By the Sliding Rule.

As one on A, is to the area on B; so is the depth on A,

to the content on B.

3. If the length of a rectangular cooler be 162.7, and its breadth 86.3 inches; how many gallons of ale does it contain, when the depth of the liquor is 6.8 inches? Ans. 338.572 gallons.

4. If the sides of a rectangular wine-vat measure 74.6 and 65.7 inches; required the area and content, in wine gallons, supposing the depth of the liquor to be 24.7 inches?

Ans. The area is 21.217, and the content 524.0599 wine gallons.

5. A brewer has a rectangular mash-tun which measuree 64 inches in length, and 52 in breadth; how many bushels of malt had been brewed, when the Excise Officer found the depth of the grains to be 32 inches; admitting that each gallon of malt uniformly produces one gallon of grains? (See Note 2, Page 78.)

Ans. 58.64 bushels. 6. A maltster has a rectangular cistern whose length is 124.5 inches, and breadth 98.2; required the area and content, in malt bushels, when the depth is 14.8 inches. Ans. The area is 5.685, and the content 84.138 malt bushels.

7. A floor of malt measures 245 inches in length, 152 in breadth, and 5.9 in depth; required the area and content in malt bushels.

Ans. The area is 17.317, and the content 102.1703 malt bushels.

PROBLEM III.

To find the area of a rhombus or rhomboides.

RULE.

By the Pen.

Multiply the length of the base by the perpendicular breadth, and the product will be the area in square ininches; which being divided by 282, 231, 227, and 2150.42, the respective quotients will be the area in ale, wine, and mash-tun gallons, and malt bushels.

EXAMPLES.

1. Let ABCD bè a rhombus, whose base A B is 50 inches, and perpendicular DE 40 inches; what is the area in ale, wine, and mash-tun gallons, and malt bushels ?

Sq. inches.

Divisor 227)2000(8.810 mash-tun gallons.

1816

As the square divisor on A, is to the base on B; so is the perpendicular breadth on A, to the area on B.

2. Let the foregoing figure denote the base of a vessel whose sides are perpendicular; required the content in ale, wine, mash-tun gallons, and malt bushels, at 17 inches from the bottom?

Here 7.092 x 17=120.564 ale gallons; 8.658 × 17= 147.186 wine gallons; 8.81 x 17-149.77 mash-tun gallons; and .93 × 17=15.81 malt bushels.

By the Sliding Rule.

As one on A, is to the area on B; so is the depth on A, to the content on B.

3. There is a cooler in the form of a rhomboid, whose base is 73.6, and perpendicular breadth 56.2 inches; required the area and content, in ale gallons; the depth of the liquor being 2.7 inches?

Ans. The area is 14.667, and the content 39.6009 ale gallons.

4. Required the area and content of a rhomboidal vessel, in ale gallons, the length of the base being 108.4 inches, the perpendicular breadth 70.6, and the depth of the liquor eight-tenths of an inch.

Ans. The area is 27.138, and the content 21.7104 ale gallons.

PROBLEM IV.

To find the area of a triangle, when the base and perpen

dicular are given.

RULE.

By the Pen.

Multiply the base by the perpendicular, and half the the product will be the area in square inches; which being divided by 282, 231, and 2150.42, the respective quotients will be the area in ale and wine gallons, and malt-bushels.

Note. If the base be multiplied by half the perpendicular, or the perpendicular by half the base, the product will be the area in square inches.

EXAMPLES.

1. Required the area of the triangle ABC, in ale and wine gallons, and malt bushels; the base AB, being 216.8, and the perpendicular D C, 94.6 inches.

C

Note. The perpendicular CD, is the shortest distance from the angle C, to the base A B; and may be found by one person holding the end of the measuring-tape at C, while another, by trials, determines the point D.

K