2. What is the volume of a cask whose length is 40 in., the diameters 21 and 30 in. respectively? 3. How many gallons in a cask of slight curvature, 3 ft. 6 in. long, the head diameter being 26 in., the bung diam. 31 in.? METRIC SYSTEM. 488. The metric system of weights and measures is based upon the decimal notation. 489. The meter is the base of the system, and is one tenmillionth part of the distance on the earth's surface from the equator to the north pole, and is equal to 39.37079 inches. 490. The metric system has three standard units; viz., the me'ter (mee'ter) or unit of length, the li'ter (lee'ter), 01 unit of capacity or volume, and the gram, or unit of weight. The ar and ster are the units of square and cubic measures Each of these units has its multiples and sub-multiples. 491. The multiple units, or higher denominations. are formed by prefixing to the standard unit the Greek numerals, děk'a (10), hěk'to (100), kilo (1000), mýr'ia (10000). 492. The sub-multiple units, or lower denominations, are formed by prefixing to the standard unit the Latin ordinals, děc'i (5), cent'i (100), mil'li (1000). Hence, it is apparent from the name of a unit, whether it is greater or less than the standard unit, and also how many times. Thus, 1 deka-meter (Dm.) denotes 10 meters; 1 hekto-meter (Hm.), 100 meters; 1 kilo-meter (Km.), 1000 meters; and 1 myria-meter (Mm.)* 10000 meters. Also, 1 deci-meter (dm.) denotes (1) of a meter; 1 centimeter (cm.), Too (.01) of a meter; 1 millimeter (mm.), Tobo (.001) of a meter. 494. The metric system being based upon the decimal scale, the denominations correspond to the orders of the Arabic notation, and hence are written like United States money, the lowest denomination at the right. Thus, m. The number is read, 67015.638 me'ters. It may be expressed in different denominations by placing the decimal point at the right of the required denomination, and writing the name or abbreviation after the figures. Thus, the above may be read, 670.15638 Hm.; or 67.015638 Km.; or 670156.38 dm.; or 6701563.8 cm.; or it may be read, 6 Mm. 7 Km. 0 Hm. 1 Dm. 5 m. 6 dm. 3 cm. 8 mm. Write 3672.045 meters, and read it in the several orders read it in kilometers; in hektometers; in dekameters; ín decimeters; in centimeters. The names mill, cent, and dime, used in U. S. money, correspond to milli, centi, and deci in the metric system. Hence, the eagle might be called a deka-dollar, since it is 10 dollars; the dime, a deci-dollar, since it is of a dollar, etc. MEASURES OF LENGTH. 495. The me'ter is the unit of length, and is equal to 39.37 in., or 1.0936 yd. +. 4 in. 1 dm. 3) One Deci-meter = 10 Centi-meters = 100 Milli-meters = 3.973 inches. 21 41 19 Four Inches. 10 Hěk'to-me'ters 10 Ki'lo-me' ters Units of length form a scale of tens; hence, in writing numbers expressing length, one decimal place must be allowed for each denomination. Thus, 9652 mm. may be written 965.2 cm., or 96.52 dm., or 9.652 m., or .9652 Dm. 1. The meter is used in measuring cloths and short distances. 2. The kilo-meter is commonly used for measuring long distances, and is about g of a common mile. 3. The cen'ti-meter and milli-me'ter are used by mechanics and others for minute lengths. 4. In business, dec'i me'ters are usually expressed in cen'ti me'ters. 5. The děka-mēter, hěkto-meter, and myr'ia-mè'ter are seldom used, but their values are expressed as kilo-mē'ters. Write the following, expressing each in three denominations: 2. 24379 dm.; 15032036 cm.; 2475064 mm.; 30471 Dm. 3. 6704 Hm.; 85 Km.; 120000 m.; 780109 cm. ; 75 m. MEASURES OF SURFACES AND SOLIDS. 496. The square meter is the unit of ordinary surface measures, and is 1.196 sq. yd., or 10.764 sq. ft. 1 sq. cm, exact size. .00155 sq. in 1 Sq. Mil'li-me'ter. sq. mm. 100 Sq. Mil'li-me'ters = 1 Sq. Cen'ti-me'ter. sq. cm. 100 Sq. Cěn'ti-me'ters = 1 Sq. Děc'i-mē'ter. 100 Sq. Děc'i-me' ters = 1 Sq. Me'ter. .155 sq. in. sq. dm. 15.5 sq. in. sq. m. 1.196 sq. yd. 497. The ar is the unit of land measures, and is a square whose side is 10 meters, and contains 100 sq. meters. 1. The meter is used in measuring cloths and short distances. 2. The kilo-meter, equal to § of a mile, nearly, is used for measuring long distances. 3. The dec'i-är is of an är; the děk är is 10 a.; an acre is 40 ärs, nearly. 498. The cubic meter is the unit of ordinary solid measures. 1 cu. cm., exact size. 1 Cu. Mil'li-mē'ter. cu. mm. .000061 cu. in. 1000 Cu. Milli-me'ters = 1 Cu. Cen'ti-me'ter. cu. cm. 1000 Cu. Cěn'ti-me'ters 1 Cu. Děc'i-me'ter. cu dm. .061 cu. in. .0353 cu. ft. 35.3166 cu. ft. 499. The ster is the unit of wood or stone measures, and is a cubic meter, equal to 35.3166 cu. ft., or .2759 cord. 1. The square and cubic measures are only the squares and cubes of the measures of length. 2. The cubic deci-meter is called a -ter when used as a unit of liquid or of dry measures. MEASURES OF CAPACITY. 500. The li'ter is the unit of capacity, both of liquid and of dry measures, and is equal in volume to 1 cu. dec'i-me'ter, equal to 1.0567 qt. liquid measure, or .908 qt. dry meas. 1 DRY ml. LIQUID Dry M. Liquid M. 1 Děk'a-li'ter. .845 gi. 1.0567 qt. 2.64175 gal. 264.175 " 10 Kil'o-li'ters = 1 Mỹr'ia-lï'ter. MI. 283.72 bu. 2641.75" 1. The liter is used in measuring liquids in moderate quantities. 2. The hek'to-liter is used for measuring grain, fruit, roots, etc., in large quantities, also wine in casks. MEASURES OF WEIGHT. 501. The gram is the unit of weight, and is equal to the weight of a cu. cen'ti-me'ter of distilled water. A gram is equal to 15.432 gr. Troy, or .03527 oz. Avoir. |