THE METRIC SYSTEM. 372. THE METRIC SYSTEM of Weights and Measures is based upon the decimal system of notation. It was authorized to be used in the United States, and its use introduced into some departments of public service, in 1866, by an Act of Congress. 373. The Principal Units, or those from which the others are derived, are: The METER, which was intended to be, and is nearly, one ten-millionth of the distance on the earth's surface from the equator to the pole. The SQUARE METER, which is the square whose side is one meter; and the ARE (pronounced air), which is the square whose side is ten meters. The Cubic METER, or STERE (pronounced stair), which is the cube whose edge is one meter ; and the LITER (pronounced leeter), which is one thousandth of a cubic meter. The Gram, which is the weight, in vacụum, of a cubic centimeter of distilled water, at the greatest density. 374. The HIGHER DENOMINATIONS are expressed by prefixing to the name of the principal unit, DEKA, 10; HECTO, 100; Kilo, 1000; MYRIA, 10,000; and the LOWER DENOMINATIONS by prefixing DECI, 10th ; CENTI, 100th ; Milli, 1000th 375. MEASURES OF LENGTH. 10 millimeters (mm.) - 1 centimeter, cm., .3937 inch. 10 centimeters, 1 dec'imeter, dcm., 3.937 inches. 10 decimeters, 1 METER, me., 39.37 inches. 10 meters, 1 dek'ameter, dkm., 393.7 inches. 10 dekameters, 1 hectometer, hm., 328 ft. 1 in. 10 hectometers, 1 kilometer, km., 3280 ft. 10 in. 10 kilometers, 1 myrliameter, mym., 6.2137 miles. 1 ARE, 100 ares, NOTE 1. The meter is used as the unit of measure in measuring cloth, and common lengths and distances, and the kilometer in measuring long distances, as the length of roads and rivers, distances between cities, etc. NOTE 2. A meter is very nearly 3 feet, 3 inches, and 3 eighths of an inch in length; and a kilometer is about 200 rods, or of a mile. 376. MEASURES OF SURFACE. 100 sq. millimeters (mm2.)=1 sq. centimeter, cm'.,=.00155 sq. in. 100 sq. centimeters, 1 sq. decimeter, dem?., .1076 sq. ft. 100 sq. decimeters, 1 SQ. METER, m., 1.196 sq. yd. Also, 100 cen'tiares (ca.), or sq. me., ar., 119.6 sq. yd. 1 hectare, ha., 2.471 acres. Note 1. The square meter is used in general in measuring surfaces. The are is the principal unit in measuring land; and the hectare is also taken as a unit of the same kind of measurement. NOTE 2. A square meter is about 11 square yards, and an are nearly 4 square rods. 377. MEASURES OF VOLUME. 1000 cu. millimeters, (mm.), 1 cu. centimeter, cmo., .061 cu. in. 1000 cu. centimeters, 1 cu. decimeter, dcm., 61.022 cu. in. 1000 cu. decimeters, 1 cu. METER, mo., 1.308 cu. yd. Also, 10 dec'isteres (dcs.) =1 STERE, or cu. meter, st.,=1.308 cu. yd. 10 steres, 1 dēklastere, dks., 13.08 cu. yd. And 10 milliliters (ml.) 1 centiliter, cl., It., .338 fluid oz. .845 liq. gill. 1.0567 liq. qt. 2.6417 liq. gal. 2 bu. 3.35 pk. 1.308 cu. yd. NOTE 1. The cubic meter is used in general in measuring volume, and the stere in estimating wood. NOTE 2. The liter is used in measuring liquids; it is about 117 liquid quarts, or of a dry quart; 1000 liters are equal to 1 cubic meter. 10 grams, Note 3. The hectoliter, or for brevity hecto, is generally taken as the unit in measuring dry articles, such as grains, salt, etc., and is about 2 bushels, or of a barrel. 378. WEIGHTS. 10 milligrams (mg.)=1 cen'tigram, cg., = .1543 grains. 10 centigrams, 1 dec'igram, dcg., 1.543 grains. 10 decigrams, 1 GRAM, gm., 15.432 grains. 1 dek'agram, dkg., .3527 av. oz. 10 dekagrams, 1 hec'togram, hg., 3.5274 av. oz. 10 hectograms, 1 kilogram, k., 2.2046 av. lb. 10 kilograms, 1 myr'iagram, myg., 22.046 av. lb. 10 myriagrams, 1 quin'tal, 9., 220.46 av. Ib. 10 quintals, 1 tonneau, t., 2204.6 av. Ib. Note 1. The gram is the unit in weighing gold, silver, and jewels, in mixing medicines, determining postage, etc.; the kilogram, or, for brevity, kilo, is the ordinary weight of commerce; and the tonneau, or metric ton, is used in weighing coal, hay, and all very heavy articles. NOTE 2. A kilo is about 24 avoirdupois pounds, or 2.68 Troy pounds ; and a metric ton a little more than 2200 avoirdupois pounds. 379. Equivalents of denominations of common weights and measures in metric denominations are exhibited in the following COMPARATIVE TABLE. An inch 2.54 centimeters. A gallon 3.786 liters. A foot =30.48 centimeters. A bushel .3524 hectoliter. A mile =1.6094 kilometers. A cu. inch = .01639 liter. A sq. inch=.0006452 sq. meter. A cu. yard = .7646 stere. A sq. foot=.0929 sq. meter. A cord 3.625 stere. A Troy lb. .373 kilo. mile=259 hectares. A com. ton =.9071 tonneau. The numbers in the tables are determined approximately, but are sufficiently exact for all ordinary purposes. 380. In expressing Metric Weights and Measures the decimal point, as in United States money, is placed between the unit, and its subdivisions decimally written. One, two, or three orders of figures are required to express A grain = .0648 gram. each metric denomination, lower than the unit, according as the scale is 10, 100, or 1000. Thus, We write according to the unit and scale, 6 kilometers, 3 dekameters, 5 meters, 7 decimeters, and 2 centimeters, as 6.03572 kilometers, or 6035.72 meters. 16 hectares, 35 ares, and 25 centiares, as 16.3525 hectares, or 1635.25 ares. 41 cubic meters, 5 cubic centimeters, and 428 cubic millimeters, as 41.000005428 cubic meters. 381. The metric system is made very simple of application by the practice of using in general but a few of its denominations. Thus, Of LENGTHS, the meter, or kilometer; of SURFACES, the square meter, are, or hectare; of voLUME, the cubic meter or stere, the liter, or hectoliter ; and of weights, the gram, kilo, or metric ton. 382. In a metric expression, a decimal part, if any, may be either read as a decimal of the unit; or, which is better, as a number of the lowest metric denomination denoted. Thus, 15.75 meters may be read as fifteen meters and seventy-five centimeters. 25.0035 hectares, as twenty-five hectares and thirty-five centiares. EXERCISES. 1. Copy and read 45.63 meters. This mixed number may be read forty-five and sixty-three hundredths meters, or forty-five meters and sixty-three centimeters. Write and read, 2. 136.5 st. 6. 120.05 ha. 3. 170.301 km. 7. 31.55 hl. 4. 61.58 lt. 8. 561.038 k. 5. 3.6054 m2 9. 15.47894 m. 10. Write in figures eight meters, four centimeters. Regarding a meter the unit, we write 8, which will denote the number of meters, as the integral part of a decimal expression, and place the decimal point. Then, as there are no decimeters, we write 0 in the place of decimeters, and 4, which will denote the number of centimeters, in the place of centimeters, and have as the required expres sion, 8.04 me. Write in figures, 11. Twenty-four meters and three centimeters. Ans. 24.03 me. 12. Sixteen meters and twenty-one millimeters. 13. As hectares, thirty-five hectares, four ares, and fourteen centiares. Ans. 35.0414 ha. 14. Fifteen ares and seventy-five centiares. 15. Forty-five square meters, three square decimeters, and forty-one square centimeters. Ans. 45.0341 m2. 16. One hundred square meters and fifty-six square millimeters. Ans. 100.000056 m2. 17. Three cubic meters and sixty-two cubic centimeters. Ans. 3.000062 m. 18. Sixty-three liters, four deciliters, and five centiliters. Ans. 63.45 lt. 19. Five steres and seven decisteres. Ans. 5.7 st. 20. Two hundred twenty-five kilos and seventy-two grams. Ans. 225.075 k. 21. As tonneaux, three tonneaux, seven quintals, and five kilos. Ans. 3.705 t. 22. Reduce 9.607 kilometers to meters. Since in 1 kilometer there are 1000 meters, in 9.607 kilometers there must be 9.607 times 1000 meters, or 9607 meters. 23. In 568 ares, how hectares ? Since there is 1 hectare in 100 ares, there are as many hectares in 568 ares as 100 ares are contained times in 568 ares, or 5.68 hectares. 24. Reduce 15.045 m2. to square centimeters. Ans. 150450 cm?. 25. In 185.67 liters, how many hectoliters ? Ans. 1.8567 It. 26. In 43.61 kilograms, how many grams ? Ans. 43610 gm. 27. In 1064.000 cm3, how many cubic meters ? Ans. 1.064 m. 28. In 3.05 ms, how many cubic millimeters ? Ans. 3050000000 mm. 29. Add 31.04 meters, 67.05 meters, and 11.05 meters. Ans. 109.14 me. 30. Find the sum of 416.54 kilos, 312.065 kilos, and 100.5 kilos. Ans. 829.105 k. |