EXAMPLE.

Suppose a round stick to be 24 inches diameter, how much will it square to? Ans. 17 inches.

is the girt?

"the quarter girt?

18

Round timber loses almost of its solidity by being squared, and the quarter girt makes about more than the side of the square would. The solid content being to that by the quarter girt as 9 to 7, and to the content, if squared, as 30 to 19.

To find the Cubic Feet in Round Timber.

RULE. Multiply the square of the girt by the length, from the product reject two figures to the right, and divide the remaining figures by 18, or more concisely by 3, and then by 6 for cubic feet. If by custom or agreement the quarter girt is taken, multiply the square of it by the length in feet, and divide by 144 for the content in cubic feet.

A

EXAMPLES.

1. Required the content of a round log, the girt of which is 80 inches, and the length 26 feet.

by the girt 80

80

80X,225—18 in. for side 18 [of the square.

quarter 20 inc.

20

2. Required the contents of the following pieces of round

12)702

cub. ft. 58,6 if squared.

Suppose the six pieces, last mentioned, were pine logs, brought by A. to a saw-mill, and when measured at the quar

50 65

"39 311 » 5t

45

623

"'49 - 40

ter girt, he sold them at $9 per thousand: Allowing as usual 115 feet to make a thousand feet of boards, and deducting one fourth for sawing, what was the amount?

115: 1000 :: 226 the contents as before.

8. Required the difference in the solid contents of the two following pieces of timber, equal in length and circumference, viz.

One round piece, 24 feet long, and 60 inches in circumference. The other piece 24 feet long, 18 inches wide and 12 inches thick.

Ans. 12 feet, the first being 43, and the other 36 cubic ft. This difference accounts for the custom in N. England of paying one-third more for the hauling round timber from the forests to the ship-yards, than for that which is roughhewn; each being taken there at the quarter girt.

RULES FOR PILLARS.

1. Multiply the square of of the girt by twice the length in feet, and divide by 144 for the content.

2. Multiply of the circumference by of the diameter, and the product by the length in feet, and divide the last product by 1 14 for the answer.

3. Multiply the square of the diameter by the length in feet and that product by 11, and then divide by 14 for the solid content in feet.

EXAMPLE.

Required the content in cubic feet of a pillar, the diameter of which is 30 inches, equal to 94 inches girt, and the length 24 feet.

1st. method.

2d.

3d.

To find the content of round or unsquared timber, whose ends or bases are unequal in circumference.

RULE. To the products of the girts of the two bases, add of the square of the difference, the sum will be the square of the mean girt, then proceed as before.

EXAMPLE.

Required the solidity of a mast, the length of which is 72 feet, and the girt at one end is 57 inches, and at the other 38 inches.

CIRCLES.

To find the area of a circle from its circumference. Multiply its square by 07953. And to find its area by the diameter, multiply its square by,7854.

To find the side of a square equal to any given superfices.

RULE. The square root of the given area is the side required.

If the diameters of circles be as 1 to 2, the circumferences will be in the same proportion. But the areas of the same circles will be as 1 to 4, or as the squares of their diameters. Therefore, while the circumference is twice as large, the area is four times as much.

SPHERES OR GLOBES.

The superfices of every sphere or globe is equal to four times the area of its greatest circle. Multiplying its diameter by its circumference will also give its convex surface.

To find the solidity of a Sphere or Globe.

Multiply the cube of its axis by,5236.

Spheres are to each other as the cubes of their diameters; and their surfaces as the squares of their diameters.

GAUGING.

GAUGING teaches to find the content of any vessel by having the proper dimensions given, which are usually taken in inches and tenths of an inch.

Bushel

Cubic Foot

1728

The Alc gallon is to the Wine gallon as 53 to 71 nearly.

PROBLEM I.

To find the content in Ale or Wine gallons, &c. of a box, chest,

or cistern.

RULE. Multiply the length, breadth, and depth together, and divide the last product by the cubic inches in a gallon or bushel, and the quotient will be the answer required.

EXAMPLES.

1. Required the content in ale gallons, of a square vessel, the sides of which are 80 inches and the depth 20 inches? 80X80 6400×20=128000÷282=454 Ale gallons. 2. How may bushels in a cistern 8 feet long, 4 feet wide, and 4 feet deep, equal to a cord, wood measure?

.

96X48×48=221184 cubic inches, and divided by 2150,42, the cubic inches in a bushel, give 1023 even bushels.*

To find the contents of a vessel in form of a part of a pyramid.

RULE. Multiply the sides of the two bases together, and to the product add of the square of their difference; theu multiply the sum by the height, and divide the product by the cubic inches in the measure required.

EXAMPLE.

Required the contents in wine gallons of a vessel in form of a part of a pyramid that has the sides of the base 96

*The difference between heaped and even bushels, in measuring loads of charcoal, does not appear to be fixed.