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10. SOLID MEASURE. 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. 1313286. 3. In 21 cords of wood, how many solid feet ?

Ans. 21 x 128=2688. 4. In 12 cords of wood, how many solid feet and inches?

Ans. 1536ft, and 2654208inchi 5. In 4608 solid feet of wood, how many cords,

Ans. 36cds.

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1. In 41 weeks, how many days, hours, minutes, and seconds !

Ans. 287d. 6888h. 415280min, and 24796800sec. 2. In 214d. 15h. Sim. 25sec. how many seconds ?

Ans. 18545485 sec. §. In 24796800 seconds; how many weeks

Ans: 41 weeks. 4. În 184009 minutes; how many days

'Ans. 1278, 18h. 49min. 5. Ilow many days from the birth of Christ, to Christmas, 1797, allowing the year to contain 365 days, 6 hours.

- Ans, 656854d. 6h. 6. Suppose your age to be 16 years and 20 days, how many seconds old are you, allowing 365 days and 6 hours to the year?

Ans. 506649600sec. 7. From March 2d, to November 19th following, inclusive, how many days ?

Ans. 262.

12. CIRCULAR MOTION. 1. In 7 signs, 15° 24' 40" how many degrees, minutes, and seconds ?. Ans. 2250 15524' and 811480" 2. Bring 1020500 seconds into signs.

Ans9 signs, 13° 25'

QUESTIONS TO EXERCISE REDUCTION. 1. In 1259 groats, how many farthings, pence, shillings, and guineas at 28s.

Ans. 20144grs. 5056d. ; 4198. 8d. and 14guineas, 27 s. 8d.

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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 ?

Ans. 20. 3. Four men brought each 171. 10s. sterling value in gold into the mint, how many guineas at 21s. each inust they receive in return?

Ans, 66 guin. 14s. 4. A silversmith received three ingots of silver, each weighing 27 ounces, with directions to make them into spoons of 2 oz. cups of 5 oz. salts of 1 oz. and snuff boxes of 2 oz. and deliver an equal number of each ; what was the number?

Ans, 8 of each, and 1 oz. over.. 5. Admit a ship's cargo from Bordeaux to be 250 pipes, 150 hhds. and 150 quarter casks [hhds.] how inany 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, 12cwt. 2yrs. 6. In 15 pieces of cloth, each piece 20 yds. how many French Elis?

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. Ans. 200. 7. In 10 bales of cloth, each bale 12 pieces, and each piece 25 Flemish Ells, how many yards ? Ans. 2250.

8. The forward wheels of a waggon are 14) feet in circumference, and the hind wheels 15 feet 9 inches, how marty more times will the forward wheels turn round than the hind 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 niile in 7 seconds ; how long would a cannon ball be, at that rate in flying from here to the sun ?

Ans. 22yr. 216d. 12h. 40m. 11. The Sun travels through 6 signs of the Zodiac in: half a year ; how many degrees, minutes and seconds ?

Ans. 180deg. 10800min. 648000sec. 12. How many strokes does a regular clock strike in 365 days, or a year?

Ans, 56940. 18. How long will it take to count a million at the rate of 50 a minute? Ans. 33Sh. 20m. or 13d. 21h. 20m.

14. The national debt of England amounts to about 279 millions of pounds sterling; how long would it take to count this debt in doilars (4s. Cd. sterling) reckoning without interinission twelve hours a day at the rate of 59 dollars a minute, and 305 days to the year?

Ans. 94 years, 134 days, 3 hours, 23 min."

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

VULGAR AND DECIMAL. A Vulgar Fruction, is represented by two numbers placed one above another, with a line drawn between them, thus, , , &c. signifies three-fourtis, ve-eights, &c.

The figure above the line, is called the numerator, and that below it, the denominator,

S5 Numerator.

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Thus, 33 Denominator.

The denominator (which is the divisor in division). shows 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 terins will be ), and is equal to , &e.

PROBLEM I.
To abbreviate or reduce fractions to their lowest terms.

RULE.
Divide the terms of tre given fraction by any number
which will divide them without a remainder, an'i the quo-
tients again in the same inanner; and so on), till · appears
that there is no number greater than 1, which wil divide
them, and the fraction will be in its least terms

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EXAMPLES.
1. Reduce 144 to its lowest terins.

(3) (2)
8)4= = = the Answer.
2. Reduce to its lowest terms. Ans.
3. Reduce 1 to its lowest terins. Ais.
4. Recluice to its lowest terms. Ans.
5. Abbreviate 66 as much as possible. . ins.
6. Reduce 825 to its lowest terms.

Ans. 55 7. Reduce 14% to its lowest terms.

Ans. And 8. Reduce to its lowest terms.

Ans. ] 9. Peduce 171 to its lowest terms. 10. Reduce to its lowest terms, Aus.

PROBLE1 1. : To find the value of a fraction in the known parts of the integer, as to coin, weighit, measure, &c.

RÜLE.
Multiply the numerator by the cominon parts of the
integer, and divide by the denominator, &c.

EXAMPLES.
What is the value of of a pound sterling ?

Numer. 2

20 shillings in a pound. Denom. 3)40(138. 4d. Ans.

Veloch

Ans.

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2. What is the value of 1 of a pound sterling?

ins. 188. 5d. 2grs.
3. Reduces of a shilling to its proper quantity.

Ans. 41d. 4. What is the value of 3 of a shilling? Ans, 44d. 5. What is value of it of a pound troy? Ans. 90%.

6. How much is is of an hundred weight ?

:: Ans. 3qrs. 71b. 10-40z. 7. What is the value of of a mile?

Ins. 6fur. 26po. 11ft. 8. How much is į of an cwt. ?

Ans. 3qrs. 3lb. 1oz. 124dr. 9. Reduce of an Ell English to its proper quantity,

Ans. 2grs. 3 na. 10. How much is of a bhd. of wine ? Ans. 54gal. 11. What is the value of of a day?

Ans. 16h. 36min. 55. sec.

PROBLEM III. To reduce any given quantity to the fraction of any greater denomination of the same kind.

RULE. . Reduce the given quantity to the lowest term mention. ed for a numerator ; then reduce the integral part to the same term, for a denominator ; which will be the fraction required.

EXAMPLES. 1. Reduce 13s. '6d. 2qrs. to the fraction of a pound.

20 Integral part - 13 6 2 given sum.
12

12

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960 Denominator. 650 Num. Ans. 47915 2. What part of an hundred weight is Sqrs. 141b..

3qrs. 141b.=9815. Ans. 3. What part of a yard is Sqrs. Sna.. Ans. * 4. What part of a pound sterling is 138. 4d.? Ans. 5. What part of a civil year is 3 weeks, 4 days ? 6. What part of a mile is 6fur. 26po. Syds. 2it. ?" fur. po. yd. ft. feet. is 6 203 2=4400 Num.

a mile =520 Den m. Ans. 440031 7. Reduce 7oz. 4pwt. to the fraction of a pouni riy. 8. What part of an acre is 2 roods, 20 poies ? jins.

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