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Article 88. To meafure the Surface of a Fruftum or Segment of a Globe.

Rule. Find the Diameter of the Globe, by Art. 73, and the Superficies of the whole Globe, by Art. 86; then tay, as the Diameter of the Globe is to the Height of the Fruftum, fo is the Superficies of the Globe to the Superficies of the curve Part of the Fruftum; then find the Area of the Bafe, by Art. 64, and add these two together, which will be the whole Surface of the Fruftum.

Exam. The Diameter AC being 72, and the Height BE 13, to find the Superficies?

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13) 1296 (99 Refidue of the Diameter.

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5184 Square of the Diameter of the Base.

.7854

20736 25920 41472 36288

4071.5136 Area of the Base of the Fruftum,
4574
Area of the curve Surface add.

8645.5 Area of the whole Segment.

The Operation explained: Squaring the Half of the Diameter of the Bafe, and dividing by the Height, or verfed Sine BE, the Quotient is the Refidue of the Diameter of the Globe; to which adding the verfed Sine 13, it gives 112 for the whole Diameter: Then, by Art. 61, finding the Circumference, and multiplying that by the Diameter, the Product 39408 (omitting the fractional Part) is the Area of the Surface of the whole Globe: Then, by the Rule of Three, finding the Area of the Segment's curve Surface 4574, we next compute the Area of the Bafe, by Art. 63; and, adding thefe Sums together, we have 8645.5 for the Area of the Surface of the whole Segment or Fruftum.

As to the measuring the Surfaces of the other Solids, I efteem it ufelefs, fince the Rules laid down in fuperficial Measure are fufficient to find the Superficies of any of the foregoing Bodies: Unless it is neceffary to inform the Learner, that the curve Surface of a Cone is a Sector, whofe Arch-Line is equal to the Cone's Bafe, and the Radii equal to the Side of the Cone; fo that, if Half the Circumference of the Cone's Base is multiplied by the Length of its Side, the Product is the Area of the curve Surface; to which if the Area of the Base is added, the Sum is the Area of the whole Surface of the Cone.

Article 89. To measure a Spheroid.

Definition. A Spheroid is a folid Body like an Egg, only both its Ends are the fame.

Rule Multiply the Square of the Diameter of the greateft Circle, that is, the Diameter of the Middle, by the Length; then multiplying that Product by .5236, this Product is the

folid Content.

Exam. The Diameter AC being 24, and the Length BD 30, to find the Content?

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Art. 9o. To find the Side of a Cube equal to any folid Body. Rule. The folid Content of any Body being given, extract the Cube Root of the given Solidity, which will be the Side of a Cube equal to the Body whofe folid Content was fo given. Exam. 1. Find the Side of a Cube equal to a Globe whofe Content is 16974-593. 16974.593 (25.7 Side of (the Cube.

8

8974

1200 60

1260

25 300 1200

1525

5

7625

Exam. 2. Find the Side of a Cube equal to a Spheroid whofe Content is 9047.808. 9047.808 (20.8 Side of the

1047

1200

60

1260

1047808

120000
600

120600

(Cube.

1349593

187500
750

188250

64 4800

120000

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If the Dimensions of any folid Body were given, and it was required to find the Side of a Cube that is equal to that folid Body, find the Content of the given Body, by the Rules already laid down, and extract the Cube Root of that Number, which will be the Side of the Cube required.

Article 91. To measure the Solidity of any irregular Body, whofe Dimensions cannot be taken.

Get any regular Veffel, either fquare or round, and into it put the Body to be measured; then pour Water into the Veffel fo as to cover the Body, and measure the dry Part from the Top of the Veffel to the Surface of the Water; then take out the Body, and measure again from the Top of the Veffe! to the Water, and fubtract the firft Measure from the second, which is the Fall of the Water: Then, if the Veffel is fquare, measure one Side and multiply it by itself, and that Product by the Fall of the Water, which laft Product is the Content of the Body: But, if it is a long Square, as a Ciftern, multiply the Length by the Breadth, and that Product by the Fall of the Water: Or, laftly, if it is a round Veffel, fquare the Diameter, and multiply the Square by .7854, and that Product by the Fall of the Water, which gives the folid Content of the Body.

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Exam. 1. Eighteen Inches is 1.5 Foot; which being squared is 2.25 Feet, and that being multiplied by .5, the Decimal of 6 Inches, gives 1.125 Foot; which is Foot and an eighth Part of a Foot.

Of

Of Board and Timber Measure.

The Meafuring of Boardsis fuperficial Measure, the Thickness of a Board not being taken into the Account in measuring; fo that a Board is a Parallelogram, the Measuring of which is taught Art. 53. In regard to how much in Length is required to make a Foot to any affigned Breadth, there is a Table on the Joint-Rules, which every Carpenter is acquainted with; and when any Breadth is given, to find how much in Length makes a Foot, divide 144, the Square Inches in a Foot, by the given Breadth, and the Quotient is the Number of Inches required to make a Foot.

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Of Timber there are three different Sorts: If it is fquare, and of the fame Bignefs all the Way, it is a Parallelopipedon, the Measuring of which is taught Art. 79; if it is bigger at one End than the other, it is a Fruftum of a fquare Pyramid, the Measuring of which is taught Art. 84; and, if it be round Timber, it is the Fruftum of a Cone, the Measuring of which is fhewn Art. 82.

But there is a cuftomary Way of measuring both round and fquare Timber, which, tho' it be erroneous, is used by all Dealers: It will therefore be useless to repeat what has been fo often proved, of the Errors of thofe Rules. In round Timber, they ufually girt the Piece in the Middle with a Cord, which they divide into four Parts; this fourth Part of the Circumfe rence they call the Side of a Square equal to the Circumference; this fourth Part fquar'd, and the Square multiply'd by the Length, they call the folid Content: In which there are two Errors; for the Bignefs in the Middle is not a Mean between the greater and leffer Bafes, neither is the fourth Part of the String equal to the Side of a Square, of equal Area with the Circumference: And as to the Timber, after it is squar❜ð, if the Sides are unequal, they add the two Sides together, and

take

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