the folidity of which latter fegment may be found out by the rule before given in Art. 777. the area of each base (or circle) being known.

782. A Cylinder is a folid, which may be well represented by a ftone-roll, fuch as are used in gardens for the rolling of walks. Now if the circumference of a Cylinder be 4.57 feet, and the length 3.25 feet, what is the folid content of that Cylinder?

Anfw. 5.4+ feet, thus found out: Firft, by the help of the given circumference 4.57, find out the fuperficial content of that circle, (being the bafe of the Cylinder;) which content (by Art. 769.) will be found 1.661967 foot; then multiplying the faid 1.661967 by the given length 3.25, the product will be 5.401393, which is the folid content required.

783. If the Base of a Cylinder be 1.6619 feet, how much in length of that cylinder will make a foot folid?

Anfw. .6017 parts of a foot; for I (to wit, I folid foot) being divided by the bafe 1.6619, gives in the quotient the decimal .6017 for the length required.

784. A globe is a perfect round body contained under one furface; in the middle of the globe there is a point called the center, from whence all ftraight lines drawn to the outfide are of equal length, and called femi-diameters, the double of any one of which is equal to the diameter of the globe; now if the diameter of a globe of ftone be 1.75 foot, how many feet folid are contained in that globe?

Anfw. 2.80616 feet; for as I is to .5235988, fo is the cube of the diameter to the folid content of the globe: Therefore multiplying the cube of the diameter by the faid decimal 5235988, the product will be the folid content required: So the diameter 1.75 being firft multiplied by itself, the product will be 3.0625, which multiplied by the faid 1.75, gives in the product 5.359375, to wit, the cube of the diameter, which being multiplied by .5235988, the product thence arifing will be 2.80616, which is the folidity of the globe propounded.

785. What is the diameter of a globe of stone, which contains 4 cubical or folid feet?

Anfw. 1.96+foot; for as I is to 1.9098593, fo is 4 (the folid content given) to a fourth proportional, to wit, 7.639437, whofe cubic root is 1.96949, the diameter required.

786. In Timber and Stone. The Content is given by the

Solid Foot.

787. In Digging. The Content is given by the Solid Yard.

Examp. 2. A vault digged 9 feet deep, 4 feet long, and 3 feet 9 inches broad, how many folid yards?

·27) 151. 10. 6 Fards. Feet. Inches. Parts.

Anfw. 5. 16. ΙΟ

6

88. If a bullet of brafs of 8 inches diameter weigh 72 pounds, what fhall a bullet of brafs weigh whofe diameter is 4 inches ?

Since like folids are in triple proportion to their homologous fides, diameters, lines, &c. it holds.

A$

As the cube of the diameter given,

To the weight thereof:

So is the cube of the other diameter,
To the weight thereof.

That is, As 8x8x8: 72: 4X4X4 :

789. If a fhip of 100 tun be 44 foot long at the keel, of what length fhall the keel be of a ship of 220 tun?

As 100 44X44×44 :: 220: 44X44X44X28.
That is, 44X44X44X2 is the cube the length required.

√44X44

3

And 44X44X44 × 23 = 44 X 2,2 the length.

But

2,2 1,30059; therefore 442,2 = 57,22596. 790. The fide of the cube being given to find the fide of that cube that fhall be double, treble, quadruble, &c. in quantity to the given cube.

Multiply the cube-root of 2, 3, 4, &c. by the fide of the given cube, and the product will be the fide of the cube required, &c..

Examp. There is a cubical veffel, whofe fide is 12 inches, and it is required to find the fide of that vessel which shall contain 3 times as much.

The cube-root of 3 is (per Table in Art. 482.)

Multiply by

1,442250

12

Answer 17,307000

If you would find a fide that fhall contain as much, as much, as much, &c. then divide the fide of the given cube by the cube-root of 2, 3, 4, &c.

791. The concave diameter of two guns, being known, together with the quantity of gunpowder fufficient to charge one, to find what will be fufficient to charge the other.

Rule. The capacities are one to another, as the cubes of their diameters.

Examp. If 45 pounds of gunpowder be fufficient to charge a gun, whofe concave diameter is 1 inch, how much gunpowder will fuffice to charge a gun whose concave diameter is 7 inches?

As

As XX:45 :: 7×7X7:45×××4.

792. Questions relating to Solids.

1. If a piece of timber 48 feet long, 6 inches broad, and 14 inches thick, coft 10l. what is the value of five fuch pieces which are 6 feet long, 4 inches broad, and 7 inches thick?

Conditional terms

Correfponding

Pieces. Feet. Br. Thickn. Len.

2. If 300 men, in 15 days, dig a trench 5600 feet long, 6 deep, and 12 wide, how long muft that trench be, whofe depth is 8 feet, width 14 feet, dug by 2700 men in 25 days. Men. Days. Len. Dep. Wid. 300 15 5600 6 2700 25 A. 8

Conditional terms
Correfponding

Therefore A 2700X25X 5600X6X12

300 × 15X8X 14

= 54000.

12.

14

3. If 248 men, in 5 days, dig a trench 23 yards long, 2 deep, and 3 wide; in how many days will 24 men dig a trench 33 yards long, 3 deep, and 53 wide?

4. If 24 men, working 189 days, 14 hours each day, dig a trench 33 yards long, 31 deep, and 53 wide; how many hours per day muft 217 men work to dig a trench 23 yards long, 21 deep, and 33 wide in 5 days?

A

Conditional terms
Corresponding

Men. Days. Hours. Len. Dep. Wid.

24X189X14X93×7 × 11 ×2×4×2×5

24

189

135

14

4

글

28

4×3×3×217X11X135X7X28

So find the fide of a cube that fhall be equal in folidity to
any given folid, as a Globe, Cylinder, Prifm, Cone, or fuch

like.

The Cube-root of the folid content of any folid body given,
is the fide of a Cube of equal folidity. So if the content of a
Globe were found to be 15625 folid inches, feek the Cube-
root of 15625, which is 25, which is the fide of a Cube of
equal capacity.