaldron, a measure of coal, consists of 36 bushels; and in other parts of the country it consists of 32 bushels, or of 4 quarters, each consisting of 8 bushels. The quarter, however, in England is 8 Imperial bushels, a measure of grain equal to 560lb., or one quarter of a ton of 2240lbs.
EXAMPLES. 1. How many pints in 35bu. 3pk. ? 2. In 2288 pints how many bushels ? 3. In 676 chaldrons, of 36 bushels each, how many pecks?
4. How many chaldrons, of 36 bushels each, in 97344 pecks?
5. A grocer purchased 50 bushels of potatoes, by “heaped” measure, at 60 cents a bushel, and sold the same, by “even” measure, at 15 cents a peck ; did he gain or lose by the operation ?
Ans. Gain $ 7.50. 6. If I purchase by measure 96 bushels of oats, weighing 2304 pounds, at 42 cents a bushel, and sell the same by weight in Ohio, at 45 cents a bushel, shall I gain or lose by so doing?
Ans. Lose $ 7.92. DRY, LIQUID, AND BEER MEASURES COMPARED. 141. The relative value of the gallon and its subdivisions, of the several measures, in cubic inches, and in denominations of each other, are shown in the following
TABLE. cu. in. 1 gal. B. M.
282 1gal. 1pt. 35gi. L. M. igal. kpt. D. M. 1 gal. D. M. 2684 = 1gal. 1pt. 13zgi. L. M. 3qt. 119pt. B. M. 1 gal. L. M.
3qt. kpt. B. M. 1 qt. B. M.
1qt. ll.pt. D. M. 1 qt. D. M.
1 pt. 3191gi. B. M. 1 qt. L. M. 133pt. D. M.
139 pt. B. M. 1 pt. B. M.
= 1,9.pt. D. M.
3991gi. B. M. 1 pt. L. M. 287 pt. D. M.
Japt. B. M. 1 gi. L. M. sapt. D. M.
34.pt. B. M.