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The Measuring of Solids.

HE folid Foot is compofed of 1728 Inches: For a Solid that is I Foot, or 12 Inches, every Way, the folid Content is 1728 Inches, as appears by the following Article.

Article 78. To measure a Cube.

Definition. A Cube is a Solid of fix equal Sides, each of which is an exact Square, in the Form of a Die.

Rule. Multiply the Side by itfelf, and that Product by the fame Side, and this laft Product is the folid Content of the Cube.

Exam. The Side of a Cube being 15 Inches, or 1 Foot and 3 Inches, to find the Content?

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I have done this two different Ways, that the Learner may fee they come out the fame. The Content in Inches is 3375, which being divided by 1728, the Inches in a folid Foot, and the Divifion continued by annexing more Cyphers, it will come out exactly 1.953125, as in the Decimal Operation.

Article

Article 79. To measure a Parallelopipedon.

Definition. A Parallelopipedon is a Solid of three Dimenfions, Length, Breadth, and Thickness; as a Piece of Timber exactly fquared, whofe Length is more than the Breadth or Thickness. The Ends are called Bafes, which are equal.

Rule. Find the Area of the Bafe, then multiplying that by the Length, it gives the folid Content.

Exam. I. The Side A B is 1.125, and the Length CD 4.5, to find the solid Content ?

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Exam. 2. A Veffel being 2.5 Feet each Side within, and 3 Feet deep, to find the Content?

2.5 2.5

125

50

6.25

3

18.75 the Content.

If a Piece of Timber, or any other Thing, is of an equal Bignefs through its whole Length, tho' there is a Difference between the Breadth and Thickness, if the Breadth and Thickness are multiplied together, and that Product multiplied by the Length, this laft Product is the folid Content. The fame is the Cafe with Regard to a Veffel of three different Dimenfions, as a Cistern.

Exam.

C

Exam. A Piece of Timber being 1 Foot and 3 Inches, or 15 Inches, broad, 9 Inches thick, and 8 Feet and 6 Inches, or 102 Inches, long, to find the Content?

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Article 80. To meafure a Cylinder.

Definition. A Cylinder is a round Body, whofe Bases are Circles, like a round Column, or a Rolling-Stone of a Garden.

Rule. The Diameter of the Bafe being given, find the Area, by Art. 64; then multiplying the Area of the Bafe by the Length, that Product is the Content of the Cylinder.

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Exam. The Diameter of the Base AC being 2 Feet and, 6 Inches, and the Length BD 3 Feet and 9 Inches, to find the Content?

If the Inches are changed into the Decimal Fractions of a Foot, as in the laft Article, then,

2.5 Feet, Diameter of the Bafe.

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4.9086510 Area of the Bafe.
3.75 Length.

2454325

3436055

1472595

18.4074375 Content.

The Reader may, for his Practice, reduce the Dimensions to Inches, and find the folid Content in Inches, which being divided by 1728, the Quotient will be the folid Content in Feet, as in the last Article.

This is a general Rule for finding the Content of any ftraight folid Body, of equal Bignefs from End to End, of whatever Form the Bafes are: For, if the Area of the Bafe is multiplied by the Length, the Product is the folid Content. In fuperficial Measure, we have given Rules for computing the Area of all Kinds of Figures; and, in Art. 60, a Table of Multipliers for all regular Figures: It will, therefore, be fuperfluous to trouble the Learner with Examples of triangular of multangular Prifms.

Article 81. To measure a Cone.

Definition. A Cone is a Solid, which, from a circular Bafe, leffens regularly 'till it ends in a Point at the Top, in the Form of a round Spire.

Rule. Having the Diameter of the Bafe, find the Area, by Art. 64; then multiplying the Area of the Bafe by one Third of the perpendicular Height, that Product is the Content of the Cone,

Exam.

Exam. The Diameter AC being 26, and

B

the Height BD 60, to find the Content?

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Article 82. To measure the Fruftum of a Cone,

Definition. The Fruftum of a Cone is the Part that remains when the Top is cut off by a Plane parallel to the Base.

Rule. Multiply the Diameters of the two Bafes together, and to this Product add one Third of the Square of the Difference of the Diameters; then multiplying this Sum by 7854, it will be a mean Area between the two Bafes, which, being multiplied by the Length of the Fruftum, gives the folid Content. Ex. The former Cone being cut off in the Middle, the greater Diameter A D is 20, the leffer Diameter BC 10, and the Height EF 30, to find the Content of the Fruftum ?

20
10

200

33.333

B

10

C

F

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