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COMPOUND RULES.
1. TABLES

DENOMINATIONS OF OF THE RELATIVE VALUE OF THE

COIN, WEIGHT AND MEASURE, WHICH ARE USED IN THE TRANSACTION OF BUSINESS.

Those which are essentially necessary to be understood by every individual, are expressed in the text, and should be perfectly committed to memory. Those which are less common, and less essential, will be found in the notes.

1. FEDERAL MONEY.* 10 mills, m.

cent, marked ct.
dime,

d. 10 cents

make one 10 dimes, or 100 cts.

dollar,

E. 10 dollars

eagle,
2. ENGLISH MONEY.
4 farthings, qr.
12 pence

make one

shilling, 20 shillings

pound, 3. TROY WEIGHT. 24 grains, grs.

pennyweight, marked,pwt. 20 pennyweights

make one
ounce,

16. 12 ounces

pound, By this weight, are weighed gold, silver, jewels, electuaries and liquors.

4. AVOIRDUPOIS WEIGHT. 16 drams, dr.

ounce,

marked oz. 16 ounces

pound,

lb. 28 pounds

make one
quarter of a hundred,"

qr. 4 quarters

hundred weight,

66 cwt. 20 hundred weight

ton,

7. By this weight, are weighed all

things of a coarse, or drossy nature, such as butter, cheese, meat, groceries and inetals, except gold and silver.

See * The nature of this currency will be more fully explained hereafter. Federal Money.

+ The value of the several denominations of English money, is different in different places. An American dollar is equal to 45. 60. in England, or 5s in Canada and Nova-Scotia, or 6s. in New-England, Virginia, and Kentucky, or 8s. in New York, Ohio, and North Carolina, or 7s. 60. in Pennsylvania, NewJersey, Delaware, and Maryland, or 4s. 84. in South ('arolina, and Georgia. A guinea is 21s. in England, or 28s. in New-England. A moidore in N, E. is 36s.

# The weight used by Apothecaries in compounding their medicines, is the same as Troy weight, having only some different divisions. The following is the table of Apothecaries' weight. 20 grains, grs.

scruple, marked sc. 3 scruples

dram, 8 drams

make one 12 ounces

pound

16. • The practice of grossing, as it is called, that is, of considering the quarter

dr.

ounce,

2.

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W.

mo.

Julian year

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5. OF TIME.* 60 seconds, s.

minute, marked, m. 60 minutes

hour

h. 24 hours

day

d. 7 days

week 4 weeks

lunar month 13 mno. 1 d. 6 h. 2

Y. or 365 d. 6 h. S

6. CIRCULAR MOTION.
60 seconds"

minute, marked'
60 minutes

make one

degree 30 degrees

sign 12 signs, or 360°

circle. Every circle, without regard to its size, is supposed to be divided in 360 equal parts, called degrees; and these again to be subdivided into minutes and seconds ; so that the absolute quantity expressed by any of these denominations, must always depend upon the size of the circle.

7. CLOTH MEASURE. 24 inches, in.

nail,

marked na. 4 nails, or 9 in.

make one
quarter

qr. 4 quarters

yard

yd. 5 quarters

English ell 6 E. E. to be 28lbs. and the hundred weight to be 112 lb. is now pretty generally laid aside, and, both in buying and selling, 25 lb. are, as they should be, considered a quarter, and 100lbs. a hundred weight. 144 lb Avoirdupois equals 175 lb. Troy; and 192 oz. Avoirdupois equals 175 oz. Troy. An Avoirdupois pound weighs 7000 grains; a Troy pound, 5760 grains. A firkin of butter is 56 lb. A firkin of soap, 64 lb. A barrel of pot ashes, 200 1h. A barrel of candles, 120 lb. A barrel of soap, 265 1b. A barrel of butter, 224 lb. A barrel of pork or beef is 220 lb.

A quintal of fish, 112 lb. * In civil reckoning, the year is divided into 12 Calendar months, and the number of days in each, may be readily called to mind by the following verse.

Tbir y days hath September, April, June and November;

February twenty-eight alone, and all the rest have thirty-one. Another day is added to February every fourth year, making the month consist of 29 days. This is called Bissextile, or Leap year. Leap-year is found by dividing the year of our Lord by 4; if nothing remain, it is Leap-year ; but if 1, 2 or 3 remain, it is 1st, 2d, or 3d after Leap-year. The true solar year con-sists of 365 day, 5h. 48m. 57s, or nearly 365 1 4 days. A common year consists of only 365 days, and one day is added in Leap years to make up the loss of one quarter of a day in each of the three preceding years. This inethod of reckoning was ordered by Julius Cæsar 40 years before the birth of Christ, and is called the Julian Account, or Old Style. But as the true year fell 11m. 3s. short of 365 1.4 days, the addition of a day to every fourth year was too much by 44m. 12. This amounted to 1 day in about 130 years. To correct this error, in 1581, Pope Gregory ordered 10 days to be struck out of the Calendar, by calling the 5th of October the 15th, and to prevent its recurrence, ordered that each succeeding century divisible by 4, should be a Leap-year, and each not divisible by 4, should be a common year. This is called the Gregorian, or New Style. The difference between the New Style and Old, is now 12 days.

† A Flemish-ell is 3 qrs. a French-ell, 6 qrs. a Scotch-ell, 37 1-5 inches, and a Spanish var, 33 inches.

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8. LONG MEASURE* 3 barley corns, bar.

rinch, marked in. 12 inches

foot

ft. 3 feet

yard

.yd. 51 yds. or 16% ft.

rod, or pole, “rd.orpo. 40 rods make one furlong

fur. 8 furlongs

mile

mile. 60 geographical, or

degree 69 1-5 English miles

deg. 360 degrees

circumference of earth. The use of this measure is to find the distance of places, or to measure any thing where length only is concerned, without regard to breadth.

9. SQUARE MEASURE. 144 inches า

square foot.

น 9 feet

yard. or

rod. 2724 feet

make one
40 rods

rood.
4 roods
640 acres

mile. This measure is employed in measuring land, and all things where length and breadth are concerned.

10. SOLID MEASURE.I 1728 inches

foot. 27 feet

yard. 40 ft. of round, and

make one 50 ft. hewn timber

ton. 128 ft. i. e. & in length, 4 in

cord of wood. breadth and 4 in height

By this, are measured all things which have length, breadth and thickness.

acre.

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* For measuring considerable distances, as in surveying, a chain 4 rods in length, and divided into 100 links, or a half chain 2 rods long, and divided into 50 links, is usually employed. In this measure, 25 links enake one rod, 100 links one chain, 10 chains ope furlong, and 8 furlongs one mile. In addition to the above, in long measure, 60 geographical miles make a degree, 6 points make a line, 12 lines an inch, 4 inches a hand, 3 hands a fuot, 5 feet a pace, 6 feet a fathom.

A mile is equal to 320 rods, or 1760 yards, or 5280 feet. A league is equal to 3 miles.

f The numbers in this table are produced from the preceding by multiplying the several numbers into themselves, as 12 times 12 is 144, 3 times 3 is 9, &c. We may further observe, that an acre is equal to 160 square rods, or 4840 yards, or 43560 feet.

| This is also called cubic measure. For the ease of reckoning, the cord of wood is sometimes called 8 feet. In this case, 4 feet in length, 4 in breadth, and one in height, equal to 16 solid feet, is called a foot, or 8 in length, 4 in breadth, and 6 inches in height, a foot ; that is, 1-8 of a cord is called i foot, 2-8, 2 feet, &c.

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11. WINE MEASURE.* 4 gills, gs.

pint,

marked pt. 2 pints

quart 4 quarts

gallon
42 gallons

make one
tierce

tier.
63 gallons

hogshead

hhd. 2 hogsheads

pipe

P. 2 pipes

tun

T. By wine measure are measured rum, brandy, gin, perry, cider, mead, vinegar and oil.

12. ALE AND BEER MEASURE.* % pints, pts.

quart,

marked qt. 4 quarts

gallon

gal. 8 gallons

firkin of ale 9 gallons

firkin of beer « B. f.

make one 2 firkins

kilderkin

kil. 2 kilderkins

barrel

bar. 3 kilderkins

hogshead

hhd. 3 barrels

butt

butt.
13. DRY MEASURE.I
2 pints, pts.

quart, marked qt.
8 quarts

peck

pk.
4 pecks

make one
bushel

bu.
8 bushels

quarter

qr. 4 quarters

chaldron

ch. By this measure, all dry goods, as corn, grain, salt, fruit, roots, &c. are measured.

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* The other denominations of this ineasure, which are sometimes used, are anchors, runlets and half-hogsheads. An anchor of brandy is 10 gals. a runlet is 18 gals. a half-hogshead, 31 1-2 gals. A pint, wine measure, is equal to 28 7.8 cubic inches, and a gallon to 231 cubic inches. A common cider barrel contains from 32 to 36 gallons.

+ A pint in ale and beer measure, is 35 1-4 cubic inches, and a gallon is 282 cubic inches.

# The following denominations of this measure are sometimes used : 2 quarts make one pottle, narked pot. 2 pottles one gallon, 2 gals. one peck, 4 pks. one bushel, 2 bushels one strike, 2 strikes one coom, 2 cooms one quarter, 5 quarters one load, or wey. A gon, dry measure, is 268 4 5 cubic inches. A Wincherter bushel is 18 1-2 inches diameter, and 8 mcbes in depth. By act of the Legislature, 1816, the bushel in Vermont, for measuring coal, ashes and lime, was ordered to contain 38 qt« or 2553 3 5 cubic incbes. A common bushel of 4 pecks, contains 2150 2-5 cubic inches. The inconveniences which result from so great a diversity in weights and mea

bave already eng ged the attention of Congress, and we ardently hope that they in their wisdom, may devise some method of removing the evil. and establishing a uniformity. By doing this, they will at the sanie time promote the welfare of the people, and render an essential aid to the cause of science.

Not E.-20 particular things make one score, 12 one dozen, 12 dozen one gross, 12 gross one great gross. The habit of reckoning by dozens originated out of the English method of reckoning money; articles which were 4s. a dozen, being 4d. a piece, 3s. a doz. 8d. a piece, &c.

sures,

2. Compound addition. COMPOUND Addition is the adding of pumbers which consist of different denominations, as pounds, shillings, pence and farthings. The operations in this and the four following rules, are to be regulated by the values expressed in the 13 preceding tables.

Rule. * Place the numbers so that those of the same denomination may stand directly under each other.

Add the lowest denomination and carry for that number which it takes for that denomination to make one of the next higher, setting down the remainder. Proceed with the columns of each denomination in the same way till you come to the last, which is to be added as in Simple Addition.

Proof.
The method of proof is the same as in Simple Addition.

Examples.

1. FEDERAL MONEY. 1. What is the sum of 4E. $5.3d. 4cts. Om. and 12E. $0.9d. 8cts. 7m. added together?

OPERATION, E. $ d. cts. m. As the value of the denominations increase in a ten

4 5 3 4 6 fold proportion, we here carry by 10 from one deno12 09 8 7 mipation to another, and the operation is performed

precisely as in Simple Addition. In business, we com16 6 3 3 3 monly reckon by dollars and cents only, as in the

third and fourth examples. 2.

3.

4. E. S d. cts.

$ cts.

cts. 25 8 2 6

1259 43

2228

53 12 8 many 4

2568 74

3262 44 13 2 1 3

7289 95

120 36

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51 9 1 3

11118 10

2. ENGLISH MONEY. 1. What is the sum of £9 16s. 10d. £7 10s. 9d. and 188 6d. when added together?

Ans. £18 6s. 1d.

* The reason of this rule must be evident from what has been already said ; for in carrying from one denomination to another, we only express in the higher, the value which we omitted to write down in the lower.

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