the circumference. the side of an equal square. = the side of an inscribed equi lateral triangle. = the side of an inscribed square the diameter. the side of an equal square. = the side of an inscribed equilateral triangle. = the side of an inscribed square. the radius. = the square of the radius. =the square of the diameter. } = the sq're of the circumference. SPHERES. Circumference × its diam. Radius x 12.5664. Diameter x 3.1416. Circumference2 × .3183. Surface its diameter. Radius x 4.1888. Diameters x .5236. Circumferences × .0169. Of surface x .5642. Of volume x 1.2407. Of surface x 1.77255. Of volume × 3.8978. √Of surface × .2821. Of volume x .6204. Radius x 1.1547. METRIC SYSTEM. The edges of this cube are each 1 Me'ter, or 10 Dec'i-me'ters, or 100 Cen'timelters, in length. 941. The Metric System of weights and measures is based upon the decimal notation, and is so called because its primary unit is the Me'ter. 942. The Me'ter (m.) is the base of the system, and is the one ten-millionth part of the distance on the earth's surface from the equator to either pole, or 39.37079 inches. Meter means measure; and the three principal units are units of length, capacity or volume, and weight. 943. The Multiple Units, or higher denominations, are named by prefixing to the name of the primary units the Greek numerals, Dek'a (10), Hek'to (100), Kilo (1000), and Myr'ia (10000). Thus, 1 dek'a-me'ter (Dm.) denotes 10 meters (m.); 1 hek'to-meʼter (Hm.), 100 meʼters; 1 kilo-me'ter (Km.), 1000 meters; and 1 myr'ia-me'ter (Mm.), 10000 meters. 944. The Sub-multiple Units, or lower denominations, are named by prefixing to the names of the primary units the Latin ordinals, Dec'i (†), Cen'ti (1ʊ), Mil'li (1000). Thus, 1 dec'i-meʼter (dm.) denotes, or .1 of a me'ter; 1 cen'ti-me/ter (cm.), da, or .01 of a meʼter; 1 milli-meʼter (mm.), rooo, or .001 of a me/ter. 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. 945. 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, The number is read, 67015.638 meters. It may be expressed in other 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, 670.15638Hm.; 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 me'ters, and read it in the several orders; read it in kil'o-me'ters; in hek'to-me'ters; in dek'a-me'ters; in dec'ime'ters; in cen'ti-me'ters. The names mill, cent, dime, used in United States Money, correspond to mil'li, cent'i, dec'i, in the Metric System. Hence the eagle might be called the dek'a-dollar, since it is 10 dollars; the dime, a dec'i-dollar, since it is of a dollar, etc. MEASURES OF LENGTH. 946. The Me'ter is the unit of length, and is equal to 39.37 in. or, 1.0936 yd. +. Metric Denominations. 10 Mil'li-me'ters, mm. = 1 Cen'ti-me'ter= .3937 in. = 1 Dec'i-me'ter = 3.937 in. = 39.37 in. m. = 1 Dek'a-me'ter 32.899 ft. 10 Cen'ti-me'ters, cm. 10 ME'TERS, = Units of long measure 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 Me'ter is used in measuring cloths and short distances. 2. The Kil'o-me'ter is commonly used for measuring long distances, and is about g of a common mile. 3. The Cent'i-me'ter and Mil'li-me'ter are used by mechanics and others for minute lengths. 4. In business, Dec'i-me'ters are usually expressed in Cent'ime'ters. 5. The Dek'a-me'ter, Hek'to-me'ter, and Myr'ia-me'ter are seldom used, but their values are expressed as Kil'o-me'ters. EXERCISES. Read the following: Four Inches. 1] 31 One Deci-meter = 10 Centi-meters = 100 Milli-meters = 3.973 inches. 2 9 10 |