MENSURATION OF LUMBER.

To find the contents of a board.

RULE. Multiply the length in feet by the width in inches, and divide the product by 12; the quotient will be the contents in square

feet.

EXAMPLE. A board is 16 feet long and 10 inches wide; how many square feet does it contain?

16 X 10 = 160 ÷ 12 = 13. Ans.

To find the contents of a plank, joist, or stick of square timber.

RULE.-Multiply the product of the depth and width in inches by the length in feet, and divide the last product by 12; the quotient is the contents in feet, board measure.

EXAMPLE.

- A joist is 16 feet long, 5 inches deep, and 2 inches wide; how many feet does it contain, board measure?

1

5 X 2.5 X 16 ÷ 12 = 16. Ans.

To find the solidity of a plank, joist, or stick of square timber. RULE.-Multiply the product of the depth and width in inches by the length in feet, and divide the last product by 144; the quotient will be the contents in cubic feet.

EXAMPLE.A stick of timber is 10 by 6 inches, and 14 feet in length; what is its solidity?

10 X 660 X 14

= 840 144 = 5 feet. Ans.

NOTE.If a board, plank, or joist is narrower at one end than the other, add the two ends together and divide the sum by 2; the quotient will be the mean width. And if a stick of squared timber, whose solidity is required, is narrower at one end than the other, take the measurements of its sides at half its length.

To measure round timber.

RULE (IN GENERAL PRACTICE.) Multiply the length, in feet, by the square of the girt, in inches, taken about the distance from the larger end, and divide the product by 144; the quotient is considered the contents in cubic feet. For a strictly correct rule for measuring round timber, see MENSURATION OF SOLIDS - Frustum of a

Cone.

EXAMPLE. —A stick of round timber is 40 feet in length, and girts 88 inches; what is its solidity?

88÷4=22×22=484 X 40=19360÷144134.44 cub. ft. Ans

The following TABLE is intended to facilitate the measuring of Round Timber, and is predicated upon the foregoing RULE.

To find the solidity of a log by help of the preceding TABLE.

RULE.-Multiply the tabular area opposite the corresponding girt, by the length of the log in feet, and the product will be the solidity in feet.

EXAMPLE. -The girt of a log is 22 inches, and the length of the log is 40 feet; required the solidity of the log.

3.362 X 40 134.48 cubic feet. Ans.

=

NOTE.Though custom has established, in a very general way, the preceding method as that whereby to measure round timber, and holds, in most instances, the solidity to be that which the method will give, there seems, if the object sought be the real solidity of the stick, neither accuracy, justice, nor certainty, in the practice.

Thus, in the preceding example, the stick was supposed to be 40 feet in length, and 88 inches in circumference at the distance from the larger end, and was found, by the method, to contain 134.44 cubic feet: now 883.141628 inches,: the diameter at the distance from the greater base, and retaining this diameter and the length, we may

suppose, with sufficient liberality, and without being far from the general run of such sticks, the diameter at the greater base to be 30 inches, and that of the less to be 24 inches, and

30 24 720-12=732.7854 X 40=22996-144-159.7 cubic feet, or 19 per cent. more than given by the method under consideration; and we need hardly add that the nearer the stick approaches to the figure of a cylinder, the wider will be the difference between the truth and the result obtained by the method referred to. Thus, suppose the stick a cylinder, 28 inches in diameter, and 40 feet in length; and we have, by the fallacious rule, as above, 134.44 cubic feet; and—

By a correct method, we have

282.7854 X 40=24630144-171 cubic feet, or over 27 per cent. more than furnished by the erroneous mode of practice.

Again: suppose the stick in the form of a cone, 30 inches at the base, and tapering to a point at 150 feet in length; and we have, by a correct rule

3023=300.7854 X 150-35343144245.44 cubic feet; and by the ordinary method of gauging, or the aforementioned practice, we have

20 3.141662.832÷4=15.7082 × 150 = 37011.19÷144=257 cubic feet, or nearly 44 per cent. more than the stick actually contains.

In short, without taking into account anything for the thickness of the bark, that may be supposed to be on the stick, the method is correct only when the stick tapers at the rate of 5 inches diameter per each 10 feet in length, or over inch diameter to each foot in length of the stick.

If, however, we suppose the stick as before, (30 inches at the greater base, 24 inches at the smaller, and 40 feet in length,) and suppose the bark upon it to be 1 inch thick, we shall have, by the usual method, 134.44 cubic feet, as before. And, exclusive of the bark, by a correct method, we shall have.

30-224-2=616+12=628 X.7854 X 40=19729144 137 cubic feet, or only about 2 per cent. more than that furnished us by the usual practice.

The following simple rule for measuring round timber is sufficiently correct for most practical purposes:

RULE.Multiply the square of one-fifth of the mean girt, (exclusive of bark,) in inches, by twice the length of the stick in feet, and divide the product by 144; the quotient will be the solidity in feet.

To find the solidity of the greatest rectangular stick that may be cut from a given log, or from a stick of round timber of given dimen

sions.

RULE. Multiply the square of the mean diameter of the log, in inches, by half the length of the log, in feet, and divide the product by 144.

EXAMPLE.

The diameter (exclusive of bark) of the greater base of a stick of round timber is 30 inches, and that of the less base is 24 inches, and the stick is 40 feet in length; required the solidity of the greatest rectangular stick that may be cut from it.

30 × 24+ (30—24)2=732=square of mean diameter,* and

732×20=14640 ÷ 144=101} cubic feet. Ans.

* Except in the case of a cylinder, there is a difference betwixt the solid having circular bases, and the middle diameter of that solid. reduces the solid to a cylinder; the middle diameter is the diameter two bases.

mean diameter of a The mean diameter midway between the

1464016 915 feet of square-edged boards 1 inch thick;

Or, 10139915.

To find the solidity of the greatest square stick that may be cut from a given log, or from a stick of round timber of given dimensions.

RULE.-Multiply the square of the diameter of the less end of the log, in inches, by half the length of the log, in feet, and divide the product by 144.

EXAMPLE.The preceding supposed log will make a square stick containing

242X401152÷144–80 cubic feet.

Diameter multiplied by .7071-side of inscribed square.

To find the contents, in Board Measure, of a log, no allowance being made for wane or saw-chip.

RULE.-Multiply the square of the mean diameter, in inches, by the length in feet, and divide the product by 15.28.

Or, Multiply the square of the mean diameter in inches, by the 'length in feet, and that product by .7854, and divide the last product by 12.

The cubic contents of a log multiplied by 12, equal the contents of the log, board measure.

The convex surface of a Frustum of a Cone

=

(C+c) X slant length; C being the circumference of the greater base, and c the circumference of the less.

GAUGING.

RULES for finding the capacity in gallons or bushels of different shaped Cisterns, Bins, Casks, &c., and also, by way of examples, for constructing them to given capacities.

RULE -1. When the vessel is rectangular. Multiply the interior length, breadth, and depth, in feet together, and the product by the capacity of a cubic foot, in gallons or bushels, as desired for its capacity.

RULE-2. When the vessel is cylindrical. Multiply the square of its interior diameter in feet, by its interior depth in feet, and the product by the capacity of a cylindrical foot in gallons or bushels, as desired for its capacity.

RULE-3. When the vessel is a rhombus or rhomboid. Multiply its interior length, in feet, its right-angular breath in feet, and its depth in feet together, and the product by the capacity of a cubic foot in the special measure desired for its capacity.

RULE 4. When the vessel is a frustum of a cone—a round vessel larger at one end than the other, whose bases are planes. Multiply the interior diameter of the two ends together, in feet, add the square of their difference in feet to the product, multiply the sum by the perpendicular depth of the vessel in feet, and that product by the capacity of a cylindrical foot in the unit of measure desired for its capacity.

RULE 5. When the vessel is a prismoid or the frustum of any regular pyramid. To the square root of the product of the areas of its ends in feet, add the areas of its ends in feet, multiply the sum by its perpendicular depth in feet, and that product by the capacity of a cubic foot in gallons or bushels, as desired for its capacity.

If it is found more convenient to take the dimensions in inches, do so; proceed as directed for feet, divide the product by 1728, and multiply the quotient by the capacity of the respective foot as directed. Or, multiply the capacity in inches by the capacity of the respective inch in gallons or bushels; - by the quotient obtained by dividing the capacity of the respective foot in gallons or bushels by 1728 — for

the contents.

RULE-6. When the vessel is a barrel, hogshead, pipe, &c. Multiply the difference in inches between the bung diameter and head diameter, (interior,) if the staves be

and add the product to the head diameter, taken in inches; then multiply the square of the sum by the length of the cask in inches, and divide the product by the capacity in cylindrical inches of a gallon or