Mathematics

duct add the next preceding remainder; and so on till you have used all the divisors and remainders.

To explain this rule from the example, we may observe, that every unit of the first quotient may be looked upon as containing 9 of the units in the given dividend; consequently every unit of it, that remains, will contain the same; therefore this remainder must be multiplied by 9, in order to find the units of the given dividend, which it contains. Again, every unit in the next quotient will contain 4 units of the preceding, or 36 of the given dividend, that is, 9 times 4; therefore what remains must be multiplied by 36; or, which is the same thing, by 9 and 4 continually. Now this is the same as the rule; for instead of finding the remainders separately, they are reduced from the bottom upward step by step, to the first, and the remaining units of the same class taken in as they occur.

III. To perform division more concisely than by the generál

rule.

RULE.*

Multiply the divisor by the quotient figures as before, and subtract each figure of the product when you produce it, always remembering to carry so many to the next figure as were borrowed before.

EXAMPLES.

1. Divide 3104675846 by 833.
833)3104675846(37271017 the quotient.

6056

2257

5915

848

1546

713

2. Divide 29137062 by 5317. 3. Divide 62015735 by 7803.

4. Divide 432756284563574 by 873469.

Ans. 5479317.

Ans. 7947294

7803

Ans. 495445498- 18

REDUCTION.

Reduction is the method of bringing numbers from one name or denomination to another without changing the val

ue.

In order to perform reduction it is necessary to be acquainted with the relative value of the different denominations of coin, weight, and measure, that are used; for which purpose see the following

TABLES of COIN, WEIGHT, and MEASURE.

* The reason of this rule is the same as that of the general

rule.

By this weight are weighed jewels, gold, silver, corn,

1 pound

i or lb.

8 dr.

12 oz.

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

AVOIRDUPOIS WEIGHT.

16 drams make 1 ounce, marked dr. oz.

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

lb.t

* A firkin of butter.. is. 56 A gallon of train oil

A firkin of soap

64 A faggot of steel

A barrel of pot-ashes... 200 A stone of glass

A barrel of anchovies.... 30 A seam of glass is 24 stone,

120

lb. oz. dr.

weighs.....

17 6 1

A half peck . .

8 11

....

A barrel of butter..... 224 A peck loaf of bread

A fother of lead is 194 cwt

A stone of iron. ...

.......

A stone of butcher's meat. 8

DRY MEASURE.

Marked

2 pints make 1 quart pts. qts. 8 bushels 1 quarter

Marked

qr.

pot. 5 quarters 1 wey or load wey gal. 4 bushels 1 coomb

2 quarts

1 pottle

str. 12 weys

CO.

pe. 5 pecks 1 bushel water meas. bu. 10 coombs 1 wey

NOTE. The diameter of a Winchester bushel is 18 inches, and its depth 8 inches. And one gallon by dry measure contains 2684 cubic inches.

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

ALE AND BEER MEASURE.

Marked

2 pints mske 1 quart pts. qts. 2 firkins

4 quarts

Marked

1 kilderkin kil.

1 gallon gal. 2 kilderkins 1 barrel bar.

8 gallons 1 firkin of Ale fir. [3 kilderkins 1 hogshead hhd. 9 gallons 1 firkin of Beer fir. 13 barrels 1 butt

butt.

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