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NOTE.-The higher denominations are not generally used.

I indicate

the cubic measures with an exponent, instead of writing cu. before the denominations.

MENTAL EXERCISES.

1. How many centisteres in a stere?
2. How many decisteres in a decastere?
3. How many decasteres in a kilostere?
4. How many cubic meters in a hectostere?

MEASURES OF CAPACITY.

795. The Liter is the unit of capacity. It equals a cubic decimeter; that is, a cubic vessel whose size is onetenth of a meter.

796. This measure is used for measuring liquids and dry substances. The liter is a cylinder, and holds 2.1135 pints wine measure, or 1.816 pints dry measure.

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NOTES.-1. The liter is principally used in measuring liquids, and the hectoliter in measuring grains, etc.

2. The liter equals nearly 1 liquid quarts, or of a dry quart, or nearly of a bushel measure.

3. The hectoliter is about 28 bushels, or of a barrel. 4 liters are a little more than a gallon; 35 liters, very nearly a bushel.

MENTAL EXERCISES.

1. How many liters in a hectoliter?
2. How many liters in a kiloliter?
3. How many deciliters in a decaliter?
4. How many liters in a cubic meter?
5. How many liters in a stere?

MEASURES OF WEIGHT.

Ans. 1000.

Ans. 1000.

797. The Gram is the unit of weight. It is the weight of a cubic centimeter of distilled water at the temperature of melting ice. The gram equals 15.432 Troy grains.

TABLE.

10 milligrams (mg.) equal 1 centigram, eg.

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NOTES.-1. The gram is used in weighing letters, and mixing and compounding medicines, and in weighing all very light articles. The new 5-cent coin (dated 1866) weighs 5 grams.

2. The kilogram is the ordinary unit of weight, and is generally abbreviated into kilo. It equals about 2 pounds avoirdupois. Meat, sugar, etc., are bought and sold by the kilogram.

3. In weighing heavy articles, two other weights, the quintal (100 kilograms) and the tonneau (1000 kilograms), are used. The tonneau is between our short ton and long ton.

4. The avoirdupois ounce is about 28 grams; the pound is a little less than a kilo.

MENTAL EXERCISES.

1. How many grams is a kilogram?
2. How many milligrams in a gram?
3. How many decigrams in a kilogram?
4. How many hectograms in a myriagram?

MEASURES OF VALUE.

798. The Franc is the French money unit.

It equals

$0.193. The principal gold coin is the 20-franc piece; the principal silver coins are the franc and the 3-franc piece.

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NOTE. It has been suggested that the American dollar and the English pound be so modified that we shall have the following money table : 5 francs = 1 dollar.

5 dollars 1 pound.

The franc equals about 19.3 cents of our present money.

NUMERATION AND NOTATION.

799. In the Metric System the decimal point is placed between the unit and its divisions, the whole quantity being regarded as an integer and a decimal. Thus, 3 decagrams, 5 grams, 6 decigrams, 8 centigrams, are written 35.68 grams.

800. The initials of the denomination may be placed either before or after the quantity, though they are most frequently placed after it; thus, 27 grams may be written 627, or 276.

EXERCISES IN NUMERATION.

1. Read 48.05M.

SOLUTION.-This is read 48 and 5 hundredths meters; or it may be read 4 decameters, 8 meters and 5 centimeters.

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EXERCISES IN NOTATION.

1. Write 6 meters and 5 centimeters. SOLUTION. We write the 6 meters with a decimal point to the right, and then, since there are no deci meters, we write a naught in the tenths place, and then write the 5 centimeters in the place of centimeters.

OPERATION.

6.05M

2. Write 17 meters, 4 decimeters, 8 centimeters.
3. Write 7 decameters, 2 decimeters, 5 centimeters.
4. Write 15 ares, 9 deciares, 8 milliares.

5. Write 4 hectares, 8 ares, 5 centiares.

6. Write 12 decasteres, 6 decisteres, 8 centisteres.

7. Write 9 kilosteres, 7 decasteres, 5 centisteres.

8. Write 3 hectoliters, 8 liters, 7 deciliters.

9. Write 16 grams, 4 decigrams, 8 centigrams.

10. Write 8 myriagrams, 7 hectograms, 6 centigrams, and 5 milligrams.

REDUCTION OF THE METRIC SYSTEM ·
TO THE COMMON SYSTEM.

MEASURES OF VALUE.

1. How many dollars in 25 francs?
2. How many dollars in 47.50 francs?

3. How many francs in $15.50?

4. How many francs in $37.75?

Ans. $4.825.

Ans. $9.164. Ans. 80.31 fr.

Ans. 195.595 fr.

MEASURES OF WEIGHT.

5. How many grains in 12 grams? 6. Pounds Troy, in 480.5 grams?

Ans. 185.184 gr.

Ans. 1 lb. 3 oz. 8 pwt. 23% gr.

7. Pounds Av., in 976.25 grams?

Ans. 2 lb. 2 oz. 190.49 gr.

8. Grams in 480 grains? 9. Grams in 12 Troy pounds? 10. Grams in 12 Av. pounds?

MEASURES OF LENGTH.

11. How many feet in 24.5 meters?

12. Yards in 136.54 meters?

13. Meters in 120 yards?

14. Meters in 2 mi. 120 rd. ?

16. Meters in 3 mi. 272 rd.?

Ans. 31.104G.

Ans. 4479.0046.
Ans. 5443.2346.

Ans. 80.38 ft.

Ans. 149.3216 yd.

Ans. 109.73M.

Ans. 3822.199M.

15. Miles in 4000 meters? Ans. 2 mi. 155 rd. 5 ft. 10 in.

Ans. 6195.9867M.

MEASURES OF SURFACE.

17. How many ares in 360 sq. yd.?
18. Sq. yd. in 142.5 ares?
19. Acres in 505.6 ares?

Ans. 3.01A. Ans. 17043 sq. yd.

Ans. 12 A. 78.1312 P.

20. How many ares in 30 acres?
21. How many ares in 5 A. 104 P.?

Ans. 1214.574A.

MEASURES OF VOLUME.

Ans. 228.744A.

22. How many cu. ft. in 46 steres? Ans. 1624.5636 cu. ft.

23. Cu. ft. in 214.78 steres ?

Ans. 7585.2993 cu. ft.

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MISCELLANEOUS PROBLEMS.

1. If a letter weighs 2.5 grams, how many such letters will it take to weigh a kilogram? Ans. 400.

2. A lady bought 11.5 meters of silk for a dress, at the rate of $4.75 a meter; what did it cost her? Ans. $54.625. 3. My butcher's bill one month was 87.5 kilograms of beef, at 18 cents a kilo; what was the bill? Ans. $16.40§. 4. How much must I pay for 56.25 liters of coal oil, at the rate of 18 cents a liter? Ans. $10.546 +.

5. A kilogram weighs 2.2046 lb.; what is the weight of 56 tonneaux? Ans. 124559.9 lb.

6. A bought 2500 ares of land, at $4.50 an are, and sold it for $525 a hectare; what was the gain? Ans. $1875. 7. If 15 steres of wood cost $22.50, what must I pay for 24.5 steres at the same rate? Ans. $36.75. 8. If a kilogram of sugar is worth 21 cents, how many kilos can I buy for $100?

Ans. 459.77 +. 9. The height of a pole is 68.325M; how long would it take a worm to climb to its top, at the rate of 15 meters a day?

Ans. 4.555 days.

how many kilome

Ans. 112.

10. A kilometer is about of a mile; ters from Lancaster to Philadelphia, 70 miles? 11. How much must I pay for 23 meters of silk, at 8 francs 25 centimes a meter? Ans. 195.94- fr. 12. What cost 3 kilares, 7 hectares, 6 deciares of land, at $275.25 a hectare? Ans. $10185.90. 13. It is about 100 miles from Philadelphia to New York; how many kilometers is it?

Ans. 160.

14. How much will it cost to excavate 12 cubic meters Ans. $476.80.

of earth, at $37.25 a cubic meter?

15. What is the width of the Atlantic in kilometers, the width being about 3000 miles? Ans. 4800 kilometers. 16. What must I pay for 25 steres, 2 decisteres, and 5 centisteres of wood, at the rate of $2.65 a stere? Ans. $66.914. 17. How long will it take a man to walk from Philadelphia o New York, at 8 kilometers an hour? Ans. 20 hours.

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