5. A piece of timber is 32 inches broad, and 20 inches deep, at the greater end; 16 inches broad, and 8 inches deep, at the less end; and its length is 25 feet what is its solidity?

Ans. 583 feet.

Note. The true content, measured as a prismoid, is 61 feet. See Example 2, Problem X., Section I.

PROBLEM III.

To find the solidity of round or unsquared timber.

RULE I.

;

Multiply the square of of the circumference, or quarter girt, by the length, and the product will be the content, according to the common practice.

By the Sliding Rule.

As the length upon C, is to 12 upon D; so is of the girt in inches upon D, to the content upon C.

RULE II.

Multiply the square of of the girt by twice the length, and the product will be the solidity nearly.

By the Sliding Rule.

As twice the length upon C, is to 12 upon D; so is of the girt upon D, to the content upon C.

Note 1. The girt must be taken in the middle of the tree, if it taper regularly; if not, take several girts, and their sum divided by their number, will give something near a mean girt. If the tree be very irregular, divide it into two or more parts, and find the content of each separately.

2. The girt of a tree is generally taken with a string, which being folded into four equal parts, and applied to a carpenter's rule, gives the quarter girt ; but it is more expeditions to take the girt with a tape divided into equal parts of 4 inches each: and numbered at 4 inches from the end with 1, at 8 inches with 2, at 12 inches with 3, &c. by which means the quarter girt can be ob. tained by merely girting the tree.

If the second Rule be used, the girt may be taken with a tape divided into equal parts of 5 inches each.

Each division of 4 or 5 inches, may also be subdivided into halves and quarters, and numbered successively with,,; hence the quarter girt may be obtained with accuracy. The other side of the tape may be divided into feet and inches.

3. In measuring a tree which has its bark on, an allowance is generally made, by deducting so much from the girt as is judged sufficient to reduce the tree to such a circumference as it would have without its bark. This deduction may be most easily made from the quarter girt; and should be proportioned according to the thickness of the bark.

For ash, beecb, elm, young oak, &c. or of an inch for every foot of the quarter girt, will generally be sufficient; but for old oak, whose bark is much thicker, it will be found necessary to allow an inch, an inch and a half, and sometimes two inches, for every foot of the quarter girt.

4. That part of the boughs, or of the trunk of a tree, which is less than 24 inches in circumference, or 6 inches quarter girt, is generally cut off, and sold at an inferior price; not being considered timber.

5. The first Rule in this Problem gives the solidity about & part less than the true quantity, or nearly what the quantity would be if the tree were squared; so that it seems intended to make an allowance for the squaring of the tree.

6. The second Rule gives nearly the true content, whether the tree be a cylinder or the frustum of a cone; and as it is full as easy in practice as the first, it ought always to be used when accuracy is required; if the Rules for a cylinder, the frustum of a cone, &c. be thought too prolix. (See Examples 3 and 4.)

7. If a piece of round tapering timber be cut through exactly in the middle, the two parts will measure to the most possible; and to more than the whole by either of the Rules.

8. To find where a round tapering tree must be cut, so that the part next the greater end may measure the most possible: From the greatest girt take 3 times the least; then, as the difference of these girts, is to the remainder; so is one third of the whole length, to the length to be cut off from the less end, Or, cut the tree where the girt is one-third of the greatest girt.

When the greatest girt does not exceed 3 times the least, this Rule is im practicable.

9. Forty feet of round timber, measured by the quarter girt method, are called a load; but when the content of timber is correctly found, fifty feet are accounted a load.

Fifty feet of dry oak weigh rather more than a ton and a quarter.

10. The content of a piece of timber, according to the quarter girt method, may be readily found from the following Table, thus: Multiply the area cor responding to the quarter girt, in inches, by the length of the timber, in feet; and the product will be the solidity in feet and decimal parts.

EXAMPLES.

1. What is the solidity of a tree whose girt in the middle is 100 inches, and length 18 feet?

As 18 upon C: 12 upon D::25 upon D: 78 upon C.

By Rule II.

By the Sliding Rule.

As 36 upon C: 12 upon D:: 20 upon D: 100 upon C. 2. The length of a tree is 32 feet 6 inches, and its girt in the middle, after allowing for the bark, is 60 inches; what is its content?

Ans.

3. The circumfer ber is 6 feet 8 inches, is its solidity?

By the first Rule, 50.78125 feet.
By the second Rule, 65 feet.

of a cylindrical piece of timand its length 24 feet; what is

By the first Rule, 66 ft. 8 in. Ans. By the second Rule, 85 ft. 4 in.

Note. The true content measured as a cylinder, is 84 feet 10 inches. See Example 3, Problem IV., Section I.

4. The circumference of a piece of round, tapering timber is 65 inches at the greater end, 35 inches at the less end, and its length 33 feet 9 inches; what is its solidity?

J By the first Rule, 36.621 feet.
By the second Rule, 46.875 feet.

Note. The true content measured as the frustum of a cone, is 48 feet. See Example 3, Problem VIII., Section I.

5. What is the content of an oak tree whose dimensions are as follow: The length of the trunk is 45 feet, and its quarter girt, in the middle, 30 ches; the length of a large bough 16 feet, and its quater girt 14 inches; and the length of another bough 12 feet, and its quarter girt 10 inches? Ans. 311.36111 feet.

PROBLEM IV.

To measure and value standing Timber.
To find the content.

RULE.

Obtain the dimensions by some of the methods described in the following pages; and find the solidity by the Rules given in the last Problem. The first Rule is generally adopted, and the content found by the Sliding Rule.