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Tables of Coin, Weights, and Measures. Denominations of Federal money as determined by an Act of Congress, Aug. 8, 1786.

10 mills make 1 cent marked c.
10 cents 1 dime

d.
10 dimes 1 dollar
10 dollars
1 Eagle

E. The coins of Federal money are two of gold, four of silver, and two of copper. The gold coins are an eagle and half-eagle; the silver, a dollar, half-dollar, double-dime, and "dime; the copper, a cent and half-cent. The standard gold and silver is eleven parts fine, and one part alloy. The weight of fine gold in the eagle is 246.268 grains; of fine silver in the dollar, 375.64 grains ; of copper in 100 cents 21 lbs. avoirdupois.*

ENGLISH MONEY.

4 farthings make 1 penny d. value in U. S. $0.019
1 shilling s.

.228
20 shillings
1 pound £.

4.4444 21 shillings 1 guinea

4.6724

12 pence

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FRENCH MONEY.

100 centimes make 1 franc, value $.1875.

TROY WEIGHT.

OZ.

24 grains (gr.) make 1 penny-weight dwt.
20 dwt.

1 ounce
1 pound

Ib. By this weight are weighed jewels, gold, silver, corn, bread, and liquors.

12 oz.

APOTHECARIES WEIGHT.

3 sc.

20 grains (gr.) make 1 scruple SC.

1 dram

dr. or 3 8 dr.

1 ounce oz. or 3 12 oz.

1 lb. * The above are the coins which were at first contemplated, but the double-dime has never been coined. Twenty-five-cent piecco and wall-dimes nave been coined.

Apothecaries use this weight in compounding their medicines ; but they. buy and sell their drugs by Avoirdupois weight. Apothecaries' is the same as Troy, having only some different divisions.

AVOIRDUPOIS WEIGHT.

16 oz.

4 qrs.

10 drams (dr.) make 1 ounce

OZ.
1 pound

Ib.
28 lbs.
1 quarter

qr.

hundred-weight cwt.
20 cwt.
1 ton

T. By this weight are weighed all things of a coarse and drossy nature ; such as butter, cheese, flesh, grocery wares, and all metals except gold and silver.

DRY MEASURE.

8 qts.

2 pints (pt.) make 1 quart

qt. I peck

pk. 4 pks.

1 bushel bu. 8 bu.

1 quarter

fr. The diameter of a Winchester bushel is 184 inches, and its depth 8 inches.—And one gallon by dry measure contains 2682 cubic inches.

By this measure salt, lead ore, oysters, corn, and other dry goods are measured.

ALE OR BEER MEASURE.

4 qts.

9 gals.

2 pints (pt.) make 1 quart

qt. 1 gallon

gal. 3 gals.

1 firkin of ale fir.

I firkin of beer fir. 2 fir.

1 kilderkin kil. 2 kil.

1 barrel

bar. 3 kil.

1 hogshead hhd. 3 bar.

1 butt

butt. The ale gallon contains 282 cubic inches. In Londou the ale firkin contains 8 gallons, and the beer firkin 9 ; other measures being in the same proportion

WINE MEASURE.

4 qts

qt. gal.

63 gals.

2 pints (pt.) make 1 quart

1 gallon 42 gals.

I tierce

tier.

1 hogshead hhd. 84 gals.

1 puncheon pun. 2 hhds.

1 pipe or butt 2 pipes

1 tun

T. 18 gals.

I runlet 31, gallons

1 barrel

bar. The wine gallon contains 231 cubic inches.

By this measure brandy, spirits, perry, cider, mead, vine, gar, and oil are measured.

p. or b.

run.

CLOTH MEASURE.

21 inches make 1 nail
4 nls.

1 quarter
1 yard
1 ell Flemish

I ell English
5
qrs.

1 aune or ell French. The French aune is 42 inches.

nl.
qr.
yd.
Ell Fl.

4 qrs. 3 qrs. 5 qrs.

Ell Eng.

LONG MEASURE.

ft.

1 yard

3 barley corns make 1 inch

in. 12 in.

1 foot 3 ft.

yd. 5) yds.

I pole or rod pole 40 poles

I furlong fur. 8 fur.

I mile

ml. 3 mls.

1 league

I.
60 geographical miles, or
691 statute miles 1 degree nearly, deg. or •
360 degrees the circumference of the earth.

Also, 4 inches make 1 hand
5 feet

1 geometrical pace
6 feet

1 fathom 6 points

1 line 12 lines

1 inch

SQUARE MEASURE.

ft.

yd.

144 inches make 1 foot
9 ft

1 yard
301 yds. or
2721 ft.

1 pole, rod, or perch.
40 poles 1 rood.
4 roods

1 acre.

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The true length of the solar year is 265 days, 5 hours, 48 min. 57 seconds

Reflections on Mathematical Reasoning.

If the learner has studied 'he preceding pages attentively, he has had some practice in mathematical reasoning. It may now be pleasant, as well as useful, to give some attention to the principles of it.

By attending to the objects around us, we observe two properties by which they are capable of being increased or diminished, viz. in number and extent.

Whatever is susceptible of increase and diminution is the object of mathematics.

Arithmetic is the science of numbers.

All individual or single things are naturally subjects of number. Extent of all kinds is also made a subject of number, though at first view it would seem to have no connexion with it. But to apply number to extent, it is necessary to have recourse to artificial units. If we wish to compare two distances, we cannot form any correct idea of their relative extent, until we fix upon some length with which we are familiar as a measure. This measure we call one or a unit. We then compare the lengths, by finding how many times this measure is contained in them. By this means length becomes an object of number. We use different units for different purposes. For some we use the inch, for others the foot, the yard, the rod, the mile, &c.

In the same manner we have artificial units for surfaces, for solids, for liquids, for weights, for time, &c. And in all there are different units for different purposes.

When a measure is assumed as a unit, all smaller measures are fractions of it. If the foot is taken for the unit, inches are fractions. If the rod is the unit, yards, feet, and inches are fractions, and the smaller, being fractions of the larger, are fractions of fractions. It may be remarked, that gll parts are properly units of a lower order. As we say sin

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