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2. Troy Weight. 24 grains (gr.) make 1 penny-weight, marked put. . 20 penny-weights, 1 ounce, 12 ounces,

1 pound,

3. Avoirdupois Weight. 16 drams (dr.) make 1 ounce, 16 ounces,

1 pound, 28 pounds, 1 quarter of a hundred weight, 4 quarters,

1 hundred weight, cwt. 20 hundred weights 1 ton,

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

4. Apothecaries Weight. 20 grains (gr.) make 1 scruple, S scruples, . 1 dram, 8 drams,

1 ounce, 12 ounces,

1 pound, Apothecaries use this weight in compounding their medicines.

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5. Cloth Measure.

4 nails (na.) make 1 quarter of a yard, qr. 4 quarters,

1 yard,

yd. 3 quarters,

1 Ell Flemish, E.H. 5 quarters,

1 Ell English, E. E. 6 quarters,

1 El French, E.Fr.

6. Dry Measure. 2 pints (pt.) make 1 quart, 8 quarts,

1 peck, 4. pecks, .

1 bushel, This measure is applied to grain, beans, flax-sced, salt, oats, oysters, coni, &c.

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All brandies, spirits, mead, vinegar, oil, &c. are meagured by wine measure. Note.-231 solid inches, make a gallon.

8. Long Measure.

in.

s barley corns (b.c.) make 1 inch, marked 12 inches,

I foot, 3 feet,

1 yard, • 5 yards,

1 rod, pole, or perch, rd. 40 rods,

1 furlong,

1 mile, . Smiles,

1 league, 69} statute miles,

1 degree, on the earth. 360 degrees, the circumference of the earth.

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The use of long measure is to measure the distance of places, or any other thing, where length is considered, without regard to breadth.

N. B. In measuring the height of horses, 4 inches make i hand. In measuring depths, six feet make 1 fathom, or French toise. Distances are measured by a chain, four rods long, containing one hundred links.

9 Land, or Square Measure. ', 144 square inches make 1 square foot. 9 square feet,

1 square yard. 304 square yards, or 2724 square feet,

1 square rod. 40 square rods,

1 square rood. 4 square roods,

1 square acre. 640 square acres,

1 square mile. 10. Solid or Cubic Measure. 1728 solid inches make

1 solid foot.. 40 feet of round timber, or

{ 1 ton or load.

1 to
50 feet of hewn timber, S
128 solid feet or 8 feet long,

feet long, } 1cord of wood.! 4 wide, and 4 high, : S All solids, or things that have length, breadth and depth, are measured by this measure. N. B. The wine gallon contains 231 solid or cubic inches, and the beer gallan, 282. A bushel contains 2150,42 solid inches.

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11. Time. 60 seconds (S.) make 1 minute, marked S.M. 60 minutes,

1 hour, 24 hours, : 1 day, 7 days,

1 week, 4 weeks,

1 month, 18 months, 1 day and 6 hours, 1 Julian year, yr. Thirty days hath September, April, June, and November, February twenty-eight alone, all the rest have thirty-one.

N. B. In bissextile, or lea) year, February hath 29 days.

12. Circular Motion 60 seconds (TM) make 1 minute, 60 minutes,

1 degree, 30 degrees,

.1 sign, 12 signs, or 360 degrees, the whole great circle of the

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Explanation of Characters used in this Book.

- Equal to, as 12d.

equal to 1 shilling.

1s. signifies that 12 pence are

+ More, the sign of addition, as 5+7=12, signifies

that 5 and 7 added together, are equal to 12.

---- Minus, or less, the sign of subtraction, as 6-2-4,

signifies that 2 subtracted from 6, leaves 4.

X Multiply, or with, the sign of Multiplication; as 4x3=12, signifies that 4 multiplied by 3, is equal to 12.

The sign of Division; as 8+2=4, signifies that divided by 2, is equal to 4; or thus, =4, each of which signify the same thing.

{ : Four points set in the middle of four numbers, denote

them to be proportional to one another, by the rule of three; as 2:4::8:16; that is, as 2 to 4, so is 8 to 16.

Prefixed to any number, supposes that the square root

of that number is required.

3 Prefixed to any number, supposes the cube root of that number is required.

Denotes the biquadrate root, or fourth power, &c.'

ARITHMETIC is the art of computing by numbers, and has five principal rules for its operation, viz. Numeration, Addition, Subtraction, Multiplication, and Division.

NUMERATION. Numeration is the art of numbering. It teaches to express the value of any proposed number by the follow: ing characters, or figures :

1, 2, 3, 4, 5, 6, 7, 8, 9, D or cypher." Besides the simple value of figures, each has a local value, which depends upon the place it stands in, viz. any figure in the place of units, represents only its simple value, or so many ones, but in the second place, 0.

NOTE.-Although a cypher standing alone signifies nothing; yet when it is placed on the right hand of figures, it in creases their value in a tenfold proportion, by throwing them into higher places. Thus 2 with a cypher annexed to it becomes 20, twenty, and with two cyphers, thus, 200, two hundred.

2. When numbers consisting of many figures, are given to be read, it will be found convenient to divide them into ag many periods as we can, of six figures each, reckoning from the right hand towards the left, calling the first the period o. units, the second that of millions, the third billions, the fourth. trillions, &c. as in the following number:

2 O 3 6 2 5 4 6 2 7 8 9 0 1 2 5 0 6 y 9 2 4. Period of 1 3. Period of 2. Period of 1. Period of

Trillions. Billions. Millions. Units.

890

8078
625462

789012 1 506792 The foregoing number is read thus-Eight thousand and seventy-three trillions; six hundred and twenty-five thousand, sour hundred and sixty-two billions ; seven hundred and eighty-nine thousand and twelve millions ; five hundred and six thousand, seven hundred and ninety-two.

N. B. Billions is substituted for millions of millions.
Trillions for millions of millions of millions.
Quatrillions for millions of millions of millions of millions.

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