3. How many cubic feet in a stick of timber whose larger end is 25 feet by 20, the smaller 15 feet by 10, and the length 12 feet?

Ans. 3700.

4. What is the number of cubic feet in a stick of hewn timber, whose ends are 30 inches by 27 and 24 inches by 18, the length being 24 feet?

Ans. 102.

5. The length of a piece of timber is 20.38 feet, and the ends are unequal squares: the side of the greater is 191 inches, and of the less 97 inches: what is the solid content? Ans. 30.763 cubic ft.

6. The length of a piece of timber is 27.36 feet: at the greater end, the breadth is 1.78 feet and the thickness 1.23 feet; and at the less end, the breadth is 1.04 feet and the thickness 0.91 feet: what is its solidity? Ans. 41.8179 cubic ft.

8. How do you do when the timber does not taper regularly?

If the timber does not taper regularly, measure parts of the stick, the same as if it had a regular taper, and take the sum of the parts for the entire solidity.

9. Knowing the area of the end of a square piece of timber which does not taper, how do you find the length which must be cut off in order to obtain a given solidity?

1st. Reduce the given solidity to cubic inches.

2d. Divide the number of cubic inches by the area of the end expressed in inches, and the quotient will be the length in inches.

EXAMPLES.

1. A piece of timber is 10 inches square: how much must be cut off to make a solid foot?

10 x 10 = 100 square inches.

Then, 1728 100 17.28 inches.

2. A piece of timber is 20 inches broad and 10 inches deep: how much in length will make a solid foot?

Ans. 81 in.

3. A piece of timber is 9 inches broad and 6 inches deep: how much in length will make 3 solid feet?

Ans. 8 ft.

10. How do you find the solidity of round or unsquared timber?

1st. Take the girt or circumference, and then divide it by 5.

2d. Multiply the square of one-fifth of the girt by twice the length, and the product will be the solidity very nearly.

EXAMPLES.

1. A piece of round timber is 93 feet in length, and the girt is 13 feet: what is its solidity?

First, 135 2.6 the fifth of the girt.

Also, 2.62

6.76; and 9.75 x 2 = 19.50.

Again, 6.76 x 19.5 = 131.82 cubic feet, which is the required solidity.

2. The length of a tree is 24 feet, and the girt throughout 8 feet: what is the content?

Ans. 122.88 cubic ft.

3. Required the content of a piece of timber, its length being 9 feet 6 inches, and girt 14 feet.

Ans. 148.96 cubic ft.

11. How do you do when the timber tapers?

Gird the timber at as many points as may be necessary, and divide the sum of the girts by their number for the mean girt, of which take one-fifth, and proceed as before.

4. If a tree, girt 14 feet at the thicker end and 2 feet at the smaller end, be 24 feet in length, how many solid feet will it contain?

Ans. 122.88.

5. A tree girts at five different places as follows: in the first 9.43 feet; in the second 7.92 feet; in the third 6.15 feet; in the fourth 4.74 feet; and in the fifth 3.16 feet: now, if the length of the tree be 17.25 feet, what is its solidity?

12. What is often necessary for lumber merchants?

It is often necessary for lumber merchants to ascertain the number of feet of boards which can be cut from a given log; or, in other words, to find how many logs will be necessary to make a given amount of boards.

13. What is a standard board?

A standard board is one which is 12 inches wide, 1 inch thick, and 12 feet long: hence, a standard board is 1 inch thick and contains 12 square feet.

14. What is a standard saw-log?

A standard log is 12 feet long and 24 inches in diam

eter.

15. How will you find the number of feet of boards which can be sawed from a standard log?

If we saw off, say 2 inches, from each side, the log will be reduced to a square 20 inches on a side. Now, since a standard board is one inch in thickness, and since the saw cuts about one quarter of an inch each time it goes through, it follows that one-fourth of the log will be consumed by the saw. Hence we shall have

the number of boards cut from the log.

Now, if the width of a board in inches be divided by 12, and the quotient be multiplied by the length in feet, the product will be the number of square feet in the board.

20

Hence, x length of the log in feet the square feet

12

length; and the same may be shown for a log of any length.

16. What then is the rule for finding the number of feet of boards which can be cut from any log whatever ?

From the diameter of the log, in inches, subtract 4 for the slabs. Then multiply the remainder by half itself and the product by the length of the log, in feet, and divide the result by 8: the quotient will be the number of square feet.

EXAMPLES.

1. What is the number of feet of boards which can be cut from a standard log?

2. How many feet can be cut from a log 12 inches in diameter and 12 feet long?

Ans. 48.

3. How many feet can be cut from a log 20 inches in diameter and 16 feet long?

Ans. 256.

4. How many feet can be cut from a log 24 inches in diameter and 16 feet long?

Ans. 400.

5. How many feet can be cut from a log 28 inches in diameter and 14 feet long?

Ans. 504.

SECTION III.

BRICKLAYERS' WORK.

1. In how many ways is artificers' work computed?

Artificers' work, in general, is computed by three different measures, viz.:

1st. The linear measure, or, as it is called by mechanics, running measure.

2d. Superficial or square measure, in which the computation is made by the square foot, square yard, or by the square containing 100 square feet, or yards.