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CAPACITY OF CISTERNS, ETC. 503. The Capacity of Cisterns, etc., is usually expressed in gallons or barrels.
504. The Standard Liquid Gallon of the United States contains 231 cubic inches, and is equal to about 8} lb. Avoirdupois of pure water.
505. The Barrel of 31.5 gallons and the hogshead of 63 gallons, are used in measuring the capacity of cisterns, vats, tanks, etc. When used as the names of vessels, these terms express no definite quantity.
The Imperial Gallon of Great Britain contains 277.274 cubic inches, and is equal to about 1.2 U. S. gallons. The beer gallon contains 282 cubic inches, but is now seldom used. A cubic foot of pure water weighs 1000 oz. Avoirdupois, or very nearly 62} lb.
Rule 1.— To find the capacity of a cistern or vessel in gallons, divide the contents in cubic inches by 231.
Rule II. - To find the cubic inches in a given number of gallons, multiply the given number of gallons by 231.
EXAMPLES FOR PRACTICE. 1. How many gallons of water are contained in a tank 9 ft. long, 5 ft. wide, and 4 ft. deep?
SOLUTION.—The contents of the tank equal 9x 5X4, which are 180 cubic feet; multiplying by 1728 to reduce to cubic inches, and dividing by 231, the number of cubic inches in a gallon, we have 1346 gal.
2. A trough 8 ft. long, 5 ft. wide, and 3 ft. deep, will hold how many gallons of water ?
Ans. 897-1 gal. 3. A vat 12 ft. long, 8 ft. wide, and 6 ft. deep, will contain how many gallons of beer?
Ans. 352935. 4. A cistern whose length was 10 ft. and width 7 ft., contained 50 hogsbeads; what was its depth? Ans. 624 ft.
5. How many hogsheads of water can be contained in a well whose diameter within the curb is 3ft., and depth 15 ft. ?
Ans. 17.136 bhd. 6. The diameter of a cylindrical cistern is 6 ft., and it contains 40 barrels of water; what is the depth of the water ?
Ans. 5.958+ st. 7. A cistern 18 ft. 3 in. long and 7 ft. 4 in. wide is full of
water; how many gallons must be drawn off to lower the surface 1 foot?
Ans. 1001+ gal. 8. How many imperial gallons will a cistern contain that is 8 ft. 4 in. long, 3 ft. 3 in. wide, and 2 ft. 6 in. deep?
Ans. 421.965+ gal. 9. A cistern 6 ft. long, 3 ft. 4 in. wide, and 4 ft. 9 in. deep, is emptied by a pipe in 1 h. 45 min.; how many gallons are discharged in 1 minute ?
Ans. 643 gal. 10. If 40 gal. 3 qt. of water flow through an orifice in 21 hours, how long will it require to fill a cistern 6 ft. long, 3.5 ft. wide, and 8.663 ft. deep ?
Ans. 3 da. 11 h. 31 min. 29+ sec. 11. What will be the expense of pumping the water out of a reservoir 24 ft. long, 18 ft. wide, and 8 ft. deep, at 10 cents a hogshead, the reservoir being half full ?
Ans. $20.52—. 12. A man wishing to construct a tank in his attic, found that it would not be safe to place there a weight of more than 4500 lb. of water; what length can he make the tank with a width of 4 ft., and a depth of 3 ft., water weighing 1000 oz. a cubic ft. ?
Ans. 6 ft.
CAPACITY OF BINS, ETC. 506. The Capacity of Bins, etc., is usually expressed in bushels.
507. The Standard Bushel of the United States is a cylindrical measure 181 in. in diameter and 8 in. deep, containing 2150.42 cubic inches.
The bushel heaped measure is the standard bushel heaped in the form of a cone 19 in. in diameter and at least 6 in. high, and containing 2747.7167 cu. in., while the even measure is called stricken measure. Grains, seeds, and small fruit are sold by stricken measure; but potatoes, corn in the ear, coarse vegetables, large fruits, coal, and other bulky articles are sold by heaped measure. In practice we may call 5 stricken measures equal to 4 heaped measures.
A Register Ton, used in measuring the internal capacity or tonnage of vessels, is 100 cubic feet, while a shipping ton, used in measuring cargoes, is only 40 cubic feet in the United States and 42 cubic feet in England.
Grain is shipped from New York by the quarter of 480 lb. (8 U. S. bu.), or by the Ton of 33} U. S. bushels. The Imperial Bushel of Great
Britain contains 2218.192 cu. in., and the English Quarter contains 8 Imperial or 81 U. S. bushels.
Coal is bought and sold in large quantities by the ton, in small quantities by the bushel, 28 heaped bushels or about 43.5 cu. ft. being considered equal to a ton. Ordinary anthracite coal measures from 36 to 40 cu. ft. to the ton; bituminous from 36 to 45 cu. ft. to the ton; Lehigh white ash, egg size, measures about 341 cu. ft. to the ton; Schuylkill white ash, 35 cu. ft., and pink, gray, or red ash, 36 cu. ft. to the ton.
A ton of hay upon a scaffold measures about 500 cu. ft.; on a mow, 400 cu. ft.; and in well-settled stacks, 10 cubic yards.
Rule 1.— To find the capacity of a bin in bushels, divide the contents in cubic inches by 2150.42.
Rule II.— To find the cubic feet in a given number of bushels, multiply the number of bushels by 2150.42, and divide by 1728.
NOTE.—2150.42 is to 1728 as 5 to 4, nearly ; hence a bushel is nearly equal to 11 cubic feet. Therefore, for practical purposes, any number of cubic feet, diminished by }, will give their equivalent in bushels, and any number of bushels, increased by 1, will give their equivalent in cubic feet. The 6th example, and those following, will be solved by these rules.
EXAMPLES FOR PRACTICE. 1. How many bushels of grain are contained in a bin 9 ft. long, 4 ft. wide, and 21 ft. deep ?
SOLUTION.—The contents equal 9X4X 21, or 90 cubic feet, which equals 155520 cubic inches ; dividing by 2150.42, the number of cubic inches in a bushel, we have 72.32 bushels.
2. How many bushels of grain are contained in a bin 10 ft. long, 5 ft. wide, and 3 ft. deep? Ans. 120.53+bu.
3. What must be the width of a bin which is 8 ft. long and 3 feet deep, in order to contain 96 bushels ? Ans. 4.97 ft.
4. A farmer built a granary 25.5 ft. long, 3.25 ft. wide, and 5.6 ft. high; how many bushels of grain will it hold ?
Ans. 372 bu. 3 pk. 5 qt. 1.8-pt. 5. An elevator containing 5000 bushels is 32 ft. long and 16 ft. wide ; what is its depth ?
Ans. 12.15 ft. 6. A bin 11 ft. 3 in. long, 6 ft. 6 in. wide, and 4 ft. 9 in. deep, was filled with wheat; what is it worth at $1.875 a cental, reckoning 60 lb. to a bushel ? Ans. $312.61.
7. A farmer has a wagon whose box is 12 ft. 3 in. long, 3 ft. 2 in. wide, and 2 ft. 3 in. deep; how many bushels of oats and how many of potatoes will it hold ?
Ans. 69.825 bu. oats; 55.86 bu. potatoes.
8. A bin 12 ft. 7 in. long, 6 ft. 3 in. wide, and 3 ft. 9 in. deep, is filled with w beat; how many barrels of flour will it make if one bushel of wheat makes 48 lb. of flour ?
Ans. 57.78 bbl. 9. A dealer has a bin of coal 80 ft. long, 10 ft. wide, and 8 ft. deep; how many tons of Lehigh wbite ash does it contain, and how many of Schuylkill gray ash?
Ans. 185.5+; 177.77+. 10. A shed 8 yd. long, 64 yd. wide, and 72 feet high, is full of Schuylkill white ash coal ; what is its value, at $4.50 a ton ?
Ans. $289.29. 11. I have a baymow 22 ft. long, 17 ft. 6 in. wide, and 11 ft. 8 in. high; what is its value, when filled, at $11.50 a ton ?
Ans. $129.14. 12. Mr. Barr had a rectangular stack of hay 9 ft. long, 71 ft. wide, and 6 ft. high, which he sold at $13.25 a ton; what did he receive for his hay?
Ans. $21.53. 13. A crib filled with corn in the ear measures on the inside 17 ft. 2 in. in length by 6 ft. 9 in. in width, and 8 ft. 3 in. in height; what is the value of the corn when shelled at 85€ a busbel, if 2 busbels of ears make 1 bushel of shelled corn?
COMPARISON OF MEASURES OF CAPACITY.
508. The Dry Gallon, or half peck, contains 268.8 cubic inches; hence 6 dry gallons equal nearly 7 liquid gallons.
Note.-The pupil will remember that the liquid gallon contains 231 cuin., and the old beer gallon 282 cu. in.
EXAMPLES FOR PRACTICE. 1. Reduce 4 gal. 3 qt. wine measure to the old beer measure.
Ans. 3 gal. 3 qt. 12 pt. 2. Reduce 57 gal. 3 qt. dry measure to wine measure.
Ans. 67 gal. 13 pt. 3. Reduce 336 gal. wine measure to dry measure.
Ans. 288 gal. 3 qt. 4. Reduce 8 bu. 3 pk. 2 qt. dry measure to the old beer measure.
Ans. 67 gal. 13 pt.
5. A farmer has a bin which contains 924 bu. of grain; how much water would it hold ? Ans. 8601.68 gal.
6. If a man should buy 28 qts. of milk at 5 cts. a quart, beer measure, and sell it at 6} cts. a quart, wine measure, what would be gain ?
Ans. 82 4 cts. 7. If a milkman bought 141 gal. milk, wine measure, at 25 cents a gallon, and sold it at 8 cts. a quart, beer measure, what did he gain ?
Ans. $1.71. 8. A grocer bought 33 bushels of berries, at $2.25 per bushel, and sold them by mistake by wine measure at 8 cents a quart; what was his gain or loss? Ans. Gain, $24.055.
MISCELLANEOUS PROBLEMS. 1. How much alloy must be mixed with 2 lb. 1 oz. 12 pwt. 15 gr. of pure gold, that the mixture may be 18 carats fine ?
Ans. 8 oz. 10 pwt. 21 gr. 2. What costs the excavation for a cellar 61 ft. deep under the main building of a dwelling-house 40 x 32 ft., and an excavation for the walls of an L 20 ft. square, 11 ft. wide and 2 ft. deep, at 50€ per cu. yd ?
Ans. $150.81. 3. James Morton & Co., New York, bought of a firm in Chicago 15600 bu. of wheat @ $1.25, delivered in New York, and shipped the same to Liverpool, the freight being $1.371 per quarter, where they sold the whole cargo at 60 3. per English quarter; what was the gross gain in U. S. money?
Ans. $5525.08. 4. Required the cost of the cellar aud brickwork of a dwelling-house in the form of an L, the main building being 40 x 30 ft., and the L projecting 24 ft., and being 14 ft. wide, the walls of the main building being 24 ft. high, and 13 in. thick, and those of the L 14 ft. high and 9 in. thick; chimneys and gables being reckoned as 400 sq. ft., 13 in. thick, and equal to windows and doors; the estimate being as follows: 50¢ per cubic yard for excavating a cellar 5 ft. deep; cellar wall, 17 ft. thick, $2.25 a perch, for lower part of wall, 5 ft. high, and 15¢ per sq. ft. for cut stone 2 ft. high; brick $10 p M., and laying $2 p M.