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Note.—The teacher should present this subject orally before attempting the pages that follow. It will be well if this oral work can be commenced many weeks before this page is reached in the regular work of the class. A meter stick, a liter measure, and metric weights should be provided and each pupil should weigh and measure until he can easily think quantity in the units of this system without reference to the units of any other system.
319. All units in the metric system of measures and weights are derived from the primary unit known as the meter.
When the length of the primary unit of this system was determined it was supposed to be one ten-millionth of the distance from the equator to the pole. A pendulum that vibrates seconds is nearly one meter long.
In the names of the derived units of this system the prefix deka means 10; hekto means 100; kilo means 1000; myria means 10000; deci means tenth; centi means hundredth; milli means thousandth.
320. Linear Measure.
10 millimeters (mm.) = 1 centimeter (cm.).*
10 centimeters = 1 decimeter (dm.).
10 decimeters = 1 meter (m.).
10 meters = 1 dekameter (Dm.).
10 dekameters = 1 hektometer (Hm.).
10 hektometers = 1 kilometer (Km.).
10 kilometers = 1 myriameter (Mm.).
* In the common pronunciation of these words the primary accent Is on the first syllable and a secondary accent on the penultimate syllable; thus, cen'timfiter. In the better pronunciation the accent is on the vowel preceding the letter m, that is, on the antepenultimate syllable; thus, centim'eter, dekam'eter, etc.
321. The names of the units of surface measurement are the same as those used for linear measurement, combined with the word square; thus, a surface equivalent to a square whose side is a meter is 1 square meter.
The pupil, if properly taught to this point, will be able, without difficulty, to fill the blanks in the table of—
100 square millimeters (sq. mm.) = 1 square centimeter (sq. cm.).
square centimeters = 1 square decimeter (sq dm.).
square decimeters — 1 square meter (sq. m.).
square meters = 1 square dekameter (sq. Dm.).
square dekameters = 1 square hektometer (sq. Hra.).
square hektometers = 1 square kilometer (sq. Km.).
square kilometers = 1 square myriameter (sq. Mm.).
Note.—The special unit of surface measure for measuring land is equivalent to a square whose side is ten meters. This unit is called an ar.
100 centars (ca.) = 1 ar (a.).
100 ars = 1 hektar (Ha.).
1. In a square decimeter there are sq. cm.
2. In 2 square decimeters there are sq. cm.
3. In a 2-decimeter square there are sq. cm.
4. In a square meter there are sq. dm.
5. In 2 square meters there are sq. dm.
6. In a 2-meter square there are sq. dm.
7. In a square meter there are sq. cm.
8. In 2 square meters there are sq. cm.
9. In a 2-meter square there are sq. cm.
322. The names of the units of volume measurement are the same as those used for linear measurement, combined with the word cubic; thus, a volume equivalent to a cube whose edge is a meter is 1 cubic meter.
The pupil should be able easily to All the blanks in the table of—
1000 cubic millimeters (cu. mm.) = 1 cubic centimeter (cu. cm.).*
cubic centimeters = 1 cubic decimeter (cu. dm.).
cubic decimeters = 1 cubic meter (cu. m.).
cubic meters = 1 cubic dekameter (cu. Dm.).
cubic dekameters = 1 cubic hektometer (cu. Hm.).
Note 1.—The special unit of capacity for measuring liquids, grain, small fruits, etc., is the liter. It is equal to 1 cubic decimeter. 10 liters (1.) = 1 dekaliter (Dl.), and 1 tenth of a liter = 1 deciliter (dl.), etc.
Note 2.—The special unit for measuring wood is the ster. It is equal to 1 cubic meter.
1. A cubic meter equals liters.
2. A cubic meter equals . cubic decimeters.
3. A cubic meter equals cubic centimeters.
4. A cubic decimeter equals cubic centimeters.
5. Two cubic decimeters equal . cubic centimeters.
6. A 2-decimeter cube equals cubic centimeters.
7. A 5-centimeter square equals square centimeters.
8. A 5-centimeter cube equals cubic centimeters.
9. One tenth of a liter equals cubic centimeters.
10. One deciliter equals cubic centimeters.
* The abbreviation cc. is often used for cubic centimeter.
323. The primary unit of weight is the gram. This equals the weight of one cubic centimeter of pure water.
10 milligrams (mg.) = 1 centigram (eg.).
10 decigrams = 1 gram (g.).
10 grams = 1 dekagram (Dg.).
10 dekagrams = 1 hektogram (Hg.).
10 hektograms = 1 kilogram (Kg.).
Note.—The special unit for the weight of very heavy articles is the tonneau. It equals the weight of a cubic meter of pure water, or 1000 kilograms.
1. The weight of 1 liter of water is grams.
2. The weight of 6 cubic centimeters of water is .
3. The weight of a cubic decimeter of water is .
4. One kilogram of water equals cubic centimeters.
5. One hektogram of water equals cc.
6. One dekagram of water equals . cubic centimeters.
7. If the specific gravity of iron is 7.5, what is the weight of a cubic centimeter of iron?
8. If the specific gravity of cork is -^, what is the weight of a cubic decimeter of cork?
9. If the specific gravity of oil is .9, what is the weight of a liter of oil?
10. What is the weight of a cubic meter of stone whose specific gravity is 2.5?
11. What is the weight of a cubic decimeter of wood whose specific gravity is .8?
1. Find the area of a rectangular surface that is 1 meter long and 6 decimeters wide. Make a diagram of this surface upon the blackboard.
2. Find the area of a rectangular surface that is 2 decimeters long and 5 centimeters wide. Make a diagram of this surface on your slate or paper.
3. Find the solid content of a 5-centimeter cube. A 5centimeter cube is what part of a cubic decimeter?
4. Find the solid content of a 4-decimeter cube. A 4decimeter cube is what part of a cubic meter?
5. Find the entire surface of a 4-centimeter cube. The surface of a 4 centimeter cube is what part of a square decimeter?
6. Find the area of a rectangular surface that is 2.4 yards by 5 yards; of a rectangular surface that is 2.4 meters by 5 meters.
7. Which is the larger of the two surfaces described in problem 6?
8. Find the area of a rectangular surface that is 3.5 yards by 2.5 yards; of a rectangular surface that is 3.5 meters by 2.5 meters.
9. Find the volume of a rectangular solid that is 3.4 feet by 3 feet by 2 feet; of a rectangular solid that is 3.4 meters by 3 meters by 2 meters.
10. Find the volume of a rectangular solid that is 3.5 meters by 2.3 meters by 4.6 meters.
11. What is the weight of a cubic decimeter of wood whose specific gravity is .5?