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Problem 10.

To measure a Sphere or Globa.

Def. A Sphere or Globe is a round folid Body, every Part of whose Surface is equally distant from a Point within, called its Center.

Rule.

Find the Area of a Circle in the middle of the Globe, and multiply it by (two thirds) of the Height, that Product will be the Solid Content. *

Example.

Let ABCD be a Globe whose Diameter is 20 Inches, what is its Solid Content?

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Operation. 20×20=400×.7854=314.16×1.33333

4188.798 Inches, &c. the Solidity required.

For the Superficial Content, multiply the Diameter by the Circumference, and that Product will be the Superficial Content required.

• Every Globe is equal to of a Cylinder of the fame Diameter

and Altitude,

3

Problem 11.

Another Way to measure a Globe.

* All Globes are to each other as the Cube of their Diameters; and it is found, that if a Globe be 1 in Diameter, its Solid Content will be .5236; therefore this

Rule.

Cube the Diameter, and multiply that by .5236, it will give the Solidity required.

Crample.

Let ABCD be a Globe, whose Diameter A B is 20 Inches, (as before) what is its Content ?

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Operation.

20×20×20=800×.52364188.8, nearly Problem 12.

the fame as in the last Problem.

Another Way to measure a Globe. A 21:11::Cube of the Diameter to the Solid Content. This Rule will ferve for those who do not understand Decimals.

To measure the Fruftum of a Globe.

Def. The Fruftum of a Globe is a Part cut off less than Half the Globe.

Rule.

To three Times the Square of the Semidiameter of the Fruftum's Top, add the Square of the Frustum's Height; this Sum multiplied by the Frustum's Height, and that Product again multiplied by .5236, will give the Solid Content.

Crample.

Let ABCD be the Fruftum of a Globe; let A B, the Diameter at Top, be 16 Inches, and CD, the Height, be 4 Inches, what is the Solidity?

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8×8=64×3=192+16=208×4=832×

Operation.

5236435.6352 Inches, the Solidity required.

For the Curved or Superficial Content, multiply the whole Circumference of the Sphere by the Height of the Segment, and the Product will be the Content required. The Diameter and Circumference of the Sphere may be found by Problems 15 and 10 of Planometry.

Problem 13.

To meafure an Oblong, or an Oblate Sphere.

Def. If a Globe be supposed to be pushed out of its real Figure, fo as to become longer than before, like an Egg, it is called an Oblong Sphere; if it be comprefled so as to make it flatter, like an Orange, it is called an Oblate Sphere; and the Rule for measuring each is thus.

Rule.

Square the Diameter in the Middle, and multiply that Product by the Length, which Product multiply again by .5236, and it will give its true Solidity or Content. *

Example.

Let ABCD be an Oblong Sphere; and let the Diameter DC be 30 Inches, and the Length AB 50 Inches, what is its Solid Content?

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30×30=900×50=45000×.5236=23562

Operation.
Inches, the Content fought.

* See the Reason of this Rule in the Cubature of the Conic Sections.

Problem 14.

To measure an Irregular Solid.

All Irregular Bodies must be reduced as near as poffible to regular ones; no particular Rule therefore can be laid down; but from a due Confideration of the foregoing Rules, a Method may be found for taking the Dimensions of any folid Body, how irregular foever, that shall give the Content near enough the Truth.

Crample.

Let ABCD be a Piece of Timber 28 Feet long; and the Circumference at AB 24 Inches, at E F 20 Inches, and at CD 16 Inches, what is its Content?

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Workmen usually add the three Circumferences together, taking of the Sum for a mean Circumference; then of which Circumference they make the mean Side of a Square, and measure it as square Timber, by multiplying that Side by itself, and that Product by the Length, and dividing by 1728, if the Length was Inches; or by 144, if the Length was given in Feet; this Quotient gives the Content in square Feet.

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