NOTE II. The standard unit for liquid measure is the GALLON.

NOTE III. The standard unit for dry measure is the BUSHEL.

NOTE IV. In buying and selling grain and many other kinds of produce, the bushel is reckoned at a certain number of pounds. Thus, potatoes have 60 pounds to a bushel and corn has 56 pounds to a bushel.

a. How many half-pint tumblers can a person fill with 1 gallon of jelly?

b. How many quart measures can be filled with 1 bushel of cranberries?

c. What does a vender receive for 1 peck of peanuts which he sells at 5 cents a pint?

d. Which is larger, 1 quart of milk, or 1 quart of berries? e. How many pints in a bushel? How many gills in a gallon?

f. I bought 3 bushels of pears for $2 a bushel, and sold them at 10 cents a quart; what did I gain by the sale?

CIRCULAR AND ANGULAR MEASURES.

143

CIRCULAR AND ANGULAR MEASURES.

331. A plane surface bounded by a line every point of which is equally distant from a point

within, called the centre, is a circle.

332. The bounding line of a circle is the circumference. Any part of the circumference is an arc.

333. The circumference of a circle is divided into 360 equal arcs, called degrees (°), each degree into 60 minutes ('),

A Circle.

and each minute into 60 seconds ("). These are the units of

Circular Measure.

60 seconds = 1 minute.

60 minutes = 1 degree.

360 degrees = 1 circumference.

NOTE. As the circumference of every circle has 360 degrees, the length of the degree differs in different circles.

334. A degree of the circumference of the earth at the equator is about 69.16 common miles in length.

335. A minute of the circumference of the earth at the equator is a geographical or nautical mile, and equals about 1.15 common miles.

336. If the centre of a circle is placed at the vertex of an angle, the arc included between the sides is the measure of the angle. Thus, if the

arc contains 30 degrees, the angle is called an angle of 30 degrees. (See illustration.)

NOTE.

An angle of one degree has always the same size, but the arc that measures it differs in different circles.

337. Oral Exercises.

a. How many degrees are there in a semi-circumference? in of a circumference, or a quadrant? in of a circumference, or a sextant?

b. The torrid zone is 47° wide.

How would you find its

width in nautical miles? in common miles?

c. Through how many degrees does the hour hand of a clock move in 3 hours? in 1 hour? in 2 hours?

d. Through how many degrees does the minute hand of a clock move in 5 minutes of time? in 1 minute? in a quarter of an hour? in half an hour?

e. How many degrees in a right angle?

f. How long does it take the hour hand of a clock to move through a right angle? How long does it take the minute hand?

g. The hour and minute hand of a clock form an angle of how many degrees at 3 o'clock? at 4 o'clock? at 10 o'clock ? at 7 o'clock? at 12 o'clock ?

MEASURES OF TIME.

338. In measuring time we employ the century, year, month (mo.), week (w.), day (d.), hour (h.), minute (m.), and second (s.). These are the units of

365

or 52 weeks day day} = 1 common year (c. y.).

366 days = 1 leap year (1. y.).

100 years

= 1 century (C.).

339. Any year is a leap-year when the number denoting the year is divisible by 4 and not by 100, and when it is divisible by 400. (See Appendix, page 307.)

Which of the following named years are leap-years:

1878? 1892 ? 1888 ? 1900? 2000? 1864? 1880 ?

340. The year begins with the first of January, and is divided into four seasons of three months each,

as follows: The winter months are December, January, and February. The spring months are March, April, and May. The summer months are June, July, and August. The autumn months are September, October, and November. 341. April, June, September, and November have 30 days each. February has 28 days, in leap year 29. The other months have 31 days each.

342. Oral Exercises.

a. What date is three months from Jan. 5? July 10? b. What date is 6 months from May 2? Feb. 11? Nov. 1? c. What months contain 30 days each? 31 days each? d. At 10 cents an hour for 5 hours of every working day, how much can you earn in 4 weeks?

e. 8 years and 9 months are how many months?

f. How many years are there in 100 mo. ? in 200 mo. ?
g. What date is 30 days from May 5? from Apr. 4?
h. How many days from May 3 to June 5?

NOTE. For other measures sometimes used, see Appendix, page 307.

SECTION XII.

COMPOUND NUMBERS.

345. In 2 feet 7 inches, how many inches? Ans. 31 inches.

The number 31 inches expresses a quantity by reference to a single integral unit. Such a number is a simple

number.

346. The number 2 feet 7 inches expresses a quantity by reference to two units of different denominations. A number expressing a quantity by reference to two or more units of different denominations is a compound number.

The compound number 2 feet 7 inches expresses the same quantity that the simple number 31 inches does.

347. When the name of the units is given, the number is a denominate number. Thus, 31 inches and 2 feet 7

inches are both denominate numbers.

348. When the name of the unit is not given, the number is a general number. Thus, 31 is a general number. NOTE. Denominate numbers are sometimes called concrete numbers, and general numbers are called abstract numbers.

Name a simple number; a compound number; a denominate number; a general number. Is 5 feet 2 inches a denominate or general number? a simple or compound number? Is 25 a denominate or a general number? a simple or a compound number?

349. Written Exercises.

Write from memory the table for Long Measure, Square Measure, Cubic Measure, Liquid Measure, Dry Measure, Avoirdupois Weight, Troy Weight, Circular or Angular Measure, Numbers, Paper.