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MISCELLANEOUS.

360. To determine how big a stick you can hew square out of a round log.(317.)-Multiply the diameter by 0.7071, and the product will be one side of the square.

EXAMPLE.

How big will a log square, that is 2.5 feet diameter?
Ans. 0.7071X2.5=1.9635 feet for one side of the square.

361. To take off the corners of a square so as to form an octagon.(66)-Multiply the side of the square by 0.2922, 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.

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ABCD is a square tower of 20 feet each way, on which it is required to erect an octagon. Then 0.2922×20=5.84 = AE FB, and ABAE+FB-EF=8.32 G for one side of the octagon. If it is required to form a diagonal equare within the tow- K er, as HIKL :-Then AC X 0.7071: 142 HI, being one side of the inscribed diagonal square. Then to form an octagon on this square, HLX 0.2928 Lm = 4.13, and Lm+PK-LK= mp 5.88, for one side of the octagon formed on the inscribed square.

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14.

EXAMPLE.

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362. The most common pitch for roofs of barns is to rise one third of the length of the beam, as KB=} of AE=8.

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

Braces are generally placed equi

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distant each way from the corner, as FG, and 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 0.6666X9-6 feet.

If the roof is raised 30 degrees to C, then 12X1.1546819.856 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 12X1.118054-13.416 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 given is 6 feet each way from the corner; then CX1.4142-8.485 for the length of the brace. FG.

The brace HI, being 8 feet one way and 4 feet the other from the corner, is subject to the same proportion as the last case of rafters, that is, 8×1.118-8.944 feet for the length of the brace HI. Braces running in any direction, and subtending a right angle, can be found by the square root; and those and all other braces, let the angles be what they may, can be found by trigonometry, which it is not my purpose here to explain.

LOG MEASURE.

363. LOG TABLE FOR THE STATE OF NEW-YORK.

8 9 10 11 12 13 13 14 15 16 17 18 10.122.137 .153 .168 .183.198 .207.213 .223 .244 .259.274 14.148.166 185 .203 .222 .240 .250 .258 .276 .296 .314 .332 12.175.197.219 .240 .262 .284 .297 .306 .328] .350 .372 .394 13 .206 .232 .257 .283 .309 .335 .349 .360 .385 .412 .437 .464 14.240 .270 .300 .330 .360 .390 .405 .420 .450 .480 .510 .540 15 .275 .309 .344 .378 .412] .447 .465 .482 .516 .550 .584 .618 16 .313 .352 .391 .430 .469 .509 .529 .548 .587 .626.665.704 17 .354 .398 .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 .973 1.039 1.100 21.540 .607 .675 .742 .810 .877 .910 .945 1.012 1.080 1.147 1.215 22 .592 .666 .740 .814 .828 .962 1.000 1.036 1.1101.1841.258 1.332 23 648 729 .810 .891 .972 1.053 1.093 1.134 1.215 1.296 1.377 1.458 24 705 .793.881 .9691.057 1.146|1.190 1.233 1.3221.410 1.498|1.586 25 .765 .861 .956 1.052 1.147 1.243 1.2911.339 1.434 1.530 1.626 1.722 26.827 .930 1.034 1.137 1.240 1.344 1.396 1.447 1.550 1.6541.757 1.860 27 892 1.003 1.115|1.226|1.338 1.449 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 2.160 291.029 1.1571.2861.415|1.543|1.672|1.737|1.800|1.929|2.058|2.176 2.314 301.101 1.238 1.376 1.514 1.651 1.789 1.859 1.926 2.064 2,202 2.339 2.476 311.175 1.322 1.469 1.616 1.762|1.909|1.985|2.056 2.203 2.350 2.497 2.644 321.2521.408 1.565 1.7211.878 2.034 2.115|2.191|2.347 2.504 2.660 2.816 33 1.332 1.498 1.665 1.831 1.998 2.164 2.249 2.831 2.497 2.664 2.830 2.996 34 1.414 1.591 1.767 1.944 2.121|2.298|2.587|2.474|2 651|2.828 3.005 3.182 35 1.499 1.686 1.874 2.061|2.248|2.436|2.529 2.6232.811 2.9983.185 3.372 36 1.585 1.783 1.981 2.179 2.377 2.577|2 6752.7742.972 3.170 3.368 3.566 37 1.676 1.885 2.095 2.304 2 5142,723 2,828 2.933|3.1423.352 3.561 3.771 38 1.767 1.988 2.209 2,430 2.651|2.871|2 9833.092|3.313 3.534 3.755 3.976 391.861 2.0942.327|2.560 2.792|3.025|3,142|3.257|3.490 3.723|3.9564.183 401 9582.2082 448|2.693|2.937|3,182|3,305/3.427′3.672 3.917|4.1614.406

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In the state of New-York, logs for sawing are calculated by their number; a log 13 feet long and 22 inches diameter, is considered one log, and logs of all other sizes and lengths are calculated according to their respective cubic quantities, in conformity to which the preceding table is constructed. The left hand column is the diameter of the logs in inches, and the top line is the length of the logs in feet. The number at the angular point is the proportional cubic quantity.

To use the foregoing table, take the numbers therefrom agreeably to your bill of logs, add them together, and you have the number of logs equal to standard, according to the custom of the state of New-York.

In the state of Vermont, logs for sawing are calculated according to the quantity of square edged inch boards which they will make by being sawed. For this purpose many log tables have been formed, varying from each other, none of which that I have seen are on true principles, because not proportioned according to the cubic quantity of the respective logs. I have with great care formed the following table, which is proportioned to the cubic quantity of the logs, and to determine the quantity of boards which each log would make, I drew various circles at full size, and marked them out into boards and saw cuts; the mean result of which is, that for a log 12 feet long, multiply the square of the diameter in inches by 0.51, and it will give the quantity of boards such log will make, if carefully sawed. The little discrepancies in the table are occasioned by the omission of fractions of 5 or under, and adding one when over 5.

In the following table the figures on the top show the length of the logs in feet, and the left hand column is the diameter in inches. The number standing at the angular point is the quantity of boards such log will make.

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LOG TABLE. BOARD MEASURE.

9 10 11 12 55 61 67 13 65 72 79 14 75 83 92 15 86 96 105 16 98 109 120 17110 122 134 18 124 137 151

12

73 86

13 14 15 16 17 18 19 20 21 22 79 85 91 97 103 109 115 121 128 134 93 100 107 114 121 129 136 143 150 157 100 108 116 125 133 141 150 158 166 175 183 115 125 134 144 154 163 172 182 191 201 211 131 142 153 164 175 185 196 207 218 229 230 147 159 171 184 196 208 220 232 244 257 269 165 179 192 206 220 234 247 260 274 289 302 19 138 153 169 184 199 215 230 245 261 276 291 307 322 337 20 153 170 187 204 221 238 255 272 289 306 323 340 357 374 21 169 187 206 225 244 262 281 300 319 337 356 375 394 412 22 185 206 226 247 268 288 309 329 350 370 391 412 432 453 23 202 225 247 270 292 315 337 360 382 405 427 450 472 495 24 220 245 269 294 318 343 367 392 416 441 465 490 514 539 25 239 266 292 319 346 372 399 425 452 478 505 532 558 585 26 258 287 316 345 373 402 431 460 489 517 546 575 604 632 27 279 310 341 372 403 434 465 496 527 558 589 620 651 682 28 300 333 367 400 433 467 500 533 567 600 633 667 700 733 29 322 357 3931 429 464 500 536 572 608 643 679 715 751 786 30 344 382 421 459 497 535 574 612 650 688 727 765 803 841 31 367 408 449 490 531 572 612 653 694 735 776 817 857) 398 32 391 435 478 522 565 609 652 696 73 783 826 870 913 957 33 416 462 509 555 601 647 694 740 786 832 879 925 9711017 34 442 492 541 590 639 688 737 787 836 885 934 983 1032 1082 35 469 521 573 625 677 729 781 833 885 937 9901042 1094 1146 36 496 551 606 661 716 771 826 881 936 9911047 1102 1157 1212 37 524 582 640 698 756 814 872 931 989 1047 1105 1163 1221 1280 38 552 613 675 736 797 859 920 981 1043 1104 1165 1227 1288 1349 39 582 647 711 905 9701035 1099 1164 1229 1293 1358 1423 40 612 680 748 884 952 1020 1088 1156 1224 1292 1360 1428 1496 41 642 714 786 857 928 1000 1071 1143 1214 1285 1357 1428 1500 1571 42 675 750 825 900 975 1050 1125 1200 1275 1350 1425 1500 1575 1650 43 707 786 864 943 1022 1100 1179 1257 1336 1414 1493 1572 1650 1729 44 730 812 895 987 1069 1151 1234 1316 1398 1480 1563 1645 1727 1809 45 775 861 947 1033 1119 1205 1291 1377 1463 1549 1636 1722 1808 1894

776 816

841

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