61.25 the content.

=

If a piece of timber, or any other thing, be of an equal bigness through its whole length, though there be a difference between the breadth and thickness, if the breadth and thickness are multiplied together, and that product multiplied by the length, this last product will be the solid content.

EXAMP. 3. A piece of timber being 1 foot and 6 inches, or 18 inches broad, 9 inches thick, and 9 feet 6 inches, or 114 inches long, to find the content?

1 foot, 6 inches = 1.5 foot

9 inches=75 foot.

10.6875 content.

Note. When the end is given in inches and the length in feet, find the area at the end in inches, multiply that by the length in feet, and divide this product by 144 (the square inches in a foot) and the quo sient will be the feet.

810

1458

length.

By the Sliding Rule.

Set 12 inches on the girt line D to the side of the square end on C, then, against the length on D, you will have the answer on C.

By Gunter.

Extend the compasses from 12 inches to the length of the side of the square end; that distance, twice turned over from the length,

144)1539(10-6875= content. will reach to the content.

144

990

864

1260

1152

1080

1008

720

720

When the side of a square solid is given, in inches, to find how much in length will make a foot solid.

RULE. As the given side is to 12, so is 12 to a fourth number, and so is that fourth number to its required length. Or divide 1728 by the area at the end, and the quotient will be the length making a solid foot.

If the given side is in foot measure, then,

RULE. As the given side is to 1; so is 1 to a fourth number, and so is that fourth number to the required length.

When two sides of an equal square solid (that is, of unequal breadth) are given, to find what length will make any number of solid feet.

RULE.--Multiply the proposed number of feet by 144 divide that product by the product of the breadth and depth, and the quoient will be the length required.

ART. 30. To measure a Cylinder.

Definition. A cylinder is a round body, whose bases are circles, fike a round column, or a rolling stone of a garden.

RULE. The diameter of the base being given, find the area of the end by Art. 15, then, multiplying the area of the base by the length, that product will be the content of the cylinder.

EXAMP. The diameter of the base AC being 1 foot and 9 inches, and the length BD 12 feet and 6 inches, to find the content.

A

12025

175

4810

2405

3.0625

⚫7854

30'0625 content.

If the square of the diameter of a cylinder be multiplied by 7854 and the solidity divided by that product, the quotient will be the length.

The learner may, for his practice, reduce all the dimensions te inches, and find the solid content in inches, which being divided by 1728, the quotient will be the solid content in feet: or, if he finds the area at the end in inches, and multiplies that by the length in feet, and divides by 144; the quotient will be feet.

This is a general rule for finding the content of any straight solid body, of equal bigness from end to end, of whatever form the bases are for, if the area of the base be multiplied by the length, the product will be the solid content.

By the Sliding Rule.

Set 13.5, the square root of 183-34 (which is a gauge point arising from the division of 144 by 7854) found on D, to the diameter found on C, and opposite to the length, on D, you will find the content on C,

Or,

Or, as 42.54 is to the circumference; so is the length in feet to a fourth number, and so is that fourth number to the answer.

Note. The superficial content of a cylinder is found by multiplying the circumference of one of the bases into the length, and to the product adding the areas of the two bases, or ends.

When the diameter is given in inches, to find what length will make a solid foot.

:

RULE. As the given diameter is to 13-531 so is 12 to a fourth number, and so is that fourth number to the required length. If the diameter be given in foot measure: Rule, as the given diameter is to 1128: so is 1 to a fourth number, and so is that fourth number to the required length. Or, divide 1728 by the area at the end in inches, and the quotient will be the required length.

To find how much a Cylindrick or round Tree, that is equally thick from end to end, will hew to, when made square.

RULE. Multiply twice the square of its semidiameter by the length, then divide the product by 144, and the quotient will be the

answer.

If the diameter of a round stick of timber be 24 inches from end to end, and its length 20 feet: how many solid feet will it contain, when hewn square; and what will be the content of the slabs which reduce it to a square?

solidity, whence 62.8-40-22.8 feet, the solidity of the slabs.

ART. 31. To measure a Prism.

Definition. A prism is a body with two equal or parallel ends, either square, triangular, or polygonal, and three or more sides, which meet in parallel lines, running from the several angles at one end, to those of the other.

RULE. Prisms of all kinds, whether square, triangular or polygonal, are measured by one general rule, viz. Find the superficial content, or area at the base (or end) by the proper rule of Sect. 1. and this multiplied by the length, or height of the prism, will give the solid content.

EXAMP. The side of a stick of timber, AB, hewn three square, is 10 inches, and the length, AC, is 12 feet, to find the content?

Note. The superficial content is found by adding the areas of the several quadrilateral and triangular figures which compose it.

ART. 32. To measure a Pyramid,

Definition. Solids, which decrease gradually from the base till they come to a point, are generally called pyramids, and are of dif ferent kinds, according to the figure of their bases; thus, if it has a square base, it is called a square pyramid: if a triangular base, a triangular pyramid: If the base be a circle, a circular pyramid, or simply acne. The point, in which the top of a pyramid ends, is called a Vertex, and a line drawn from the vertex, perpendicular to the base, is called the height of the pyramid.

RULE-Find the area of the base, whether triangular, square, polygonal or circular, by the rules in superficial measure: then, multiply this area by one third of the height, and the product will be the solid content of the pyramid.

EXAMP. 1. In a triangular pyramid, the height BE, being 48, and each side of the base 13: the base being a triangle, let the perpendicular height DE be 11; to find the content.

B

87

D

E