269. The sides of a triangular garden are 52.64, and 72 yds. respectively. Find the area.

270. Find the circumference and area of a circle whose radius is 2 ft. 4 in.

271. The side of an equilateral triangle is 12 ft. Find its

area.

272. How many bricks, each 9 in. long, 4

in. wide, and 3 in. thick, will be required for a wall 175 yds. long, 12 ft. high, and 1 ft. 10 in. thick?

273. The diameter of a circular shaft in a railway tunnel is 5 ft. and its depth 30 fathoms. How many cubic feet of earth were dug out in making it?

274. Find the cost f plastering a room 25 ft. 6 in. long, 17 ft. 3 in. wide, and 10 ft. 8 in. high. The price for the wills is 21 cts., and for the ceiling 32 cts. a square yard, and no allowance is made for doors and windows.

275. A line 62 ft. long reaches from the top of a house 48 ft. high, to the bottom of a house on the opposite side of the street. Find the width of the street.

276. Find the capacity in bushels of a round basket 20 in. in diameter and 28 in. deep.

277. The diameter of a spherical balloon is 25 ft. How many square yards of silk were required to make it, and how many cubic feet of gas will be required to fill it?

278. Find the weight of an ivory ball 2 in. in diameter, the weight of ivory being 1825 oz. a cubic foot.

279. How many cubic feet in a stone roller 6 ft. 6 in. long and 5 ft. 4 in. in circumference?

CHAPTER XVI.

METRIC MEASURES.

320. The Metric System is a system of weights and measures expressed in the decimal scale.

321. 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 nations.

322. The principal units of the metric system are : The meter (m) for lengths;

The square meter (m) for surfaces;

The cubic meter (cbm) for large volumes;

The liter (') (lee'-ter) for smaller volumes;
The gram (8) for weights.

323. 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.

324. 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.

NOTE. A meter is a trifle more than 39.37 inches, and all the units of the system are derived from the meter. All the compound names are accented on the first syllable; thus, millimeter. The teacher should be supplied with a meter stick, a liter, and a cubic centimeter.

326. 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.

327. 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.

328. Remember that, before adding or subtracting, the quantities must be written in the same units of measure.

Ex. 165. (Oral.)

1. How many meters in a dekameter? hectometer? kilometer? How many dekameters in a hectometer? kilometer?

2. What part of a meter is a decimeter? centimeter? millimeter? What part of a centimeter is a millimeter?

3. Read 32.3; 12.6em; 15.4km; 59.8mm.

4. Express 3256m as kilometers; as centimeters.
5. Express 5368mm as centimeters; as meters.
6. Express 12.4km as meters; as centimeters.

Ex. 166.

Find the value of each of the following expressions in

meters:

1. 0.435m+852cm +4263mm +0.1595km.

2. 0.927km 6495cm; 4.37cm - 42.87mm.

3. 8× 0.0457km; 3.04 × 60.93cm; 5.43 × 67.2mm.

4. 38,019mm 0.097; 0.41km ÷ 25.625.

5. A book is 2.1cm thick; if the average thickness of the leaves is 0.05mm, find the number of pages in the book. 6. The expense of building a certain railroad is $25,000 on the average per kilometer. What is the whole cost of the road, if its length is 72km and 53m.

7. The wheels of a locomotive that makes 45km an hour are 7.5m in circumference.

will they make a minute?

How many revolutions

8. A locomotive runs 1284m in 13 min. How many kilometers will it go in 1 hr. 35 min. 15 sec.?

9. The top of a monument is 143.9m, and the base 67.19m above the level of the sea; the steps which lead from the base to the top of the monument are each 19cm high. How many steps are there?

MEASURES OF SURFACE.

329. The principal unit of surface is a square meter (9). 330. 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. The square meter, therefore, contains 10 x 10 or 100 square decimeters.

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.

In like manner, a square meter contains 1,000,000 square millimeters.

331.

A

UNITS OF SURFACE.

square millimeter (mm)=0.000001 of a square meter. A square centimeter (qcm)

A square decimeter

=

= 0.0001

A square hektometer

A square kilometer (km)

=

10,000

332. It will be observed that while centimeters are in the second, and millimeters in the third decimal place from meters, square centimeters are in the fourth and square millimeters in the sixth decimal place from square meters.