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SOLID MEASURE.

By this measure the solid or cubic contents of all things are ascertained which have length, breadth, and thickness, For instance, a piece of square timber has length, breadth, and thickness. A cord of wood has lenght, breadth, and height. A bin of grain has length, breadth, and depth.

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The usual form of a cord, is 8 feet long, 4 feet high, and 4 feet wide.

LESSON 1.

If a stick of timber be 18 inches in breadth, 15 inches thick, and 28 feet in length, how many solid feet? And how much will it amount to at 8 cents a foot? Answer, 521 feet, and it cost 4 dol. 20 cents.

1. Find the superficial content of one end, by multiply. ing the breadth by the thickness.

2. Multiply this superficial content, by the inches in the length.

3. Divide the last product by 1728, the quotient will be solid feet.

4. If inches remain, multiply them by 12 and divide again by 1728, the quotient will be inches or parts of a solid foot.

* 12 x 12 x 12 makes the inches of a solid foot.

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N. B. The 6 inches in the quotient, must not be considered as merely of 6 square inches, or 6 superficial inches, because they consist of half a cubic foot, or foot, or .5 of a solid foot, &c.

of a solid

And if 3 had happened in place of 6, then the number would be, or, or .25 of a solid foot. If the quotient had been 4, it would be or,33333+ of a solid foot.

Rules for a second operation.

or

1. Multiply the breadth 18, by the length, to find the superficial content of one side.

2. Multiply that superficial content by the thickness 15, and divide the product by 1728. solid content.

28 feet the length. 12 inches in a foot. 336 inches in length. 18 inches in breadth.

2688 336

6048

The quotient will be the

6048 inches of one side must be 15 times that sum.

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Rules for a third operation decimally.

1. Reduce 1 ft. 3 in. the thickness, and 1 ft. 6 in. the breadth, into decimals of a foot, by Case 3, in decimals; then we shall have 1.25 foot for the thickness, and 1.5 foot for the breadth at the end of the stick.

2. Multiply the thickness by the breadth, the product will be the superficial content of the end, in a foot and decimals of a foot.

3. Multiply this superficial content by the length in feet, the product will be the answer.

1 ft. 3 in.

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1.25

1.5

625 125

1.875 the superficial content of one end, 28 feet the length.

15000

3750

Feet, 52.500 Answer. And as to the price,

52.5 x 8420.0 4 dolls. 20 cents.

X

See a short method; Lesson 11th in Duodecimals.

LESSON 2.

In a cellar 28 feet long, 14 feet wide, and 8 feet deep, how many solid feet? Answer, 3332 feet..

LESSON 3.

In a pile of wood 12 feet long, 4 feet wide, and 7 feet high, how many cords? And how much will it amount to

in dollars and cents at 4 dol. 25 cents a cord?

Ans. 2 cords and .625 of a cord at 425 cents = 11 dol.

5.625 cents.

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A farmer bought a cider mill wheel by the solid foot; the diameter, that is, the breadth across the middle, was 5 ft. 9 in. and the thickness 13 inches; how many solid feet in the wheel? Answer, 28.

RULE.

1. Multiply the square of the diameter by .7854 the product will be the superficial content of the wheel.

2. Multiply the superficial content by the thickness, the product will be the answer.

5 ft. 9 in.-5.75 feet to be multiplied by itself.

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25.96728750 superficial content. 1.08 thickness.

13 inches=1.08+ foot.*

25967287500

20773830000

28.0446705000

N. B. Multiply the square of the diameter of any circle by .7854, the product will be the superficial content.

LESSON 5.

How many solid feet in a well that is 8 feet across and 30 feet deep?

Ans. 1507 ft. 11 in.

8 feet the diameter multiplied by itself.

8

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In a stick of round timber 40 feet long, and 15 inches

thick, how many solid feet?

Answer, 49.

15 inches = 1 ft. 3 in. = 1.25 diameter.

1.25

625

1500

1.5625 the square of one end.†

Lesson 6, continued.

The sign of addition + annexed to a decimal,denotes that it is a surd.

+ For distinction, call the square end of a stick, the base.

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