176. A stationer buys 25 reams of commercial note paper at $1.75 a ream, and retails it at 12 cents a quire, with the exception of one outside quire of each ream, which he sells at 8 cents. How much does he make?

177. How many years, months, and days did a man live who was born March 15, 1767, and died June 8, 1845?

178. Bought a cask of oil, containing 68 gallons, at 72 cents a gallon; having leaked out, the remainder was sold at 90 cents a gallon. Did I make or lose, and how much?

179. Show that any article is worth as many five-cent pieces a cental as dollars a ton.

180. A carpenter sent two of his apprentices to ascertain the length of a certain fence. The first made it 17 rd. 16 ft. 11 in., and the second made it 18 rd. 5 in. The carpenter, fearing they might both be wrong, measured for himself, and found it to be 17 rd. 5 yd. 1 ft. 11 in. What was the difference in their measurements?

181 If A and B should commence, March 5, 1882, to go to bed at the same hour, and A should rise at before 6 o'clock and B at past 7, how much more time for labor would A have had than B, by March 5, 1900, paying attention to the leap years?

QUESTIONS.

183. What is a denomination?

184. A denominate number?

185. A simple number? 186. A compound number?

187. What is reduction descending? 188. How is a denominate number reduced to smaller denominations?

189. What is reduction ascending? 190. How is a denominate number reduced to larger denominations?

191. What is a denominate fraction? 192. How is a denominate fraction reduced to integers of smaller denominations? 193. How are denominate integers reduced to fractions of larger denominations? 196. How is the difference between dates, in years, months, and days, found?

THE METRIC SYSTEM.

197. The Metric System of weights and measures, now coming into use in the United States, has for its base a unit called the meter.

NOTE.

This system, in extensive use in the arts and sciences, adopted for the United States Coast Survey, and partially employed in the Mint and General Post Office, was legalized for use in the United States by Congress in 1866.

198. The Meter, which was intended to be, and is very nearly, the ten-millionth part of the distance on a meridian from the equator to the pole, is the principal unit of lengths, and the standard unit from which all metric measures are derived.

199. The Are,* the principal unit of the measures of land, is a square whose side is ten meters.

200. The Stere, the principal unit of the measures of wood and stone, is a cube whose edge is a meter.

201. The Liter, the principal unit of the measures of capacity, is a cube whose edge is the tenth of a meter.

202. The Gram, the principal unit of weight, is the weight of a cube of pure water at its greatest density, whose edge is a hundredth part of a meter.

203. The Names of the divisions of the unit are formed by prefixing to the name of the unit the Latin words, milli for 1000th, centi for 100th, and deci for 10th; and the names of multiples, by prefixing the Greek, deka for 10, hekto for 100, kilo for 1000, and myria for 10000.

* Are is pronounced air; stere, stair; and liter, lee'ter. All metric names have the accent on the first syllable.

204. In the metric system, as in United States money, only a few of the denominations are much used. These will be distinguished in the tables by the difference in type. The unit corresponds to the dollar, and deci, centi, milli to dimes, cents, mills.

205. LENGTH MEASURES.

10 millimeters (mm) are 1 centimeter, cm.

10 centimeters

10 decimeters

10 meters

10 dekameters 10 hektometers 10 kilometers

Km

Dm

Centimeters.

1 decimeter, or 10 centimeters, or 100 millimeters.

1 5 Hm 7 3 m m 4 dm 2 cm, written as meters, is 1573.42", and, written as kilometers, is 1.57342 Km.

207. In reading metric numbers, the name of the unit may be applied to all on the left of the decimal point, and the name of the smallest denomination denoted to all on the right of the point.

m

Thus,

42.73 may be read forty-two, and seventy-three hundredths meters; or, forty-two meters, and seventy-three centimeters.

8.675 Km may be read eight, and six hundred seventy-five thousandths kilometers; or, eight kilometers, and six hundred seventy-five meters.

1. How many meters and hundredths of a meter are expressed by 7.25 m ?

2. How many kilometers and thousandths of a kilometer are expressed by 8.407 Km?

?

3. How many meters and centimeters does 7.25 m express 4. How many kilometers and meters does 8.407 Km express?

5. How many centimeters in 4.15 m? How many meters in 7.384 Km ?

6. Reduce 784 centimeters to meters; 6453 meters to kilometers.

208. SURFACE MEASURES.

100 square millimeters (sq mm) are 1 square centimeter, sq cm ̧

1. The square meter is used in measuring ordinary surfaces; the square kilometer, in measuring the area of countries; and the are and hektare, in measuring land.

2. The square meter is about 10 square feet, or 1 square yards; and the hektare, about 2 acres.

3. As 100 units of a smaller denomination make a unit of a denomination next larger, the scale is 100, and two places of figures must be allowed for each denomination. Thus,

1 Square Centimeter.

31 Ha 14 a 17 ca, written as ares, is 3114.17 a, which may be read 3114 ares, and 17 centares; and, written as hektares, is 31.1417 Ha, which may be read 31 hektares, and 1417 centares.

7. In 4 square meters how many square decimeters?

square centimeters how many square millimeters?

8. Express 65.41 as centares; as hektares.

In 4

9. How many ares in 5734 ca? How many hektares in 6893 a?

209. VOLUME MEASURES.

1000 cubic millimeters (cu mm) are 1 cubic centimeter, cu cm.

1 cubic centimeter = 0.061 cu. inch. 1 cubic meter = 1.308 cu. yards.

1 cubic decimeter = 61.022 cu. inches. 1 stere

= 0.2759 cord.

1. The cubic meter, the unit of ordinary solids, takes the name of stere when applied to the measuring of wood and lumber.