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COMPOUND RULES.

1. TABLES

OF THE RELATIVE VALUE OF THE

DIFFERENT DENOMINATIONS OF

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.

10 cents

cent, marked ct.
dime,

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d.

make one

10 dimes, or 100 cts.

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10 dollars

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12 ounces

make one

24 grains, grs.

pennyweight, marked,pwt.

ounce,

66 0%.

66 lb.

By this weight, are weighed gold, silver, jewels, electuaries and

liquors.

4. AVOIRDUPOIS WEIGHT.&

{

pound,

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marked oz. 66 lb.

make one

quarter of a hundred, " qr. hundred weight,

ton,

cwt.

66 T.

By this weight, are weighed all things of a coarse, or drossy nature, such as butter, cheese, meat, groceries and metals, except gold and silver.

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

See

+ The value of the several denominations of English money, is different in different places. An American dollar is equal to 4s. 6d. 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. 6d. in Pennsylvania, NewJersey, Delaware, and Maryland, or 4s. 8d. in South Carolina, and Georgia. A A moidore in N. E. is 36s. guinea is 21s. in England, or 28s. in New-England.

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.

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♦ The practice of grossing, as it is called, that is, of considering the quarter

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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.

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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 lb. A barrel of candles, 120 lb. A barrel of soap, 265 lb. 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.

Thirty 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 days, 5h. 48m. 57. or nearly 365 14 days. A common year con-
sists 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 method 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. 12s. 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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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.

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

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breadth and 4 in height

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

* 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 make one rod, 100 links one chain, 10 chains one 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 foot, 5 feet a pace, 6 feet a fathom. A mile is equal to 320 rods, or 1760 yards, or 5280 feet. league is equal to 3 miles.

A

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 1 foot, 2-8, 2 feet, &c.

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By wine measure are measured rum, brandy, gin, perry, cider,

mead, vinegar and oil.

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

* The other denominations of this measure, 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, marked 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 gallon, dry measure, is 268 4 5 cubic inches. A Winchester bushel is 18 1-2 inches diameter, and 8 iuches in depth. By act of the Legislature, 1816, the bushel in Vermont, for measuring coal, ashes and lime, was ordered to contain 38 qts or 2553 3 5 cubic inches. A common bushel of 4 pecks, contains 2150 2-5 cubic inches.

The inconveniences which result from so great a diversity in weights and measures, have already engaged 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 same time promote the welfare of the people, and render an essential aid to the cause of science. NOTE. 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.

2. Compound Addition.

COMPOUND ADDITION is the adding of numbers 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. 6m. and 12E. $0. 9d. 8cts. 7m. added together?

OPERATION.

E. $ d. cts. m.
4 5 3 4
12 0 9

8

6

As the value of the denominations increase in a tenfold proportion, we here carry by 10 from one deno7mination to another, and the operation is performed precisely as in Simple Addition. In business, we com 16 6 3 3 3 monly reckon by dollars and cents only, as in the third and fourth examples.

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1. What is the sum of £9 16s. 10d. £7 10s. 9d. and 18s 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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