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COBB'S

EXPLANATORY ARITHMETICK.

Ques. What is COMPOUND ARITHMETICK? Ans. It is the working of figures employed to express quantities of different denominations.

Note. To TEACHERS. All the EXPLANATIONS should be thoroughly and carefully read by the young scholar, as they are intended to impress deeply on his mind the principles of the rules, and their importance in his operations.

EXPLANATIONS.

You have already learned the five fundamental rules of Arithmetick. You have learned, to enumerate, to add, to substract, to multiply, and to divide numbers; that is, simple, whole numbers. You must now learn to work figures employed to express quantities of different denominations; as, bushels, pecks, quarts, and pints; pounds, ounces, and drachms; leagues, miles, and furlongs; yards, feet, and inches; years, months, and days; and for describing things of different values; that is, money of various sorts; as, eagles, dollars, dimes, cents, and mills. To work figures employed in these most useful purposes, is the present object of your attention. As the quantities and values are so various, and as several of them are occasionally joined to

gether in one sum, or are compounded, the working of figures thus employed, is called COMPOUND ARITHMETICK.

You must not be alarmed, or apprehend any dif ficulty, in consequence of the extent or apparent intricacy of this branch of the study; for the prin ciples in compound quantities do not materially differ from those in simple numbers, such as you have been working. You have, I presume, found it easy to express and to manage sums of the largest amount, by making yourself acquainted with the principles on which they are stated, and by which they are worked; and by a similar attention to a very simple rule or two, you will, also, see every difficulty vanish here; and will find it easy to work figures, however new and strange to you, the several quantities and values they may be employed to express.

If there had been only one unit for each kind of quantity, or if there had been different units increasing or decreasing in a tenfold proportion, then all Arithmetical operations, on the values of quantities, might have been expressed by the common or simple rules of Arithmetick. But for the sake of practical convenience, and from other causes, different units or denominations, for the same kind of quantity, and increasing in various proportions, have been introduced; and it is necessary that you should be acquainted with these units and their proportions; and that certain rules should be given for the convenient calculation of quantities, when represented in their various units or denominations.

Before you commence any operation in these compound rules, it is highly important, and, indeed, it is absolutely necessary, that you thoroughly learn the following Arithmetical tables.

FEDERAL MONEY.

This money increases in a tenfold proportion, and accounts are generally kept in it throughout the United States.

The denominations are, Eagle, Dollar, Dimes Cent, and Mill.

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The denominations of this money are, Pound,

Shilling, Penny, and Farthing.

4 farthings qr.

12 pence

20 shillings

make 1 penny, d.

1 shilling, s.

1 pound, £

TIME.

The denominations of time are, Year, Month, Week, Day, Hour, Minute, and Second.

60 seconds, sec. make 1 minute, min.

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AVOIRDUPOIS WEIGHT.

By this weight, all coarse and drossy goods, gro. ceries, and all metals, except gold and silver, are weighed.

The denominations are, Tun, Hundred-weight, Quarter, Pound, Ounce, and Drachm.

16 drachms, dr. make 1 ounce, oz.

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1 pound, lb.

- 1 quarter, qr.

1 hundred-weight, cut. 1 tun, T.

APOTHECARIES WEIGHT.

This weight is used by apothecaries in compounding medicines; but all goods of this kind are bought and sold by Avoirdupois Weight.

The denominations are, Pound, Ounce, Drachm, Scruple, and Grains

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This weight is used for weighing gold, silver, jewellery, liquors, &c.

The denominations are, Pound, Ounce, Pennyweight, and Grain.

24 grains, gr. make 1 penny-weight, pwt.
20 penny-weights - 1 ounce, oz.

12 ounces

- 1 pound, lb.

DRY MEASURE.

This measure is used for grain, salt, coal, fruit, &c. The denominations are, Chaldron, Bushel, Peck, Gallon, Quart, and Pint.

A gallon in this measure contains 268% solid inches, and a bushel 2150,4%.

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This measure is applied to all spirituous liquors, vinegar, oil, &c.

The denominations are, Tun, Pipe, Puncheon, Hogshead, Tierce, Barrel, Gallon, Quart, Pint, and Gill.

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2 pipes, or4hogsheads, 2

or 252 gallons

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1 hogshead, hhd.
1 puncheon, pun.
1 pipe, P.

1 tin, T.

The wine gallon contains 231 solid or cubick inches.

LONG MEASURE.

This measure is required where length is considered, without reference to breadth, as, for instance, the distance from one place to another.

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