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2. Troy Weight. 24 grains (gr.) make

1 penny-weight, marked prot. 20 penny-weights, 1 ounce,

Oz. 12 ounces,

1 pound,

3. Avoirdupois Weight. 16 drams (dr.) make

1 ounce, 16 ounces,

1 pound,

16. 28 pounds, 1 quarter of a hundred weight,

9r. 4 quarters,

1 hundred weight, crot. 20 hundred weight,

1 tun.

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

4. Apothecaries Weight. 20 grains (gr.) make 1 scruple, 3 scruples, 1 dram,

3 8 drams,

1 ounce, 12 ounces,

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

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

1 yard,

yd. 3 quarters,

1 El Flemish, E. FI. 5 quarters,

1 Ell English, E. E. 6 quarterz,

1 Eli French, E. Fr.

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

2t. 8 quarts, 1 peck,

pk. 4 pecks, i bushel,

bu. This measure is applied fo grain, beans, flax-seed, salt dats, oysters, coal, &c:

7, Wine Measure.

9t.

gal.

1 pipe, 1 tun,

4 gills (gi.) make

1 pint, 2 pints,

1 quart, 4 quarts,

1 gallon, 314 gallons, 1 barrel,

bl. 42 gallons, 1 tierce,

tier. 63 gallons, 1 hogshead,

ehhd 2 hogsheads,

f: 2 pipes,

All brandies, spirits, mead, vinegar, oil, &c. are measur. ed by wine measure.

Note. 231 solid inches, make a gal lon. 8. Long Measure.

in. 3 barley corns (b. c.) make 1 inch, marked 12 inches,

1 foot, 3 feet,

1 yard, 5} yards,

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

1 furlong,

fur. 8 furlongs,

1 mile, 3 miles,

1 leaguc,

lca. 69, statute miles,

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

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 1 hand, In measuring depths, 6 feet make 1 fathom or French toise. Distances are measured by a chain, four rods long, containing one hundred links.

yd.

m.

1 square rood.

9. Land, or Square Measure. 144 square inches make

1
square

foot. 9 square feet

1 square yard. 394 square yards, or 2721 square feet, }

1 square rod. 40 squarc rods, 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 50 feet of hewn timber,

1 tun or load. 128 solid feet, or 8 feet long,

I cord of wood. 4 wide, and 4 high, 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 gallon, 282. A bushel contains 2150,42 solid inches.

1 day,

mo.

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

1 hour,

h. 24 hours,

d. 7 days,

I week, 4 weeks,

I month, 13 months, 1 day and 6 hours, 1 Julian year, yr. Thirty days hath September, April, June, and November, February twenty-eight alone, all the resi have thirty-one. N. B. In Bissextile, or leap year, February hath 29 days.

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

1 degree, 30 degrees,

s. 12 signs, or 360 degrees, the whole great círcle of the Zodiack.

1 sign,

B

Explanation of Characters used in this Book,

Equal to, as 12d. = ls. signifies that 12 pence are equal to 1 shilling

+ 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, 82=4, signifies that 8 divided by 2, is equal to 4; or thus, 54, 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 hy the following characters, or figures :

1, 2, 3, 4, 5, 6, 7, 8, 9, 0-or cipher. Besides the simple value of figures, each has a local value, which depends upon the place it stands in, viz. any ågure in the place of units, represents only its simple value, or so many ones; but in the second place, or place of tens, it becomes so many teps, or ten times its simple value ; and in the third place, or place of hundreds, it becomes a hundred times its simple value, and so on, as in the following

Note. -Although a cipher standing alone signifies nothing ; yet when it Is placed on the right hand of figures, it increases their value in a tenfold proportion, by throwing them into higher places. Thus, 2 with a cipher annexed to it, becomes 20, twenty, and with two ciphers, 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 as many periods as we can,

of six figures each, reckoning from the right hand towards the left, calling the first

the period of units, the second that of millions, the third billions, the fourth trillions, &c. as in the following number :

8 0 7 3 6 2 5 4 6 2 7 8 9 0 1 2 5 0 6 og 92 4. Period of 3. Period of 2. Period of 1. Period of Trillions. Billions. Millions.

Units.

8073
625462
789012

506792 The foregoing number is read thus-Eight thousand and seventy-three trillions ; six hundred and twenty-five thousand, four hundred and sixtytwo 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, foc.

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