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CUBIC MEASURE. 1 cu. inch = 16.387 cu. centimeter. 1 cu. centimeter =.061 of a cu. inch. 1 cu. foot = 28.317 cu. decimeter.

1 cu, decimeter = .0353 of a cu. foot. 1 cu. yard = .7645 of a cu. meter. 1 cu. meter = 1.308 cu. yard. 1 cord 3.624 ster.

1 ster = .2759 of a cord.

MEASURES OF CAPACITY. 1 liquid quart = .9463 of a liter.

1 liter = 1.0567 liquid quarts. 1 dry quart = 1.101 liter.

1 liter = .908 of a dry quart. 1 liquid gallon = .3785 of a dekaliter. 1 dekaliter = 2.6417 liquid gallons. 1 peck =.881 of a dekaliter.

1 dekaliter = 1.135 pecks. 1 bushel = .2524 of a hektoliter.

1 hektoliter = 2.8375 bushels.

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1 ounce, Avoir.

MEASURES OF WEIGHT. 1 grain, Troy = .0648 of a gram.

1 gram

: .03527 of an ounce, Avoir. = 28.35 gram.

1 gram

= .03215 of an ounce, Troy. 1 ounce, Troy = 31.104 grams.

1 gram = 15.432 grains, Troy.

. 1 pound, Avoir. = .4536 of a kilogram. 1 kilogram = 2.2046 pounds, Avoir. 1 pound, Troy = .3732 of a kilogram. 1 kilogram = 2.679 pounds, Troy. 1 ton (short) = .9072 of a tonneau. 1 tonneau = 1.1023 tons (short).

REMARK.—Metric quantities of any unit are read like ordinary decimals.

FRENCH MONEY.

498. The Legal Currency of France is decimal, its unit being the silver Franc. 499. The French coins are as follows: (100 francs,

10 centimes,
40 francs,
5 francs,

5 centimes,
Gold 20 francs,

Silver { 2 francs,

Bronze

2 centimes,
10 francs,
1 franc.

l centime.
5 francs.

Table.
10 millimes (m.) = 1 centime (ct.) = $.00193.
10 centimes = 1 decime (dc.) .0193.
10 decimes = 1 Franc (fr.)

=

.193.

MONEY OF THE GERMAN EMPIRE.

500. The Unit is the Mark = $.2385 United States money. It is divided into 100 pfennigs (pennies).

The silver Thaler = $.726 United States money.
501. The German coins are:
20 marks,

20 marks,
Gold10 marks, Silver

10 pfennigs,
1 mark,

Nickel
5 marks.
20 pfennigs.

5 pfennigs.

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MISCELLANEOUS EXAMPLES.

502. 1. What is the value, in English money, of $1750 in United States gold coin?

2. It required 12 yr. 6 mo. 1 da. to build the Brooklyn bridge. If it was completed July 4, 1882, when was its construction begun ?

3. What is the board measure of 7 planks, cach 16 ft. long, 15 in. wide, and 3 in, thick ?

4. How many acres of land can be bought for $25000, if a square foot costs 254?

5. A cellar is 24 ft. square inside of the wall, which is 9 ft. high, and 2 ft. thick. How many perches of 104 cu. ft. each does the wall contain?

REMARK.-Sometimes 244 cubic feet are reckoned as a perch, but this is rarely done by contractors or architects; girt measurements are taken.

nuns.

6. How many shingles, 4 inches wide, laid 6 inches to the weather, would be required to cover the roof of a barn 60 ft. long and 24 ft. wide on each side?

7. The highest chimney in the world is at Port Dundas, Scotland, it being 450 ft. high. How many rods in hight is it ? 8. The Italian Government pays out yearly $2140000 to 32590 monks and

What is the average sum received by each ? 9. What will be the cost of the plank, at $18 per M, that will cover a floor 24 ft. by 13 ft., if the plank is 24 inches in thickness ?

10. A farm having 225 rods fronting the road, is 95 rods wide at one end and 72.5 rods at the other. How many acres does the farm contain ?

11. If the capacity of a cask is 641 wine gallons, how many quarts of berries will it hold ?

12. A bird can fly 1° in 1 hr. 10 m. 12 sec. At that rate, in what time can it encircle the earth ?

13. What will be the cost in Paris of a cargo of 38500 bu. United States wheat, at 10 fr. 60 cent. per hektoliter?

14. How many francs are equal to $275.

15. The largest shipping lock in the world is at Cardiff, it being 600 ft. long, 80 ft. wide, and 32 ft. deep. What is its capacity in barrels ?

16. When it is noon at the point of your observation, what is the time at a point 1500 statute miles due south-west ?

17. If your coal costs $5.60 per ton, and you use 65 lb. per day, what will be the expense of your fire for the months of the winter of 1891–2 ?

18. How many barrels of water in a cistern 12.5 ft. long, 10 ft. wide, and 7.5 ft. deep?

19. A carriage wheel 4 ft. 3 in. in diameter will make how many revolutions in going 62.5 miles ?

20. If Wm. H. Vanderbilt died worth two hundred millions of dollars, in what length of time could his fortune, in silver dollars, be counted by one person, counting 60 per minute and working 10 hours per day for 305 days each year ?

21. What will be the cost of 10 sticks 2 in. Ly 4 in., 10 sticks 2 in. by 6 in., 10 sticks 4 in. by 4 in., and 10 sticks 2 in. by 10 in., if the sticks are each 16 ft. long and the cost is $15 per M ?

26.

22. How many yards of Axminster carpeting, of a yard in width, and laid lengthwise of the room, will be required to cover a floor 21 ft. long and 18} ft. wide, making no allowance for waste in matching the design ?

23. How many tons of 324 cu. ft. each, in a mow of hay 36 ft. 3 in. long, 18 ft. 10 in. wide, and 13 ft. 6 in. high ?

24. Two astronomers, located at different points, observed at the same instant of time an eclipse of the moon, one seeing it five minutes after 9 P. M., local time, and the other five minutes before midnight. How many degrees of longitude separated the observers ? 25. How many Avoirdupois pounds in 10 myriagrams 4 kilograms.

If the sun is 93 millions of miles from the earth, and a cannon ball travels nine miles per minute, at what time would a ball fired from the earth at one minute after 3 o'clock P. M., Dec. 25, 1889, reach the sun at that rate ?

27. How many francs are equal to £425 ?

28. Allowing 305 sq. ft. for doors and windows, what will be the cost, at 40¢ per square yard, of plastering the ceiling and walls of a room 45 ft. long, 354 ft. wide, and 12 ft. 3 in. high ?

29. How many German marks are equal to $1500 United States money ?

30. A pile of wood built 10 ft. high and 22 ft. wide must be how long to contain 125 cd.?

31. The main centennial building at Philadelphia in 1876 was 1880 ft. long and 464 ft. wide. What was its area in acres, square rods, and square feet ?

Reduce 47 mi. 216 rd. 11 ft. 5 in. to metric units. 33. If £2 4 s. 6 d. is paid for a coat and vest, and the coat costs 4 s. more than twice as much as the vest, what is the cost of each, in United States money?

34. From .001 of a section, plus .01 of an acre, take .001 of a quarter section, plus .01 of a square rod.

A grocer bought 12 bu. of chestnuts, at $3.50 per bushel dry measure, and sold them at 15¢ per quart liquid measure. Did he gain or lose, and how much ?

36. How many dollars are equal to 2150 francs ?

37. How many square feet of sheet lead will be required to line a tank y ft. in diameter and 12 ft. deep ?

38. If bricks cost $5.50 per M, what will be the cost of the brick for a wall 12 ft. high and 3 ft. thick, enclosing an acre of land 10 rd. wide and 16 rd. long ?

39. The gold coin of the commercial world suffers each year a loss of one ton by wear or abrasion. What is the value, in United States gold dollars, of the loss thus sustained?

40. Reduce 250 hektars to common units.

41. What will be the cost, at $16.00 per M, of a tapering board 18 ft. long, and 9 in, wide at one end and 161 in. wide at the other ?

42. A German immigrant having 1000 thalers and 500 marks, exchanges them for United States money. How many dollars should he receive ?

43. The hight, width, and length of a shed are equal. What are its dimensions, if it will contain 125 cords of wood ?

32.

44. A train of 45 cars of Lehigh coal averages, by the long ton, 23 T. 7 cwt 3 qr. 10 lb.

per car.

What is the value of the coal, at $5.25 per short ton ? 45. How many feet of lumber in a box 64 ft. long, 54 ft. wide, and 31 ft. deer, inside measurements given, and lumber 1 inch in thickness ?

46. What will be the cost of carpeting & yd. wide, and lining yd. wide, to cover a room 24 ft. long and 20 ft. wide, if the strips of carpet are laid the long way

of the room and there is a waste of 9 inches at one end in matching, also an allowance of 10% in width and 6% in length for shrinkage of the lining, the carpet selling at $2.25 per yd., and the lining at 30$ per yd.

47. A pile of wood 56 meters long, 181 meters wide, and 3 meters high, was sold at $6

per

cord. How much was received for it? 48. A farmer filled a bin 9 ft. wide, 12 ft. long, and 71 ft. deep, with wheat grown from a field yielding 324 bu. per acre. How long was the field, if its width was 50 rods ?

49. Seasoned pine in freighting is estimated to weigh 3000 lb. per M, and green oak 5000 lb. per M. How much freight must I pay, at $1 per ton, on a car load of 3265 ft. of pine and 3795 ft. of oak ?

50. How long is the side of the largest cube that can be cut from a spherical snow ball 5 ft. in diameter ?

51. Glenn's California reaper will in 12 hours cut, thresh, winnow, and put into bags, 30 A. of wheat. How many days, of 15 working hours each, will it require to harvest and thresh the wheat of a field 125 rods wide and 240 rods long? 52. An ounce of gold can be so beaten as to cover 146 sq.

ft. What weight of gold would be required for a sheet which will cover an acre of ground ?

53. A farmer having 1240 bu. of corn in the ear to store in two rail cribs, builds each 9 ft. square on the inside. If one is built 10 ft. high and filled, how high must the other be built to hold the remainder ?

54. The Hercules ditcher, of Michigan, removes 750 cu. yd. of earth per hour. In how many days, of 12 working hours each, can it dig a ditch 7 miles in length, 8 ft. in depth, 24 ft. wide at the surface, and 16 ft. at the bottom ?

55. If a car carrying 20 tons of freight is with its couplings 42 ft. long, what would be the length of a train carrying Vanderbilt's two hundred millions of dollars, if it is all in standard silver dollars, and any fractional part of a car load is rejected ?

PERCENTAGE.

503. Percentage is a term applied to computing by hundredths.

504. The Elements of Percentage are, the Base, the Rate, the Amount Per Cent., the Difference Per Cent., the Percentage, the Amount, and the Difference.

505. The Base is the number upon which the percentage is computed.

506. The Rate Per Cent. denotes how many hundredths of the base are to be taken, and is usually expressed as a decimal.

507. Per Cent. is an abbreviation of the Latin words per centum, signifying by the hundred, or a certain number of each one hundred parts.

508. The Sign, %, is used to denote per cent.

509. The Rate may be expressed as a part in a common fractional form, as * ; in the form of an extended decimal, as .01625 = 15%; but only when expressed in hundredths can it with strict propriety be considered a rate per cent. Thus, .12, .06, .15}, .054, are each a rate per cent.

510. To read per cent., call the first two places per cent., and the added places, if any, fractions of 1 per cent.; as, .2125 read as 21 and one-fourth per

cent. 511. To express per cent. as a common fraction, write the per cent. for a numerator and 100 for a denominator, and reduce; thus, 25% = = 1.

512. To change a common fraction to an equivalent per cent., apply the decimal explanation, Art. 245. Divide the numerator by the denominator, and give the quotient at least two decimal places.

513. Every rate per cent., being as many hundredths, requires at least two decimals places; hence, if the per cent. be less than 10, a cipher must be prefixed to the figure denoting it; thus, 2%=.02.

514. The Amount Per Cent. is 100 per cent. increased by the rate, or 1 plus the rate.

515. The Difference Per Cent, is 100 per cent. diminished by the rate, or 1 minus the rate.

REMARK.— Where the rate per cent. is the equivalent of a common fraction, use in solution whichever is most convenient.

516. The Percentage is the sum obtained by multiplying the base by the rate. 517. The Amount is the sum of the base and percentage.

518. The Difference is the remainder after deducting the percentage from the base.

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