CHAPTER IX. * MEASURES. 175. Continuous quantities (such as length, surface, bulk, value, heat) cannot be counted; they are measured. 176. To measure a quantity is to find how many times it contains a known quantity of the same kind, called the unit of measure. 177. The unit of measure for lengths is a meter; and from this are derived the units of surface, volume, and weight. The meter was intended to be one ten-millionth of the distance from the equator to the north pole, but more careful measurements of meridians show that this distance is 10,001,887 meters. 178. The standard meter, as defined by law, is the length of a bar of very hard metal, carefully preserved at Paris, accurate copies of which are furnished to the governments of all civilized countries. 179. The principal units of measure are: The meter (m) for lengths; The square meter (m) for surfaces; The cubic meter (cbm) for large volumes; The liter () (leé-ter) for smaller volumes; Chapters IX. and XIV. may be taken or omitted, at the option of the teacher. 180. All these units are divided and multiplied decimally, and the size of the measures thus produced is shown by one of seven prefixes; namely, deka, meaning 10; hekto, meaning 100; kilo, meaning 1000; myria, meaning 10,000; and deci, meaning 0.1; centi, meaning 0.01; milli, meaning 0.001.* But, as in United States money we seldom speak of anything else than dollars and cents, so in other measures it is only those printed in black letter in this chapter that are in common use. MONEY. 181. The unit of commercial values is the dollar. It is compared with the gram of gold by laws fixing the weight of gold which shall constitute a dollar; but these laws are changed from time to time. Coins are also made of silver, nickel, and bronze. Cents are made of bronze; half-dimes of nickel; dimes, quarter-dollars, half-dollars, and dollars, of silver; quartereagles, half-eagles, eagles, and double eagles, of gold. But the eagle is usually called ten dollars, and the dime ten cents. That is to say, $137.875 is read 137 dollars 87 and a half cents, and not 13 eagles 7 dollars 8 dimes 7 cents 5 mills. *All the compound names are accented on the first syllable, thus: mil'limeter. A kilometer (km) = 184. A length given in any one of these measures may be expressed in terms of another measure by simply moving the decimal point to the right or left. Thus, 17,856,342mm may be written as kilo-meters by observing that milli-meters are changed to meters by moving the point three places to the left; and these meters into kilo-meters by carrying it three places further, making, in all, six places. Therefore, 17,856,342mm 17.856342km Again, 4.876326km may be written as centimeters, by observing that kilo-meters are changed to meters by moving the point three places to the right, and meters to centi-meters by moving it two places further, making, in all, five places. Therefore, 4.876326km 487,632.6cm. = 185. The rule, therefore, for this conversion is: First change the point so as to convert the given measures into terms of the principal unit; then change the point so as to convert the principal into the required units. 186. Remember that, before adding or subtracting, the quantities must be written in the same units of measure. 1. Convert 5427m into kilometers; into millimeters; into centimeters. 2. 6853mm contain how many meters? how many centime ters? what part of a kilometer? 3. Write 49.7m as centimeters; as millimeters; as part of a kilometer. 4. How many centimeters in 12.4km? how many millimeters? 5. Change 1230 meters into kilometers; into centimeters. 6. Write 1230cm as meters; as millimeters. Find the value of each of the following expressions in meters: 7. 0.435m+852cm +4263mm+0.1595km. 8. 0.927km 6495cm 4.37cm 42.87mm 9. 8×0.0457km; 3.04 × 60.93cm; 5.43 x 67.2mm 10. 38,019mm 0.097; 0.41km ÷ 25.625. 11. At $1.87 the meter what is the cost of 6.20m of cloth? 12. At $0.75 the meter what is the cost of 60m of cloth? 13. From a piece of cloth containing 47.60m a tailor cuts off three pieces: the first of 3.80m, the second of 1.30m, and the third of 45cm. How much of the cloth is left? 14. What is the value of 60cm of cloth, worth $5.20 a meter? 15. If $6.00 are paid for a railroad ticket to travel 440km, what is the fare per kilometer? 16. If a train run 288km in 9 hours, how many meters does it run in a minute? 17. If a man walk at the rate of 6km an hour, what part of an hour will it take to walk 420 meters? 18. A railroad carried 412 passengers 18 kilometers, and received $88.992; at the same rate, what will it receive for carrying 350 passengers 35 kilometers? Square Centimeter. MEASURES OF SURFACE. 187. The unit of surface is a square, each side of which is a linear unit. The principal unit of surface is, therefore, a square meter (m). 188. But in square measure, the multiplication and division of units is by hundreds and hundredths, instead of by tens and tenths. Suppose the square in the margin to represent a square meter. It is divided into ten equal horizontal bands, and each band is one-tenth of the square meter. Each band can be divided, as the upper one is, into ten little squares measuring one-tenth of a meter on a side. Each of these squares will be 0.1 of the band, or 0.01 of the whole square. square meter, therefore, contains 10 × 10 or 100 square deci meters. The If the square meter were divided into 100 equal horizontal bands, each band would be 0.01 of the square; and if each of the 100 bands were divided into 100 squares, that is, into 100 square centimeters, the whole square would contain 100 x 100 or 10,000 square centimeters. A square meter, therefore, contains 10,000 square centimeters. If the square were divided into 1000 equal bands, each band would be 0.001 of the square; and if each of the 1000 bands were divided into 1000 squares, that is, into 1000 square millimeters, the whole square would contain 1000 × 1000 or 1,000,000 square millimeters. A square meter, therefore, contains 1,000,000 square milli meters. That is, |