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REDUCTION. 6. If from the creation of the world, to the end of the present year, 1830 of the Christian era, 184107038400 seconds will be elapsed, required the number of years since the creation of the world.

Ans. 5834. 7. How many days from June 6th included, to October 9th included ?

Ans. 126 days. 8. Reduce a solar year to seconds. Ans. 31556937sec. 9. Reduce 126227748 seconds to solar years. Ans. 4.

MOTION, OR CIRCULAR MEASURE. This measure is used by astronomers, navigators, &c. The denominations are, revolution or circle, sign, degree, minute, and second. 60 seconds

equal=1 minute, 60 minutes

1 degree, 30 degrees

1 sign, sig 12 signs, or 360°

1 revolution of a

planet, or circle.

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EXAMPLES.

1. In 4sig. 23° 15' 34" how many seconds ?

Ans. 515734". 2. How many minutes and seconds in one complete revolution of a planet? Ans. 21600' and 1296000". 3. In 1131385 seconds how many signs?

Ans. 10sig. 14° 16' 25". 4. The planet Venus at its greatest elongation appears about 166800 seconds from the sun--required the number of degrees.

Ans. 46° 20'. LAND OR SQUARE MEASURE. This measure is applied to land, and has respect to length and breadth. The denominations åre, mile, acre, rood, square perch, square yard, square foot, and square inch. 144 square inches in. equal=1 square foot, ft.

9 square feet, or 1296 square inches 1 square yard, yd. 30.25 square yds, or 272.25 square ft. 1 square perch?. 40 square P. or 1210 square yds. or 10890 square feet,

1 rood,

R. 4 roods, or 160 square perchés

A. 640 acres

1 mile,

M. OTE. --See the Chain denomination under Long Measure.

1 acre,

EXAMPLES.

1. In 29 acres, 3 roods, 19 perches, how many perches?

Ans. 4779P. 2. In 1997 perches, how many acres ?

Ans. 12A. 1R. 37P. 3. In 89763 square yards, how many acres, &c. ?

Ans. 18A. 2R. 7P. 101ft. 36in. 4. A tract of land, containing 1299600 square perches, is to be divided into -25 plantations—required the contents of each plantation.

Ans. 324A, 3R. 24P. 5. One square mile is called a section of land-how many perches does it contain ?

Ans. 102400P. CUBIC, OR SOLID MEASURE. By this measure is ascertained the solid content of all things in which length, breadth, and thickness are considered; such as stone, timber, wood, or bark, grain, coal, &c. The denominations are, ton, cord, perch, bushel, yard, foot, and inch.

1728 cubic inches c. in. equal=1 cubic foot, c. ft. 46656 cúbic inches, or 27 cubic feet l cubic yard, c. yd. 2150.4252 c. in. or 1.24446 c. ft. 1 bushel, of strick

measure, 2553.6299 c. in. or 1.47779+ c. ft. 1 bushel, of heaped

c. bu..

measure.

24.75 c. feet, or 42768 с. inches 1 perch,

ph. 128 c. feet, or 221184 c. inches 1 cord,

cd. 40 c. feet of round, or 50 of square (sawn) timber

1 ton,

7. Fire-wood is usually cut 4 feet in length, and corded in tiers of 4 feet in height; when so corded, every 8 feet in length equal=1 cord.

EXAMPLES. 1. In 15 tons of hewn timber, how many solid inches?

Ans. 1296000. 2. In 622080 solid inches, how many tons of round timber?

Ans. 9. 3. In 25 cords of wood, how many inches?

Ans. 5529600. 4. In 5529600 cubical inches, how many cords?

Ans. 25cds.

REDUCTION.

16
5. In 12 tons of hewn timber, how many inches ?

Ans. 1036800.
LIQUID MEASURE.
This measure is used for beer, cider, wine, &c.
The gallon contains 231 cubic inches; or.13368ft.

The denominations are, ton, pipe or butt, puncheon, hogs. nead, tierce, barrel, half-barrel, gallon, quart, pint, and gill.

equal=1 pint, 2 pints

1 quart, 4 quarts

1 gallon, 16 gallons

1 half-barrel,

hf. bar. 31.5 gallons

1 barrel, bar. 42 gallons

1 tierce,

tier. 63 gallons

1 hogshead, hhd. 84 gallons

1 puncheon, punch. 2 hogsheads

1 pipe or butt, p. or b. 2 pipes or butts

1 ton,

T.

4 gills g

pt.
qt.
gal.

EXAMPLES.

1. Reduce 9hhds. 15gals. 3qts. of wine, into gills.

Ans. 18648 g. 2. Reduce 19152 pints to hhds.

Ans. 38hhds. 3. In 11 barrels of beer, how many quarts ?

Ans. 1386qts. 4. How mary dozens of gallon, quart, and pint bottles, of each a like number, will be contained in a cask of Madeira of 165 gallons ?

Ans. 10 dozen.

DRY MEASURE. This measure is used for all dry goods. The Winchester bushel is 18.5 inches in diameter, and 8 inches deep, and contains 21502 or 2150.4252 cubical inches. Wheat, beans, flax-seed, salt, &c. are measured by struck or level measure ; but fruit, roots, oysters, charcoal, &c. by heaped measure, which is about of a bushel more than the struck measure. The bushel contains 2553.6299 (or 2553.6:3) cubical inches. The denominations are, bushel, peck, quart, and pint.

2 pints pt. equal=1 quart, qt.
8 quarts

1 peck, p.
4 pecks

1 bushel, bu.

EXAMPLES.

1. Reduce 27 bushes, 3 pecks, to pints. Ans. 1776pts. 2. In 5054 pints, how many

bushels ?

Ans. 78bu. 3p. 7qt. 3. Reduce 11 bushels, 3 pecks to pecks.

Ans. 47p. 4. Reduce 518 pints to bushels.

Ans. 8bu. 3qt.
PARTICULARS.
The denominations are, great gross, common gross, hun-
dred, score, dozen, and single thing.

12 single things equal=1 dozen, doz.
12 dozen

1 gross,

gro. 12 gross or 144 dozen

1 great gross, G.

gro.
ALSO,
20 single things equal=1 score,
5 score

1 hundred, hund.

SCO.

EXAMPLES.

1. How many buttons in 1 great gross? Ans. 1728.

2. Admitting the button factory at Bridgeton to make 34716 buttons per day, how many, at that rate, will they manufacture in one week, or six days' labor ?

Ans. 120G.gro. 6gro. 6doz. 3. In 820 single things, how many score, and how many hundred, &c.

Ans. 41sco. or Bhund. 1sco.

PAPER.
The denominations are, bundle, ream, quire, and sheet.

24 sheets, or 23.6
20 quires
2 reams

equal =1 quire, qr.

1 ream,

re.

1 bundle, bun.

The two outside quires of a ream of paper contain only 20 sheets each, which are broken, or defective, and termed cassie. The sizes of paper are designated by, post, foolscap, super-royal, imperial, elephant, atlas, and antiquarian.

EXAMPLES. 1. In 10 reams of paper, how many sheets ? Ans. 4720.

2. In 19722 sheets of paper, how many quires, reams, and bundles?

Ans. 20bun. 1re. 15qr. 16 sheets.

66

or 36
or 24

66

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68

12 pence

EXAMPLES.

48

REDUCTION.

SIZES OF PAPER. The sizes of paper are designated by quarto and folio post, coloured letter-paper, foolscap, crown, demy, medium, royal, superroyal, imperial, elephant, atlas, and antiquarian.

BOOKS. The denominations are, folio, quarto, octavo, duodecimo, 18mo. 24mo. 36mo., &c.

36mo. is when 1 sheet makes 36 leaves, or 72 pages.
24mo.

24 or 48
18mo.

18 12mo.

12 Octavo, or 8vo. 6

8

or 16 Quarto, or 4to.“

4

or 8 Folio, or fol.

2

or 4
ENGLISH MONEY.
The denominations are, pound, shilling, pence, and farthing.
4 farthings gr. equal = 1 penny, d.

= 1 shilling, s.
20 shillings

1 pound, £ A sovereign, or pound sterling of Great Britain = $4 44cts. 1. In £27 15s. 6d. 2qrs. how many farthings? 20

PROOF. 12

4)26666 6666 d

12)6666—2 qrs. 4

2,0)55,5—6 Ans. 26666 qrs.

$27 15 6 2qrs. In multiplying by 20 we add the 15s, by 12 the 6d, and by 4 the 2qrs., which must always be done in like cases.

2. In £36 12s. 10d. Iqr. how many farthings ? Ans. 35177qrs. 3. In 24615 farthings, how many pounds ? Ans. £25 12s. 9d. 3qr. 4. In 19200 pence, how many sovereigns ?

Ans. 80.
REDUCTION OF GOLD COINS.

EXAMPLES.
1. Required the value of llb. of pure gold.

Ans. $248.27535 2. Required the value of llb. of standard gold of the United States.

Ans. $223.2553 3. Required the value of llb. of standard gold of G. Britain, it being 11 parts fine and 1 part alloy-containing 5280gr. of pure gold per Ib.

Ans. #227.58629. Questions.—How are pounds troy reduced to ounces? Why? Ounces to pennyweights ?. Why? Pennyweights to grains ? Why? &c. &c. going throngh all the weights and measures, including English money, Reduction of Gold Coins.

555 s.

and

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