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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. 10X4=40 pro.
Sides 10_4=6X6=36==12 add.

Sum 52
Sum 52X32=1664--144=119 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 15 x 12=180 area of largest end.
Sides 9X 6= 54 area of smallest end.

2

234 sum of the two areas. A. 180 X 54= 9720=987 root add.

Sum 332x7=2324--144167ft.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- =7 mean side.

Mean side 7x7x32=1568 = 144=109 Ans. Solidity too small by 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=27=313 mean side.
Ends 9+ 6=15+1=7 mean side.

Sides XX*! „144 =14741 ft. Ans, and is 1**ft. smaller than the true answer, See question 2, case 22.)

Note.--This last method of measuring hewn tapering tim. ber, 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 4.4, 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 Use answer will be very near the true solidity.

CASE XXIV.

WOOD AND BARK MEASURE.*

RULE.Multiply the length of the pile in feet and inches, by the width, and that product again by the height of the pile, the last product is the solidity ; which divided by 128 the quotient is cords ; if any thing remains, divide it by 16, the quotient is feet of wood ; if any thing still remains, divide by 4, the quotient will be quarters of a foot of wood, &c.

Examples.

1. What is the quantity of wood in a pile, that is 9 feet 6 inches long, 6 feet wide, and 4 fect 6 inches high? ft. ft. ft. 9 6'X60X46=256 6' ;-128=2 cords f solid ft. Ans.

2: What is the solidity of a pile of wood 22 ft. 9 in. long, 5 ft. 8 in. wide, and 2 feet 6 inches high?

Ans. 23+ cords. 3. What is the solidity of a pile of bark that is 9 feet long, 10 ft. 6 in. high, and 4 ft. 6 in. thick?

Ans. 4251 sol. ft. or 3 cords 241 ft.

CASE XXV.

Having the base, or bottom of a pile of wood, or bark give .ch, to find how high to build, that the pile may contain

any quantity of wood, or bark required. RULE.

Find the solid feet contained in the pile of wood you would build ; reduce these feet to solid inches, and use them for a dividend; find the superficial area of the base in inches, and use them for a divisor; divide, and the quotient is the inches in height.

* Wood and bark are sold by the cord, and 1728 inches make 1 solid foot; 18 solid feet make 1 foot of wood; 8 Peet of wood I cord; 128 solid feet one cord.

Examples. 1. How high must a pile of wood, or bark be to contain 8 ft. or 1 cord; which stands upon a base 48 in. by 48 in. ?

1 cord=128 sd. ft. x1728=22118 4 sd. in, dividend.
48 in. X 48 in. =2304 area of the base, divisor.

221184--230496 in., or 8 ft. in height, Ans. 2. I demand the height of a pile of wood that will contain 4į feet, the base, or bottom of which is 4 by 5 feet. Ans. 43 17 in. or 3 ft. 7 in.

3. I demand the height of a pile of wood, that shall contain 9 feet, that stands upon a base, that is 6 by 5 feet. Ans. 57 in. or 4 ft. 9 in.

CASE XXVI.

To find the sotidity of a parallelopipedon. DEFINITION.-A parallelopidedon is a figure haying six rectangular sides, every opposite pair of which are equal and parallel.

Rule.-Multiply the length breadth and thickness together the product is the solidity.

Example. 1. A farmer would make a large chest 21 ft. long, 5 ft. 6 in. wide, and 3 ft., 9 in, high, the solidity of which is required.

21 ft. O in. x 5 ft. 6 in. X 3 ft. 9 in. 433 ft. 1' 6" Ans. 2. How many solid feet in a cart that is 8 ft. long, 4 ft. 4 in. wide, and 2 ft. 4 in. high?

Ans 80 ft. 10 8".

CASE XXVII.

To find the solidity of any cubical Agure, DEFINITION—Any figure having six square, or equal sides is called a cube.

RULE.-Multiply one side into another, and this product by the third, the last product is the solidity.

Examples. 1. What is the solidity of a tea chest that is 3 ft. 6 in. every way?

3 ft. 6' x 3 ft. 6' x 3 ft. 6'42 ft. 10'6" Ans. 2. How many solid feet will 60 bales of goods occupy in a store ; each bale measuring 4 ft. 3 in. every way?

Ans. 4605 ft. 11' 3". 3. How many solid feet are in a square room that is 12 feet long, 12 feet wide and 12 feet high?

Ans. 1728. 4. How many solid feet in a pillar that is 16 feet square?

Ans. 4096. 5. There is a pit dug 8 feet deep, 8 feet long and 8 feet wide ; how many solid feet of sand were thrown out of it?

Ans. 5120

GUAGING.

DEFINITION.-Guaging is the art of measuring all kinds of vessels, determining the quantity of liquor contained in them; practitioners in the art, generally make their calculations by means of instruments, the instruments used in guaging, are the calipers, Gunter's sliding rule, Gunter's scale, &c. the guaging rod is used 10 take, or find the outs. The vessels used for liquor are various in shapes and names, viz. pipes, hogsheads, barrels, runlets, &c. also among brewers, coolers, backs, vats, &c. are used.

Solidity of liquid measure, &C.
A gallon of wine occupies a space equal to 231 sol. in.

gallon of beer occupies a space equal to 282 sol. in. A gallon in corn measure is equal to 268:8, sol. in. Á bushei in corn measure is equal to 2150:4 sol, in,

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