from those of the circumference table in that they are not fractional or decimal parts of the number but form the last digit before the decimal point. To find the square of 12, for instance, we locate the 1 in the number column on the left edge and the 2 in the top row of figures. Its square, 144, will be found on a level with the 1 and in the column beneath the 2. Likewise the square of 25 is on a level with the 2 and in the column beneath the figure 5. Twenty-five squared (252) equals 625. The square of 407 is on a level with the 40 and in the column beneath the 7. Four hundred seven squared (4072) = 165,649. Check the following squares from the table: The method of using the tables of square roots, cubes, and cube roots, also given in this chapter, is exactly the same as explained for the table of squares. Examples: 1. What would be the length of a steel sheet from which to make a 28-in. circular drum, allowing 1 in. extra for lapping and riveting the ends? The circumference of the drum is measured in the direction of the length of the sheet. In this case the length of the sheet will be equal to the circumference of the drum, plus the amount required for lapping and riveting. Squares, cubes, etc., of mixed numbers can also be found from the tables by the proper manipulation of the decimal point. 2. Find the square of 83.2. The actual figures in the square of 83.2 will be the same as in the square of 832. From the table, the square of 832 is 692,224. However, 83.2 has one decimal place, and its square will, therefore, contain two decimal places. The square of 832 is then found by shifting the decimal point two places to the left in the square of 832. PROBLEMS 131. Extract the square root of the following numbers by the method explained in Arts. 69-72: (a) 64,516 (b) 198.1369 (c).571428 Answer, 254 Note. One answer is given so that the student can see if he understands the operations of square root before proceeding further. 132. From the tables, find the squares, cubes, square roots, and cube roots of the following numbers: (a) 123 (b) 956 (c) 56.7 133. The hand-power derrick of Fig. 28 has a mast AB 15 ft. in height, and the leg BC is fastened to AC at a distance of 16 ft. from the foot of the mast AB. Calculate the length of the leg AC. 134. Figure 29 shows an end view of the roof framing for a barn. If the run is to be 12 ft. and the rise 8 ft., what rafter length is required, allowing 16 in. for the extension? 135. From the tables, determine the circumferences of the following circles: (a) Diameter 6 in. (c) Diameter 21.7 in. 136. A steel stack 75 ft. high is supported by 4 guy wires fastened to a ring two-thirds of the way up the stack and having the other ends -Rafter Length Extension -Run Rise FIG. 29.-Roof framing for barn. anchored at a distance of 50 ft. from the base of the stack and on a level with the base. guys, allowing 10 % How many feet of wire are required for all four extra for fastening the ends? 137. An electric hoist is designed for a nominal capacity of 7000 lb. with a rope speed of 150 f.p.m. at the drum. If the hoisting drum makes 36 r.p.m., what diameter of drum is required? Note. The hoisting rope is wound up on the drum. 138. A 30-in. pulley and a 24-in. pulley are keyed to the same shaft. If the belt on the large pulley has a speed of 3000 f.p.m., what is the belt speed of the small pulley? TABLE 1 CIRCUMFERENCES OF CIRCLES Diameters to 50, advancing by eighths Dia. 0 0.3927 0.7854 1.1781 1.5708 1.9635 2.3562 2.7489 3.1416 3.5343 3.9270 4.3197 4.7124 5.1051 5.4978 5.8905 6.2832 6.6759 7.0686 7.4613 7.8540 8.2467 8.6394 9.0321 9.4248 9.8175 10.2102 10.6029 10.9956 11.3883 11.7810 12.1737 12.5664 12.9591 13.3518 13.7445 14.1372 14.5299 14.9226 15.3153 15.7080 16.1007 16.4934 16.8861 17.2788 17.6715 18.0642 18.4569 18.8496 19.2423 19.6350 20.0277 20.4204 20.8131 21.2058 21.5984 21.9911 22.3838 22.7765 23.1692 23.5619 23.9546 24.3473 24.7400 25.1327 25.5254 25.9181 26.3108 26.7035 27.0962 27.4889 27.8816 28.2743 28.6670 29.0597 29.4524 29.8451 30.2378 30.6305 31.0232 31.4159 31.8086 32.2013 32.5940 32.9867 33.3794 33.7721 34.1648 34.5575 34.9502 35.3429 35.7356 36.1283 36.5210 36.9137 37.3064 37.6991 38.0918 38.4845 38.8772 39.2699 39.6626 40.0553 40.4480 40.8407 41.2334 41.6261 42.0188 42.4115 42.8042 43.1969 43.5896 43.9823 44.3750 44.7677 45.1604 45.5531 45.9458 46.3385 46.7312 47.1239 47.5166 47.9093 48.3020 48.6947 49.0874 49.4801 49.8728 50.2655 50.6582 51.0509 51.4436 51.8363 52.2290 52.6217 53.0144 53.4071 53.7998 54.1925 54.5852 54.9779 55.3706 55.7633 56.1560 56.5487 56.9414 57.3341 57.7268 58.1195 58.5122 58.9049 59.2976 59.6903 60.0830 60.4757 60.8684 61.2611 61.6538 62.0465 62.4392 62.8319 63.2246 63.6173 64.0100 64.4026 64.7953 65.1880 65.5807 65.9734 66.3661 66.7588 67.1515 67.5442 67.9369 68.3296 68.7223 69.1150 69.5077 69.9004 70.2931 70.6858 71.0785 71.4712 71.8639 72.2566 72.6493 73.0420 73.4347 73.8274 74.2201 74.6128 75.0055 75.3982 75.7909 76.1836 76.5763 76.9690 77.3617 77.7544 78.1471 78.5398 78.9325 79.3252 79.7179 80.1106 80.5033 80.8960 81.2887 81.6814 82.0741 82.4668 82.8595 83.2522 83.6449 84.0376 84.4303 84.8230 85.2157 85.6084 86.0011 86.3938 86.7865 87.1792 87.5719 87.9646 88.3573 88.7500 89.1427 89.5354 89.9281 90.3208 90.7135 91.1062 91.4989 91.8916 92.2843 92.6770 93.0697 93.4624 93.8551 94.2478 94.6405 95.0332 95.4259 95.8186 96.2113 96.6040 96.9967 97.3894 97.7821 98.1748 98.5675 98.9602 99.3529 99.7456 100.138 100.531 100.924 101.316 101.709 102.102 102.494 102.887 103.280 103.673 104.065 104.458 104.851 105.243 105.636 106.029 106.421 106.814 107.207 107.600 107.992 108.385 108.778 109.170 109.563 109.956 110.348 110.741 111.134 111.527 111.919112.312 112.705 113.097 113.490 113.883 114.275 114.668 115.061 115.454 115.846 116.239 116.632 117.024 117.417 117.810 118.202 118.596 118.988 119.381 119.773 120.166 120.559 120.951 121.344 121.737 122.129 122.522 122.915 123.308 123.700 124.093 124.486 124.878 125.271 125.664 126.056 126.449 126.842 127.235 127.627 128.020 128.413 128.805 129.198 129.591 129.983 130.376 130.769 131.161 131.554 131.947 132.340 132.732 133.125 133.518 133.910 134.303 134.696 135.088 135.481 135.874 136.267 136.659 137.052 137.445 137.837 138.230 138.623 139.015 139.408 139.801 140.194 140.586 140.979 141.372 141.764 142.157 142.550 142.942 143.335 143.728 144.121 144.513 144.906 145.299 145.691 146.084 146.477 146.869 147.262 147.655 148.048 148.440 148.833 149.226 149.618 150.011 150.404 150.796 151.189 151.582 151.975 152.367 152.760 153.153153.545 153.938 154.331 154.723 155.116 155.509 155.902 156.294 156.687 157.080 157.472 157.865 158.258 158.650 159.043 159.436 159.829 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 |