2. What will be the cost of digging a cellar 42 ft. long, 28 ft. wide, and 6 ft. 6 in. deep, at $.42 a load, each load being a cubic yard ? Ans. $118.903.

3. How many perches (244 cu. ft.) of stone, laid dry, will build a wall around a lot 20 rd. long and 18 rd. wide, the wall to be 5 ft. high and 2 ft. 6 in. thick ? Ans. 6283 perches.

4. What will be the cost of filling in a street 600 feet long and 65 feet wide, averaging 4 ft. below grade, at $.52 a cubic yard? Ans. $3380.

5. How many bricks of average size will it require to build the walls of a house 48 ft. long, 25 ft. wide, and 21 ft. high, the wall being 13 in. thick (21 bricks to sq. ft.), allowing 240 sq.ft. for doors and windows? Ans. 57,435 bricks.

SUPPLEMENTARY PROBLEMS,

To be omitted unless otherwise directed.

6. Mr. Wilson had a well dug in his yard, 6 ft. in diameter and 15 ft. 9 in. deep; what did it cost at 50% a load? Ans. $8.25-.

7. What will be the cost of the bricks in a house 40 ft. square, 22 ft. high, the walls being three bricks thick, of Philadelphia brick, at $15 per M.? Ans. $1027.75.

8. What will be the cost of digging and walling the cellar of a house 45 ft. by 24 ft., the cellar being 6 ft. deep and the wall 7 ft. high and 1 ft. thick, if the excavating cost 45% a load, and the masonry $4.25 a perch? Ans. $374.59.

MEASURES OF CAPACITY.

365. Measures of Capacity are volumes used to determine the quantity of fluids and many dry substances.

366. The Principal Measures of capacity are the gal lon for liquid substances, and the bushel for dry substances.

CAPACITY OF CISTERNS, ETC.

367. The Capacity of Cisterns, etc., is usually expressed in gallons or barrels.

368. The Standard Liquid Gallon of the United States contains 231 cubic inches, and is equal to about 8 lb. Avoirdupois of pure water.

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. Avoirdupois.

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.

WRITTEN EXERCISES.

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 6×4×24, 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 4037 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. 1178 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. 3788 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. 466 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+ hhd.

SUPPLEMENTARY PROBLEMS,
To be omitted unless otherwise directed.

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

9. A tank 4 yd. long, 2 yd, wide, and 6 ft.

of water; what is the weight of the water?

Ans. 14.44+ ft.

deep, is half full

Ans. 13,500 lb.

10. A tank 7 ft. long, 5 ft. wide, and 3 ft. deep, 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 it hold, and what will be the weight?

Ans. 10.72hhd.; 564437 lb.

12. A reservoir 32 ft. long, 27 ft. wide, and 10) ft. deep, is full when it becomes necessary to draw off the water to clean it out; what will be the expense of pumping the water ont at 10 cents a hogshead? Ans $76.94+.

CAPACITY OF BINS, ETC

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

371. The Standard Bushel of the United States is a cylindrical measure 18 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 in the ear, large fruits, coal and other bulky articles are sold by heaped measure.

In practice we may call 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, 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 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 nearly equa to 1 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.

WRITTEN EXERCISES.

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

SOLUTION. The contents equal 8×6×3, or 144 cubic feet, which equals 248832 cubic inches; dividing by 2150.42, the number of cubic inches in a bushel, we have 115.714 bushels.

2. A bin is 16 ft. long, 7 ft. wide, and 24 ft. deep; how many bushels will it hold? 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?

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

Ans. 9.95+ ft. 15 ft. wide, and Ans. 6.63+ft. 6 in. deep; how

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

Ans. 2041 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? Ans. $12.534.

7. A shed 6 yd. long, 4 yd. wide, and 8ft. high, is half full of Lehigh white ash coal (34 cu. ft.); what is the value of the coal at $7.50 a ton? 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 tons.

SUPPLEMENTARY PROBLEMS.

To be omitted unless otherwise directed.

9. 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. 172

bu.; 223 bu.

10. A bin 8 ft. long, 6 ft. wide, and 3 ft deep, is what is its value at $1.25 a bushel?

11. How many barrels of flour (196 lbs.) contents of a bin 12 ft. long, 7 ft. wide, bushel of wheat makes 48 lb. of flour?

full of barley;

Ans. $108.

can be made from the and 4 ft. deep, if one Ans. 7039 lb.

12. A hay-mow is 24 ft. long by 19 ft. wide and 16 ft. high; what is the value of the hay when it is filled, valued at $12 a ton, 400 cu. ft. to a 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.

MISCELLANEOUS PROBLEMS.

IN PRACTICAL MEASUREMENTS.

1. How many planks laid crosswise, 1 ft. wide, will it take for a board walk 1 mi. 16 rd. long, and 4 ft. wide?

Ans. 5544.

2. How many bushels of grain can a farmer store in a hogshead containing 122 gallons?

Ans. 13.1+bu.

3. How much stair carpet will be required for a flight of 18 steps, each 10 in. wide and 7 in. high ?

Ans. 83 yd.

4. To dig a sewer 1 miles long, 5 ft. wide, and 8 ft. deep, cost $3716; what was the price per cubic yard?

Ans. $.31.

5. A has a mow 20 ft. long, 12 ft. wide, and 10 ft. deep; how many tons of hay (400 cu. ft.) does it hold?

Ans. 6 tons.

6. From a quartz rock yielding silver at the rate of $123.75 per ton, a miner obtained $75.64 worth; what was the weight of the rock? Ans. 12 cwt. 224 lb.

7. If 4 persons can stand on one square yard of ground, how many people can be contained in a public square 32 rods on each side? Ans. 123904.

8. How many bunches of lath will be required for the walls and ceiling of a room 18 ft. long, 14 ft. wide, 10 ft. high, each bunch being estimated to cover 5 sq. yd.? Ans. 19.

9. I wish to cover my parlor 25 ft.X17 ft. 6 in. with carpet 26 in. wide; what will it cost me at $1.87 per yard, the pattern requiring an allowance of 2 yd. for waste? Ans. $131.25.

10. A street 36 ft. wide was paved with Nicholson pavement, at $3.25 per square yard; what did it cost to pave a "square" 32 rods long? Ans. $6864.