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72. CUBIC MEASURE is used in measuring timber, earth, and such other things as have length, breadth, and thickness.

TABLE.

1728 cubic inches (cu. in.) make 1 cubic foot

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1. In 1 cord how many cubic feet? Ans. 128 cu. ft. 2. In 1 cord how many cubic inches?

Ans. 221184 cu. in.

3. In of a cord how many cubic feet?

Ans. 96 cu. ft.

4. In 1 cubic yard how many cubic inches?

Ans. 46656 cu. in.

5. In 1 ton of round timber how many cubic inches?

Ans. 69120 cu. in.

6. In 1 ton of hewn timber how many cubic inches?

Ans. 86400 cu. in.

Ans. 663552 cu. in.

7. In 3 cords of wood how many cubic inches?

166

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REMARK.-The Wine Gallon contains 231 cubic inches.

EXERCISES.

1. In 1 tun how many hogsheads? gallons? quarts? pints? gills?

Ans. 4 hhd.; 252 gal.; 1008 qt.; 2016 pt.; 8064 gi. 2. In 1 hogshead how many cubic inches?

Ans. 14553 cu. in.

3. In 1 cubic foot how many gallons?

Ans. 1728-231-7.48 gallons.

4. In 1 hogshead how many cubic feet?

Ans. 8.42 cu. ft.

5. How many quarts in a cubic foot? How many pints? Ans. 29.92 qt.; 59.84 pt.

74. DRY MEASURE is used in measuring such articles as grain, fruit, etc.

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1 quarter

qr.

REMARK.—The Winchester Bushel contains 2150.4 cubic inches.

EXERCISES.

1. In 1 bushel how many quarts?

pints?

How many

Ans. 32 qt.; 64 pt.

2. How many quarts in 9 bushels? 13 bushels? 26 bushels? 78 bushels? Ans. 288 qt.; 416 qt., etc.

3. In 6464 pints how many bushels? Ans. 101 bu.

75. TIME is divided into DAYS by the revolution of the earth on its axis, and into YEARS by the revolution of the earth round the sun.

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REMARK 1.-A SIDEREAL DAY consists of 23 h. 56 m. 4 sec. REMARK 2.-A Tropical Year consists of 365 d. 5 h. 48 m. 47.57 sec.

REMARK 3.-The Civil Year consists of 365 days, except Leap Year, which consists of 366 days.

REMARK 4.-Every year which is divisible by 4 without a remainder is Leap Year, excepting those centennial years not divisible by 400 without a remainder. Thus: 1868; 1872; 1876, etc., will be Leap Years: 1900; 2100; 2200; 2300; 2500, etc., will not be Leap Years; but 2000; 2400; 2800, etc., will be Leap Years.

REMARK 5.-February has 28 days, except in Leap Year, when it has 29 days. April, June, September, and November have 30 days each. Each of the other months of the year has 31 days.

EXERCISES.

1. How many seconds in 1 day? 5 days? 15 days?

45 days? 90 days?

2. How many seconds in 1 weeks? 21 weeks? 84 weeks?

Ans. 86400, etc. week? 7 weeks? 14 Ans. 604800, etc.

3. How many days in 604800 seconds; 1814400 seconds? 16329600 seconds?

Ans. 7 days, etc.

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76. CIRCULAR MEASURE is used in estimating Latitude and Longitude, and in measuring the relative distances of the planets and other heavenly bodies.

TABLE.

60 seconds (") make 1 minute, marked

60 minutes

::0 degrees

12 signs

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1 circumference of circle. circ.

REMARK 1.—The length of a degree, measured on the equator, is 69.161 miles. The length of a degree, measured on a meridian, 169.042 miles.

EXERCISES.

1. In 1 circumference of a circle how many degrees?

Ans. 360 degrees.

2. In 1 circ. how many minutes? seconds?

Ans. 21600'; 1296000".

3. How many miles in 1' on the equator?

Ans. 1.153 m.

4. How many miles in 1' on a meridian?

Ans. 1.151 m.

5. How many miles in 1" on the equator?

Ans. 0.019 m.

6. How many miles in 1" on a meridian?

7. It is 90° from the equator to many miles is it?

8. The Torrid Zone is 47° wide. is that zone in width?

Ans. 0.019 m. each pole. How

Ans. 6213.78 m.

How many miles Ans. 3244.974 m.

9. Each of the Temperate Zones is 43° wide. How many miles is each zone in width? Ans. 2968.806 m. 10. Each of the Frigid Zones is 23° wide. How many miles is each zone in width? Ans. 1622.487 m. 11. The City of Mexico is in north latitude 19° 25' 45". How many miles is it from the equator? Ans. 1341.428 m.

REDUCTION OF COMPOUND NUMBERS. 77. A NUMBER is a unit (one), or a collection of units (ones).

78. An ABSTRACT NUMBER is a number whose unit has no name other than that given it as a mere number. Thus: 3, 7, 15 are abstract numbers, since the name of their unit is one.

79. A CONCRETE or DENOMINATE number is a number whose unit has a name other than that given it as a mere number. Thus: 3 dollars, 7 feet, 15 apples, are concrete numbers, since the names of their units are one dollar, one foot, one apple.

So. A SIMPLE NUMBER is a unit or a collection of units of the same kind. It may be abstract or it may be concrete. Thus: 5 is a simple abstract number; 5 peaches is a simple concrete number.

81. A COMPOUND NUMBER is a number consisting of two or more concrete numbers of different unit values, but reducible to a simple number. Thus: 3£ 2 s. is a com

pound number, and equal to 62 shillings, which is a simple number. But 3 £ 2 pt. is not a compound number, because pounds can not be reduced to pints.

82. REDUCTION consists in making some change in the method of representing a number. Thus: 3 s. 6 d.=42 d.

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