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NOTE.-Work equivalent to that found on pp. 154, 164, 174, etc., of the Werner Arithmetic, Book II, should be done by the pupils before this chapter is attempted. If such work has not been done the teacher should present the subject orally in the order given on the pages named. Pupils must learn to think of quantity in metric units.
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.
1 decimeter (dm.).
1 meter (m ).
= 1 dekameter (Dm ).
1 myriameter (Mm.).
* The teacher must see that a meter stick is provided and that the pupils use it in measurement until they can think its multiples and its divisors without reference to other units of measurement.
+ 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'timoter. In the better pronunciation the accent is on the vowel preceding the letter m, that is, on the antepen ultimate syllable: thus, centimeter, 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
SQUARE MEASURE. 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. Hm.). 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
100 centars (ca.) = 1 ar (a.).
= 1 hektar (Ha.).
1. In a square decimeter there are
sq. cm. sq. dm. sq. dm.
sq. dm. sq. cm. sq. cm. 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 fill the blanks in the table of
VOLUME MEASURE. 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 (D1.), 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.
EXERCISE. 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. 11. One dekaliter equals cubic decimeters.
* 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 (cg.).
1 decigram (dg.).
1 gram (g.). 10 grams
1 dekagram (Dg.). 10 dekagrams = 1 hektogram (Hg.). 10 hektograms = 1 kilogram (Kg.).
Note.—The speciál 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
CC. 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 1, 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?
Metric System. 324. MISCELLANEOUS PROBLEMS. * 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 4 decimeter 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?
* Pupils should draw or image every magnitude whose dimensions are given on this page.