Εικόνες σελίδας
PDF
Ηλεκτρ. έκδοση

timber; multiply the two sides together; find the difference between the two sides; square the difference, and add one third of its square to the product of the two sides, and multiply this sum by the length, the last product is the solidity required.

Examples.

1. How much hewn timber is in a stick of round timber, that is 24 ft. long, and its circumference at one end is 44 in. and at the other 22 in. ?

Cir. 440 4410 a side of the largest square.
Cir. 22.0÷4.4 5 a side of the least square.
Sides of the two squares 10×5=50 product.
Sides 10-5 5 X5=25÷3 = 8 added.

58 sum.

Sum 58x24 ft.=1400÷144-9 ft. Ans.

144

2. How much hewn timber is in a stick that is 21 feet long, and its circumference at one end is 88 in. and at the other 44 in. ? Ans. 34,4 ft.

NOTE. If it is required to find how much hewn timber is contained in a round stick, allowing the square timber to be all its length of equal bigness, the round stick must be girted only at the smallest end.

CASE XX.

To find the solidity of a round stick of timber which is of a true taper from end to end, including the four segments, or slabs.

RULE. Apply the rule for finding the solidity of the frustum of a round cone.

(See Frustum of Cones, Case Sixth, Solids.)

Examples

1. What is the solidity of a stick of timber whose largest circumference is 63, and smallest 43 in.; and is 21 feet long?

Cir. 63-00-3-14 20:0† diam.

Cir. 43.00 3.14 13-7 diam. nearly.

Cir, and diam. 63x20=1260 315 area, large end.
Cir. and diam. 43×13·7589·1÷÷=147† area, small end.
Areas 315×147= 46305 =215† root add.

2

677 sum.

Sum 677×21÷=4739÷144—32443 ft. Ans.

NOTE.-This method of operation would be too lengthy for ́common use; and if the following rule be adopted the solidity may be found very near the truth (although a little too small) with much more convenience.

RULE 2.-Girt the stick near the middle (but rather nearer the but end), the girt is the circumference; annex two cyphers to the circumference; and divide by 3.14 the quotient is the diameter nearly ;multiply the circumference and diameter together, and of the product multiplied into the length will give the solidity very near.

Examples.

1. What is the solidity of a round stick of tim ber (including the four segments) which is 12 ft. long and its middle girt, or circumference it 62.8 inches?

Cir. 62.80÷3∙14=20 diam.; and 20×62·8—1256·0— 314X12-3768-144 26 ft. Ans..

2. What is the solidity of a round stick of timber that is 10 ft. long; and its mean girt 314 in. including the four segments or slabs?

[blocks in formation]

3. What is the solidity of a round stick of timber, whose mean girt is 94.2 in.; and 30 ft. long? Ans. 147 27 ft.

CASE XXI.

T44

To find the solidity of a hervn stick of timber that has all its sides parallel.

RULE.-Multiply one side by the other, and the product multiplied by the length, will be the solidity.

Examples.

1. What is the solidity of a stick of hewn timber that is 30 ft. 6 in. long; and one side is 1 ft. 3 in.; the other side 6 in. ?

30 ft. 6'x1 ft. 3'×0 ft. 6'19 ft. 0′ 9′′ or 19

1

16 ft. Ans. NOTE.-Stone is measured in the same manner as square or hewn timber.

2. What is the solidity of a stone that is 12 ft. 6 in. long, 4 ft. 10 in. wide, and O ft. 9 in. thick? Ans. 45 ft. 3' 9".

NOTE.--When two sides, of the stick are parallel, multiply the mean width and the other side together, and the product by the length.

3. What is the solidity of a stick of timber that is 12 in. wide at one end, and 8 at the other; and is 8 in. thick, and 3 ft. 4 in. long?

Ans. 1 ft. 10′ 2′′ 8'".

CASE XXII.

[ocr errors]

To find the solidity of a tapering hewn stick of timber, which has no two sides parallel.

RULE. Apply the rule for finding the solidity of the frustum of a cone or pyramid,(see case sixth;) if the stick is square at each end, measure it as in case 6th, rule 2.

Examples.

1. What is the solidity of a stick of hewn timber that is 10 in. square at one end, and 4 in. at the other, and is 32 feet long?

Sides of Sq. 10×440 pro.

Sides 10-4-6X6=36÷-12 add.

Sum 32

Sum 52×321664÷144—115 ft. Ans.

2. What is the solidity of a stick of timber that is 15 in. by 12 at one end; and 9 by 6 in. at the other end, and 21 ft. long?

Sides 15x12=180 area of largest end.
Sides 9 × 6= 54 area of smallest end.

2

234 sum of the two areas.

A, 180×549720=98† root add.

Sum 332X72324-144-16ft.Ans.

NOTE. The preceding method of measuring hewn tapering timber gives the exact solidity; but the method of taking the dimensions in the middle of the stick does not give the ex. act solidity, except in such sticks as have two or more sides parallel.

1. Required the solidity of a stick of timber that is 10 by 10 in. at one end, and 4 by 4 in. at the other end; and is 32 feet long: measured by taking the mean be tween the two ends?

Sides 10+4 14-17 mean side.

Mean side 7X7X32=1568144-10 Ans. Solidity too small by 6 of a foot, (see quest. 1, case 22.)

2. What is the solidity of a stick of timber, which on one side is 15 in. at one end, and 12 the other; and on

the other side, it is 9 in. at one end, and 6 the other; and is 21 feet in length;

Ends 15+12=2713 mean side.

Ends 9615÷7 mean side.

Sides 27 × 15 × 21÷144

15

14441 ft. Ans,

(See

and is 1218 ft. smaller than the true answer, question 2, case 22.)

NOTE.--This last method of measuring hewn tapering timber, being more convenient than the method of measuring it as a frustum of a cone, it is generally put in practice.

CASE XXIII.

To find the solidity of timber by Gunter's sliding rule allowing of the circumference to be a side of square timber in the round stick.

RULE 1. Look first for the length of the stick in feet upon the brass slider, slip the slider to bring the figures expressing the length, to 12 on the girt line below, then look on the girt line for the quarter girt of the stick, and against the quarter girt (on the slider) stands the figures expressing the solidity of

the stick.

To find the solidity of a stick of timber, allowing 4.4 of the circumference to be a side of square timber.

RULE 2. Girt the stick where it would tip easy if it were lying upon another log, annex a cypher to the girt in inches, and divide by 44, the quotient is a side of square timber: then proceed as above.

To find the solidity of hewn timber by Gunter's rule.

RULE. 3-Add the four sides together, take of the sum for the mean side, proceed as above, and the will be very near the true solidity.

answer

« ΠροηγούμενηΣυνέχεια »