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344, 346.




344. Having two dimensions in feet of a bin, box, or coal-house, to find what the other must be in order to hold a given quantity.

RULE.-Multiply the given dimensions together for a divisor, and multiply the given quantity by the cubic feet in a bushel, as expressed in the above table; the quotient will be the other dimension.

1. A coal-box is 25 feet wide and 4 feet long; how high must it be to hold 10 bushels ? 2.5X4=10 divisor, 10X1.4777=14.777 & 14.777-10=1.4777 ft.=lft. 5@in. 2.5X4=10 divisor, 10X1.5555=15.555 & 15.555--10=1.5555 ft.=1 ft.6 in.

2. If I build a coal-house 40 feet wide and 18 feet high, how long must it be to hold 30000 bushels common coal measure ? Ans. 64.81 feet.

3. I have a garner of wheat which is 20 feet long, 8 feet wide, and 6 feet high; how many bushels are there?

Ans. 20X8X6X0.8—768 bushels. 4. How high must the above garner be to hold 1000 bushels of wheat?

· Ans. 20X8=160 for a divisor, and 1000X1.2444=1244.4 for a dividend. Then 1244.4;160—7.77 feet, for the height of the garner.

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The two first columns contain the size of the timber in inches, and the third column contains the area of a section of such stick in feet; so that if you find the size of the stick in the two first columns, and multiply its length in feet into the number in the third column, marked "areas of sections," the product will be the cubic feet and decimal parts which such stick of amber contains. One example will be sufficient :

What number of cubic feet in a stick of timber 18 by 15 igches, and 25 feet long? Ans. 1.875X25–46.875 cubic feet

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347. To determine how big a stick you can hew square ow of a round log (317), and how big a round log is required to be to make a square stick of given dimensions. In the first case, multiply the diameter of the log by 0.7071, the natural sine of 45° ; and in the second case, multiply the side of the stick required by 1.4142, the natural secant of 45°.

1. How big will a log square that is 2.5 feet diameter?

Ans. 0.7071X2.5=1,76775 feet for one side of the square. 2. A stick of timber is required 1.5 feet square; how large a round log is required to make it?

Ans. 1.4142x1.5=2.1213 feet diameter. 318. To take off the corners of a square 80. as to form an octagon.-Multiply the side of the square by 0.2929, and the product will be the distance to measure from the corners to form the octagon. Deduct twice the product from the side of the square, and it will leave one side of the octagon required

EXAMPL.E. ABCD is a tower, 20 À F

G : B feet square, on which an octagon is to be erected; what will be its side, and what dis, tance from the corner to the octagon post ?

Ans. TAB=20X E 0.2929 = 5.853 = AF and AB-AF-GB= FG=8.284 for one siden of the octagon. • If a diagonal square, as HIKL, is required. to be formed on the abuve said square tow. er, then multiply one side by 0.7078 °(360, and the product will be one side of the inscribed diagonal square. That is, AB=20X0.70713 14.142=HI. HL, KL, or KI.

If the side of a square tower be 16 feet, what will be the side of an octagon erocted upon it?

Ans. 6.6272 feet

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349. The most common pitch for roofs of barns is to rise one third of the length of the beam, as KB-5 of AE=8. Roofs of one and A

12. K H a half story houses are usually pitched to at about 30°, as KC, and two story houses, or higher, the roof is. F usually raised one fourth of the length of the beam, as KD.

Braces are generally placed equidistant each way from the corner, as FG, but sometimes farther one way than the other, as HI.

To find the length of rafters when they rise one third of the length of the beam, inultiply one half the length of the beam or the base of the rafter by 1.20185; and to get the length of studs under the rafters, multiply so much of the base as is contained between the foot of the rafter and the foot of stud by 0.6666. Consequently the half length of the beam, 12x1.2 (bmitting the other figures), is 14.4 for the length from A to B; and if a stud is placed 9 feet from the foot of the rafter, its length will be 0.6666X96 feet.

If the roof is raised 30 degrees to C, then 12X 1.15468 13.856 for the length of the rafter; and the length of studs under the rafter will be obtained by multiplying as above by 0.57735.

If the roof rises one fourth of the length of the beam, then 12x1.118034—13.416 for the length of the rafter; and the length of the studs in this case will be half the distance from the foot of the rafter to the foot of the stud.

For the length of braces subtending a right angle, and extending equidistant each way, multiply the length of one of the sides containing the right angle by 1.4142; or if you have the brace, and wish to know how far from the corners to make the mortices for it, multiply the. Jength of the brace by 0.7071.

The brace FG is 6 feet each way from the corner, and 6X1.4142_8485. its length. The brace HI is found by the bast case of rafters, thus 8X1.1188.944 its length. They may also be found by the square root. (268)

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USE OF THE TABLE, I have four log's, oncis 14 in. rliameter and 13.} 11. long, one 21 in. and 17 n., one 30 in. and 16 n., and one 35 in. and 1. 1. long: how many logs have I, log measure ? Against 14 under 13 we find 405

- 21 " 17" 16 1.147

35 6 12 16 2.2 18

Ans. 6.002 logs, or a little more than 6 lomme

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