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11. 3 qt. 1 pt. to a decimal of a gallon.

12. of 5 qt. 1 pt. to a decimal of 2 bushels. 13. f37 m 15 to a decimal of Cong. 3.

14. A merchant bought 5860 bushels wheat in Ohio at $1.25, and sold the whole in Connecticut at the same price. How much did he gain on the transaction?

15. A grocer bought 12 firkins of butter, each containing 73 lb. 13 oz., at 36 cts. a pound; 7 bu. 3 pk. clover seed, at $1.15 a peck; and 5 loads of potatoes, each load containing 43 bu. 3 pk., at $.32 a bushel. How much was the cost?

Comparative Table of Units of Capacity.

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1. The Standard Bushel of United States contains 2150.42 cu. in. and the Imperial Bushel of Great Britain contains 2216.192 cu. in. 2. An English Quarter contains 8 imp. bu. or 81 U. S. bu. A quarter of 8 U. S. bu., or 480 lb., is used in shipping grain from New York.

3. A Register Ton is 100 cu. ft.; used in measuring the internal capacity or tonnage of a vessel. A Shipping Ton is 40 cu. ft. in the U. S. and 42 cu. ft. in England.

4. A cubic foot of pure water weighs 1000 oz. or 621 lb. Avoir.

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423. 1. How many U. S. bushels in a bin of wheat 6 ft. long, 5 ft. 6 in. wide, and 4 ft. 9 in. deep?

How many cubic feet in a space that holds

2. 1000 U. S. bushels?

3. 1000 imp. bushels ?

4. 120 bbl. water?

Ans.

5. 240 English quarters?

6. 18 T. 16 cwt. of pure water? 7. 804 bu. 3 pk. U. S. bu.?

8. A cistern containing 5300 gal. of water is 10 ft. square. How deep is it?

Ans. 7.085+.

9. How many ounces in gold are equal in weight to 9 pounds 14 ounces of iron?

UNITS OF TIME.

424. The mean solar day is the Standard Unit of time.

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3. In computing interest, 30 days are usually considered one month. For business purposes the day begins and ends at 12 o'clock midnight.

425. The reason for common and leap years will be seen from the following:

The true year is the time the earth takes to go once around the sun, which is 365 days, 5 hours, 48 minutes and 49.7 seconds. Taking 365 days as a common year, the time lost in the calendar in 4 years will lack only 44 minutes and 41.2 seconds of 1 day. Hence we add 1 day to February every fourth year, making the year 366 days, or Leap Year. This correction is 44 min. 41.2 sec. more than should be added, amounting in 100 years to 18 hr. 37 min. 10 sec.; hence at the end of 100 years we omit adding a day, thus losing again 5 hr. 22 min. 50 sec., which we again correct by adding a day at the end of 400 years; hence the following rule for finding leap year:

426. RULE.-Every year, except centennial years, exactly divisible by 4, is a leap year. Every centennial year exactly divisible by 400 is also a leap year.

This will render the calendar correct to within one day for 4000 years.

427. PROB. 10.-To find the interval of time between two dates.

How many yr., mo., da. and hr. from 6 o'clock P. M., July 19, 1862, to 6 o'clock A. M., April 9, 1876.

yr.

mo. da.

hr.

1876

4

9

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1862

7

19

18

13 8 19

13

SOLUTION.-1. Since the latter date denotes the greater period of time, it is the minuend, and the earlier date, the subtrahend.

2. Since each year commences with January, and each day with 12 o'clock

midnight, 7 o'clock A. M., April 9, 1876, is the 7th hour of the 9th day of the fourth month of 1876; and 6 o'clock P. M., July 19, 1862, is the 18th hour of the 19th day of the 7th month of 1862. Hence the minuend

and subtrahend are written as shown in the margin.

3. Considering 24 hours 1 day, 30 days 1 month, and 12 months 1 year, the subtraction is performed as in compound numbers (392), and 13 yr. 8 mo. 19 da. 13 hr. is the interval of time between the given dates.

Find the interval of time between the following dates: 1. March 14, 1776, and August 3, 1875.

2. 5 A. M. May 19, 1854, and 7 P. M. Sept. 3, 1876.

3. 10 P. M. October 3, 1812, and 8 A. M. April 17, 1879. 4. 7 P. M. November 25, 1754, and 2 A. M. May 13, 1873. 5. The American revolution began April 19th, 1775, and ended Jan. 20, 1783. How long did it continue?

6. Washington died Dec. 14th, 1799, at the age of 67 yr. 9 mo. 22 da. At what date was he born?

CIRCULAR MEASURE.

428. A Circle is a plane figure bounded by a curved line, all points of which are equally distant from a point within called the centre.

429. A Circumference is the line that bounds a circle.

430. A Degree is one of the 360 equal parts into which the circumference of a circle is supposed to be divided.

30.

Sextant.

60°

60°

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Semi-Circle.

Quadrant.

431. The degree is the Standard Unit of circular

measure.

TABLE OF UNITS.

60" 1'

=

60' = 1° 30° 1 S.

12 S. 1 Cir. 360°1 Cir.

1. Denominations.-Seconds (''), Minutes ('), Degrees (°), Signs (S.), Circle (Cir.).

2. One-half of a circumference, or 180°, as shown by the figure in the margin, is called a Semi-circumference; One-fourth, or 90°, a Quadrant; One-sixth, or 60°, a Sextant; and Onetwelfth, or 30°, a Sign.

3. The length of a degree varies with the size

of the circle, as will be seen by examining the foregoing diagram.

4. A degree of latitude or a degree of longitude on the Equator is 69.16 statute miles. A minute on the earth's circumference is a geographical or nautical mile.

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432. Reduce and explain the following:

1. 5° 27' 43" to seconds. 4. 7° 4' to a fraction of a sign. 2. 1 cir. 5 s. to minutes. 5. 9° 12' to a decimal of a circle. 3. 3 s. 17° 9' to seconds. 6. .83 of a cir. to a compound number. 7. What part of a circumference are 60°? 90° ? 180°?

8. Reduce of a quadrant to a compound number.

9. How many sextants in 120° ? In 150°? In 165°? In 248°? In 295°?

10. In 5 cir. 7 s. 17°, how many sextants and what left? 11. How many degrees, minutes, etc., in § of a quadrant ? 12. America was discovered Oct. 14, 1492. What interval of time between the discovery and the Centennial Exposition, July 4, 1876 ?

13. Washington was born Feb. 22, 1732, and Napoleon Aug. 15, 1769. How much older was Washington than Napoleon?

14. How many dozen in 7 gross? In 133 gro. ?

15. How many dozen in 83 great gross? In 151⁄2?

16. How many dozen in 174 scores? In 1967? In 843? 17. Reduce 13 bundles 1 ream 15 quires of paper to sheets. 18. 136 sheets are what decimal of 1 bundle? Of 17 quires?

UNITS OF MONEY.

UNITED STATES MONEY.

433. The gold dollar is the Standard Unit of United States money.

TABLE OF UNITS.

10 m.

10 ct.

1 ct.
1 d.

10 d. = $1. $10 = 1 E.

1. Denominations.-Mills (m.), Cents (ct.), Dimes (d.), Dollars ($), Eagles (E.).

2. The United States coin, as fixed by the "New Coinage Act" of 1873, is as follows: Gold, the double-eagle, eagle, half-eagle, quarter-eagle, three-dollar, and one-dollar; Silver, the trade-dollar, half-dollar, quarter-dollar, and ten-cent; Nickel, the five-cent and three-cent; Bronze, one-cent. 3. Composition of Coins.—Gold coin contains .9 pure gold and .1 silver and copper. Silver coin contains .9 pure silver and .1 pure copper. Nickel coin contains .25 nickel and .75 copper. Bronze coin contains .95 copper and .05 zinc and tin.

4. The Trade-dollar weighs 420 grains and is designed for commercial purposes solely.

CANADA MONEY.

434. 1. Denominations.—Mills, Cents, and Dollars. These have the same nominal value as in United States Money.

2. The Coin of the Dominion of Canada is as follows: Gold, the coins in use are the sovereign and half-sovereign; Silver, the fiftycent, twenty-five cent, ten-cent, and five-cent pieces; Bronze, the onecent piece.

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