MEASURES OF VOLUME.

298. The principal unit of capacity or volume is a cubic meter (am).

299. The cubic meter can be divided into 10 layers, each a meter square and a deci

meter thick. Each layer will, therefore, be 0.1 of a cubic meter.

Again, each layer can be divided into 10 equal parts. Each part will, therefore, be 0.1 of the layer, or 0.01 of the meter, and will be a decimeter square and a meter long.

A

B

Also, each one of these parts can be divided into 10 equal parts, each of which will be a cubic decimeter, and will be 0.1 of 0.01, that is, 0.001 of the cubic meter.

The cubic meter, therefore, contains 1000 cubic decimeters. In like manner, each cubic decimeter can be divided into 1000 cubic centimeters, and each cubic centimeter into 1000 cubic millimeters.

A cubic millimeter (mm) = 0.000000001 of a cubic meter. A cubic centimeter (ccm) = 0.000001

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301. It will be seen that cubic centimeters are in the sixth and cubic millimeters are in the ninth decimal place from cubic meters.

302. In measuring wood, the cubic meter is called a ster (st); and in measuring liquids, grain, etc., the cubic decimeter is always called a liter.

When the liter is the unit, the numeral prefixes have the same value as in linear measure.

Ex. 167. (Oral.)

1. In a cubic meter, how many cubic decimeters? cubic centimeters?

2. What part of a cubic meter is a cubic decimeter? 3. What part of a cubic meter is a cubic centimeter? 4. What part of a cubic decimeter is a cubic centimeter? 5. How many liters in a hektoliter?

6. How many liters in a cubic meter?

7. How many cubic centimeters in a liter?

8. Express 7685.25' as cubic meters; as hektoliters.

9. If the water in the liter represented in the margin

Liter Cubic Decimeter.

stands 6em high, how many cubic centimeters of water are there in the measure? How many will be required to fill it? If the faucet be turned, and the water allowed to run out until the measure is only a quarter full, how

many cubic centimeters will run out? How many will still remain ?

Ex. 168.

1. How many cubic meters in a rectangular box 125cm long, 112cm wide, and 80cm deep? how many liters? 2. How many cubic meters of earth must be removed to dig a ditch 90m long, 85cm wide, and 50cm deep? 3. How deep must a cistern be to hold 6000', if the bottom is a square measuring 2.25m on a side? 4. How many hektoliters in a bin 4m long, 2m wide, and 1m high?

5. How high must a box be to hold 30', if it is 50cm long and 20cm wide?

UNITS OF WEIGHT.

303. The units of weight are the weights of units of pure water taken at its greatest density,

that is, a little above the freezing

point.

The principal unit is the gram,

which is the weight of a cubic centi- Cubic Centimeter. Gram Weight.

meter of water.

The numeral prefixes have the same value as in linear

measure.

304. A cubic centimeter of water weighs a gram. A liter of water weighs a kilogram.

A cubic meter of water weighs a ton (1000).

Ex. 169. (Oral.)

1. How many grams in a kilogram? dekagram? hektogram? 2. What part of a gram is a centigram? decigram? milligram? 3. In a ton, how many kilograms? grams?

4. A hektoliter of water weighs how many kilograms? what part of a ton?

5. What is the weight in grams of 5ccm of water?

6. Change 12,260mg into grams.

7. Give the weight in kilograms of 0.275cm of water.

8. Change 0.546kg to grams; to milligrams.

9. Change 0.563 of a ton to kilograms.

Ex. 170.

1. What is the weight of water required to fill a vat 98cm long, 71cm wide, and 38cm deep?

2. A mass of 21.7% is divided into 70 pills. What is the weight of each pill?

3. At 2 cts. a kilogram, what will 2.25 tons of hay cost? 4. At $6 a ton for coal, what will it cost to heat a building 30 days, if it takes 400** of coal a day?

SPECIFIC GRAVITY.

305. The specific gravity of any substance is the number found by dividing the weight of the substance by the weight of an equal bulk of water.

306. Therefore the specific gravity of a substance is the number that expresses the weight of a cubic centimeter of it in grams; or of a liter in kilograms; or of a cubic meter in

tons.

307. The volume of a body is found by dividing its weight by its specific gravity.

Ex. 171.

1. A bar of iron 50cm long, 4cm wide, 1cm thick has a specific gravity of 7.8. Find its weight in kilograms. 2. A piece of iron weighing 117 is made into a bar 6cm wide and 2em thick. What is its length, if the specific gravity of the iron is 7.8?

3. A cubical vessel, 40cm on an edge, is full of water. If 14' are drawn off, and replaced by a liquid of which the specific gravity is of that of water, what is the weight of the mixture?

4. What will be the weight in air, in water, and in olive oil, of which the specific gravity is 0.915, of a cube of iron 6em on an edge, if the specific gravity of the iron is 7.8?

cm

NOTE. A body weighed in a liquid weighs less than in air by the weight of the volume of the liquid which it displaces. 5. What is the specific gravity of a substance of which. 7.3ccm weighs 31.5%?

6. A block of granite 60cm long, 50cm wide, 15cm thick weighs 130.5. Find its specific gravity.

7. What is the weight of a load of 250 paving stones, 15cm square and 8cm thick, if the specific gravity of the stone is 2.90?

8. A stick of timber 8m long, 25cm wide, and 23cm thick is carried by 4 men. What weight does each carry, if

the specific gravity of the timber is 0.53 of that of water?

9. Allowing that water in freezing is increased by of its volume, find the volume and the weight of a block of ice 80cm long, 50cm wide, 20cm thick, and find how much water it will give on melting.

10. A hall has a capacity of 450cbm. Compute the weight of oxygen in the air that fills the hall, knowing that air contains 23% of its weight of oxygen, and weighs 773 as much as water.

11. A bottle empty weighs 650; full of oil, it weighs 1075%. What part of a liter will the bottle hold, if the specific gravity of the oil is 0.905?

12. A vessel full of water weighs 9.68%, and, full of oil, of which the specific gravity is 0.91, weighs 9.266*o. Find its capacity and its weight when empty.

NOTE. To find the capacity, divide the difference of the two weights by the difference of the weights of a liter of water and a liter of oil.

13. In a decimeter cube full of water is placed a chain of iron, of which the specific gravity is 7.8. When the chain is removed, the height of the water is just 5cm. Find the volume and weight of the chain.

14. If a body weighs 3.71kg in air, and 2.38** in water, what is its specific gravity?

15. From 106.25 of rhubarb are made 125 powders. What is the volume of water of which the weight is equal to the weight of a powder?