5. CLOTH MEASURE.

1. In 95 yards, how many quarters and nails?

Ans. 380grs. 1520na.

2. In 341 yards, 3qrs. 1na. how many nails?

s. In 3783 nails, how many yards?

Ans. 5469.

Ans. 256yds. 1qr. Sna.

4. In 61 Ells English, how many quarters and nails?

Ans. 305qrs. 1220na.

5. In 56 Ells Flemisn, how many quarters and nails?

Ans. 168grs. 672na,

6. In 148 Ells English, how many Ells Flemish?

Ans. 246E. F, 2qrs.

7. In 1920 nails, how many yards, Ells Flemish, and Ells English?

Ans. 120yds. 160E. F. ard 96E. E. 8. How many coats can be made out of 564 yards of broadcloth, allowing 14 yards to a coat ?

6. DRY MEASURE.

Ans. 21.

1. In 136 bushels, how many pecks, quarts and pints ? Ans. 544pks. 4352qts. 8704pts.

2. In 49 bush. Spks. 5qts. how many quarts?

3. In 8704 pints, how many bushels? 4. In 1597 quarts, how many bushels ?

Ans. 1597.
Ans. 136.

Ans. 49bus. Spks. 5qts. 5. A man would ship 720 bushels of corn in barrels, which will hold 3 bushels, 3 pecks each, how many barrels must he get ?

7. WINE MEASURE.

Ans. 192.

1. In 9 tuns of wine, how many hogsheads, gallons and quarts?

Ans. 36hhds. 2268gal. 9072qts.

2. In 24 hhds. 18 gals. 2 qts. how many pints?

Ans. 14
Ꭿ

3. In 9072 quarts, how many tuns ?
4. In 1905 pints of wine, how many hogshead
Ans. 3hhds. 49gali

5. In 1789 quarts of cider, how many barrels

Ans. 14bls. 25qts.

6. What number of bottles, containing a pint and a nalf each, can be filled with a barrel of cider ? Ans. 168. 7. How many pints, quarts, and two quarts, each an equal number, may be filled from a pipe of wine?

8. LONG MEASURE.

Ans. 144.

1. In 51 miles, how many furlongs and poles ?

corns?

Ans. 408fur. 16320 poles. 2. In 49 yards, how many feet, inches, and barley, Ans. 147ft. 1764inch. 5292b.c. 3. How many inches from Boston to New-York, i being 248 miles?

Ans. 15713280inch

4. In 4352 inches, how many yards?

5. In 682 yards, how many

Ans. 120yds. 2ft. 8in.

rods?

Ans. 682×2÷÷11=124rods. 6. In 15840 yards, how many miles and leagues?

Ans. 9m. Slea.

7. How many times will a carriage wheel, 16 feet and 9 inches in circumference, turn round in going from New-York to Philadelphia; it being 96 miles?

Ans. 30261 times, and 84 feet over. 8. How many barley-corns will reach round the globe it being 360 degrees? Ans. 4755801600

9. LAND OR SQUARE MEASURE.

1. ID 241 acres, 3 roods and 25 poles, how many square? rods or perches ? Ans. 58705perches. 2. In 20692 square poles, how many acres?

Ans. 129a. 1r. 12po. 3. If a piece of land contain 24 acres, and an inclosure of 17 acres, 3 roods, and 20 rods be taken out of it, how miny perches are there in the remainder ?

Ans. 980 perches. 4. Three fields contain, the first 7 acres, the second 10 res, the thad 12 acres, 1 rood; how many shares can by be divided into, each share to contain 76 rods ?

Ans. 61 shares, and 44 rods over.

1. In 14 tons of hewn timber, how many solid inches? Ans. 14x50x1728-1209600.

2. In 19 tons of round timber, how

many inches?

Ans. 1313280.

3. In 21 cards of wood, how many solid feet?

Ans. 21×128=2688.

4. In 12 cords of wood, how many solid feet and inches? Ans. 1536ft. and 2654208inch. 5. In 4608 solid feet of wood, how many cords? Ans. S6cds.

11. TIME.

1. In 41 weeks, how many days; hours, minutes, and sonds ?

Ans. 287d. 6888h. 413280min. and 24796800'sec. 2. In 214d. 15h. 31m. 25sec. how many second's? Ans. 18545485sec.

3. In 24796800 seconds, how many weeks?

Ans. 41 weeks.

4. In 184009 minutes, how many days?

Ans. 127d. 18h. 49min. 5. How many days from the birth of Christ, to Christas, 1797, allowing the year to contain 365 days, 6 hours. Ans. 656554d. 6h. 6. Suppose your age to be 16 years and 20 days, how any seconds old are you, allowing $65 days and 6 hours the year? Ans. 506649600sec. 7. From March 2d, to November 19th following, inusive, how many days?

12. CIRCULAR MOTION.

Ans. 262.

1. In 7 signs, 15° 24′ 40′′ how many degrees. minutes, and seconds?

Ans. 225 13524 and 811480"

2. Bring 1020300 seconds into signs.

Ans. 9 signs, 13° 25′

QUESTIONS TO EXERCISE REDUCTION.

1. In 1259 groats, how many farthings, pence, shilling

and guineas at 988.

Ans. 20144grs. 50368, 419s. 94. and 14guineas, Ms. Sd.

2. Borrowed 10 English guineas at 28s. each, and 24 English crowns at 6s. and 8d. each; how many pistoles at 22s. each will pay the debt? Åns. 20. 3. Four men brought each 177. 10s. sterling value in gold into the mint, how many guineas at 21s. each must they receive in return? Aus. 66 guin. 148.

4. A silversmith received three ingots of silver, each weighing 27 outices, with directions to make them into spoons of 2oz. cups of 5 oz. saits of 1 oz. and suufl' boxes of 2 oz. and deliver an equal number of each; what was the wumber? Ans. 8 of each, and Voze over.

5. Admit a ship's cargo from Bordeaux to be 250 pipes, 150 hlds. and 150 quarter casks [} hhds.} how many gallons in all; allowing every pint to be a pound, what burden was the ship of? Ans. 44415 gals, and the ship's burden was 158 tons, 12ewi. 2yrs. 6. In 15 pieces of cloth, each piece 20 yds. how many French Eils? Ans. 200.

7. In 10 bales of cloth, each bale 12 pieces, and each piece 23 Flemish Ells, how many yards? dus. 2250.

8. The forward wheels of a waggon are 143 feet in ircumference, and the hind wheels 15 feet 9 inches, how Lany more times will the forward wheels turn round than the kind wheels, in running from Boston to New-York, it being 248 miles ? Ans, 7167. 9. How many times will a ship 97 feet 6 inches long, sail her length in the distance of 12800 leagues and ten yards? Ans. 2079508. 10. The sun is 95,000,000 of miles from the earth, and a cannon ball at its first discharge flies about a mile in 73 seconds; how long would a caŭnon ball be, at that rate in flying from here to the sun ?

Aus. 22yr. 216d. 19h. 40m. 11. The Sun travels through 6 signs of the Zodiac in halt a year; how many degrees, minutes and seconds? Ans. 1802eg. 10800min. 648600see.

2. How many strokes does a regular clock strike in
days, or a year?
Ans. 56940.
3. How long will it take to count a million at the rate
10 a minute? Ans. 333h. 20m. `or 15d, 21k. 20ri.

14. The national debt of England amounts to about 279 millions of pounds sterling; how long would it take to count this debt in dollars (4s. 6d. sterling) reckoning without intermission twelve hours a day at the rate of 50 dollars a minute, and 365 days to the year ?

Ans. 94 years; 134 days, 5 hours, 20 min.

FRACTIONS.

FRACTIONS, or broken numbers, are expressions fo any assignable part of an unit or whole number, and (ir general) are of two kinds, viz.

VULGAR AND DECIMAL.

A Vulgar Fraction, is represented by two numbers pla ced one above another, with a line drawn between them thus,,,&c. signifies three-fourths, five-eights, &c. The figure above the line, is called the numerator, ane hat below it, the denominator,

Thus,

S5 Numerator.
28 Denominator.

The denominator (which is the divisor in division) shews how many parts the integer is divided into; and the numerator (which is the remainder after division) shews how many of those parts are meant by the fraction.

A fraction is said to be in its least or lowest terms, when it is expressed by the least numbers possible, as when reduced to its lowest terms will be, and equal to 4, &c.

PROBLEM I.

To abbreviate or reduce fractions to their lowest terms

RULE.

Divide the terms of the given fraction by any number which will divide them without a remainder, an the quetients again in the same manner; and so on, tillit appears that there is no number greater than 1, which will divide then and the fraction will be in its least terins