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3. One week to minutes.
4. 20,160 minutes to weeks.
5. 4 da. 6 h. 56 min. to min.
6. 5776 min. to days.
7. 32 hr. 32 min. 41 sec. to seconds.
8. 87,990 sec. to hours.

PROBLEMS. 1. Express 49,796 sec. in higher denominations. 2. Express 49,598 sec. in units of higher orders. 3. How many days from April 10th to September 12th ? 4. How many days from March 22d to July 17th ?

5. Giving three months to each, which is the longer, summer or winter ?

6. Which of these are leap years: 1600, 1660, 1666, 1700, 1776, 1790, 1794, 1800, 1898, 1900 ?

7. How many seconds are there in 7 hr. 38 min. 49 sec. ? 8. How many days and hours in week ? 9. Find the number of hours in a week. 10. What part of a week is 1 day 18 hours ?

11. A man borrows some money July 17 and promises to repay it in 60 days. On what day is it due ?

12. How many leap years in the nineteenth century? 13. How many hours in the month of August?

14. If you read French 30 min. each day for 5 much time do you thus spend ?

15. On what day will of a common year end ? of a leap year?

a

yr., how

CIRCULAR MEASURE.

Circular Measure is used to measure angles.

A Circle is a figure made by a bounding line which is everywhere equally distant from a centre-point.

E

The Circumference of the circle is the bounding line.

An Arc is any part of the circumference, as BD.

A Quadrant is an arc equal to 1 of the circumference, as BE.

A Degree is to of the circumference of a circle.

B

An angle whose sides meet at the centre is measured by the arc included between its sides. The angle BCD is measured by the arc BD. A right angle is measured by a quadrant, or 90°.

Table. 60 seconds ()

1 Minute (). 60 Minutes

1 Degree (0) 30 Degrees

1 Sign (S.). 12 Signs, or 360° 1 Circumference (C.). The Sign is used in astronomical calculations.

EXERCISES. 1. Reduce:

1. 56' 25" to seconds. 5. 35° 48' 59" to seconds.
2. 3830" to minutes. 6. 99,800"' to degrees.
3. 23° 36' to minutes. 7. 4 S. 29° 26' 33" to seconds.

4. 856' to degrees. 8. 490,833" to signs.
2. How many minutes in 2 quadrants ?
3. How many seconds in a right angle?
4. 2ị quadrants are what part of a circumference ?
5. In 811,480" how many signs ?

6. In what time does a fixed point in the earth's surface pass through 15° 15' 15' ?

7. Where is a degree of latitude equal to 60 geographical miles?

8. Sixty-nine and 16 hundredths statute miles equal one degree on what surface?

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MISCELLANEOUS TABLES.

Counting. 12 Units 1 Dozen.

12 Gross 12 Dozen 1 Gross.

20 Units 1 Score.

1 Great gross.

24 Sheets
20 Quires

1 Quire. 1 Ream.

Paper.

2 Reams 1 Bundle.
5 Bundles = 1 Bale.

Books.

A book composed of sheets folded in : 2 leaves is a folio.

12 leaves is a duodecimo. 4 leaves is a quarto.

16 leaves is a 16mo. 8 leaves is an octavo.

18 leaves is an 18mo.

EXERCISES.
Reduce :

1. 45 gross of crayons to units.
2. 222 dozen bottles of ink to gross.
3. 12 great gross to units.
4. 3 reams of paper to quires.
5. 5 bundles of paper to sheets.

PROBLEMS. 1. What would 9600 sheets of foolscap cost at $.25 per quire?

2. Find the cost of 4 dozen brushes @ $.55 each.

3. A dealer bought paper at $8 per ream and sold it at $.30 a quire. Did he gain or lose, and how much ?

4. In an octavo book of 960 pages how many sheets ?
5. How many years are 3 score and 10 ?
6. How many sheets in 2 bundles

sheets in 2 bundles 1 ream 15 quires 10 sheets?

7. How many units in 8 gross 9 dozen ?

8. If 12 dozen of buttons are worth $1.08, what are 11 buttons worth?

9. The use of 48 screws per day implies the use of h'w many gross in 6 weeks ?

10. 500,000 copies of a daily newspaper are sold on an average per diem. Reckoning 3 sheets for each copy, how many reams of paper are used in a month ?

REDUCTION OF DENOMINATE FRACTIONS.

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15

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12

15 in.

SPECIAL EXERCISES.

Reduction Descending. 1. Reduce of a rod to units of lower denominations. Process.

Explanation. 4 of 4 yd. = 14 yd. 15 yd. 54 yd. = 4yd. Since 1

rd. 2 of 3 ft. = 5 ft. = 24 ft.

4 yd., rd.

= of 4

yd. 49 yd. Since 1 yd. 1 of 12 in. = in. = 14 in.

3 ft., \ yd. = of 3 ft. = 4 yd. 2 ft. 14 in.

ft.

24 ft. Since 1 ft. in., 1 of a ft. 1 of 12 in. 12 in.

Hence rd.

4 yd. 2 ft. 1 in. 2. Reduce .795 lb. Troy to units of lower denominations. Process.

Explanation. .795 lb.

Since 12 oz. = 1 lb., 12 times the number of pounds 12

the number of ounces ; 12 times .795 9.540 oz. 9.540 Since 20 pwt.

1 oz., 20 times the number of ounces = 20 the number of pwt. .540 X 12= 10.8 pwt. Hence

.795 lb. 9 oz. 10.8 pwt. 190.800 3. Reduce 258 gal. to gills. Process.

Explanation. 5 x 4 x 2 X 4=

Since 1 gal. = 4 qt., 1 qt. = 2 pt., 288

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and 1 pt. = 4 gi., we multiply by the 72

numbers of the scale, 4, 2, 4, and ob36

tain by cancellation ý gills.

gi.

1. 3618

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EXERCISES. 1. Reduce :

21% of a bushel to the fraction of a pint. 2. 64o da. to minutes. 3. šrd. to yards, feet, and inches. 4. .065 of a gallon to integers of lower denominations. 5. 4 of a ton to lower denominations. 6. I of an acre to lower denominations. 7. .007 of a bushel as a decimal of a pint. 8. .796 of a lb. troy to lower denominations. 9. £.686 to lower denominations. 10. .436 of a ream to integers. 11. .875 of a leap year to integers. 12. .795 of a league to integers. 13. cu. yd. to lower denominations.

14. .115625 lb. troy to integers. 2. Reduce :

1. & bu. to pints. 9. 12000 T. to ounces. 2. £1728 to pence.

10. 18727 mi, to inches. 3. lb. troy to integers. 11. 5 da. to integers. 4. ß mi. to integers. 12. 14 of a rod to integers. 5. § bu. to integers.

13. .03125 T. to integers. 6. 5 A. to integers. 14. Į yd. to integers. 7. .1845 gal. to integers. 15. mi. to yards. 8. .15625 bu. to integers. 16. 4 mi. to rod.

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Reduction Ascending. 1. Reduce ş gi. to the fraction of a gal. Process.

Explanation. 4 gi.

1 pt., therefore the number of 1 1

the number of pt. ; 2 pt. X Х

gi. x 9 2

36

therefore { the number of pt. the number of qt. ; 4 qt. 1 gal., therefore the number of qt.

1

the number of gal. ; hence % gi. = $ x į X 1 X = 36 gal.

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1 qt.,

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