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 ? 2.5X4=10 divisor, 10X 1.4777=14.777 & 14.777--10=1.4777 ft.=lft. 5ğin. 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. 12/0.7854||19|1.9689112013.686313315.9395||101 8.7179||47|12.0482) 13|0.9218||20|2.18171127 3.9753||34 6.3050||41 9.1684|48|12.5664 14 1.0691||212.4018||28|1.2760||35|6.6813,12 9.6211|49|13.0954 15 1.2272 122 2.6393||29 4,5869 ||36|7.0686143 10.0847 150 13.6354 16 1.3963||232.8847 30 4.908737 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 11811.7671112513.40821|325.585 3918.29571146 11.5410115315.3201| 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 oubic feet in a round stick of timber, 20 feet fong, 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, 1.7671X20=35.342 cubic feet. 2. How many cubic feet in a round log: 24 inches diameter and 16 feet long? Ans. 3.1416X16350.2656 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 bow many bushels of wheat will it hold; Ans. 7.0686X5335.343 cubic ft., which X0.8–28.2744 bustha 346. TABLE OF SQUARE TIMBER MEASURE. 1 81 81 0.4444|| 12 13) 1.0833 16/201 2.232211 21/21/ 3.0625 90.5000 14 1.1666 21 2.3333 22 3.2083 10! 0.5555 (15! 1.2500!! 17 17 2.0069 23 3.3541 11 0.6111 (16) 1.3333 18 2.1250 24 3.5000 12 0.6666 17 1.4166 19 2.2430 25 3.6458 13 0.7222 18 1.5000 20 2.3611 26 3.7916 14) 0.7777 13 13 1.1736) 21 2.4971 271 3.9375 9 9 0.5625 14) 1.2638 22 2.5972|| 22 22 3.3611 10 0.6250 15 1.3541 18/18 2.2500 23 3.5138 11 0.6875 16 1.4444 19 2.3750 24 3.6666 12 0.7500! 17 1.5344! 20! 2.5000! 25 3.8191 13 0.8125 18 1.6250 21 2.6250 26 3.9722 14 0.8750 14 14 1.3611 22 2.7500 1:27 4.1250 15 0.9255 15 1.4583 23 2.8750 | 2323 3.6736 10 10.0.6944 16 1,5555 19 19 2.5069 :24 3.9333 11 0.7638 171 1.6528 (25/ 3.9930 112 0.8333 181 1.7916 23:6388 261 4.1528 131 0.9028 19 1.8472 22 2.9028 127 4.3125 14 0.9722!! 15 15! 1.5625 23 3.0347|| 24 24 4.0000 115 1.0416 16 1.6666 24 3.1414 25 4.1666 116| 1.1111 17 1.7708 25 3,2986 261 4.3333 11 11 0.8403 18 1.8750|| 20 20 2.7777 127 4.5000 12 0.9166 19 1.9791 21 2.9166|| 25254.3403 113 0,9932 120 2.0833 22 3,0555 26 4.5138 114 1.0666|| 16|16| 1.7777 23 3.1944 27 4.6875 15j 1.1458 17 1.8888 24 3.3333|| 26 26 4.6944 161 1.2222 18! 2.0000 25 3.4722; 27 4.8750 (17| 1.2986|| 191 2.1111 261 3.6111|| 27(27) 5.0625 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 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 347, 348. PRACTICAL RULES AND TABLES. 15) 347. To determine how big a stick you can hew square owo 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. 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 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 A F 1 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. AB=20X E 0.2929 = 5.853 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 abuve 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=20x0.70713 D 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 WA 12 8 9 one 349. B KH А a half story houses are usually pitched at about 30°, as KC, and two story houses, or higher, the roof is F usually raised 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, 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 fumitting 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, theo 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 6X 1.4142_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) PRACTICAL RULES AND TABLES. 153 350. Logs, in the state of New York, and some other places, are calculated by number; a log 133 feet long and 22 inches diameter being considered one log, and logs of other diameters and lengths calculated according to their cubic quantities. O 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 fect, and the figures at the angle of meeting the number of logs and decimal parts. LOG TABLE-LOG MEASURE. 8 9 10 11 12 13 13 14 15 16 17 | 18 10.122.137.159.169 .183.198.207.213.222.214 .2591 .274 11 J48 .166 .135 .203 0296 .20.950 .252.276.296.311.332 12 175 197 .219.2.10 .262.281.297.3061.24.2001.372 .394 131 2061 232 277 ...I .360 .395.412 .437 464 11 .210 .270 .300.3301 .360.3.16 .465 120 450.480.510 .510 151 .275 .399 .314 .378 .412 .4.17 465 .482.516.550.584.618 16! .313 .352.3911 .430 4691 .509.529 .518.587 .626.665 704 17 .351.338 442 487 .531 .575.597 .620 .661.7081 .752 796 18.396 415 .495 .544.594 613.669,693 .742.792.841 .890 19.441 496.5511 .6061.661.717 .745.779.827| .882.947.992 20.489 .550.6111.672.733 .791 .8251.256 .917 .9781.039 1.100 211 .510.607.675.782.810,877 .910 .915 1.012/1.080.1.1471.215 22.394 666 .710 .814 .888.962|1.000 1.0301110|1.181/1.259 1.332 23 .618 .729.810.891 .9721.053 1.093 1.131 1.21.51.290 1.377 1.458 24.705 .793 .881 .9611.057 1.146|1.190(1.2331.3221:4101.498 1.586 25 .765 .86.11.950 1.052|1.14711.243 1.2911.339 1.131|1.530 1.626 1.722 261,827 .93011.034 1.1371.240 1.344 1.396/1.4171.55011.651 1.757 1.860 27.892 1.003 1.115 1.2261.338.1.4-9 1.500 1.561 1.679 1.784 1.895 2.006 28 .960 1.080 1.200 1.320 1.140 1.560 1.620 1.6801.800 1.920 2.040 2.160 29(1.029|1.157 1.2:361.41515431.0741.757|1.0 1.9292.054 2.1762.314 30/1.101'1.9381.57611.51411.65111.789 1.859|1.9262.6612.209 2.339 2.476. 31 1.17511:322 1.4691.616 107621.909 1.985 2.0502.203 2.350 2.4972.644 |321.2521.4081.565 1.72111.878|2.0342.115 2.191 2.3-172,504 2.6602.816 3311.332 1.4981.665 1.831 1.9982,164 2.249 2.331|2.497 2.0642.830 2.996 311.4111.591 1.767 1.9142.1212.298 2.387|2.471/2.651 2.828 3.00 3.182 351.1991.686/1.8742.06112.218 2.436 2.5292.6232.311 2.998|3.1853.372 36 1.5951.783 1.98119.3799.577 2.577 2.67512.7742.97213.170 3.3683.566 37 1.676|1.8952.0952.304/2.31.12.723 2.9232.9333.142|3.352 3.561 3.771 3811.767 1.938|2.200/2.1302.651 2.8712.983.0923.3133.531 3.756 3.976 391.8612.0942.32712.500 2.7923.0252.119,957 2.10.2013.72313.956 4.188 10/1.9552.23.2.1-132.6932.93713.18215.30513.12713.67243.917/4.16114.406 USE OF THE TABLE. I have four log's, one is 14 in. sliameter and 13.} 11. long, one 21 in. and 17 n., one 30 in. an:1 16 n., and one 35 in. and 12 ft. fong: how many logs have I, log measure ? Against 14 under 13 we find .405 17 1.147 2.202 2.2 18 66 Aps. 6.002 logs, or a little more than 6 loro |