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.

2. The beer gallon of 282 inches is retained in use only by custom A bushel is commonly estimated at 2150.4 cubic inches.

EXAMPLES FOR PRACTICE.

1. A fruit dealer bought a bushel of strawberries, dry measure, and sold them by wine measure; how many quarts did he gain? Ans. 5 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. 894 quarts.

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

TIME.

Ans. 302 cu. in.

206. Time is used in measuring periods of duration, as

What is the U. S. standard unit of dry measure? How is it obtained? What is the relative size of the wine and the dry gallon What is the size of a beer gallon? What is time? Repeat the table.

1 = 12 =

3668784 527040 31622400

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

NOTES. 1. The exact length of a solar year is 365 da. 5 h. 48 min. 48 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 :

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, Ans. 86400. beating seconds, vibrate in one day?

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.

A sheet folded in 4 leaves
A sheet folded in 8 leaves
A sheet folded in 12 leaves
A sheet folded in 16 leaves
A sheet folded in 18 leaves
A sheet folded in 24 leaves
A sheet folded in 32 leaves

66

a quarto, or 4to.

an octavo, or 8vo.

66

a 12mo.

66

a 16mo.

66

an 18mo.

66

a 24mo.

66

a 32mo.

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

paper. For indicating the size of books.

EXAMPLES FOR PRACTICE.

1. If in Birmingham, England, 150 million Gillott pens are manufactured annually, how many great gross will they make? Ans. 86805 great gross 6 gross 8 dozen.

2. In 100000 sheets of paper, how many bales?

Ans. 20 bales 4 bundles 6 quires 16 sheets. 3. What is the age of a man 4 score and 10 years old? 4. How many printed pages, 2 pages to each leaf, will there be in an octavo book, having 8 fully printed sheets? Ans. 128 pages.

5. How large a book will ten 32mo. sheets make, if every page be printed? Ans. 640 pages.

PROMISCUOUS EXAMPLES IN REDUCTION.

1. How many suits of clothes, each containing 6 yd. 33 qr., can be cut from 333 yards of cloth? Ans. 48.

2. A man bought a gold chain, weighing 1 oz. 15 pwt., at seven dimes a pennyweight; what did it cost? Ans. $24.50.

3. A physician, having 2 lb 33 53 19 19 gr. of medicine, dealt it out in prescriptions averaging 15 grains each; how many prescriptions did it make? Ans. 886.

4. A man bought 1 T. 11 cwt. 12 lbs. of hay, at 14 cents a pound; what did it cost? Ans. $38.90.

5. What will be the cost of a load of oats weighing 1456 pounds, at 37 cents per bushel?

6. If one bushel of wheat will make 45 many barrels will 1000 bushels make? 7. A load of wheat weighing 2430 much, at $1.20 a bushel?

Ares. $17.0625. pounds of flour, how Ans. 229 bbl. 116 lb. pounds is worth how Ans. $48.60.

8. Paid $12.50 for a barrel of beef; how much was that per pound? Ans. 6 cents.

9. If a silver dollar measure one inch in diameter, how many dollars, laid side by side on the equator, would reach round the earth? Ans. 1577511936.

10. In 10 mi. 7 ch. 4 rd, 20 l., how many links?

Ans. 80820 links.