344, 346.

PRACTICAL RULES AND TABLES.

149

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?

2.5×4=10 divisor, 10×1.4777=14.777 & 14.777÷10=1.4777 ft.=1ft. 5gin. 2.5×4=10 divisor, 10×1.5555=15.555 & 15.555÷÷10=1.5555 ft.=1 ft.6ğ 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. 20X8X6×0.8-768 bushels.

4. How high must the above garner be to hold 1000 bushels of wheat?

Ans. 20X8 160 for a divisor, and 1000×1.2444-1244.4 for a dividend. Then 1244.4-160-7.77 feet, for the height of the garner.

1210.7854||19|1.9689||26|3.6863||33|5.9395||40| 8.7179||47|12.0482|

13 0.9218 20 2.1817 27 3.9753||34|6.3050||41| 9.1684 48 12.5664 14 1.0691 212.404828 4.2760||35|6.681342 9.6211||49 13.0954 15|1.2272||22|2.6393||29|4.5869|36|7.0686 43 10.084750 13.6354 16 1.3963 23 2.8847 30 4.9087 37 7.4667||44|10.5592 51 14.1861 171.5762 24 3.1416 31 5.2414 38 7.8758 45 11.0447 52 14.7479 18/1.7671253.408232 5.585139 8.2957146 11.541053 15.3201

The column marked diameter is the diameter in inches, and the column marked area is the area of a section of the cylinder in feet and decimal parts. To illustrate the use of this table, I will give a few examples, viz.

1. How many cubic feet in a round stick of timber, 20 feet long, and 18 inches diameter ?

Look in the table under the head of diameter, and against 18 in the column of areas is 1.7671, which multiplied into the length in feet, will give the number of cubic feet such stick contains that is, 1.7671×20=35.342 cubic feet.

2. How many cubic feet in a round log. 24 inches diameter and 16 feet long? Ans. 3.1416x16 50.2656 cubic feet. 3. Suppose the mean diameter of a cask to be 3 feet, and its length 5 feet, how many cubic feet will it contain, and how many bushels of wheat will it hold

Ans. 7.0686X5-35.343 cubic ft., which X0.8 28.2744 bush.

EXPLANATION OF THE TABLE OF SQUARE TIMBER MEASURE

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 timber contains. One example will be sufficient :

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

26 4.3333

22 3,0555

23 3.1944

24 3.3333

25 3.47221

26 3.6111

347, 348.

PRACTICAL RULES AND TABLES.

151

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°.

EXAMPLES.

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. 1.4142x1.52.1213 feet diameter.

348. To take off the corners of a square so 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,

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

Ans. 6.6272 feet,

tant 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, multiply 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 (omitting 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 0.6666×9—6 feet.

If the roof is raised 30 degrees to C, then 12×1.15468= 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 length 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 last case of rafters, thus 8x1.1188.944 its length. They may also be found by the square root. (268)

950.

PRACTICAL RULES AND TABLES.

153

350. Logs, in the state of New York, and some other places, are calculated by number; a log 134 feet long and 22 inches diameter being considered one log, and logs of other diameters and lengths calculated according to their cubic quantities. On this principle the following table is constructed, in which the left hand column is the diameter of the logs in inches, the top line the length in feet, and the figures at the angle of meeting the number of logs and decimal parts.

LOG TABLE-LOG MEASURE.

510 540]

618

704

8 9 10 11 12 13 134 14 15 16 17 18 10.122 .137 .153 .163] .183 .198 207 213.228 244 .259 .274 11 148 .166 .185 203 222 210 .950 .258 .276 296 .314 .332 12.175.197 219 .240 262 284 297 306,328 350 372 .394 13 206 232.257.200 09 33519 360 895 .412 437 464 11 240 270 300 330 360.390] .465] .420 450 480 15 275 309 344 378 412 417 465 482 516 .550 584 16 .313 .352 .391 430 469 509 529 518 .587 .626.665 17 351 338 442 487 .531 .575 .597 .626.664 .708 752 796 18 .396 .445 495 544 .594 .643 .669 .693.742.792 .841 .890 19 441 496.551 .606 .661 .717 745.772 827.882.947 992 20 489 550 .611 672 733 791 825 856.917 .978 1.039 1.100 21.540.607 675 742 810 877 910 .915|1.0121.080 1.147 1.215 22.592 666 .740 .814 888 .962 1.000 1.036|1.110|1.1841.258 1.332 23.648 729 .810 .891.972 1.053 1.093 1.1341.2151.296 1.3771.458 24 .705 .793 .881 .9611.057 1.146 1.190 1.233 1.322 1.410 1.498 1.586 25 .765.861| .956|1.052|1.147 1.243 1.291 1.339 1.4341.530 1.626 1.722 26.827.930|1.034 1.137|1.240 1.3441.396 1.447 1.550 1.654 1.7571.860 27.892 1.003 1.115 1.226 1.3381.449 1.506 1.5611.672 1.784 1.895 2.006 28 .960 1.080 1.200 1.320 1.440 1.560 1.620|1.680|1.800 1.920 2.040 2.160 29 1.029 1.1571.2361.4151.543 1.61.787|1,600|1.929 2.058 2.176 2.314 301.101 1.258 1.5761.514 1.651|1.789|1.859|1.926|2.061|2.202 2.339 2.476 |31|1.1751.322|1.469 1.61617621.909 1.985 2.056 2.2032.350 2.4972.644| 321.2521.408 1.565 1.721 1.878 2.034 2.1152.191 2.3472.504 2.6602.816) 331.3321.498 1.665 1.831 1.9982.164 2.249 2.331 2.497|2.064 2.850 2.996 311.4141.591 1.767 1.9142.121 2.298 2.387 2.474 2.651|2,828|3.005 3.182 35 1.199 1.686 1.874 2.061 2.248 2.436 2,529 2.623 2.811 2.9983.1853.372 36 1.585 1.783 1.981 2.3792.5772,577 2.6752.774 2.972 3.170 3.3683.566 371.676 1.885 2.095 2.3042.5112.723 2.828 2.933 3.1423,352 3.561 3.771 381.7671.938 2.209 2.430 2.6512,871 2.983 3.092 3.3133.534 3.7553.976 391.8612.0942.3272.560 2.7923.025 3.1123.2572.4903.7233.9564.188 401.958 2.203 2.1482.6932.9373.182|3.3053.427 3.6723.9174.161 4.406|

USE OF THE TABLE,

I have four logs, one is 14 in. diameter and 133 ft. long, oue 21 in. and 17 ft., one 30 in. and 16 ft., and one 35 in. and 12 ft. fong; how many logs have 1, log measure?