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find it to be 2150.4252, the number of cubic inches in a Winchester bushel.

2. It has been ascertained by experiments, that after the saccharine substance has been extracted from malt, by the operation of mashing, its bulk is diminished a little more than one-sixth part of the whole; in consequence of which the mash-tun gallon is always taken at 227 cubic inches.

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A Table of Drams in an Ounce, a Pound, a Quarter, &c. &c. Avoirdupois Weight.

Drams.

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=

28672 1792 112= 4= 1 Hund. Wt. 573440

35840=2240=80=20=1 Ton.

REMARK.

By various Statutes made in the reign of George III., it is enacted that, "Officers of the Excise and Customs shall take the weight of candles, coffee, tea, cocoa-nuts, chocolate, glass, hides, hops, paper, salt, soap, starch, stone-bottles, tobacco, and snuff, by Avoirdupois Weight, in order to charge the respective duties upon these articles."

THE METHOD OF FINDING THE

MULTIPLIERS, DIVISORS, AND GAUGE-POINTS CONTAIN ED IN THE SUBSEQUENT TABLE.

If the area of any vessel, in square inches, be divided by the square-divisors 282, 231, 227, 268.8, and 2150.42,

the respective quotients will be the area of the vessel in ale gallons, wine gallons, mash-tun gallons, malt gallons, and malt bushels; but as dividing by these numbers is

1 1 1

the same as multiplying by 282' 231' 227 &c., it is evident, that if these fractions be reduced to decimals, we shall obtain multipliers that will answer the same purpose as the divisors, if we prefer multiplication, in making our calculations,

Again, it has been found, by Mathematicians, that if the diameter of a circle be 1, the area will be .7854, nearly; and that the area of any circle may be obtained by multiplying the square of the diameter by this number; but as the area thus found, must be divided by the square-divisors, to reduce it to ale gallons, wine gallons, &c., it becomes desirable to find numbers that will perform the work at one operation.

Now, as multiplying the square of the diameter by .7854, and then dividing the product by the square-divisors, is the same thing as multiplying the square of the .7854 .7854 .7854 &c.; it is evident that if

diameter by

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282 231 227

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these fractions be reduced to decimals, we shall obtain proper multipliers to be used in finding the areas of circles.

If we prefer division, it is the same thing to divide by

282 231

.7854' .7854'

&c. as to multiply by

.7854 .7854

&c.;

282 231 hence, if those fractions be reduced to mixed numbers, we shall have proper divisors for circles.

In the same manner we can find multipliers and divisors for ascertaining the weights of bodies from their contents, and vice versa, provided the specific gravities of the bodies be known. Thus, the solid content of a pound of hard soap cold, is found to be 27.14 cubic inches; a pound of hard soap hot, 28.0; a pound of green soap, 25.67, &c. &c.; hence, if the area of any vessel, in square inches, be divided by these numbers, the respective quotients will be the area of the vessel in pounds; and if the area in pounds, be multiplied by the depth of the vessel in inches, the product will be the content of the

vessel in pounds. Or, if the weight of any quantity of goods, in pounds, be multiplied by the cubic inches in a pound, the product will be the content in cubic inches. The multipliers for squares, in order to find their areas in pounds, are found by reducing

1

1

1

27.14' 28.0° 25.67&c. to decimals; the multipliers for circles, by reducing

.7854 7854 .7854

27.14' 28.0' 25.67' circles, by reducing numbers.

&c. to decimals; and the divisors for

27.14 28.0 25.67
.7854 .7854 7854'

&c. to mixed

The gauge-points for squares are the square roots of the square-divisors; being the sides of squares whose areas are one ale gallon, one wine gallon, one malt bushel, &c.; and the gauge-points for circles, are the square roots of the circular-divisors; being the diameters of circles whose areas are equal to one ale gallon, one wine gallon, one malt bushel, &c. &c.

Note. What has been said on this subject will be fully comprehended from the following Rules and Examples.

To find Multipliers for Squares.

RULE.

Divide unity by the square divisors, and the respective quotients will be factors for squares.

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2311.000000(.004329 Wine gallons.

268.8)1.000000(.003720 Malt gallons.

227)1.000000(.000465 Malt bushels.

2150.42)1.000000(.004405 Mash-tun gallons.

To find Multipliers for Circles.

RULE.

Divide .7854 by the square-divisors, and the respective quotients will be factors for circles.

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281).7854(.003399 Wine gallons.

268.8).7854(.002922 Malt gallons.

227).7854(.000365 Malt bushels.

2150.42).7854(.00346 Mash-tun gallons.

To find Divisors for Circles.

RULE.

Divide the square-divisors by .7854, and the respective quotients will be divisors for circles.

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whose Diameter isl. for Squares. for Circles,

.7854) 282.0000( 359.05 Ale gallons.
.7854) 231.0000 294.12 Wine gallons.
.7854) 268.8000 342.24 Malt gallons.
.7854)2150.4200(2738.00 Malt bushels.
.7854) 227.0000( 289.00 Mash-tun gallons.

To find Gauge-points for Squares.

RULE.

Extract the square roots of the square-divisors, and you will obtain the gauge-points for squares.

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Extract the square roots of the circular divisors, and you will obtain the gauge-points for circles.

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In the same manner were found all the Factors, Divi

sors, and Gauge-points in the following Table.

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