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The standard Winchester bushel* contains 2150 42 cubic inches, consequently the gallon must be 268.8 cubic inches: Hence the following table of

Cubic inches.

268.8 I gallon.

Dry meafure.

537.6= 2= 1 peck.

2150.4= 8= 4=1 bushel.

17203.2=64=32=8=1 quarter.

Note. 4 bushels=a coomb, 10 quarters a wey, and 12 weys a last of corn.

In gauging, All fuperficies or areas are derstood t be r inch deep, otherwise it could not be faid (as in the gauger's language it is) that the area of any square, circle, &c. is fo many gallons.

Most of the following problems are such as have been already proposed in the former part of this treatise, and are only here applied to practice,

PROBLEM I.

To find divisors, multipliers. and gauge-points, with their uses.

282

cubic inches make 1 ale gallon.
231
cubic inches make I wine gallon.
268 8 cubic inches make I corn gallon.
2150.42 cubic inches make I corn or malt bufhel.

* A cylindric bushel, 18 one-half inches diameter, and 8 inches deep, is e steemed a legal Winchester bushel, according to the standard in his Majesty's Exchequer, settled by act of Parliament in the year 1697.

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RULE.

Divide 1 by these numbers, and the quotient will give equivalent multipliers, and their square roots will be the gaugepoints

TABLE I. For right-lined furfaces.

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To find the area of any rectangular tun, back, or cooler, &c. in ale, wine gallons, and malt busbels.

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Multiply the length by the breadth, (both being in inches) and divide the product by the divisors, or multiply it by the multipliers in Table I. the result will be ale gallons, wine gallons, corn gallons, or malt bushels.

EXAMPLE I.

Required the area of a square cooler, whose side is 124 inches, in ale, wine, corn gallons, and malt bushels.

124.5

• Gauge-points are the sides of squares whose area is I gallon, 1 bushel, &c.

124,5X124.5 = 15500.25

First by division,

then by multiplication.

282)15500.25(54.96 A.G. 15500.258.003546-54.96 A. G 231)15500.25(76.10 WG. 15500.25 XCC4329=76.10 W.G 268-8)15500.25(57.66 C.G. 15500.25X.0037202=57.66 CG 250.42)15500.25 (7.209 Μ.Β. | 15500.25×.0004650= 7.209MB

These areas, being multiplied by the depth, produce the content of the whole vessel.

Ex. 2. A vessel in the form of a rectangle, 232 inches in length and 64 in breadth, what is its area in ale, wine, corn gallons, and malt bushels ?

Ans. 52.652 ale gallons, 64.277 wine gallons, 55.238 corn gallons, and 6.904 malt bushels.

Ex 3. Suppose the length of a brewer's tun, back, or cooler, be 2171⁄2 inches, and its breadth 85 inches, required its area in beer, wine, corn gallons, and malt bushels.

Anf. 66.014 ale gallons, 80.59 wine gallons, 69.02 corn gallons, and 8.6 malt bushels.

Ex. 4 Required the area of a square back, whose side is 30 inches, in ale, wine gallons, and malt bushels.

Ans. 3.19 ale gallons, 3.89 wine gallons, and .418 malt bushels.

By the fliding rule.

Set the divifor upon B to the side of the square on A, and against the fide of the square on B you have the content on A, in ale, wine, corn gallons, or in malt bushels, in terms of the divisor.

If the tun, back, &c. be a rectangular oblong, set the proper divisor on B to the breadth on A, then against the length on B is the content on A, as above.

PROBLEM

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PROBLEM III.

To find divisors, multipliers, and gauge-poiuts for circular areas.

RULE.

Divide 282, 231, 268.8, and 2150.42*, by 7854, (the area of a circle whose diameter is 1) and the quots will be a set of divisors; and divide .7854 by the same numbers, the quot will give a set of multipliers as exhibited in the following table. Also the square roots of these divisors will give their respective gauge-points †.

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To find the area of a circle in ale, wine, corn gallons, and malt

bufhels.

RULE.

* In practice, the decimal part is neglected, 2150 being reckoned sufficiently accurate: We shall therefore only use the integer for the future. The fame is to be observed of the divisors in the preceding table.

+ The gauge-point for circular areas is the diameter of a circle whose area, at I inch deep, is I gallon, I bushel, &c.

RULE.

Divide the square of the diameter by the divisors, or multiply the same square by the multipliers, the result will be the area in ale, wine, corn gallons, or malt bushels.

EXAMPLE I.

Required the area of a circle, whose diameter is 80 inches,

in ale, wine gallons, and malt bushels.

First by division,

80 X 80 = 6400.

359)6400(17.827 A. G.

294) 6400 (21.768 W. G.

2737)6400(2.338 Μ. Β.

then by multiplication

6400X .00278=17.792 A. G. 6400 × .0034=21.76 W. G.

6400X.000365=2.336 Μ. Β.

Ex. 2. Required the area of an ellipfe, whose diameters are 173 and 90, in ale, wine gallons, and malt bushels.

173×90 = 15600,

This may be reckoned as the square of the diameter in circular furfaces.

First by division,

then by multiplication.

359)15600(43.4

A. G. 15600 × 00278 =43.4 A. G. 294)15600(53.06 W. G. 15600 × 0034 =53.0 W. G. 2737)1.5600(5-7 M. B.

M. G. 15600×000365=5.7

Required the area of a circular back, whose diameter is 50 inches, in ale, wine gallons, and malt bushels.

Ans. 6.95 ale gallons, 8.5 wine gallons, and .91 malt

bufhels.

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