pk.

16

SCALE

bu. 1= 8

14 = 32 =64

ascending, 2, 8, 4; descending, 4, 8, 2.

NOTE. In England, 8 bu. of 70 lbs. each are called a quarter, used in measuring grain. The weight of the English quarter is of a long ton.

EXAMPLES FOR PRACTICE.

1. In 49 bu. 3 pk. 7 qt. 1 pt. how many pints?

2. In 3199 pt. how many bushels?

3. Reduce 1 bu. 1 pk. 1 qt. 1 pt. to pints.

4. Reduce 83 pints to bushels.

5. An innkeeper bought a load of 50 bushels of oats at 65 cents a bushel, and retailed them at 25 cents a peck; how much did he make on the load? Ans. $17.50.

STANDARD OF EXTENSION.

202. The U. S. standard unit of measures of extension, whether linear, superficial, or solid, is the yard of 3 feet, or 36 inches, and is the same as the imperial standard yard of Great Britain. It is determined as follows: The rod of a pendulum vibrating seconds of mean time, in the latitude of London, in a vacuum, at the level of the sea, is divided into 391393 equal parts, and 360000 of these parts are 36 inches, or 1 standard yard. Hence, such a pendulum rod is 39.1393 inches long, and the standard yard is 359983 of the length of

the pendulum rod.

203. The U. S. standard unit of liquid measure is the old English wine gallon, of 231 cubic inches, which is equal to 8.33888 pounds avoirdupois of distilled water at its maximum density, that is, at the temperature of 39.83° Fahrenheit, the barometer at 30 inches.

Repeat the table. What is a quarter? What is the U. S. standard unit of measurement of extension? How is it determined? What is the U. S. standard unit of liquid measure?

204. The U. S. standard unit of dry measure is the British Winchester bushel, which is 18 inches in diameter and 8 inches deep, and contains 2150.42 cubic inches, equal to 77.6274 pounds avoirdupois of distilled water, at its maximum density. A gallon, dry measure, contains 268.8 cubic inches.

NOTE. 1. The wine and dry measures of the same denomination are of different capacities. The exact and the relative size of each may be readily seen by the following

205. COMPARATIVE TABLE OF MEASURES OF CAPACITY.

Cu. in. in one gill.

733223

83

2. The beer gallon of 282 inches is retained in use only by custom A bushel is commonly estimated at 21504 Gubic inches.

EXAMPLES FOR PRACTICE.

1. A fruit dealer bought a bushel of strawberries, dry measure, and sold them by wine measure

did he gain?

how many quarts

2. A grocer bought 40 quarts of milk by beer measure, and sold it by wine measure; how many quarts did he gain?

Ans. 84 quarts.

3. A bushel, or 32 quarts, dry measure, contains how many more cubic inches than 32 quarts wine measure?

TIME.

Ans. 3023 cu. in.

206. Time is used in measuring periods of duration, as years, days, minutes, &c.

What is the U. S. standard unit of dry measure? tained? What is the relative size of the wine and What is the size of a beer gallon? What is time?

How is it obthe dry gallon? Repeat the table.

SCALE ascending, 60, 60, 24, 7; descending, 7, 24, 60, 60.

The calendar year is divided as follows:-
: -

=

NOTES. 1. The exact length of a solar year is 365 da. 5 h. 48 min. 46 sec.; but for convenience it is reckoned 11 min. 14 sec. more than this, or 365 da. 6 h. 365 da. This day in 4 years makes one day, which, every fourth, bissextile, or leap year, is added to the shortest month, giving it 29 days. The leap years are exactly divisible by 4, as 1856, 1860, 1864. The number of days in each calendar month may be easily remembered by committing the following lines:

"Thirty days hath September,
April, June, and November;
All the rest have thirty-one,

Save February, which alone

Hath twenty-eight; and one day more

We add to it one year in four."

2. In most business transactions 30 days are called 1 month.

EXAMPLES FOR PRACTICE.

1. Reduce 365 da. 5 h. 48 min. 46 sec. to seconds.

2. Reduce 31556926 seconds to days.

Give the scale. What is the length of each of the calendar months? What is the exact length of a solar year? Explain the use of bissextile or leap year. What is the length of a month in business transactions?

3. In 5 wk. 1 da. 1 h. 1 min. 1 sec. how many seconds? 4. In 3114061 seconds how many weeks?

5. How many times does a clock pendulum, 3 ft. 3 in. long, beating seconds, vibrate in one day? Ans. 86400.

6. If a man take 1 step a yard long in a second, in how long a time will he walk 10 miles? Ans. 4 h. 53 min. 20 sec. 7. In a lunar month of 29 da. 12 h. 44 min. 3 sec. how Ans. 2551443. many seconds?

8. How much time will a person gain in 40 years, by rising 45 minutes earlier every day? Ans. 456 da. 13 h. 30 min.

CIRCULAR MEASURE.

207. Circular Measure, or Circular Motion, is used principally in surveying, navigation, astronomy, and geography, for reckoning latitude and longitude, determining locations of places and vessels, and computing difference of time.

Every circle, great or small, is divisible into the same number of equal parts, as quarters, called quadrants, twelfths, called signs, 360ths, called degrees, &c. Consequently the parts of different circles, although having the same names, are of different lengths.

SCALE-ascending, 60, 60, 30, 12; descending, 12, 30, 60, 60.

NOTES. 1. Minutes of the earth's circumference are called geographic or nautical miles.

2. The denomination, signs, is confined exclusively to Astronomy.

Define circular measure. How are circles divided? table. Give the scale. What is a geographic mile? sign?

Repeat the
What is a

3. Degrees are not strictly divisions of a circle, but of the space about a point in any plane.

4. 90° make a quadrant, or right angle, and 60° a sextant, or of a circle.

EXAMPLES FOR PRACTICE.

1. Reduce 10 S. 10° 10' 10" to seconds.

2. Reduce 1116610" to signs.

3. How many degrees in 11400 geographic or nautical miles? Ans. 190°.

4. If 1 degree of the earth's circumference is 69 statute miles, how many statute miles in 11400 geographic miles, or 190 degrees? Ans. 13148.

5. How many minutes, or nautical miles, in the circum, ference of the earth? Ans. 21600' or mi. 6. A ship during 4 days' storm at sea changed her longitude 397 geographical miles; how many degrees and minutes did she change? Ans. 6° 37'.

The terms folio, quarto, octavo, duodecimo, &c., indicate the number of leaves into which a sheet of paper is folded.

A sheet folded in 2 leaves is called a folio.

What is a degree? Repeat the table for counting. For reckoning

paper. For indicating the size of books.