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PART IV.

MENSURATION OF SUPERFICIES

APPLIED TO

GAUGING.

PROBLEM I.

The side of a square being given, to find the area in ale gallons, wine gallons, mash-tun gallons, and melt bushels.

EXAM. 3.

By Multiplication.

Inches.

153.4 side.

153.4 side.

6136

4602

7670

1534

23331.56 area in square inches.

.003546 multiplier.

14118936

9412624

11765780

7059468

83.44291176 area in ale gallons.

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Here 82.2 × 82.2 = 6756.84, the area in square inches; and 6756.84 ÷ 282 = 23.96, the area in ale gallons; then 23.96 × 5.4 = 129.384, the content in ale gallons.

EXAM. 5.

Here 43.2 x 43.2 = 1866.24, the area in square inches; and 1866.24÷ 231 = 8.078, the area in wine gallons; then 8.078 x 52.7 = 425.710, the content in wine gallons.

EXAM. 6.

Here 75 x 755625, the area in square inches ; and 5625 2150.42 2.615, the area in malt bushels; then 2.615 × 16.4 42.886, the content in malt bushels.

EXAM. 7.

1. Here 84 x 84 = 7056, the area in square inches; and 7056 ÷ 282 = 25.021, the area in ale gallons; then 25.021 × 14 = 350.294, the content in ale gallons.

2. Here 7056231 30.545, the area in wine gallons; and 30.545 × 14 = 427.63, the content in wine gallons.

3. Here 7056÷22731.083, the area in mashtun gallons; and 31.083 x 14 = 435.162, the content in mash-tun gallons.

4. Here 70562150.42 3.281, the area in malt bushels; and 3.281 x 14 = 45.934, the content in malt bushels.

PROBLEM II.

To find the area of a rectangle..

EXAM. 3.

Inches.

162.7 length.

86.3 breadth.

4881

9762

13016

Divisor 282)14041.01 (49.79 area in ale gallons.

1128

.2761

2538

.2230

1974

.2561

2538

23

Galcas.

49.79 area.
6.8 depth.

39832

99674

338.572 the content.

EXAM. 4.

Here 74.6 x 65.74901.22, the area in square inches; and 4901.22 ÷ 231 = 21.217, the area in wine gallons; then 21.217 x 24.7 524.0599 gallons, the content.

EXAM. 5.

=

Here 64 × 52 = 3328, the area in square inches; and 3328 227 = 14.660, the area in mash-tun gallons, which, by the question, is also the area in mait gallons; then 14.660 x 32 = 469.12, the content in malt gallons; hence 469.12 ÷ 8 = 58.64, the number of bushels required.

EXAM. 6.

Here 124.5 x 98.2 = 12225.90, the area in square inches; and 12225.902150.42 = 5.685, the area in malt bushels; then 5.685 × 14.8 = 84.138 malt bushels, the content.

EXAM. 7.

Here 245 × 152 = 37240, the area in square inches; and 37240 ÷ 2150.42 = 17.317, the area in malt bushels; then 17.317 x 5.9 = 102.1703 malt bushels, the content.

PROBLEM III.

To find the area of a rhombus or rhomboides.

ЕХАМ. 3.

Here 73.6 x 56.2 = 4136.32, the area in square inches; and 4136,32 ÷ 282 = 14.667, the area in ale

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