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NOTE.--2180.42 18 to 1728 as 8 to 4 nearly; hence a bushel is nearly oqual to cu. ft. Therefore, for practical purposes, t of the number of oubio Tool will equal the number of bushels, and of the number of bushels will equal the number of cubic feet.

Notice also that i of the number of bushels stricken measure equals the number of bushels heaped measure. Examples 5, 9, 10, 11 and 11 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 8X6X3, 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 21 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. 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. 2043 bu. 6. A bin 5 ft. long, 47 ft. wide, and 3 ft. deep, is filled with Schuylkill white ash coal (35 cu. ft.); what is its value at $6.50

Ans. $12.537. 7. A shed 6 yd. long, 4t yd. wide, and 8ft. high, is half full of Lehigh white ash coal (34cu. 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 583 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 cran. berries ?

Ans. 1741 bu.; 223 bu. 10. 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. $108. 11. How many barrels of four (196 lbs ) can be made from the contents of a bin 12 ft. long, 7$ ft. wide, and 4 ft. deop, if ono bugbel of wbeat makes 48 lk. of flour ?

Ans. 704f1b.

a ton ?

18. A hay-mow is 24 ft. long by 18 ft. wide and 16 ft. high; what is the value of the bay when it is filled, valued at $12 a ton, 400 cu. it. 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 10 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. $.31ff.

ő. 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. 225$ ib. 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. 1945 9. I wish to cover my parlor 25 ft.X17 ft. 6 in. with carpet 26 in. wide; what will it cost me at $1.873 per yard, the striju running lengthwise, with 31 yd, waste? Ans. $131.25.

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

Ans. $6884

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 71 ft. long and 4f ft. wide, what is its depth ? Ans. 124 in.

14. I used the earth taken from 4 cellars in grading a lot of ground; if the cellars were 30X21 ft., 28X18 ft., 24X16 ft., and 32X24 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.

16. What costs the excavation for a cellar 54 ft. deep under the main building of a dwelling-house 30X25 ft. and an excavation for the walls of an L 16 ft. square, 11 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 14X15 ft. and a hall 30X8 ft.; the first story being 10 ft. high, the second 9} ft., and the third s} ft., allowance being also made for 24 doors 7X34 ft., and 30 windows 6X3 ft., at 30% per sq. yd.?

Ans. $357.863. 17. Required the cost of a cellar of a house 40X30 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%

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 31 ft., and 30 windows, each 6 ft. by 3 ft

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Ans. $1258.915.

per sq. ft.

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SUPPLEMENT TO DENOMINATE NUMBERS. These supplementary exercises of Arts, 372, 373 and 374 are to be omittoa 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. 2. What part of 5 gal. 2 qt. of old beer measure is 3 gal. 2 qt. 1 pt. of liquid measure ?

Ans. .53993. 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. 1287 cents.

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

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

2. What is the value of a silver pitcher weighing 21b. 10 oz Avoirdupois, at $2.25 per ounce Troy?

Ans. $86.13. 8. Which is the heavier, 524 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 ?

Ans. 1241 lb. 6. How many times 3 lb. 10 oz. Troy is 5 lb. 12 oz. A voirdupois ?

Ans. 1.8229+. 6. A young lady weighs 120 lb. Avoirdupois weight; how much would she weigh by Troy weight ?

Ans. 145f lb. 7. If a druggist buys 25 lb. Avoirdupois of drugs at $8} a pound, and sells them in prescriptions at the rate of 754 an 3, what is the gain ?

Ans. $65.10.

COMPARISON OF MONEY.

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

375. The gold Dollar weighs 25.8 gr.; the silver Dollar, 4121 gr.; the Half-dollar, 192.9 gr.; the Sovereign (gold), 123.274 gr.; and the Shilling (silver), 87.27 gr. 1. How many dollars in £25 ?

Ano 2121.661. 2. How many dollars in £14 128 ?

Ans. $71.05. 3. How many pounds in $256.16 ? Ans. £52 128. 9d.-. 4. How many dollars in 240 guineas ? Ans. $1226.358. 5. How many francs in £42 ?

Ans. 1059.03 fr. 6. How many pounds in 875 francs ? Ans. £34 14.03 8. 7. How many marks in £340 ? Ans. 6937.568 marks. 8. How many pounds in 4375 marks ? Ans. £214 88. 3d.-, 9 How many pounds Avoirdupois in 1000 sovereigns ?

Ans. 17.6104 10. An ingot of pure gold was brought from California to be voined at the Philadelphia mint; if it weighed 15 lb. 8 oz. Troy, how many gold dollars will it make, to of the coin being alloy!

Ans. $3886; 7.08 gr. rom.

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