33. How many pounds does each foot in length of the wall of Ex. 31 weigh?

34. If 60.98 cubic inches of brick weigh 4 pounds, how many cubic inches of brick weigh 1 pound? How many pounds will a cubic foot (1728 cubic inches) weigh?

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

36. Light moves through the air at the rate of 186,500 miles a second. How many times can it go around the earth in a second, if the distance round the earth is 24,897.714 miles?

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

38. A minute is 60 seconds. How many miles and how many 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, and each foot is 0.9542 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 of the earth is 7911.7 miles, and that a mile is 5280 × 12 inches.

44. How must a number be altered that its reciprocal may be doubled ?

45. What effect is produced on the sum of two numbers, if the same number is added to each of them? 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 the rate of 309,800 kilometers a second, how long would it take light to perform each of the following journeys:

49. A kilometer is about 0.6214 of a mile.

miles is each of the planets from the sun?

How many

50. If 11.75 tons of coal cost $82.25, what will 21.4 tons cost?

51. Find the number of hours it will take a locomotive running at the rate of 27 miles an hour to make the distance passed over in 13.25 hours by another locomotive that has a velocity of 43.5 miles an hour.

Review Questions.

What are units? numbers? integral numbers? decimal numbers ? abstract numbers? concrete numbers? like numbers?

What is notation? numeration ? Where is the decimal point placed? What do figures in the first place to the left of the decimal point represent? in the second place? in the third place? in the fourth place? in the first place to the right of the decimal point? in the second place? in the third place? in the fourth place? Which place do the units of a number occupy? the tens? the hundreds ? the thousands? the tenths? the hundredths? the thousandths? At what rate does the value of a figure increase from right to left? In separating a row of figures into periods where do we begin? How many figures in each period? What is the period on the right called? the second period? the third period? Which period do we write first? Which period do we read first? How do we write a decimal? How do we read a decimal? In reading, by what word do we connect the integral and decimal parts of a number?

What kind of

What is addition ? What is the result called? numbers only can be added? What is the sign of addition? Does it make any difference in what order the numbers are added? In addition how do we arrange the decimal points? How do we prove that the work of addition is correct?

What is subtraction? What is the greater number called? the smaller? the result? What kind of numbers must the minuend, subtrahend, and remainder be? What is the sign of subtraction ? In subtraction, how do we arrange the decimal points? How do we prove that the work of subtraction is correct?

What is multiplication? the multiplicand? the multiplier? the product? What kind of a number must the multiplier be? What are the factors of a product? Does it make any difference in what order the factors are multiplied? What is the sign of multiplication? How many decimal places must the product have? How do we prove that the work of multiplication is correct?

What is division? the dividend? the divisor? the quotient? If the divisor is not an integer how can we make it an integer without altering the quotient? If the divisor is an integer where do we place the decimal point in the quotient? What is the advantage of writing the quotient over the dividend in long division? What is the sign of division? How do we prove that the work of division is correct?

CHAPTER V.

METRIC MEASURES.

110. To measure a quantity is to find the number of times it contains a known quantity of the same kind, called the unit of measure.

111. The metric system is a system of weights and measures expressed in the decimal scale.

112. 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 the governments of all civilized countries.

The meter was intended to be one ten-millionth of the distance from the equator to the north pole, but more careful measurements show that this distance is 10,001,887 meters.

113. The principal units of the metric system are :

The meter (m) for lengths;

The square meter (am) for surfaces;

The cubic meter (cbm) for large volumes;
The liter (1) (lee'ter) for smaller volumes;
The gram (8) for weights.

114. All these units are divided and multiplied decimally, and the size of the measures thus produced is shown by a prefix; 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.

As in United States money we seldom speak of anything except dollars and cents, so in metric measures only measures printed in black letter are in common use.

Measures of Length.

115. The principal unit of length is the meter.

TABLE.

10 millimeters (mm) = 1 centimeter (cm

10 centimeters

10 decimeters

10 meters

10 dekameters
10 hektometers
10 kilometers

NOTE.

= 1 decimeter (dm).

= 1 meter (m).

= 1 dekameter (dkm).
= 1 hektometer (hm).
= 1 kilometer (km).
= 1 myriameter.

The names of all compound units are accented

on the first syllable; thus, millimeter, kilometer.

116. A length given in one unit may be expressed in another unit by simply moving the decimal point.

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 centi-meters 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,

117. The rule, therefore, for this conversion is:

First count the number of places needed to convert the given measure into terms of the principal measure; then the number needed to convert the principal into the required measure.

118. Before adding or subtracting, the quantities must be written in terms of the same unit of measure.