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REDUCTION OF UNITS.

212. The Units shown in the metric tables form a decimal system (Art. 19), to which apply the following

Principles. 1. Ten units, or some multiple of ten units, of any denomination make one of the next larger unit.

2. A metric number may be changed from one denomination to another next smaller, or larger, by moving the decimal point one or more places to the right, or left, as the case may be.

3. Any denomination may be taken as the unit, the number at the right of the point being read as a decimal of the unit.

213. The units of the metric and the common system may be readily compared by means of the equivalents which have been given, and by means of the following

COMPARATIVE TABLE.
Length.

1 cu. yard = 0.7646 cu. meter. 1 inch = 2.54 centimeters. 1 cord = 3.625 steres. 1 foot = 30.48 centimeters. 1 rod = 5.029 meters.

Capacity. 1 mile = 1.6093 kilometers.

1 liq. quart = 0.9465 liter.

1 gallon = 3.785 liters. Surface.

1 dry quart = 1.101 liters. 1 sq. inch = 6.452 sq. centim.

1 bushel = 0.3524 hektoliters. 1 sq. foot = 9.2903 sq. decim. 1 sq. yard = 0.8361 sq. meter.

Weight. 1 sq. rod = 0.2529 are. 1 acre = 0.4047 hektare. 1 grain troy = 0.648 centigram. 1 sq. mile = 2.59 sq. kilometers. 1 ounce troy = 31.1035 grams.

Volume.

1 ounce av. = 23.35 grams. 1 cu. inch = 16.387 cu. centimeters. 1 pound av. = 0.4536 kilogram. 1 cu. foot = 28.317 cu. decimeters. 1 common T. = 0.9072 met. ton.

WRITTEN EXERCISES.

25. Express as meters and add 1365 mm, 497 cm, and 145.51 m. 26. Express as ares and add 15.16 Ha, 111.55 a, and 3615 ca.

27. From a range of wood containing 45 steres, I have sold 276 decisteres. How many steres remain ?

28. How many liters in 6 casks, each containing 3.40 HI ?

29. Eight men shared equally 21.080 metric tons of sugar. What is each man's share worth at 20 cents a kilo ?

30. From a farm containing 365.50 Ha there have been sold two small lots; the one containing 8.42 Ha, and the other 87.25a. How much remains ? 31. Change 125 meters to feet. 39.37 in.

Solution. — As i meter = 39.37 125

inches, 125 meters must equal 125 19685

times 39.37 inches, or 4921.25 7874

inches. As 1 foot = 12 inches, 3937

there will be as many feet as 12 : 12 in.) 4921.25 in.

inches are contained times in 410.10) ft.

4921.25 inches, or 410.103 ft. 32. If your weight is 55 kilos, what is it in pounds avoirdupois ?

33. A garden plat contains 306 square meters. How many square yards are there in it ?

34. A farm is 450 hektares in extent. How many acres does it contain ?

35. A barrel of flour weighs 196 pounds. What is its weight in kilos ?

36. The produce of 7 acres was 210 bushels of wheat. What was it in hektoliters ?

37. When butter is 35 cents a pound, how much should it be a kilo ?

Solution. — At 35 cents a pound, a kilo, which is 2.2046 pounds, must cost 2.2046 times 35 cents, or 77+ cents.

38. At 65 cents a bushel, what should be the price of corn a hektoliter ?

39. What is the value of an eighth of a plantation of 600.58 hektares at $ 25 an acre ?

40. The distance by railroad between Boston and New Orleans is 1607 miles. What is it in kilometers ?

41. The dome of the capitol at Washington is 287 ft. 6 in. high, surmounted by a statue of Liberty 19 ft. 6 in. high. What is the whole height in meters ?

42. Bought a roll of carpeting of 65 yards at $ 1.20 a meter, and sold it at the same price a yard. How much did I make by the transaction ?

43. The capacity of a certain bin is 40.64 cubic meters. What is the value of the grain that can be put in it at 80 cents a bushel ?

QUESTIONS.

197. What is the metric system? 198. What is a meter ? 199. An are ? 200. A stere ? 201. A liter ? 202. A gram ?

203. How are the names of the divisions of the metric units formed ?

205. Recite the table of metric measures of length. For what is the meter used ? The kilometer ?

206. How is a metric number written ? 207. How are metric numbers read ?

208. Recite the table of metric measures of surface. How is the square meter used ? The square kilometer ? The are and hektare ?

209. Name the measures of volume. How is the cubic meter used? When does it take the name of the stere ?

210. Recite the. tạble of measures of capacity. How is the liter used ? The hektoliter ?

211. Recite the table of measures of weight. For what is the gram used ? The kilogram? The metric ton ?

212. How many units of one denomination make a unit of another in the metric system ? How may a metric number be changed from one denomination to another ? When any denomination is taken as the unit, how may the number at the right of the point be read ?

MEASUREMENTS.

SURFACES.

214 1. How many square inches in a surface 8 inches long and 1 inch wide ? In a surface 8 inches long and 2 inches wide ?

2. A path 12 feet long and 2 feet wide has how many square feet of surface in it ?

3. A table is 6 feet long and 4 feet wide. How many square feet of surface has it ?

215. A Plane Figure is a portion of a plane surface (Art. 163) bounded by lines.

216. The Perimeter of a plane figure is the sum of its bounding lines.

217. The Area of a plane figure is the surface included within its perimeter.

218. The Dimensions of a rectangle are its length and breadth.

A rectangle 3 inches long and 2 inches broad contains in one row 3 squares of 1 square inch each; and 2 such rows contain 2 times 3 square inches, or 6 square inches. That is,

The area of a rectangle is equal to the product of its length and breadth, taken in the same denomination.

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Also,

One of the dimensions of a rectangle is equal to the area divided by the other dimension.

219. A Triangle is a plane figure bounded by three straight lines.

The Base of a triangle is the line upon which it stands ; and the Altitude is its height above the base, or

the base extended. Thus, A B is the base, and C D the altitude, of the triangle A B C.

220. Draw the lines A E, D B perpendicular to the extremities of the base of the triangle A C B, and draw the line E D through C, parallel to

A B, and it is evident that the triangle A F

AC B is half the rectangle A B D E, of the same base and altitude. That is,

The area of a triangle is half the area of a rectangle of the same base and altitude.

221. A Circle may be regarded as consisting of a great number of triangles, whose bases form the circumference of a circle, and whose altitude is the radius of the circle. Hence,

[graphic]
[graphic]

The area of a circle is equal to half the product of the circumference by the radius.

222. The quotient of the circumference of a circle divided by the diameter, to the nearest ten-thousandth, is 3.1416. Hence,

The circumference is equal to the diameter multiplied by 3.1416; the diameter is equal to the circumference divided by 3.1416.

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