22. It is 3.1416 times as far round a wheel as across it. How many times will a wheel 4.5 feet across turn round in going 23 miles of 5280 feet each?

23. How many gallons of 231 cubic inches are contained in a cubic foot (1728 cubic inches)? in a bushel of 2150.42 cubic inches? How many cubic feet in a bushel? How many bushels in 31.5 gallons?

24. Seven children had left to them $7186 apiece; one died, and his share was divided among the surviving six. How much had each then?

25. What is the nearest number to 7196 that will contain

372 without a remainder?

26. How long will it take 2 men to do what 1 man can do in 6 days? what 4 men can do in 3 days? what 3 men can do in 4 days?

27. Divide $1.80 among Thomas, Richard, and Henry in such a way that Henry shall receive 3 cents for every 5 cents that Thomas gets, and Richard shall receive 2 cents for every 3 cents that Henry gets. 28. Divide $87.84 between B and C so that C shall get $19 as often as B gets $17.

29. Three partners received for goods: one, $371.63; the second, $285.40; the third, $411.91. They paid for the goods $879.34, and divided the balance equally among them. How much did each receive?

30. At 12 inches in a foot, how many inches long is a wall 35 feet in length? A brick and its share of mortar

being 8.4 inches long, how many bricks in length is the wall?

31. A brick and mortar being 2.4 inches in height, how many bricks are required to build the wall 12 feet high, if the wall be two bricks wide.

32. What is the total weight of the wall, if a brick and its share of the mortar weigh 4.13 pounds? What is

the weight after a long rain, when the weight is increased to 4.27 pounds for each brick?

33. How many pounds does each foot in length of the wall weigh?

34. If 60.98 cubic inches of brick weigh 4 pounds, how

many cubic inches of brick weigh 1 pound? How many pounds would a cubic foot (1728 cubic inches) weigh?

35. If a cubic foot of water weigh 62.5 pounds, how many times as heavy as water is brick?

36. Light moves through the air at 186,500 miles in a

second. How many times can it go around the earth

in a second, the distance round the earth being 24,897.714 miles?

37. Light moves through the air at 300,190 kilometers in a second. How many times can it go around the earth in a second, the distance round the earth being 40,007.5 kilometers?

38. A minute is 60 seconds. How many miles and how nany kilometers can light travel through air in a minute?

39. An hour is 60 minutes. How many miles and how many kilometers can light travel in an hour?

40. The distance round the earth, given in Ex. 37, is measured on a north and south line. Around the equator the distance is 40,075.45 kilometers. How many

times could light move round the equator in one

minute?

41. Find the reciprocal of the difference between 31.24 and 31.23768.

42. The Hanoverian mile is 25,400 Hanoverian feet long, each foot being .9542 of an English foot. Find to four places of decimals the fraction that an English mile of 5280 English feet is of a Hanoverian mile.

43. Express in inches the length of a meter, given that a meter is one ten-millionth of a quarter of the earth's circumference, that the circumference is 3.14159 times the diameter, that the diameter is 7911.7 miles, and that a mile is 5280 × 12 inches.

44. How must a number be altered to double its reciprocal? 45. What effect is produced on the sum of two numbers, if each number is increased by the same number? What effect on the difference?

46. What effect is produced on the product of two numbers, if both numbers are multiplied by the same number? What effect on the quotient?

47. What effect is produced on the remainder, if both divisor and dividend are multiplied by the same

number? If both are divided by the same number? 48. In going from one planet to another light probably moves faster than in air. Suppose it moves at 309,800 kilometers a second, how long would it take light to perform each of the following journeys:

49. A kilometer is about .6214 of a mile. How many miles is each of the planets from the sun?

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 (am) for surfaces;
The cubic meter (cbm) for large volumes;

The liter (1) (leé-ter) for smaller volumes;
The gram (8) for weights.

* 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.