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.

347. To determine how big a stick you can hew square ou 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. 1.4142X1.5-2.1213 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.

ABCD is a tower, 20 feet square, on which an octagon is to be erected; what will be its side, and what distance from the corner to the octagon post?

Ans. AB=20X E 0.29295.858 = AF and AB-AF-GB= FG-8.284 for one side H of the octagon.

If a diagonal square, as HIKL, is required to be formed on the above said square tower, then multiply one side by 0.7071 (360), and the product will be one side of the inscribed diagonal square. That is, AB=20X0.7071= 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 erected upon it?.

Ans. 6.6272 feet.

1

fourth of the length of the beam, as KD.

Braces are gener

ally placed equidis

F

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 8.485 its length. The brace HI is found by the last case of rafters, thus 8x1.118-8.944 its length. They may also be found by the square root. (268)

350. Logs, in the state of New York, and some other places, are calculated by number; a log 13 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.

262 .309 360 412

13 14 15 16 17 18

10 .122 .137 .153 .169.183 .198 207 213 228 244 259 .274 11.148 .166 .185 .203 292 240 .250 .258 .276 296 .314 .332 12.175.197 219 .240 284 297 .306 .328 .350 .372 .394 13.206.232 .257 .263 .335 .349 .360 .385 412 437 464 14 .240 .270 .300 .330 390 405 420 450 480 .510 .540 15 .275 .309 .344 378 417 465 482 516 .550 .584 .618 16 313 .352 .391 430 .469 .509.529 .548 .587 .626 .665 .704 17 351 393.442 487 531 575 597 .620 .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 .794 .825 .856 .917 .978 1.039 1.100 21.540 .607 675 .742 .810 .877 .910 .945 1.012 1.080 1.1471.215 22.592 666 .740 814 .888 .962 1.000 1.036 1.110|1.184 1.258 1.332 23 .648 729 .810 .891 972 1.053 1.093 1.1311.2151.2961.3771.458 24 .705 793 .881 .9611.057 1.146 1.190 1.233 1.322 1.410 1.498 1.586 25.765 .861 .956 1.0521.147 1.243 1.291 1.339 1.434 1.530 1.626 1.722 26 .827 .93011.034 1.137 1.240 1.344 1.396 1.447 1.550 1.654 1.7571.860 27 .892 1.003 1.115 1.226 1.338 1.449 1.506 1.561 1.672 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 1.157 1.236 1.415 1.543 1.672 1.7371.800 1.929 2.058 2.176 2.314 30 1.101 1.238 1.376 1.514 1.651 1,789 1.859|1.926 2.064 2.202 2.339 2.476| 31 1.175 1.322 1.469 1.616 1.762 1.909 1.985 2.056 2.203 2.350 2.4972.644 32 1.252 1.408 1.565 1.721 1.878 2.034 2.115 2.191 2.347 2.504 2.660 2.816 331.332 1.498 1.665 1.831 1.9982.164 2.249|2.331|2.4972.664 2.830 2.996 34 1.414 1.591 1.767 1.944 2.121 2.298 2.387 2.474 2.651 2.8283.005 3.182 35 1.499 1.686 1.874 2.061 2.248 2.436 2.529 2.623 2.811 2.9983.1853.372 36 1.535 1.783 1.981 2.1792.377 2,577 2.675 2.774 2.972 3.170 3.368 3.566 37 1.676 1.885 2.095 2.304 2.514 2.723 2.823 2.933 3.142 3.352 3.561 3.771 38 1.767 1.988 2.209 2.430 2.651 2.871 2.983 3.092 3.313 3.534 3:7553.976 39 1.861 2.094 2.327 2.560 2.792 3.025 3.1423.257 3.490 3.723 3.956 4.188 401.958 2.203 2.448|2.693|2.937|3.182|3.305|3.427|3.6723.917|4.1614.406

USE OF THE TABLE.

I have four logs, one is 14 in. diameter and 13 ft. long, one 21 in. and 17 ft., one 30 in. and 16 ft., and one 35 in. and 12 ft. long; how many logs have 1, log measure?

TITITE

30

16

2.202

2.248

35

12

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

351. Logs for sawing are usually calculated according to the quantity of square edged inch boards which they will make by being sawed. To facilitate this calculation, numerous tables have been constructed, but generally on erroneous principles, not being proportioned to the cubic quantities in the logs. The following table is the result of a great number of experiments and calculations, and is believed to be more accurate than any hitherto published.

LOG TABLE-BOARD MEASURE.

18124137 151 19 138 153 169 20 153 170 187 |21|169 187 206

22 185 206 226 |23 202 225 247 |24|220 245 269 (25 239 266 292

26 258 287 316

27 279 310 341

9 10 | 11 | 12 13 14 15 | 16 17 18 19 20 21 22 12 55 61 67 73 79 85 91 97 103 109 115 121 128 134 13 65 72 79 86 93 100 107 114 121 129 136 143 150 157 14 75 83 92 100 103 116 125 133 141 150 158 166 175 183 15 86 96 105 115 125 134 144 154 163 172 182 191 201 211 16 98 109 120 131 142 153 164 175 185 196 207 218 229 240 17110122134 147 159 171 184 196 208 220 232 244 257 269 165 179 192 206 220 234 247 260 274 289 302 184 199 215 230 245 261 276 291 307 322 337 204 221 238 255 272 289 306 323 340 357 374 225 244 262 281 300 319 337 356 375 394 412 247 268 268 309 329 350 370 391 412 432 453 270 292 315 337 360 382 405 427 450 472 495 294 318 343 367 392 416 441 465 490 514 539 319 346 372 399 425 452 478 505 532 558 585 345 373 402, 431 469 489 517 546 575 604 632 372 403 434 465 496 527 558 589 620 651 682 400 433 467 500 533 567 600 633 667 700 733 429 464 500 536 572 608 643 679 715 751 786 459 497 535 574 612 650 688 727 765 803 841 31 367 408 449 490 531 572 612 653 694 735 776 817 857 898 32391 435 478 522 565 609 652 696 739 783 826 870 913 957 33416462 509 555 601 647 694 740 786 832 879 925 971 1017 34 442,492 541 590 639 688 737 787 836 885 934 9831032 1082 35 469521 573 625 677 729 781 833 885 937 990 1042 1094 1146 36496 551606 661 716 771 826 881 936 991 1047 110211571212 37524 582 5640 698 756 814 872 931 989 1047 1105 1163 1221 1280 38 552 613 675 736 797 859 920 981 1043 1104 1165 12271288 1349 39 582 647 711 776 841 905 970 1035 1099 1164 1229 12931358|1423. 40 612 680 748 816 884 952 1020 1088 1156 1224 1292 1360 1428 1496 41 642714 786 857 928 1000 1071 1143 1214 1285 1357 1428 1500 1571 42675 750 825 900 975 1050 1125 1200 1275 1350 1425 1500 1575 1650 43707 786 364 943 1022 1100 1179 1257 1336 1414 1493 1572 1650 1729 44 730 812 895 987 1069 1151 1234 1316 13981480 1563 1645 1727 1809 '45 775 861947 1033 1119 12051291137714631549 1636 1722 1808 1894

28 300 333 367

29 322 357 393 30344 382 421

USE OF THE TABLE.

How many feet of inch square edged boards can be sawed

from a log 19 feet long and 27 inches diameter ?

Under 19 and against 27 we have 589 feet, the answer.