369. The Barrel of 31 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. A voirdupois.

Rule I. 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 will a tank 6 ft. long, 4 ft. wide, and 2 ft. 3 in. deep, contain?

SOLUTION. The contents of the tank equal 6×4×2, which are 54 cubic feet; multiplying by 1728 to reduce to cubic inches, we have 93312 cu. in.; dividing by 231, the number of cubic inches in a gallon, we have 40373 gallons.

2. How many gallons of water are contained in a tank 15 ft. long, 3 ft. wide, and 3 ft. 6 in. deep? Ans. 11782 gallons. 3. How many Imperial gallons would be contained in the same tank? Ans. 981.55+ Imp. gal. 4. How many cubic feet in a cistern containing 45 hogsheads? Ans. 378 cu. ft. 5. A cistern 8 ft. square contains 54 hhd.; what is its depth? Ans. 7.11- ft.

6. How many barrels of water can be contained in a tank measuring 7 ft. square by 4 ft. deep? Ans. 46 barrels. 7. How many hogsheads of water can be contained in a well whose diameter within the curb is 4 ft., and depth 12 feet? Ans. 22.66+ bbd.

SUPPLEMENTARY EXAMPLES.
To be omitted unless otherwise directed.

8. The diameter of a well is 3.5 ft., and it contains 16 hogsheads of water; what is the depth of the water?

Ans. 14.44+ ft.

9. A tank 4 yd. long, 2 yd. wide, and 6 ft. deep, is half full; what is the weight of the water? Ans. 13,500 lb. 10. A tank 7 ft. long, 5 ft. wide, and 3 ft. deep, filled with water, can be emptied by a waste pipe in 2 hours; how many gallons are discharged in 1 minute? Ans. 6 gallons.

11. Mr. Cornwell constructed a tank in his attic 8 ft. 6 in. long, 4 ft. 3 in. wide, and 2 ft. 6 in. deep; how many hogsheads of water will t hold, and what will be the weight? Ans. 10.72+ hhd.; 564417 lb. 12. A reservoir 32 ft. long, 27 ft. wide, and 10 ft. deep is fuil when it becomes necessary to draw off the water in order to clean it out; what will be the expense of pumping it out at 10 cents a hogshead?

CAPACITY OF BINS, ETC.

Ans. $76.94+.

370. The Capacity of Bins, etc., is usually expressed in bushels.

371. The Standard Bushel of the United States is a cylindrical measure 181⁄2 in. in diameter and 8 in. deep, containing 2150.42 cubic inches.

THE BUSHEL.-Grain, seeds, and small fruits are sold by stricken measure. Potatoes, corn on the ear, large fruits, coal and other bulky articles are sold by heaped measure. For practical purposes, we may regard 5 stricken bushels equal to 4 heaped bushels.

COAL.-Coal is bought and sold in large quantities by the ton; in small quantities by the bushel, 28 heaped bushels being considered equal

to a ton.

Ordinary anthracite coal measures from 36 to 40 cu. ft. to the ton; bituminous coal, from 36 to 45 cu. ft. to the ton. Lehigh white ash coal, egg size, measures about 343 cu. ft. to the ton; Schuylkill white ash, 35 cu. ft., and pink, gray, or red ash, 36 cu. ft. to the ton.

HAY.-Hay, when loose or in loads or upon a scaffold, measures about 500 cu. ft. to the ton; on a mow, 400 cu. ft.; and in large well-settled stacks, 10 cu. yd.

Rule I.-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 r early equal to 14 cu. ft. Therefore, for practical purposes, of the number of cubic feet will equal the number of bushels, and of the number of bushels will equal the number of cubic feet.

Notice also that of the number of bushels stricken measure equals the

number of bushels heaped measure. Examples 5, 9, 10, 11, and 14 are solved by this rule.

EXAMPLES FOR PRACTICE.

1. How many bushels will be contained in a bin 8 ft. long, 6 ft. vide, and 3 ft. deep?

SOLUTION. The contents equal 8X6X3, or 144 cubic feet, which quals 248832 cubic inches; dividing by 2150.42, the number of cubic inches in a bushel, we have 115.71+ bushels.

2. A bin is 16 ft. long, 7 ft. wide, and many bushels will it hold?

2 ft. deep; how Ans. 224.99 bu.

3. What is the width of a bin 24 ft. long and 3 ft. 4 in. deep, to contain 640 bushels of wheat?

Ans. 9.95 ft.

4. One division of an elevator is 25 ft. long, 15 ft. wide, and contains 2000 bu. of grain; what is its depth?

Ans. 6.63+ ft.

5. A bin is 10 ft. 5 in. long, 7 ft. wide, and 3 ft. 6 in. deep; how many bushels of shelled corn will it hold, if of the number of cu. ft. equals the number of bushels?

Ans. 2044 bu.

6. A bin 5 ft. long, 4 ft. wide; and 3 ft. deep, is filled with Schuylkill white ash coal (35 cu. ft.); what is its value at $6.50 a ton?

7. A shed 6 yd. long, 44 yd. wide, and full of Lehigh white ash coal (34 cu. ft.); of the coal at $7.50 a ton?

Ans. $12.534.

8 ft. high, is half what is the value

Ans. $211.304.

8. An ice-house 40 ft. long, 25 ft. wide, and 15 ft. high, is filled with ice; how many tons are there, if a cubic foot weighs 58 lb. ? Ans. 4351 ton

SUPPLEMENTARY EXAMPLES.

To be omitted unless otherwise directed.

9. A bin 8 ft. long, 6 ft. wide, and 3 ft. deep, is full of barley; what is its value at $1.25 a bushel?

Ans. $108.

10. There is a rectangular box 4 ft. long, 3 ft. wide, and 2 ft. 4 in. deep; how many bushels of apples will it hold? how many of cranberries? Ans. 1723 bu.; 223 bu.

11. How many barrels of flour (196 lbs.) can be made from the contents of a bin 12 ft. long, 7 ft. wide, and 4 ft. deep, if one bushel of wheat makes 48 lb. of flour?

Ans. 704 bbl.

12. A haymow is 24 ft. long by 18 ft. wide and 16 ft. high; what is the value of the hay when it is filled, quoted at $12 a ton, 400 cu. ft. to the ton? Ans. $207.36.

13. Mr. Jenkins sold a rectangular stack of hay 8 ft. long, 7 ft. wide, and 6 ft. high, at $15 a ton; what was the value of the hay, 10 cu. yd. to a ton? Ans. $18.663.

14. A crib filled with corn in the ear measures on the inside 20 ft. in length, 12 ft. in width, and 7 ft. in height; what will be the value of the corn when shelled at $1.05 a bushel, if 2 bushels in the ear make 1 bushel when shelled? Ans. $564.48.

NOTE.

Classes needing a shorter course can omit Arts. 372, 373, and 375. COMPARISON OF MEASURES OF CAPACITY. 372. 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 cu. in., and the old beer gallon 282 cu. in.

EXAMPLES FOR PRACTICE.

1. How many more cubic inches in 495.3 dry gallons than in 495.3 liquid gallons? Ans. 18722.34 cu. in.

2. What part of 5 gal. 2 qt. of old beer measure is 3 gal. 2 qt. 1 pt. of liquid measure?

Ans. .5399-.

3. How many bushels of oats can be put in a tank that holds 4550 gallons of water? Ans. 488.765- bu. 4. How many gallons of water can be poured into a pushel measure?

Ans. 9.31

5. If 32 quarts of water are put into a vessel that holds exactly 32 quarts of strawberries, will they be more or less than the vessel will hold? Ans. 302.4 cu. in. less.

SUPPLEMENTARY EXAMPLES.

To be omitted unless otherwise directed.

6. A dishonest milkman charged for milk 7 cents a quart, beer measure, but wishing to cheat his customers, he measured it by the liquid quart; what was the loss to one taking 2 gallons? Ans. 12 cents. 7. A grocer sold molasses at 15 cents a quart, but the clerk, by mistake, measured a day's sales by the dry quart; he sold 25 gallons; what did it cost a quart liquid measure? Ans. 12 cents.

COMPARISON OF WEIGHTS.

This subject may be omitted until review.

373. The Troy Pound and the Apothecaries' Pound each contains 5760 Troy grains; the Avoirdupois pound contains 7000 Troy grains. The Avoirdupois ounce contains 437 grains, while the Troy ounce contains 480 grains.

Rule. Reduce the given denominations to grains, and divide by 480 to find Troy ounces, and 437 to find ounces Avoirdupois.

1. How many rings, each weighing 23 pwt., can be made from a bar of gold weighing 1 lb. A voirdupois?

Ans. 101 rings, 31 gr. remaining.

2. What is the value of a silver pitcher weighing 2 lb. 10 oz. Avoirdupois, at $2.25 per ounce Troy? Ans. $86.13.

Ans. 12

3. Which is the heavier, 52g lb. of lead or 52.625 lb. of silver? Ans. The lead. 4. How many pounds of gold are actually as heavy as 10 lb. of iron? lb. 5. How many times 3 lb. 10 oz. Troy is 5 lb. 12 oz. Avoirdupois ? Ans. 1.8229+. 6. A young lady weighs 120 lb. A voirdupois weight; how much would she weigh by Troy weight? Ans. 145 lb.

7. If a druggist buys 25 lb. Avoirdupois of drugs at $8 a pound, and sells them in prescriptions at the rate of 75 an 5, what is the gain? Ans. $65.10.

COMPARISON OF MONEY.

This subject may be omitted until review.

374. The Pound Sterling is valued at $4.8665; and te Franc at 19.3 cents; the Mark at 23.85 cents.

375. The Dollar weighs 25.8 gr.; the Half-dollar 192.9 gr.; the Sovereign 123.274 gr.; and the Shilling 87.27 gr.

1. How many dollars in £25?

2. How many dollars in £14 12 s.?

Ans. $121.661.

Ans. $71.05.

3. How many pounds in $256.16? Ans. £52 12 s. 9 d.