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. 10.72 +hhd.; 564417 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 out at 10 cents a hogshead? Ans $76.94+.

CAPACITY OF BINS, ETU

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 34 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 equal to 1 cu. ft. Therefore, for practical purposes, of the number of oubic 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 115.71+ 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?

Ans. 9.95+ ft. 15 ft. wide, and Ans. 6.63+ft. 6 in. deep; how of the number of Ans. 2041 bu.

4. One division of an elevator is 25 ft. long, contains 2000 bu. of grain; what is its depth ? 5. A bin is 10 ft. 5 in. long, 7 ft. wide, and 3 ft. many bushels of shelled corn will it hold, if cu. ft. equals the number of bushels ?

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, 44 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. 17

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?

bu.; 223 bu. full of barley; Ans. $108.

can be made from the and 4 ft. deep, if one Ans. 701 lb.

12. A hay-mow is 24 ft. long by 18 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. $18.661.

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 hoge head 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. 8 yd.

4. To dig a sewer 14 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 tne rock? Ans. 12 cwt. 221 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 26 in. wide; what will it cost me at $1.87 running lengthwise, with 3 yd. waste?

ft. 6 in. with carpet per yard, the strips 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

32 rods long?

"square"

Ans. $6864.

11. A railroad tunnel is one-eighth of a mile long, averaging 24 ft. wide and 20 ft. high; what did the excavation cost, at $1.50 a cubic yard? Ans. $17600.

12. How many freight cars will be required to transport 12000 bu. of wheat, 60 lb. each, 24000 lb. being the weight allowed for a single car? Ans. 30 cars.

13. A coal dealer has a wagon which holds exactly one ton of Schuylkill red ash coal (36 cu. ft.); if the wagon-bed is 7 ft. long and 4 ft. wide, what is its depth? Ans. 12 in.

14. I used the earth taken from 4 cellars in grading a lot of ground; if the cellars were 30X21 ft., 28X18 ft., 24×16 ft., and 32×24 ft., respectively, and 5 ft. deep, how many loads (cu. yd.) did I use? Ans. 423 loads.

SUPPLEMENTARY PROBLEMS.

To be omitted unless otherwise directed.

15. What costs the excavation for a cellar 5 ft. deep under the main building of a dwelling-house 30×25 ft. and an excavation for the walls of an L 16 ft. square, 1 ft. wide, and 2 ft. deep, at 50% per cu. yd.? Ans. $78.88%.

16. What costs the plastering of a house of 12 rooms, there being on each story 4 rooms 14×15 ft. and a hall 30X8 ft.; the first story being 10 ft. high, the second 9 ft., and the third 8 ft., allowance being also made for 24 doors 7×3 ft., and 30 windows 6X3 ft., at 30 per sq. yd.? Ans. $357.861.

17. Required the cost of a cellar of a house 40×30 ft., the different items being as follows: excavating cellar, 4 ft. deep, at 50 per cu. yd.; cellar wall, 7 ft. high and 18 in. thick, the lower 4 ft. common masonry, @$3.15 a perch, and the upper 3 ft. cut stone at 16 per sq. ft. Ans. $263-.

18. Required the cost of brick-work of the same house, the walls being 35 ft. high and 13 in. thick, and gable 10 ft. high, using common bricks at $10 per M., bricklaying costing $3 per M., allowing for 8 doors, each 7 ft. by 3 ft., and 30 windows, each 6 ft. by 3 ft.

Ans. $1258.915.

SUPPLEMENT TO DENOMINATE NUMBERS.

These supplementary exercises of Arts, U72, 373 and 374 are to be omitted by pupils needing a shorter course, unless otherwise directed.

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.

WRITTEN EXERCISES.

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

Ans. .5399—.

2. What part of 5 gal. 2 qt. of old beer measure is 3 gal. 2 qt. 1 pt. of liquid measure? 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 bushel measure to exactly fill it? Ans. 9.31-. 5. If 32 quarts of water are put into a vessel that holds exactly 32 quarts of strawberries, will the water be more or less than the vessel will hold ? Ans. 302.4 cu. in. less,

6. 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.

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 27 pwt., can be made from a bar of gold weighing 1 lb. A voirdupois?

Ans. 101 rings, 31 gr. remaining.