4. Reduce to quarts: .8 bu.; 121% of 2 bu.; 14.2 pk. 5. Reduce to pecks: 621% of a bushel; 182 qt.

6. Change to bushels: 12.5 pt.; 1.28 qt.; 66% of a peck; .08 pk.

7. What part of a bushel is of a peck?

The Weight of a body is the measure of the attraction between it and the earth.

There are three English systems of weight. These are Avoirdupois, Troy, and Apothecaries'. The standard from which the units of these three systems are derived is the Troy pound of the mint. It is divided into 5760 equal parts called grains. The Avoirdupois pound equals 7000 grains, and the Apothecaries' pound 5760 grains.

8. For what is Troy weight used? Avoirdupois weight? Apothecaries' weight?

9. If 6 oz. of coffee are worth 124, how much are 2 lb. 8 oz. worth?

10. How much must be paid for 1200 lb. of hay at $15 a ton?

11. How much will a turkey weighing 9 lb. 12 oz. cost at 12 a pound?

12. What part of a ton is 25 lb.? 21 cwt.?

LESSON 22

1. How many spoons, each weighing 2 oz., can be made from 35 lb. of silver?

2. How many 2-grain pills can be made from 2 tb. 23 29 of quinine?

3. Change of a ton to pounds and ounces.

4. Change .45 lb. to ounces.

5. If 1 silver spoon weighs 2 oz. 15 pwt. 10 gr., find the weight of 2 dozen.

6. Find the value of 100 gold watch cases, each weighing 4 oz., at 4¢ a grain.

7. The gold dollar weighs 25.8 grains. Find the weight of ten 20-dollar gold pieces.

8. The silver and gold coins are one tenth copper. The silver dollar weighs 4121 gr. Find the weight of 1000 silver dollars. Find the amount of silver and copper respectively in 500 silver dollars. Express answers in pounds, ounces, etc.

9. How many ounces in .325 of a ton?

10. How many grains in

lb. Apothecaries' weight? 11. How many grains in .871⁄2 of a pound Troy? 871% of a pound Avoirdupois?

12. 50 lb. Troy are equal to how many pounds Avoirdupois?

13. Reduce 8.28 lb. Troy to integers of lower denominations.

14. How much are 12 T. of sugar worth at 63 a pound?

15. Which is heavier, a pound of iron or a pound of silver? How much?

16. Which is heavier, and how much, an ounce of iron or an ounce of silver?

17. How much are 12,060 lb. of wheat worth at $5 a bushel?

18. From 621% of 1 lb. Troy take 51 oz. Troy.

19. Change 627,200 oz. of flour to barrels.

20. If a ton of sugar is worth $135, how much will 5 cwt. 36 lb. cost?

LESSON 23

The unit of Time is the day.

The Solar Year is the exact time of the revolution of the earth around the sun. It contains nearly 365 da. 5 hr. 48 min. 46 sec.

As it is not convenient to reckon a fraction of a day in the year, we disregard the fourth of a day for 3 years, and add 1 day to February every fourth year. Hence we have 3 years of 365 days called civil years, and then 1 year of 366 days called leap year. By so doing we gain in 100 years about 5 hours less than a day. We rectify this by making most centennial years common years instead of leap years; but the 5 hours less than a day amounts in 400 years to nearly a full day. This we rectify by counting every 400th year a leap year.

Hence, years divisible by 4, except centennial years, are leap years; and centennial years divisible by 400 are also leap years.

1. Name the calendar months and state the number of days in each.

2. Name the months constituting each season.

3. Tell which are leap years: 1896; 1600; 1700; 1800; 1900; 1901; 1902; 1903; 1904; 2000; 1500; 1908.

4. How many hours in 1200 sec.? In 80 min.? In 35 min.? In .25 min.?

5. Change 25 da. 12 hr. 20 min. to minutes.

6. In 38,767 hr. how many days?

7. Change .26 of a common year to integers of lower denominations.

8. Change of a common year to integers of lower denominations.

9. Reduce to days: 142 hr.; 5.5 wk.

10. A note, dated July 24th, is due 60 days after date. When does it become due?

11. Change 45 da. 18 hr. to the decimal of a leap year. 12. To of a common year add of a leap year.

13. From 3 yr. 5 da. 18 hr. take 166 da. 14 hr. 32 min. 14. Divide 38 wk. 5 da. 18 hr. 21 min. 46 sec. by 7.

LESSON 24

Circular Measure is used in measuring angles, in determining latitude and longitude, etc.

When two straight lines are drawn from the same point, the opening between the lines is called an angle. Thus a, b, c, and d are angles. Their vertex is v.

a d

บ

The two straight lines are called the sides of the angle. The size of an angle depends wholly upon the difference in the direction of the sides, and not upon the length of the sides.

A Protractor is an instrument used to determine the size of an angle.

For the purpose of measuring angles the circumference is supposed to be divided into 360 equal parts called degrees (°). The degree is the unit of circular measure.

A protractor may be made out of cardboard or stiff paper.

To measure an angle its vertex is made the center of a circle, and the arc included between its sides is the "size," or measure, of the angle. Thus the angle ABC is measured by the arc AC. As the arc AC is of the circumference, the angle ABC is of 360°, or 90°.

D

B

E

A

To measure the angle DFE, for example, place the point B of the protractor upon the vertex F of the angle, and the edge BC on the side DF. Then notice the number of degrees marked on the rim of the protractor at the point where it is crossed by the side EF.

F

D

This will be the number of degrees in the angle, provided the protractor is graduated from right to left; but if the protractor is graduated from left to right, the number on the rim of the protractor must be deducted from 180° to indicate the size of the angle.

LESSON 25

An angle of 90° is called a Right Angle. Angles less than right angles are called Acute Angles; angles greater than right angles are called Obtuse Angles.

The degree does not express a fixed length. It is o

GRAD. ARITH. VI. — - 3