19. What must be the length of a pile of wood 6 feet high and 4 feet wide to contain 50 cords ? 20. If a ton of coal occupies 36 cubic feet, what must be the depth of a bin 8 feet wide and 10 feet long in order that it may hold 10 tons ? 21. The bridge over the Firth of Forth is 8296 feet long. What is its length in meters ? CHAPTER VII THE USE OF TABLES There are certain calculations which occur so frequently that to save time and labor their results have been tabulated. For example, the circumferences and areas of circles of various diameters, the square roots of numbers, the decimal equivalents of common fractions, etc., have all been arranged in tabular form in much the same way that multiplication tables are arranged, or as railroad time tables are arranged. These tables are not ordinarily memorized as the multiplication table is, or as tables of weights and measures are, but are consulted or referred to each time need arises for a particular result. For example, if one wants the square root of 20, he does not actually extract the square root but refers to a table of square roots and finds it to be 4.4721. Or if he desires to know the area of a circle whose diameter is 50 he refers to a table of areas of circles and finds it to be 1963.5. Or again, if he desires to know the interest on $ 350 for two years and six months at eight per cent, he refers to an interest table and reads his answer instantly,$ 70. Just what tables one needs most, depends upon one's occupation. The machinist has use for tables of decimal equivalents of common fractions, tables of cutting speeds, etc. Draughtsmen and designers use tables of strengths and weights of various materials, standard proportions of machine parts, etc. The actuary uses mortality tables, the banker interest tables, the merchant discount tables, the electrician wiring tables, etc. The professional computer has need for all of these and many more. There are certain mathematical tables, however, which are of general value whatever one's occupation. Among these are tables of squares, cubes, square roots, cube roots, decimal equivalents of fractions, and logarithms of numbers. The table in most common use is the multiplication table given below. Exercise Prepare a multiplication table similar to the above for numbers from 13 to 25. 1. Read from the above table the charge for a post-office money order for $ 7.50. 2. What is the charge for a $ 12 money order ? 3. What will it cost to send a money order for $ 27.50 ? 4. What is the total amount, including the money order charges, for the following amounts: $4.15, $37.50, and $ 52.00? 5. A person buys three money orders as follows: one for $ 7.20, one for $ 1.75, and one for $ 9.50. He buys also half a dollar's worth of postage stamps. What change should he get if he tenders in payment a twenty-dollar gold piece ? Min. Sec. 5 00 4 00 3 00 2 50 2 40 2 30 2 24 2 20 2 15 2 10 2 5 2 00 1 55 1 50 1 45 1 42 1 40 1 38 1 36 1 34 1 32 1 30 1 28 1 26 1 12.00 15.00 20.00 21.18 22.50 24.00 25.00 25.72 26.67 27.69 28.80 30.00 31.30 32.74 34.29 35.29 36.00 36.73 37.50 38.29 39.13 40.00 40.91 41.86 42.86 Min. Sec. 59 43.90 45.00 46.15 47.37 48.00 48.65 49.31 50.00 50.70 51.43 52.17 52.94 53.73 54.55 55.38 56.25 57.14 58.06 59.02 60.00 61.02 62.07 63,14 64.29 65.45 Min. Sec. 54 53 52 51 50 49 48 47 46 45 44 43 42 41 40 39 38 37 66.66 67.92 69.23 70.59 72.00 73.47 75.00 76.59 78.26 80.00 81.82 83.72 85.71 87.80 90.00 92.31 94.74 97.30 100.00 102.86 105.88 109.09 112.50 116.13 120.00 36 35 34 33 32 31 30 24 ORAL DRILL 1. If a vehicle is traveling at the rate of a mile in a minute, read from the above table its rate in miles per hour. 2. From the table read the rate in miles per hour if a mile is traveled in 48 seconds. |