MWWpat g w >a j >Wff * ir i Mrwirfr ni p t nMnmM FOUR FLAG UNABRIDGED EDITION E. V. HUNTINGTON Conversion Tables 0'=0°.00000 1' .01666.. .03 333.. .05 .06 666.. .08 333.. .10 .11 666.. .13 333.. .15 10' 0°.16666.. 1 .18 333.. .20 .21 666.. .23 333.. .25 .26666.. .28 333.. .30 .31 666.. 2' V 4' 5' 6' 7' 8' 9' 20' 0°.33 333.. 1 2 3 4 25' 6 7 8 .51 666.. .53 333.. .55 .56 666.. .58 333.. .60 .61 666., 8 .63 333., 9 .65 40' 0°.66 666., 1 2 3 4 35' 6 7 1 2 3 4 45' 6 7 8 9 50' 1 2 3 4 55' 6 7 8 9 // .35 .36666.. .38333.. .40 .41 666.. .43 333.. .45 .46 666.. 9 .48333.. 30' 0°.50 .68 333.. .70 .71 666.. .73 333.. .75 .76 666.. .78 333.. .80 .81 666.. 0°.83 333.. .85 .86 666.. .88 333.. .90 .91 666.. .93 333.. .95 .96666.. .98 333.. 60' 1°.00 0"=0°.00 000 1" 2" 3" 4" 5" 6" 7" 8" 9" 10" 1 2 3 4 15" 9 20" 1 2 3 4 25" 6 7 8 9 30" 1 2 3 4 35" 6 7 8 9 40" 1 2 3 4 45" 6 7 8 9 50" 1 2 3 4 55" 6 7 8 9 GO" .00 027.. .00055.. .00 083.. .00 111.. .00 138.. .00 166.. .00 194.. .00222.. .00 25 0°.00 277.. .00 305.. .00 333.. .00361.. .00388.. .00 416.. .00 444.. .00 472.. .00 5 .00 527.. 0°.00 555.. .00 583.. .00 611.. .00 638.. .00 666.. .00 694.. .00 722.. .00 75 .00 777.. .00 805.. 0°.00 833.. .00 861.. .00 888.. .00 916.. .00 944.. .00 972.. .01 .01 027.. .01 055.. .01 083.. 0°.01 111.. .01 138.. .01 166.. .01 194.. .01 222.. .0125 .01 277.. .01 305.. .01 333.. .01 361.. 0°.01 388.. .01 416.. .01 444.. .01 472.. .015 .01 527.. .01 555.. .01 583.. .01 611.. .01 638.. 0°.01666« 1°=0.01 745 329 l'=0.00 029 088 1"=0.00 000 484 radians 8 radians 814 radians 1 From Decimal Parts of a Degree into Minutes and Seconds {Exact lvalues) o°.oo= = 0'00" 0°.50= =30' l 0'36" 1 30 '36" 2 112" 2 3112" 3 1'48" 3 31 '48" 4 2 '24" 4 32 '24" 0°.05 3' 0°.55 33' 6 3 '36" 6 33 '36" 7 412" 7 3412" 8 4'48" 8 34'48" 9 5 '24" 9 35 '24" 0°.10 6' 0°.60 36' 1 6'36" 1 36 '36" 2 712" 2 3712" 3 7 '48" 3 37 '48" 4 8 '24" 4 38 '24" 0°.15 9' 0°.65 39' 6 9 '36" 6 39'36" 7 1012" 7 4012" 8 10 '48" 8 40 '48" 9 11 '24" 9 41 '24" 0°20 12' 0°.70 42' 1 12 '36" 1 42 '36" 2 1312" 2 4312" 3 13 '48" 3 43 '48" 4 14'24" 4 44 '24" 0°25 15' 0°.75 45' 6 15 '36" 6 45 '36" 7 1612" 7 4612" 8 16 '48" 8 46 '48" 9 17 '24" 9 47 '24" 0°.30 18' 0°.80 48' 1 18 '36" 1 48 '36" 2 1912" 2 4912" 3 19 '48" 3 49 '48" 4 20 '24" 4 50 '24" 0°.35 21' 0°.85 51' 6 21 '36" 6 51 '36" 7 2212" 7 5212" 8 22 '48" 8 52 '48" 9 23 '24" 9 53 '24" 0°.40 24' 0°.90 54' 1 24 '36" 1 54 '36" 2 2512" 2 5512" 3 25 '48" 3 55 '48" 4 26 '24" 4 56 '24" 0°.45 27' 0°.95 57' 6 27 '36" 6 57 '36" 7 2812" 7 5812" 8 28 '48" 8 58 '48" 9 29 '24" 9 59 '24" 0°.50 30' r.oo 60' 0°.000= 0".0 1 3".6 2 7".2 3 10".8 4 14".4 0°.005 18". 6 21".6 7 25".2 8 28".8 9 32".4 0°.010 36". Decimal Equivalents of Common Fractions {Exact Values) 06 1/8 3/16 1/4 3/8 7/16 1/2 5/8 3/4 7/8 1/32 3/32 5/32 7/32 9/32 5/16 11/32 13/32 1/64 3/64 5/64 7/64 9/64 11/64 13/64 15/64 17/64 19/64 21/64 23/64 25/64 27/64 29/64 15/32 31/64 17/32 9/16 19/32 21/32 11/16 23/32 25/32 13/16 27/32 29/32 15/16 31/32 33/64 35/64 37/64 39/64 41/64 43/64 45/64 47/64 49/64 51/64 53/64 55/64 57/64 59/64 61/64 63/64 .01 5625 .03 125 .04 6875 .0625 .07 8125 .09375 .109375 .12 5 .140625 .15 625 .17 1875 .1875 .203125 .21 875 .23 4375 .25 .26 5625 .28 125 .29 6875 .3125 .32 8125 .34375 .35 9375 .375 .39 0625 .40 625 ;42 1875 .43 75 .45 3125 .46 875 .48 4375 .50 .51 5625 .53 125 .54 6875 .5625 .578125 .59375 .609375 .62 5 .640625 .65 625 .67 1875 .68 75 .70 3125 .71 875 .73 4375 .75 .765625 .78 125 .796875 .8125 .82 8125 .84375 .85 9375 .87 5 .890625 .90625 .92 1875 .93 75 .95 3125 .96 875 .98 4375 1 radian =57°.29578 FOUR PLACE TABLES OF LOGARITHMS AND TRIGONOMETRIC FUNCTIONS .WITH AUXILIARY TABLES ( CHIEFLY TO THREE FIGURES ) OF SQUARES, SQUARE ROOTS, CUBES, CUBE ROOTS, RECIPROCALS CIRCUMFERENCES AND AREAS OF CIRCLES, EXPONENTIALS NATURAL LOGARITHMS, RADIANS, AND CONSTANTS 3?nabribgeb Cuttt'on COMPILED BY E. V. HUNTINGTON ASSISTANT PROFESSOR OF MATHEMATICS IN HARVARD UNIVERSITY Descriptive Note. — In these tables, angles are expressed in degrees and decimal parts of a degree, instead of in degrees, minutes, and seconds. A conversion table is provided. All the values of any one function, from 0° to 90°, will be found at one opening of the book ; there are also special tables for small angles and angles near 90°. The arrangement of the page is uniform, — the first figures of the argument being given at the side of the page, and the last figure along the top. Moreover, the function always increases reading to the right, and decreases reading to the left, so that a frequent cause of error in interpolating is avoided. The sign J indicates a point where the first figure of the function changes in the middle of a line. The negative characteristics, 1, 2, etc., may be modified into 9-10, 8-10, etc., if preferred. To facilitate interpolation, the tenths of the tabular differences are given at the end of each line, so that the actual differences themselves need not be considered. In using these aids, first find the nearest tabular entry, and then add (to move to the right) or subtract (to move to the left), as the case may require. Any interpolated value may be in error by one unit in the last place ; wherever the errors of interpolation may be greater than this, warning is given in the margin. A marginal index is provided throughout the table. In using the tabs at the side of the page, put the thumb on the desired tab and throw the free pages over ; do not in- sert the fingers under these tabs. The special tabs at the upper and lower edges of the page make it possible to manipulate the logarithmic part of the table entirely with the left hand, the book lying flat on the desk ; to turn forward, insert the thumb under the required tab at bottom of page; to turn backward, insert the finger under the required tab at top of page. An abridged edition is published, without the auxiliary tables. FOR SALE BY THE HARVARD COOPERATIVE SOCIETY CAMBRIDGE, MASSACHUSETTS $nce, in flexible clot& 60 cent* Copyright, 1907, 1908, 1910, by E. V. Huntington SOSTCM COLuJu^z UmiAKV CHESTNUT HILL, MASS 4 4* Squares (Moving the decimal pc equivalent to moving tint ONE place in n is t TWO places inn 2 ) n 1.0 1 2 3 4 5 6 7 8 9 10 1.000 1.020 1.040 1.061 1.082 1.103 1.124 1.145 1.166 1.188 1.210 1.1 1.210 1.232 1.254 1.277 1.300 1.323 1.346 1.369 1.392 1.416 1.440 1.2 1.440 1.464 1.488 1.513 1.538 1.563 1.588 1.613 1.638 1.664 1.690 1.3 1.690 1.716 1.742 1.769 1.796 1.823 1.850 1.877 1.904 1.932 1.960 1.4 1.960 1.988 2.016 2.045 2.074 2.103 2.132 2.161 2.190 2.220 2.250 1.5 2.250 2.280 2.310 2.341 2.372 2.403 2.434 2.465 2.496 2.528 2.560 1.6 2.560 2.592 2.624 2.657 2.690 2.723 2.756 2.789 2.822 2.856 2.890 1.7 2.890 2.924 2.958 2.993 3.028 3.063 3.098 3.133 3.168 3.204 3.240 1.8 3.240 3.276 3.312 3.349 3.386 3.423 3.460 3.497 3.534 3.572 3.610 1.9 3.61 3.65 3.69 3.72 3.76 3.80 3.84 3.88 3.92 3.96 4.00 2.0 4.00 4.04 4.08 4.12 4.16 4.20 4.24 4.28 4.33 4.37 4.41 2.1 4.41 4.45 4.49 4.54 4.58 4.62 4.67 4.71 4.75 4.80 4.84 2.2 4.84 4.88 4.93 4.97 5.02 5.06 5.11 5.15 5.20 5.24 5.29 2.3 5.29 5.34 5.38 5.43 5.48 5.52 5.57 5.62 5.66 5.71 5.76 2.4 5.76 5.81 5.86 5.90 5.95 6.00 6.05 6.10 6.15 6.20 6.25 2.5 6.25 6.30 6.35 6.40 6.45 6.50 6.55 6.60 6.66 6.71 6.76 2.6 6.76 6.81 6.86 6.92 6.97 7.02 7.08 7.13 7.18 7.24 7.29 2.7 7.29 7.34 7.40 7.45 7.51 7.56 7.62 7.67 7.73 7.78 7.84 2.8 7.84 7.90 7.95 8.01 8.07 8.12 8.18 8.24 8.29 8.35 8.41 2.9 8.41 8.47 8.53 8.58 8.64 8.70 8.76 8.82 8.88 8.94 9.00 3.0 9.00 9.06 9.12 9.18 9.24 9.30 9.36 9.42 9.49 9.55 9.61 3.1 9.61 9.67 9.73 9.80 9.86 9.92 9.99 10.05 10.11 10.18 10.24 3.2 10.24 10.30 1037 10.43 10.50 10.56 10.63 10.69 10.76 10.82 10.89 3.3 10.89 10.96 11.02 11.09 11.16 11.22 11.29 11.36 11.42 11.49 11.56 3.4 11.56 11.63 11.70 11.76 11.83 11.90 11.97 12.04 12.11 12.18 12.25 3.5 12.25 12.32 12.39 12.46 12.53 12.60 12.67 12.74 12.82 12.89 12.96 3.6 12.96 13.03 13.10 13.18 13.25 13.32 13.40 13.47 13.54 13.62 13.69 3.7 13.69 13.76 13.84 13.91 13.99 14.06 14.14 14.21 14.29 14.36 14.44 3.8 14.44 14.52 14.59 14.67 14.75 14.82 14.90 14.98 15.05 15.13 15.21 3.9 15.21 15.29 15.37 15.44 15.52 15.60 15.68 15.76 15.84 15.92 16.00 4.0 16.00 16.08 16.16 16.24 16.32 16.40 16.48 16.56 16.65 16.73 16.81 4.1 16.81 16.89 16.97 17.06 17.14 17.22 17.31 17.39 17.47 17.56 17.64 4.2 17.64 17.72 17.81 17.89 17.98 18.06 18.15 18.23 18.32 18.40 18.49 4.3 18.49 18.58 18.66 18.75 18.84 18.92 19.01 19.10 19.18 19.27 19.36 4.4 19.36 19.45 19.54 19.62 19.71 19.80 19.89 19.98 20.07 20.16 20.25 4.5 20.25 20.34 20.43 20.52 20.61 20.70 20.79 20.88 20.98 21.07 21.16 4.6 21.16 21.25 21.34 21.44 21.53 21.62 21.72 21.81 21.90 22.00 22.09 4.7 22.09 22.18 22.28 22.37 22.47 22.56 22.66 22.75 22.85 22.94 23.04 4.8 23,04 23.14 23.23 23.33 23.43 23.52 23.62 23.72 23.81 23.91 24.01 4.9 24.01 24.11 24.21 24.30 24.40 24.50 24.60 24.70 24.80 24.90 25.00 5.0 25.00 25.10 25.20 25.30 25.40 25.50 25.60 25.70 25.81 25.91 26.01 5.1 26.01 26.11 26.21 26.32 26.42 26.52 26.63 26.73 26.83 26.94 27.04 5.2 27.04 27.14 27.25 27.35 27.46 27.56 27.67 27.77 27.88 27.98 28.09 5.3 28.09 28.20 28.30 28.41 28.52 28.62 28.73 28.84 28.94 29.05 29.16 5.4 29.16 29.27 29.38 29.48 29.59 29.70 29.81 29.92 30.03 30.14 30.25 5.5 30.25 30.36 30.47 30.58 30.69 30.80 30.91 31.02 31.14 31.25 ' 31.36 5.6 31.36 31.47 31.58 31.70 31.81 31.92 32.04 32.15 32.26 32.38 32.49 5.7 32.49 32.60 32.72 32.83 32.95 33.06 33.18 33.29 33.41 33.52 33.64 5.8 33.64 33.76 33.87 33.99 34.11 34.22 34.34 34.46 34.57 34.69 34.81 5.9 34.81 34.93 35.05 35.16 35.28 35.40 35.52 35.64 35.76 35.88 36.00 6. 36.0 37.2 38.4 39.7 41.0 42.3 43.6 44.9 46.2 47.6 49.0 7. 49.0 50.4 51.8 53.3 54.8 56.3 57.8 59.3 60.8 62.4 64.0 8. 64.0 65.6 67.2 68.9 70.6 72.3 74.0 75.7 77.4 79.2 81.0 9. 81.0 82.8 84.6 86.5 88.4 90.3 92.2 94.1 96.0 98.0 100.0 Tenths of the Tabular Difference 12 3 4 5 2 4 6 810 2 5 7 911 2 5 7 10 12 3 5 8 11 13 3 6 9 12 14 3 6 9 12 15 3 7 10 13 16 3 7 10 14 17 4 7 11 15 18 112 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 2 2 2 2 2 2 2 2 2 2 2 3 2 3 2 3 2 3 2 3 2 2 2 2 2 2 2 2 2 2 2 3 4 2 3 4 3 3 4 3 3 4 3 4 4 tt 2 = 9.870 (2) 1/V = 0.10132 O'NEILL LIBRARY BOSTON CO Square Roots (Moving the decimal point TWO places in n is equivalent to moving it ONE place in */7i) Ta i l l l l l rent iula 2 3 2 2 2 1 hs of the r Difference 3 4 5 n .1 .2 .3 .4 l 2 3 4 5 6 7 8 9 10 .316 .447 .548 .632 .332 .458 .557 .640 .346 .469 .566 .648 .361 .480 .574 .656 .374 .490 .583 .663 .387 .387 .500 .592 .671 .400 .510 .600 .678 .412 .520 .608 .686 .424 .436 .529 .539 .616 .624 .693 .700 .447 .548 .632 .707 4 6 7 4 5 6 3 4 5 3 3 4 2 3 4 .5 .6 17 .8 .9 .707 .775 .837 .894 0.949 .714 .781 .843 .900 0.954 .721 .787 .849 .906 0.959 .728 .794 .854 .911 0.964 .735 .800 .860 .917 0.970 .742 .806 .866 .922 0.975 .748 .812 .872 .927 0.980 .755 .819 .877 .933 0.985 .762 .768 .825 .831 .883 .889 .938 .943 0.990 0.995 .775 .837 .894 0.949 1.000 l l l l l 1 1 1 1 1 2 3 3 2 2 3 2 2 3 2 2 3 2 2 3 1.0 1.1 1.2 1.3 1.4 1.000 1.049 1.095 1.140 1.183 1.005 1.054 1.100 1.145 1.187 1.010 1.058 1.105 1.149 1.192 1.015 1.063 1.109 1.153 1.196 1.020 1.068 1.114 1.158 1.200 1.025 1.072 1.118 1.162 1.204 1.030 1.077 1.122 1.166 1.208 1.034 1.082 1.127 1.170 1.212 1.039 1.044 1.0S6 1.091 1.131 1.136 1.175 1.179 1.217 1.221 1.049 1.095 1.140 1.183 1.225 1 1 1 1 1 12 2 12 2 12 2 12 2 12 2 1.5 1,6 1.7 1.8 1.9 1.225 1.265 1.304 1.342 1.378 1.229 1.269 1.308 1.345 1.382 1.233 1.273 1.311 1.349 1.386 1.237 1.277 1.315 1.353 1.389 1.241 1.281 1.319 1.356 1.393 1.245 1.285 1.323 1.360 1.396 1.249 1.288 1.327 1.364 1.400 1.253 1.292 1.330 1.367 1.404 1.257 1.261 U.296 1.300 1.334 1.338 1.371 1.375 1.407 1.411 1.265 1.304 1.342 1.378 1.414 1 1 1 1 1 12 2 12 2 12 2 112 112 2.0 2.1 2.2 2.3 2.4 1.414 1.449 1.483 1.517 1.549 1.418 1.453 1.487 1.520 1.552 1.421 1.456 1.490 1.523 1.556 1.425 1.459 1.493 1.526 1.559 1.428 1.463 1.497 1.530 1.562 1.432 1.466 1.500 1.533 1.565 1.435 1.470 1.503 1.536 1.568 1.439 1.473 1.507 1.539 1.572 1.442 1.446 1.476 1.480 1.510 1.513 1.543 1.546 1.575 1.578 1.449 1.483 1.517 1.549 1.581 1 1 1 1 1 112 112 112 112 112 2.5 2.6 2.7 2.8 2.9 1.581 1.612 1.643 1.673 1.703 1.584 1.616 1.646 1.676 1.706 1.587 1.619 1.649 1.679 1.709 1.591 1.622 1.652 1.682 1.712 1.594 1.625 1.655 1.685 1.715 1.597 1.628 1.658 1.688 1.718 1.600 1.631 1.661 1.691 1.720 1.603 1.634 1.664 1.694 1.723 1.606 1.609 1.637 1.640 1.667 1.670 1.697 1.700 1.726 1.729 1.612 1.643 1.673 1.703 1.732 1 1 1 1 1 112 112 112 111 111 3.0 3.1 3.2 3.3 3.4 1.732 1.761 1.789 1.817 1.844 1.735 1.764 1.792 1.819 1.847 1.738 1.766 1.794 1.822 1.849 1.741 1.769 1.797 1.825 1.852 1.744 1.772 1.800 1.828 1.855 1.746 1.775 1.803 1.830 1.749 1.778 1.806 1.833 1.860 1.752 1.780 1.808 1.836 1.863 1.755 1.758 1.783 1.786 1.811 1.814 1.838 1.841 1.865 1.868 1.761 1.789 1.817 1.844 1.871 1 1 1 1 1 111 111 111 111 1.857 111 3.5 3.6 3.7 3.8 3.9 1.871 1.897 1.924 1.949 1.975 1.873 1.900 1.926 1.952 1.977 1.876 1.903 1.929 1.954 1.980 1.879 1.905 1.931 1.957 1.982 1.881 1.908 1.934 1.960 1.985 1.884 1.910 1.936 1.962 1.987 1.887 1.913 1.939 1.965 1.990 1.889 1.916 1.942 1.967 1.992 1.892 1.895 1.918 1.921 1.944 1.947 1.970 1.972 1.995 1.997 1.897 1.924 1.949 1.975 2.000 1 1 1 1 1 111 111 111 111 111 4.0 4.1 4.2 4.3 4.4 2.000 2.025 2.049 2.074 2.098 2.002 2.027 2.052 2.076 2.100 2.005 2.030 2.054 2.078 2.102 2.007 2.032 2.057 2.081 2.105 2.010 2.035 2.059 2.083 2.107 2.012 2.037 2.062 2.086 2.110 2.015 2.040 2.064 2.088 2.112 2.017 2.042 2.066 2.090 2.114 2.020 2.022 2.045 2.047 2.069 2.071 2.093 2.095 2.117 2.119 2.025 2.049 2.074 2.098 2.121 111 111 111 111 111 4.5 4.6 4.7 4.8 4.9 2.121 2.145 2.168 2.191 2.214 2.124 2.147 2.170 2.193 2.216 2.126 2.149 2.173 2.195 2.218 2.128 2.152 2.175 2.198 2.220 2.131 2.154 2.177 2.200 2.223 2.133 2.156 2.179 2.202 2.225 2.135 2.159 2.182 2.205 2.227 2.138 2.161 2.184 2.207 2.229 2.140 2.142 2.163 2.166 2.186 2.189 2.209 2.211 2.232 2.234 2.145 2.168 2.191 2.214 2.236 111 111 111 111 111 5. 6. 7. 8. , 2.236 2.449 2.646 2.828 3.000 2.258 2.470 2.665 2.846 3.017 2.280 2.490 2.683 2.864 3.033 2.302 2.510 2.702 2.881 3.050 2.324 2.530 2.720 2.898 3.066 2.345 2.550 2.739 2.915 3.082 2.366 2.569 2.757 2.933 3.098 2.387 2.588 2.775 2.950 3.114 2.408 2.429 2.608 2.627 2.793 2.811 2.966 2.983 3.130 3.146 2.449 2.646 2.828 3.000 3.162 2 2 2 2 2 4 4 4 3 3 6 9 11 6 8 10 5 7 9 5 7 9 5 6 8 w c % $ r.0 5 W <* ^ = 1.772454 (3) n/i/7t = 0.56419 1$ Cubes (Moving the decimal point ONE place in n la equivalent to moving it THREE places in ttZ) Tenths c Tabular Di 12 3 3 7 10 4 8 12 5 9 14 5 11 16 112 f the n 1.0 1.1 1.2 1.3 1.4 12 3 4 5 6 7 8 9 10 ffennci 4 5 1.000 1.331 1.728 2.197 2.74 1.030 1.061 1.093 1.125 1.368 1.405 1.443 1.482 1.772 1.816 1.861 1.907 2.248 2.300 2.353 2.406 2.80 2.86 2.92 2.99 1.158 1.521 1.953 2.460 3.05 1.191 1.225 1.260 1.295 1.561 1.602 1.643 1.685 2.000 2.048 2.097 2.147 2.515 2.571 2.628 2.686 3.11 3.18 3.24 3.31 1.331 1.728 2.197 2.744 3.38 13 17 16 20 19 23 22 27 3 3 1.5 1.6 1.7 1.8 1.9 3.38 4.10 4.91 5.83 6.86 3.44 3.51 3.58 3.65 4.17 4.25 4.33 4.41 5.00 5.09 5.18 5.27 5.93 6.03 6.13 6.23 6.97 7.08 7.19 7.30 3.72 4.49 5.36 6.33 7.41 3.80 3.87 3.94 4.02 4.57 4.66 4.74 4.83 5.45 5.55 5.64 5.74 6.43 6.54 6.64 6.75 7.53 7.65 7.76 7.88 4.10 4.91 5.83 6.86 8.00 1 1 1 1 1 1 2 2 2 2 2 2 3 3 3 3 4 3 4 4 5 4 5 5 6 2.0 2.1 2.2 2.3 2.4 8.00 9.26 10.65 12.17 13.82 8.12 8.24 8.37 8.49 9.39 9.53 9.66 9.80 10.79 10.94 11.09 11.24 12.33 12.49 12.65 12.81 14.00 14.17 14.35 14.53 8.62 9.94 11.39 12.98 14.71 8.74 8.87 9.00 9.13 10.08 10.22 10.36 10.50 11.54 11.70 11.85 12.01 13.14 13.31 13.48 13.65 14.89 15.07 15.25 15.44 9.26 10.65 12.17 13.82 15.62 1 1 2 2 2 3 3 3 3 4 4 4 5 5 5 5 6 6 7 6 8 7 8 7 9 2.5 2.6 2.7 2.8 2.9 15.62 17.58 19.68 21.95 24.39 15.81 16.00 16.19 16.39 17.78 17.98 18.19 18.40 19.90 20.12 20.35 20.57 22.19 22.43 22.67 22.91 24.64 24.90 25.15 25.41 16.58 18.61 20.80 23.15 25.67 16.78 16.97 17.17 17.37 18.82 19.03 19.25 19.47 21.02 21.25 21.48 21.72 23.39 23.64 23.89 24.14 25.93 26.20 26.46 26.73 17.58 19.68 21.95 24.39 27.00 2 2 2 2 3 4 4 5 5 5 6 8 10 6 8 11 7 9 11 7 10 12 8 10 13 3.0 3.1 3.2 3.3 3.4 27.0 29.8 32.8 35.9 39.3 27.3 27.5 27.8 28.1 30.1 30.4 30.7 31.0 33.1 33.4 33.7 34.0 36.3 36.6 36.9 37.3 39.7 40.0 40.4 40.7 28.4 31.3 34.3 37.6 41.1 28.7 28.9 29.2 29.5 31.6 31.9 32.2 32.5 34.6 35.0 35.3 35.6 37.9 38.3 38.6 39.0 41.4 41.8 42.1 42.5 29.8 32.8 35.9 39.3 42.9 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 2 1 2 3.5 3.6 3.7 3.8 3.9 42.9 46.7 50.7 54.9 59.3 43.2 43.6 44.0 44.4 47.0 47.4 47.8 48.2 51.1 51.5 51.9 52.3 55.3 55.7 56.2 56.6 59.8 60.2 60.7 61.2 44.7 48.6 52.7 57.1 61.6 45.1 45.5 45.9 46.3 49.0 49.4 49.8 50.2 53.2 53.6 54.0 54.4 57.5 58.0 58.4 58.9 62.1 62.6 63.0 63.5 46.7 50.7 54.9 59.3 64.0 ! 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 4.0 4.1 4.2 4.3 4.4 64.0 68.9 74.1 79.5 85.2 64.5 65.0 65.5 65.9 69.4 69.9 70.4 71.0 74.6 75.2 75.7 76.2 80.1 80.6 81.2 81.7 85.8 86.4 86.9 87.5 66.4 71.5 76.8 82.3 88.1 66.9 67.4 67.9 68.4 72.0 72.5 73.0 73.6 77.3 77.9 78.4 79.0 82.9 83.5 84.0 84.6 88.7 89.3 89.9 90.5 68.9 ! 74.1 79.5 85.2 91.1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 3 2 3 2 3 2 3 4.5 4.6 4.7 4.8 4.9 91.1 97.3 103.8 110.6 117.6 91.7 92.3 93.0 93.6 98.0 98.6 99.3 99.9 104.5 105.2 105.8 106.5 111.3 112.0 112.7 113.4 118.4 119.1 119.8 120.6 94.2 100.5 107.2 114.1 121.3 94.8 95.4 96.1 96.7 101.2 101.8 102.5 103.2 107.9 108.5 109.2 109.9 114.8 115.5 116.2 116.9 122.0 122.8 123.5 124.3 97.3 103.8 110.6 117.6 125.0 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 3 3 3 3 3 3 4 3 4 5.0 5.1 5.2 5.3 5.4 125.0 132.7 140.6 148.9 157.5 125.8 126.5 127.3 128.0 133.4 134.2 135.0 135.8 141.4 142.2 143.1 143.9 149.7 150.6 151.4 152.3 158.3 159.2 160.1 161.0 128.8 136.6 144.7 153.1 161.9 129.6 130.3 131.1 131.9 137.4 138.2 139.0 139.8 145.5 146.4 147.2 148.0 154.0 154.9 155.7 156.6 162.8 163.7 164.6 165.5 132.7 140.6 148.9 157.5 166.4 1 1 1 1 1 2 2 2 2 2 2 2 2 3 3 3 4 3 4 3 4 3 4 4 4 5.5 5.6 5.7 5.8 5.9 166.4 175.6 185.2 195.1 205.4 167.3 168.2 169.1 170.0 176.6 177.5 178.5 179.4 186.2 187.1 188.1 189.1 196.1 197.1 198.2 199.2 206.4 207.5 208.5 209.6 171.0 180.4 190.1 200.2 210.6 171.9 172.8 173.7 174.7 181.3 182.3 183.3 184.2 191.1 192.1 193.1 194.1 201.2 202.3 203.3 204.3 211.7 212.8 213.8 214.9 175.6 185.2 195.1 205.4 1 216.0 1 1 1 1 1 2 2 2 2 2 3 3 3 3 3 4 5 4 5 4 5 4 5 4 5 6. 7. 8. 9. 216. 343. 512. 729. 227. 238. 250. 262. 358. 373. 389. 405. 531. 551. 572. 593. 754. 779. 804. 831. 275. 275. 422. 614. 857. 287. 301. 314. 329. 439. 457. 475. 493. 636. 659. 681. 705. 885. 913. 941. 970. 343. 512. 729. 1000. 1 1 2 2 3 2 3 3 4 5 4 4 5 7 8. 5 6 5 7 7 8 911 LI 14 7T 3 = 3U)06 (4) 1/7T 3 = 0.032252 Cube Roots (Moving the decimal point THREE places in n is equivalent to moving it ONE place in £/Ti) Tenths of the Tabular Difference n .010 1 2 3 4 5 6 7 8 9 10 1 2 1 1 3 4 5 .2154 .2162 .2169 .2176 .2183 .2190 .2197 .2204 .2210 .2217 .2224 2 3 3 .011 .2224 .2231 .2237 .2244 .2251 .2257 .2264 .2270 .2277 .2283 .2289 1 1 2 3 3 .012 .2289 .2296 .2302 .2308 .2315 .2321 .2327 .2333 .2339 .2345 .2351 1 1 2 2 3 .013 .2351 .2357 .2363 .2369 .2375 .2381 .2387 .2393 .2399 .2404 .2410 1 1 2 2 3 .014 .2410 .2416 .2422 .2427 .2433 .2438 .2444 .2450 .2455 .2461 .2466 1 1 2 2 3 .015 .2466 .2472 .2477 .2483 .2488 .2493 .2499 .2504 .2509 .2515 .2520 1 1 2 2 3 .016 .2520 .2525 .2530 .2535 .2541 .2546 .2551 .2556 .2561 .2566 .2571 1 1 2 2 3 .017 .2571 .2576 .2581 .2586 .2591 .2596 .2601 .2606 .2611 .2616 .2621 1 12 2 .018 .2621 .2626 .2630 .2635 .2640 .2645 .2650 .2654 .2659 .2664 .2668 1 12 2 .019 .2668 .2673 .2678 .2682 .2687 .2692 .2696 .2701 .2705 .2710 .2714 1 12 2 .020 .2714 .2719 .2723 .2728 .2732 .2737 .2741 .2746 .2750 .2755 .2759 1 12 2 .021 .2759 .2763 .2768 .2772 .2776 .2781 .2785 .2789 .2794 .2798 .2802 1 12 2 .022 .2802 .2806 .2811 .2815 .2819 .2823 .2827 .2831 .2836 .2840 .2844 1 12 2 .023 .2844 .2848 .2852 .2856 .2860 .2864 .2868 .2872 .2876 .2880 .2884 1 12 2 .024 .2884 .2888 .2892 .2896 .2900 .2904 .2908 .2912 .2916 .2920 .2924 1 12 2 .025 .2924 .2928 .2932 .2936 .2940 .2943 .2947 .2951 .2955 .2959 .2962 1 12 2 .026 .2962 .2966 .2970 .2974 .2978 .2981 .2985 .2989 .2993 .2996 3000 1 12 2 .027 .3000 .3004 .3007 .3011 .3015 .3018 .3022 .3026 .3029 .3033 .3037 1 112 .028 .3037 .3040 .3044 .3047 .3051 .3055 .3058 .3062 .3065 .3069 .3072 1 112 .029 .3072 .3076 .3079 .3083 .3086 .3090 .3093 .3097 3100 .3104 .3107 1 112 .03 .311 .314 .317 .321 .324 .327 .330 .333 336 .339 342 1 112 .04 .342 .345 .348 .350 .353 .356 .358 .361 .363 .366 368 1 111 .05 .368 .371 .373 .376 .378 .380 .383 .385 387 .389 391 111 .06 .391 .394 .396 .398 .400 .402 .404 .406 .408 .410 .412 111 .07 .412 .414 .416 .418 .420 .422 .424 .425 .427 .429 .431 111 .08 .431 .433 .434 .436 .438 .440 .441 .443 .445 .446 .448 111 .09 .448 .450 .451 .453 .455 .456 .458 .459 .461 .463 .464 Oil .1 .464 .479 .493 .507 .519 .531 1 3 4 5 7 .531 .543 .554 .565 .575 .585 1 2 3 4 5 .2 .585 .594 .604 .613 .621 .630 .638 .646 .654 .662 .669 1 2 3 3 4 .3 .669 .677 .684 .691 .698 .705 .711 .718 .724 .731 .737 1 1 2 3 3 .4 .737 .743 .749 .755 .761 .766 .772 .777 .783 .788 .794 1 1 2 2 3 .5 .6 .794 .843 .799 .848 .804 .853 .809 .857 .814 .819 .824 .829 .871 .875 .834 .879 .839 .884 .843 .888 1 1 12 2 .862 .866 12 2 .7 .888 .892 .896 .900 .905 .909 .913 .917 .921 .924 .928 1 12 2 .8 .928 .932 .936 .940 .944 .947 .951 .955 .958 .962 0.965 1 112 .9 0.965 0.969 0.973 0.976 0.980 0.983 0.986 0.990 0.993 0.997 1.000 1 112 1.0 1.000 1.003 1.007 1.010 1.013 1.016 1.020 1.023 1.026 1.029 1.032 1 112 1.1 1.032 1.035 1.038 1.042 1.045 1.048 1.051 1.054 1.057 1.060 1.063 1 112 1.2 1.063 1.066 1.069 1.071 1.074 1.077 1.080 1.083 1.086 1.089 1.091 1 111 1.3 1.091 1.094 1.097 1.100 1.102 1.105 1.108 1.111 1.113 1.116 1.119 1 111 1.4 1.119 1.121 1.124 1.127 1.129 1.132 1.134 1.137 1.140 1.142 1.145 1 111 1.5 1.145 1.147 1.150 1.152 1.155 1.157 1.160 1.162 1.165 1.167 1.170 111 1.6 1.170 1.172 1.174 1.177 1.179 1.182 1.184 1.186 1.189 1.191 1.193 111 1.7 1.193 1.196 1.198 1.200 1.203 1.205 1.207 1.210 1.212 1.214 1.216 111 1.8 1.216 1.219 1.221 1.223 1.225 1.228 1.230 1.232 1.234 1.236 1.239 111 1.9 1.239 1.241 1.243 1.245 1.247 1.249 1.251 1.254 1.256 1.258 1.260 111 2. 1.260 1.281 1.301 1.320 1.339 1.357 2 4 6 8 10 1.357 1.375 1.392 1.409 1.426 1.442 2 3 5 7 9 3. 1.442 1.458 1.474 1.489 1.504 1.518 1.533 1.547 1.560 1.574 1.587 1 3 4 6 7 4. 1.587 1.601 1.613 1.626 1.639 1.651 1.663 1.675 1.687 1.698 1.710 1 2 4 5 6 5. 1.710 1.721 1.732 1.744 1.754 1.765 1.776 1.786 1.797 1.807 1.817 1 2 3 4 5 6. 1.817 1.827 1.837 1.847 1.857 1.866 1.876 1.885 1.895 1.904 1.913 1 2 3 4 5 7. 1.913 1.922 1.931 1.940 1.949 1.957 1.966 1.975 1.983 1.992 2.000 1 2 3 3 4 8. 2.000 2.008 2.017 2.025 2.033 2.041 2.049 2.057 2.065 2.072 2.080 1 2 2 3 4 9. 2.080 2.088 2.095 2.103 2.110 2.118 2.125 2.133 2.140 2.147 2.154 1 1 2 3 4 ^7T = 1.46459 (5) 0.68278 f/b/Tt = 1.24070 r.v d& s W <* o°2 TTTi 1 Circumferences of Circles (n = diam.} Tenths of the ft 1. 2. 3! 4. 5. 6. 4. 8. 9. 12 3 4 5 6 7 8 9 10 Tabular Difference 12 3 4 5 3.14 6.28 9.42 12.57 15.71 18.85 21.99 25.13 2827 3.46 3.77 4.08 4.40 6.60 6.91 7.23 7.54 9.74 10.05 10.37 10.68 12.88 13.19 13.51 13.82 16.02 16.34 16.65 16.96 19.16 19.48 19.79 20.11 22.31 22.62 22.93 23.25 25.45 25.76 26.08 26.39 28.59 28.90 29.22 29.53 4.71 7.85 11.00 14.14 1728 20.42 23.56 26.70 29.85 5.03 5.34 5.65 8.17 8.48 8.80 11.31 11.62 11.94 14.45 14.77 15.08 17.59 17.91 18.22 20.73 21.05 21.36 23.88 24.19 24.50 27.02 27.33 27.65 30.16 30.47 30.79 5.97 9.11 12.25 15.39 18.54 21.68 24.82 27.96 31.10 6.28 9.42 12.57 15.71 18.85 21.99 25.13 28.27 31.42 3 6 9 13 16 3 6 9 13 16 3 6 9 13 16 3 6 9 13 16 3 6 9 13 16 3 6 9 13 16 3 6 9 13 16 3 6 9 13 16 3 6 9 13 16 1 — m^ A i-anr /-vf /""' , i*»/-»l£io ( *n A 1 n mi ~\ (Moving the decimal point OJTE place inn is 4;7rM- /\reas 01 circles yn — aiain.) equivalent to moving it two places in irn 2 /^.) Tenths of the Tabular Difference n 1.0 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 0.785 0.801 0.817 0.833 0.849 0.866 0.882 0.899 0.916 0.933 0.950 2 3 5 7 9 1.1 0.950 0.968 0.985 1.003 1.021 1.039 1.057 1.075 1.094 1.112 1.131 2 4 5 7 9 L2 1.131 1.150 1.169 1.188 1208 1.227 1.247 1.267 1.287 1.307 1327 2 4 6 810 L3 1.327 1.348 1.368 1.389 1.410 1.431 1.453 1.474 1.496 1.517 1.539 2 4 6 811 1.4 1.539 1.561 1.584 1.606 1.629 1.651 1.674 1.697 1.720 1.744 1.767 2 5 7 911 1.5 1.767 1.791 1.815 1.839 1.863 1.887 1.911 1.936 1.961 1.986 2.011 2 5 7 10 12 1.6 2.011 2.036 2.061 2.087 2.112 2.138 2.164 2.190 2.217 2.243 2.270 3 5 8 10 13 1.7 2.270 2.297 2.324 2.351 2.378 2.405 2.433 2.461 2.488 2.516 2.545 3 5 8 11 14 1.8 2.545 2.573 2.602 2.630 2.659 2.688 2.717 2.746 2.776 2.806 2.835 3 6 9 12 15 1.9 2.835 2.865 2.895 2.926 2.956 2.986 3.017 3.048 3.079 3.110 3.142 3 6 9 12 15 2.0 3.14 3.17 3.20 3.24 327 330 333 337 3.40 3.43 3.46 1112 2.1 3.46 3.50 3.53 3.56 3.60 3.63 3.66 3.70 3.73 3.77 3.80 1112 22 3.80 3.84 3.87 3.91 3.94 3.98 4.01 4.05 4.08 4.12 4.15 1112 23 4.15 4.19 423 426 430 434 437 4.41 4.45 4.49 4.52 1112 2.4 4.52 4.56 4.60 4.64 4.68 4.71 4.75 4.79 4.83 4.87 4.91 112 2 2.5 4.91 4.95 4.99 5.03 5.07 5.11 5.15 5.19 5.23 527 531 112 2 2.6 5.31 5.35 5.39 5.43 5.47 5.52 5.56 5.60 5.64 5.68 5.73 112 2 2.7 5.73 5.77 5.81 5.85 5.90 5.94 5.98 6.03 6.07 6.11 6.16 112 2 2.8 6.16 6.20 6.25 6.29 633 638 6.42 6.47 6.51 6.56 6.61 112 2 2.9 6.61 6.65 6.70 6.74 6.79 6.83 6.88 6.93 6.97 7.02 7.07 112 2 3.0 7.07 7.12 7.16 721 7.26 7.31 735 7.40 7.45 7.50 7.55 112 2 3.1 7.55 7.60 7.65 7.69 7.74 7.79 7.84 7.89 7.94 7.99 8.04 1-12 2 3.2 8.04 8.09 8.14 8.19 8.24 830 835 8.40 8.45 8.50 8.55 1 12 2 3 3.3 8.55 8.60 8.66 8.71 8.76 8.81 8.87 8.92 8.97 9.03 9.08 1 12 2 3 3.4 9.08 9.13 9.19 924 9.29 935 9.40 9.46 9.51 9.57 9.62 1 12 2 3 3.5 9.62 9.68 9.73 9.79 9.84 9.90 9.95 10.01 10.07 10.12 10.18 1 12 2 3 3.6 10.18 10.24 1029 1035 10.41 10.46 10.52 10.58 10.64 10.69 10.75 1 12 2 3 3.7 10.75 10.81 10.87 10.93 10.99 11.04 11.10 11.16 1122 11.28 11.34 1 12 2 3 3.8 11.34 11.40 11.46 11.52 11.58 11.64 11.70 11.76 11.82 11.88 11.95 1 12 2 3 3.9 11.95 12.01 12.07 12.13 12.19 12.25 . 12.32 12.38 12.44 12.50 12.57 1 12 2 3 4.0 12.57 12.63 12.69 12.76 12.82 12.88 12.95 13.01 13.07 13.14 13.20 1 12 3 3 4.1 1320 1327 1323 13.40 13.46 13.53 13.59 13.66 13.72 13.79 13.85 1 12 3 3 4.2 13.85 13.92 13.99 14.05 14.12 14.19 1425 1432 1439 14.45 14.52 1 12 3 3 42 14.52 14.59 14.66 14.73 14.79 14.86 14.93 15.00 15.07 15.14 15.21 1 12 3 3 4.4 15.21 15.27 1534 15.41 15.48 15.55 15.62 15.69 15.76 15.83 15.90 1 12 3 3 4.5 15.90 15.98 16.05 16.12 16.19 16.26 1633 16.40 16.47 16.55 16.62 1 12 3 4 4.6 16.62 16.69 16.76 16.84 16.91 16.98 17.06 17.13 17.20 17.28 17.35 1 12 3 4 4.7 17.35 17.42 17.50 17.57 17.65 17.72 17.80 17.87 17.95 18.02 18.10 1 12 3 4 4.8 18.10 18.17 18.25 1832 18.40 18.47 18.55 18.63 18.70 18.78 18.86 1 2 2 3 4 4.9 18.86 18.93 19.01 19.09 19.17 1924 1922 19.40 19.48 19.56 19.63 1 2 2 3 4 5. 19.6 20.4 21.2 22.1 22.9 23.8 24.6 25.5 26.4 27.3 283 1 2 3 3 4 6. 282 29.2 30.2 31.2 32.2 332 34.2 35.3 36.3 37.4 38.5 1 2 3 4 5 7. 38.5 39.6 40.7 41.9 43.0 442 45.4 46.6 47.8 49.0 503 1 2 4 5 6 8. 503 51.5 52.8 54.1 55.4 56.7 58.1 59.4 60.8 62.2 63.6 1 3 4 5 7 9. 63.6 65.0 66.5 67.9 69.4 70.9 72.4 73.9 75.4 77.0 78.5 1 3 4 6 7 (6) (Moving the decimal point to the RIGHT in n is equivalent to moving it to the LEFT in 1 /n) Tenths of the Tabular Differen 1© 9 S 1 6 S 4 3 2 a n 9. 1 2 3 4 5 .1000 .1010 .1020 .1031 .1042 .1053 .1064 .1075 .1087 .1099 .1111 1 2 3 4 6 .1111 .1124 .1136 .1149 .1163 .1176 .1190 .1205 .1220 .1235 .1250 go 1 3 4 6 7 .1250 .1266 .1282 .1299 .1316 .1333 .1351 .1370 .1389 .1408 .1429 7. 2 4 5 7 9 .1429 .1449 .1471 .1493 .1515 .1538 2 4 7 9 11 .1538 .1562 .1587 .1613 .1639 .1667 6. 3 5 8 10 13 .1667 .1669 .1672 .1675 .1678 .1681 .1684 .1686 .1689 .1692 .1695 5.9 1 111 .1695 .1698 .1701 .1704 .1706 .1709 .1712 .1715 .1718 .1721 .1724 5.8 1 111 .1724 .1727 .1730 .1733 .1736 .1739 .1742 .1745 .1748 .1751 .1754 5.7 1 112 .1754 .1757 .1761 .1764 .1767 .1770 .1773 .1776 .1779 .1783 .1786 5.6 1 112 .1786 .1789 .1792 .1795 .1799 .1802 .1805 .1808 .1812 .1815 .1818 53 1 112 .1818 .1821 .1825 .1828 .1832 .1835 .1838 .1842 .1845 .1848 .1852 5.4 1 112 .1852 .1855 .1859 .1862 .1866 .1869 .1873 .1876 .1880 .1883 .1887 5.3 1 112 .1887 .1890 .1894 .1898 .1901 .1905 .1908 .1912 .1916 .1919 .1923 52 1 112 .1923 .1927 .1931 .1934 .1938 .1942 .1946 .1949 .1953 .1957 .1961 5.1 1 12 2 .1961 .1965 .1969 .1972 .1976 .1980 .1984 .1988 .1992 .1996 2000 5.0 1 12 2 .2000 2004 .2008 2012 2016 2020 2024 2028 2033 2037 2041 4.9 1 12 2 2041 2045 2049 .2053 2058 2062 2066 2070 2075 2079 2083 4.8 1 12 2 2083 2088 2092 2096 2101 2105 2110 2114 2119 2123 2128 4.7 1 12 2 2128 2132 2137 2141 2146 2151 2155 2160 2165 2169 2174 4.6 1 12 2 2174 2179 2183 2188 2193 2198 2203 2208 2212 2217 .2222 43 1 12 2 2222 2227 2232 2237 .2242 2247 2252 2257 2262 2268 2273 4.4 1 1 2 2 3 2273 2278 2283 2288 2294 2299 2304 2309 2315 2320 2326 43 1 1 2 2 3 2326 2331 2336 2342 2347 .2353 2358 2364 2370 2375 2381 42 1 1 2 2 3 .2381 .2387 2392 .2398 2404 2410 2415 2421 2427 2433 2439 4.1 1 1 2 2 3 2439 2445 2451 2457 2463 2469 2475 2481 2488 2494 2500 4.0 1 1 2 2 3 2500 2506 .2513 2519 2525 2532 2538 2545 2551 2558 2564 3.9 1 1 2 3 3 2564 2571 2577 2584 2591 2597 2604 2611 2618 2625 2632 3.8 1 1 2 3 3 2632 2639 2646 2653 2660 2667 2674 2681 2688 2695 2703 3.7 1 1 2 3 4 2703 2710 2717 2725 2732 2740 2747 2755 2762 2770 2778 3.6 1 2 2 3 4 2778 2786 2793 2801 2809 2817 2825 2833 2841 .2849 2857 33 1 2 2 3 4 2857 2865 2874 2882 2890 2899 2907 2915 2924 2933 2941 3.4 1 2 3 3 4 2941 2950 2959 2967 2976 2985 2994 3003 3012 3021 3030 33 1 2 3 4 4 3030 3040 3049 3058 3067 3077 3086 3096 3106 3115 3125 32 1 2 3 4 5 .3125 3135 3145 3155 3165 3175 3185 3195 3205 3215 3226 3.1 1 2 3 4 5 3226 3236 3247 3257 3268 3279 3289 3300 3311 3322 3333 3.0 1 2 3 4 5 .333 334 336 337 338 339 340 341 342 344 345 2.9 1 345 346 347 348 350 351 352 353 355 356 357 2.8 1 357 358 360 361 362 364 365 366 368 369 370 2.7 Oil 370 372 373 375 376 377 379 380 382 383 385 2.6 Oil 385 386 388 389 391 392 394 395 397 398 .400 2.5 Oil .400 .402 .403 .405 .407 .408 .410 .412 .413 .415 .417 2.4 Oil .417 .418 .420 .422 .424 .426 .427 .429 .431 .433 .435 23 111 .435 .437 .439 .441 .442 .444 .446 .448 .450 .452 .455 22 111 .455 .457 .459 .461 .463 .465 .467 .469 .472 .474 .476 2.1 111 .476 .478 .481 .483 .485 .488 .490 .493 .495 .498 .500 2.0 111 .500 .503 .505 .508 310 .513 .515 .518 .521 .524 .526 1.9 1 111 .526 .529 .532 .535 .538 .541 .543 .546 .549 .552 .556 1.8 1 111 .556 .559 .562 .565 .568 .571 .575 .578 .581 .585 .588 1.7 1 112 .588 .592 .595 .599 .602 .606 .610 .613 .617 .621 .625 1.6 1 112 .625 .629 .633 .637 .641 .645 .649 .654 .658 .662 .667 1.5 1 12 2 .667 .671 .676 .680 .685 .690 .694 .699 .704 .709 .714 1.4 1 12 2 .714 .719 .725 .730 .735 .741 .746 .752 .758 .763 .769 13 1 1 2 2 3 .769 .775 .781 .787 .794 .800 .806 .813 .820 .826 .833 1.2 1 1 2 3 3 .833 .840 .847 .855 .862 .870 .877 .885 .893 .901 .909 . 1.1 1 2 2 3 4 .909 .917 .926 .935 .943 .952 .962 .971 .980 .990 1.0 1 2 3 4 5 # in r.O 5 1/tt = 031831 (7) 1/^ = 0.10132 *& Sine # 5 '5 o 5 JO L Jl> .1 2 3 JS .4 M 5 .4 .6 ~1T^ .8 l B s>@>° Ta 1 Tenths of the ular Difference 2 3 4 5 0.000000 0° 0.000000 001745 003491 005238 006981 008727 010472 012217 013962 015707 017452 89 175349524698873 1 01745 01920 02094 02269 02443 02618 02792 02967 03141 03316 03490 88 17 35 52 70 87 2 03490 03664 03839 04013 04188 04362 04536 04711 04835 05059 05234 87 17 35 52 70 87 3 05234 05408 05582 05756 05931 06105 06279 06453 06627 06802 06976 86 17 35 52 70 87 4 06976 07150 07324 07498 07672 07846 08020 08194 08368 08542 08716 85 17 35 52 70 87 5 03716 08889 09063 09237 09411 09585 09758 09932 10106 10279 10453 84 17 35 52 69 87 6 10453 10626 10800 10973 11147 11320 11494 11667 11840 12014 12187 83 17 35 52 69 87 7 12187 12360 12533 12706 12880 13053 13226 13399 13572 13744 13917 82 17 35 52 69 87 8 13917 14090 14263 14436 14608 14781 14954 15126 15299 15471 15643 81 17 35 52 69 86 9 15643 15816 15988 16160 16333 16505 16677 16849 17021 17193 0.17365 80° 17 34 52 69 86 10° 0.1736 1754 1771 1788 1805 1822 1840 1857 1874 1891 1908 79 2 3 5 7 9 11 1908 1925 1942 1959 1977 1994 2011 2028 2045 2062 2079 78 2 3 5 7 9 12 2079 2096 2113 2130 2147 2164 2181 2198 2215 2233 2250 77 2 3 5 7 9 13 2250 2267 2284 2300 2317 2334 2351 2368 2385 2402 2419 76 2 3 5 7 8 14 2419 2436 2453 2470 2487 2504 2521 2538 2554 2571 2588 75 2 3 5 7 8 15 2588 2605 2622 2639 2656 2672 2689 2706 2723 2740 2756 74 2 3 5 7 8 16 2756 2773 2790 2807 2823 2840 2857 2874 2890 2907 2924 73 2 3 5 7 8 17 2924 2940 2957 2974 2990 3007 3024 3040 3057 3074 3090 72 2 3 5 7 8 18 3090 3107 3123 3140 3156 3173 3190 3206 3223 3239 3256 71 2 3 5 7 8 19 3256 3272 3289 3305 3322 3338 3355 3371 3387 3404 0.3420 7Q° 2 3 5 7 8 20° 0.3420 3437 3453 3469 3486 3502 3518 3535 3551 3567 3584 69 2 3 5 7 8 21 3584 3600 3616 3633 3649 3665 3681 3697 3714 3730 3746 68 2 3 5 6 8 22 3746 3762 3778 3795 3811 3827 3843 3859 3875 3891 3907 67 2 3 5 6 8 23 3907 3923 3939 3955 3971 3987 4003 4019 4035 4051 4067 66 2 3 5 6 8 24 4067 4083 4099 4115 4131 4147 4163 4179 4195 4210 4226 65 2 3 5 6 8 25 4226 4242 4258 4274 4289 4305 4321 4337 4352 4368 4384 64 2 3 5 6 8 26 4384 4399 4415 4431 4446 4462 4478 4493 4509 4524 4540 63 2 3 5 6 8 27 4540 4555 4571 4586 4602 4617 4633 4648 4664 4679 4695 62 2 3 5 6 8 28 4695 4710 4726 4741 4756 4772 4787 4802 4818 4833 4848 61 2 3 5 6 8 29 4848 4863 4879 4894 4909 4924 4939 4955 4970 4985 0.5000 (S0° 2 3 5 6 8 30° 0.5000 5015 5030 5045 5060 5075 5090 5105 5120 5135 5150 59 2 3 5 6 8 31 5150 5165 5180 5195 5210 5225 5240 5255 5270 5284 5299 58 1 3 4 6 7 32 5299 5314 5329 5344 5358 5373 5388 5402 5417 5432 5446 57 1 3 4 6 7 33 5446 5461 5476 5490 5505 5519 5534 5548 5563 5577 5592 56 1 3 4 6 7 34 5592 5606 5621 5635 5650 5664 5678 5693 5707 5721 5736 55 1 3 4 6 7 35 5736 5750 5764 5779 5793 5807 5821 5835 5850 5864 5878 54 1 3 4 6 7 36 5878 5892 5906 5920 5934 5948 5962 5976 5990 6004 6018 53 1 3 4 6 7 37 .6018 6032 6046 6060 6074 6088 6101 6115 6129 6143 6157 52 1 3 4 6 7 38 6157 6170 6184 6198 6211 6225 6239 6252 6266 6280 6293 51 1 3 4 5 7 39 6293 6307 6320 6334 6347 6361 6374 6388 6401 6414 0.6428 B0° 1 3 4 5 7 40° 0.6428 6441 6455 6468 6481 6494 6508 6521 6534 6547 6561 49 1 3 4 5 7 41 6561 6574 6587 6600 6613 6626 6639 6652 6665 6678 6691 48 1 3 4 5 7 42 6691 6704 6717 6730 6743 6756 6769 678? 6794 6807 6820 47 1 3 4 5 6 43 6820 6833 6845 6858 6871 6884 6896 6909 6921 6934 6947 46 1 3 4 5 6 44 6947 6959 6972 6984 6997 7009 7022 7034 7046 7059' 0.7071 4S° 1 2 4 5 6 45° 0.7071 (8) Sine .0 .1 2 3 .4 M •4 J 2 1- JG> Tenths of the Tabular Difference .5 j6 .7 A j>1 4§° 12 3 4 5 0.7071 45° 0.7071 7083 7096 7108 7120 7133 7145 7157 7169 7181 7193 44 12 4 5 6 46 7193 7206 7218 7230 7242 7254 7266 7278 7290 7302 7314 43 12 4 5 6 47 7314 7325 7337 7349 7361 7373 7385 7396 7408 7420 7431 42 12 4 5 6 48 7431 7443 7455 7466 7478 7490 7501 7513 7524 7536 7547 41 12 3 5 6 49 7547 7559 7570 7581 7593 7604 7615 7627 7638 7649 7660 40° 12 3 5 6 50° 0.7660 7672 7683 7694 7705 7716 7727 7738 7749 7760 0.7771 39 12 3 4 6 51 7771 7782 7793 7804 7815 7826 7837 7848 7859 7869 7880 38 12 3 4 5 52 7880 7891 7902 7912 7923 7934 7944 7955 7965 7976 7986 37 12 3 4 5 53 7986 7997 8007 8018 8028 8039 8049 8059 8070 8080 8090 36 12 3 4 5 54 8090 8100 8111 8121 8131 8141 8151 8161 8171 8181 8192 35 12 3 4 5 55 8192 8202 8211 8221 8231 8241 8251 8261 8271 8281 8290 34 12 3 4 5 56 8290 8300 8310 8320 8329 8339 8348 8358 8368 8377 8387 33 12 3 4 5 57 8387 8396 8406 8415 8425 8434 8443 8453 8462 8471 8480 32 12 3 4 5 58 8480 8490 8499 8508 8517 8526 8536 8545 8554 8563 8572 31 12 3 4 5 59 8572 8581 8590 8599 8607 8616 8625 8634 8643 8652 0.8660 30° 12 3 4 4 60° 0.8660 8669 8678 8686 8695 8704 8712 8721 8729 8738 8746 29 12 3 3 4 61 8746 8755 8763 8771 8780 8788 8796 8805 8813 8821 8829 28 12 2 3 4 62 8829 8838 8846 8854 8862 8870 8878 8886 8894 8902 8910 27 12 2 3 4 63 8910 8918 8926 8934 8942 8949 8957 8965 8973 8980 8988 26 12 2 3 4 64 8988 8996 9003 9011 9018 9026 9033 9041 9048 9056 9063 25 12 2 3 4 65 9063 9070 9078 9085 9092 9100 9107 9114 9121 9128 9135 24 112 3 4 66 9135 9143 9150 9157 9164 9171 9178 9184 9191 9198 9205 23 112 3 3 67 9205 9212 9219 9225 9232 9239 9245 9252 9259 9265 9272 22 112 3 3 68 9272 9278 9285 9291 9298 9304 9311 9317 9323 9330 9336 21 112 3 3 69 9336 9342 9348 9354 9361 9367 9373 9379 9385 9391 0.9397 2©° 112 2 3 70° 0.9397 9403 9409 9415 9421 9426 9432 9438 9444 9449 9455 19 112 2 3 71 9455 9461 9466 9472 9478 9483 9489 9494 9500 9505 9511 18 112 2 3 72 9511 9516 9521 9527 9532 9537 9542 9548 9553 9558 9563 17 112 2 3 73 9563 9568 9573 9578 9583 9588 9593 9598 9603 9608 9613 16 112 2 74 9613 9617 9622 9627 9632 9636 9641 9646 9650 9655 9659 15 112 2 75 9659 9664 9668 9673 9677 9681 9686 9690 9694 9699 9703 14 112 2 76 9703 9707 9711 9715 9720 9724 9728 9732 9736 9740 9744 13 112 2 77 9744 9748 9751 9755 9759 9763 9767 9770 9774 9778 9781 12 112 2 78 9781 9785 9789 9792 9796 9799 9803 9806 9810 9813 9816 . 11 1112 79 9816 9820 9823 9826 9829 9833 9836 9839 9842 9845 0.9848 10° 1112 80° 0.9848 9851 9854 9857 9860 9863 9866 9869 9871 9874 9877 9 1111 81 9877 9880 9882 9885 9888 9890 9893 9895 9898 9900 9903 8 1111 82 9903 9905 9907 9910 9912 9914 9917 .9919 9921 9923 9925 7 111 83 9925 9928 9930 9932 9934 9936 9938 9940 9942 9943 9945 6 111 84 9945 9947 9949 9951 9952 9954 9956 9957 9959 9960 9962 5 111 85 9962 9963 9965 9966 9968 9969 9971 9972 9973 9974 9976 4 11 86 9976 9977 9978 9979 9980 9981 9982 9983 9984 9985 9986 3 1 87 9986 9987 9988 9989 9990 9990 9991 9992 9993 9993 9994 2 88 9994 9995 9995 9996 9996 9997 9997 9997 9998 9998 0.9998 1 89 0.9998 9999 9999 9999 9999 J 0000 0000 0000 0000 0000 1.0000 ©° 90° 1.0000 (9) M Tangent Coft&mgeimft .1 2 -T M M .4 J Ja 1 B .9 1 3 A 5 * .7 ""X" 90° 0.000000 0° 0.000000 001745 003491 005236 006981 008727 010472 012218 013964 015709 017455 89 1 01748 01920 02095 02269 02444 02619 02793 02968 03143 03317 03492 88 2 03492 03667 03842 04016 04191 04366 04541 04716 04891 05066 05241 87 3 05241 05416 05591 05766 05941 06116 06291 06467 06642 06817 06993 86 4 06993 07168 07344 07519 07695 07870 08046 08221 08397 08573 08749 85 5 08749 08925 09101 09277 09453 09629 09805 09981 10158 10334 10510 84 6 10510 10687 10863 11040 11217 11394 11570 11747 11924 12101 12278 83 7 12278 12456 12633 12810 12988 13165 13343 13521 13698 13876 14054 82 8 14054 14232 14410 14588 14767 14945 15124 15302 15481 15660 15838 81 9 15838 16017 16196 16376 16555 16734 16914 17093 17273 17453 0.17633 so° 10° 0.1763 1781 1799 1817 1835 1853 1871 1890 1908 1926 1944 79 11 1944 1962 1980 1998 2016 2035 2053 2071 2089 2107 2126 78 12 2126 2144 2162 2180 2199 2217 2235 2254 2272 2290 2309 77 13 2309 2327 2345 2364 2382 2401 2419 2438 2456 2475 2493 76 14 2493 2512 2530 2549 2568 2586 2605 2623 2642 2661 2679 75 IS 2679 2698 2717 2736 2754 2773 2792 2811 2830 2849 2867 74 16 2867 2886 2905 2924 2943 2962 2981 3000 3019 3038 3057 73 17 3057 3076 3096 3115 3134 3153 3172 3191 3211 3230 3249 72 18 3249 3269 3288 3307 3327 3346 3365 3385 3404 3424 3443 71 19 3443 3463 3482 3502 3522 3541 3561 3581 3600 3620 0.3640 7©° 30° 0.3640 3659 3679 3699 3719 3739 3759 3779 3799 3819 3839 69 21 3839 3859 3879 3899 3919 3939 3959 3979 4000 4020 4040 68 22 4040 4061 4081 4101 4122 4142 4163 4183 4204 4224 4245 67 23 4245 4265 4286 4307 4327 4348 4369 4390 4411 4431 4452 66 24 4452 4473 4494 4515 4536 4557 4578 4599 4621 4642 4663 65 25 4663 4684 4706 4727 4748 4770 4791 4813 4834 4856 4877 64 26 4877 4899 4921 4942 4964 4986 5008 5029 5051 5073 5095 63 27 5095 5117 5139 5161 5184 5206 5228 5250 5272 5295 5317 62 28 5317 5340 5362 5384 5407 5430 5452 5475 5498 5520 5543 61 29 5543 5566 5589 5612 5635 5658 5681 5704 5727 5750 0.5774 (SO 30° 0.5774 5797 5820 5844 5867 5890 5914 5938 5961 5985 6009 59 31 6009 6032 6056 6080 6104 6128 6152 6176 6200 6224 6249 58 32 6249 6273 6297 6322 6346 6371 6395 6420 6445 6469 6494 57 33 6494 6519 6544 6569 6594 6619 6644 6669 6694 6720 6745 56 34 6745 6771 6796 6822 6847 6873 6899 6924 6950 6976 7002 55 35 7002 7028 7054 7080 7107 7133 7159 7186 7212 7239 7265 54 36 7265 7292 7319 7346 7373 7400 7427 7454 7481 7508 7536 53 37 7536 7563 7590 7618 7646 7673 7701 7729 7757 7785 7813 52 38 7813 7841 7869 7898 7926 7954 7983 8012 8040 8069 8098 51 39 8098 8127 8156 8185 8214 8243 8273 8302 8332 8361 0.8391 s©° 40° 0.8391 8421 8451 8481 8511 8541 8571 8601 8632 8662 8693 49 41 8693 8724 8754 8785 8816 8847 8878 8910 8941 8972 9004 48 42 9004 9036 9067 9099 9131 9163 9195 9228 9260 9293 9325 47 43 9325 9358 9391 9424 9457 9490 9523 9556 9590 9623 0.9657 46 44 0.9657 9691 9725 9759 9793 9827 9861 9896 9930 9965jl,0000 4S° 45° 1.0000 Tenths of the Tabular Difference 12 3 4 5 175 349524698873 17 35 52 70 87 17 35 52 70 87 18 35 53 70 88 18 35 53 70 88 18 35 53 70 88 18 35 53 71 88 18 36 53 71 89 18 36 54 71 89 18 36 54 72 90 2 4 5 7 9 2 4 5 7 9 2 4 579 2 4 6 7 9 2 4 6 7 9 2 4 6 8 9 2 4 6 8 9 2 4 6 810 2 4 6 810 2 4 6 810 2 4 6 810 2 4 6 8 10 2 4 6 810 2 4 6 810 2 4 6 811 2 4 6 911 2 4 7 911 2 4 7 911 2 5 7 911 2 5 7 912 2 5 7 912 2 5 7 1012 2 5 71012 3 5 8 1013 3 5 81013 3 5 81113 3 5 8 1114 3 6 8 1114 3 6 91114 3 6 9 12 15 6 9 12 15 6 9 12 16 6 10 13 16 7 10 13 17 7 10 14 17 (10) Tangent .0 L. & .© .7 J8 .4 J5 i .6 M 2 .1 B 45° Tenths of the .1 2 .3 Tabular Difference .7 .8 ~ .9 1 12 3 4 5 1.0000 45° 1.0000 0035 0070 0105 0141 0176 0212 0247 0283 0319 0355 44 4 7 11 14 18 46 0355 0392 0428 0464 0501 0538 0575 0612 0649 0686 0724 43 4 7 11 15 18 47 0724 0761 0799 0837 0875 0913 0951 0990 1028 1067 1106 42 4 8 11 15 19 48 1106 1145 1184 1224 1263 1303 1343 1383 1423 1463 1504 41 4 8 12 16 20 49 1504 1544 1585 1626 1667 1708 1750 1792 1833 1875 1.1918 m° 4 8 12 17 21 50° 1.1918 1960 2002 2045 2088 2131 2174 2218 2261 2305 2349 39 4 9 13 17 22 ' 51 2349 2393 2437 2482 2527 2572 2617 2662 2708 2753 2799 38 5 91418 23 52 2799 2846 2892 2938 2985 3032 3079 3127 3175 3222 3270 37 5 9 14 19 24 53 3270 3319 3367 3416 3465 3514 3564 3613 3663 3713 3764 36 5 10 15 20 25 54 3764 3814 3865 3916 3968 4019 4071 4124 4176 4229 1.4281 35 5 10 16 2126 55 1.4281 4335 4388 4442 4496 4550 4605 4659 4715 4770 4826 34 5 11 16 22 27 56 4826 4882 4938 4994 5051 5108 5166 5224 5282 5340 5399 33 6 11 17 23 29 57 5399 5458 5517 5577 5637 5697 5757 5818 5880 5941 6003 32 6 12 18 24 30 58 6003 6066 6128 6191 6255 6319 6383 6447 6512 6577 6643 31 6 13 19 26 32 59 60° 1.6643 6709 6775 6842 6909 6977 7045 7113 7182 7251 1.7321 30° 29 7 14 20 27 34 1.732 1.739 1.746 1.753 1.760 1.767 1.775 1.782 1.789 1.797 1.804 112 3 4 61 1.804 1.811 1.819 1.827 1.834 1.842 1.849 1.857 1.865 1.873 1.881 28 12 2 3 4 62 1.881 1.889 1.897 1.905 1.913 1.921 1.929 1.937 1.946 1.954 1.963 27 12 2 3 4 63 1.963 1.971 1.980 1.988 1.997 2.006 2.014 2.023 2.032 2.041 2.050 26 12 3 4 4 64 2.050 2.059 2.069 2.078 2.087 2.097 2.106 2.116 2.125 2.135 2.145 25 12 3 4 5 65 2.145 2.154 2.164 2.174 2.184 2.194 2.204 2.215 2.225 2.236 2.246 24 12 3 4 5 66 2.246 2.257 2.267 2.278 2.289 2.300 2.311 2.322 2.333 2.344 2.356 23 12 3 4 5 67 2.356 2.367 2.379 2.391 2.402 2.414 2.426 2.438 2.450 2.463 2.475 22 12 4 5 6 68 2.475 2.488 2.500 2.513 2.526 2.539 2.552 2.565 2.578 2.592 2.605 21 13 4 5 7 69 2.605 2.619 2.633 2.646 2.660 2.675 2.689 2.703 2.718 2.733 2.747 20° 13 4 6 7 70° 2.747 2.762 2.778 2.793 2.808 2.824 2.840 2.856 2.872 2.888 2.904 19 2 3 5 6 8 71 2.904 2.921 2.937 2.954 2.971 2.989 3.006 3.024 3.042 3.060 3.078 18 2 3 5 7 9 72 3.078 3.096 3.115 3.133 3.152 3.172 3.191 3.211 3.230 3.251 3.271 17 2 4 6 8 10 73 3.271 3.291 3.312 3.333 3.354 3.376 3.398 3.420 3.442 3.465 3.487 16 2 4 6 9 11 74 3.487 3.511 3.534 3.558 3.582 3.606 3.630 3.655 3.681 3.706 3.732 15 2 5 7 10 12 75 3.732 3.758 3.785 3.812 3.839 3.867 3.895 3.923 3.952 3.981 4.011 14 3 6 8 11 14 76 77 4.011 4.331 4.041 4.366 4.071 4.402 4.102 4.437 4.134 4.474 4.165 4.511 4.198 4.548 4.230 4.586 4.264 4.625 4.297 4.665 4.331 4.705 13 12 3 6 10 13 16 co 35-^K) 78 4.705 4.745 4.787 4.829 4.872 4.915 4.959 5.005 5.050 5.097 5.145 11 1 40-^8 79 5.145 5.193 5.242 5.292 5.343 5.396 5.449 5.503 5.558 5.614 5.671 10° 1 48 ~ S7 80° 5.671 5.730 5.789 5.850 5.912 5.976 6.041 6.107 6.174 6.243 6.314 9 f! 59—71 81 6.314 6.386 6.460 6.535 6.612 6.691 6.772 6.855 6.940 7.026 7.115 8 Z 72—89 82 7.115 7.207 7.300 7.396 7.495 7.596 7.700 7.806 7.916 8.028 8.144 7 = 92-116 83 84 8.144 9.514 8.264 9.677 8.386 9.845 8.513 10.019 8.643 10.199 8.777 10.385 8.915 10.579 9.058 10.780 9.205 10.988 9.357 11.205 9.514 11.430 6 S " 120—157 Interpolation 85 11.430 11.664 11.909 12.163 12.429 12.706 12.996 13.300 13.617 13.951 14.301 4 accurate, except 86 87 14.301 19.08 14.669 19.74 15.056 20.45 15.464 21.20 15.895 22.02 16.350 22.90 16.832 23.86 17.343 24.90 17.886 26.03 18.464 27.27 19.081 28.64 3 2 the lasl figure Interpolation not accurate 88 28.64 30.14 31.82 33.69 35.80 38.19 40.92 44.07 47.74 52.08 57.29 1 89 57.29 63.66 71.62 81.85 95.49 114.59 143.24 191.0 286.5 573.0 00 0° 90° 00 (11) ^ < W t* c * 4/fo go" 5 Secant .0 I. .© .1 2 _J jfi J> .6 "IT" .1 .© B@° 1 Tat 1 entt ular 2 s of the Difference 3 4 5 .3 .4 "IT 1.0000 0° 1.0000 0000 0000 0000 0000 0000 0001 0001 0001 0001 0002 89 1 0002 0002 0002 0003 0003 0003 0004 0004 0005 0006 0006 88 2 0006 0007 0007 0008 0009 0010 0010 0011 0012 0013 0014 87 3 0014 0015 0016 0017 0018 0019 0020 0021 0022 0023 0024 86 1 4 0024 0026 0027 0028 0030 0031 0032 0034 0035 0037 0038 85 Oil 5 0038 0040 0041 0043 0045 0046 0048 0050 0051 0053 0055 84 111 6 0055 0057 0059 0061 0063 0065 0067 0069 0071 0073 0075 83 111 7 0075 0077 0079 0082 0084 0086 0089 0091 0093 0096 0098 82 111 8 0098 0101 0103 0106 0108 0111 0114 0116 0119 0122 0125 81 1 111 9 0125 0127 0130 0133 0136 0139 0142 0145 0148 0151 1.0154 BO° 1 111 10° 1.0154 0157 0161 0164 0167 0170 0174 0177 0180 0184 0187 79 1 112 11 0187 0191 0194 0198 0201 0205 0209 0212 0216 0220 0223 78 1 112 12 0223 0227 0231 0235 0239 0243 0247 0251 0255 0259 0263 77 1 12 2 13 0263 0267 0271 0276 0280 0284 0288 0293 0297 0302 0306 76 1 12 2 14 0306 0311 0315 0320 0324 0329 0334 0338 0343 0348 0353 75 1 1 12 2 15 0353 0358 0363 0367 0372 0377 0382 0388 0393 0398 0403 74 1 1 2 2 3 16 0403 0408 0413 0419 0424 0429 0435 0440 0446 0451 0457 73 1 1 2 2 3 17 0457 0463 0468 0474 0480 0485 0491 0497 0503 0509 0515 . 72 1 1 2 2 3 18 0515 0521 0527 0533 0539 0545 0551 0557 0564 0570 0576 71 1 1 2 2 3 19 0576 0583 0589 0595 0602 0608 0615 0622 0628 0635 1.0642 7(0° 1 1 2 3 3 20° 1.0642 0649 0655 0662 0669 0676 0683 0690 0697 0704 0711 69 1 1 2 3 3 21 0711 0719 0726 0733 0740 0748 0755 0763 0770 0778 0785 68 1 1 2 3 4 22 0785 0793 0801 0808 0816 0824 0832 0840 0848 0856 0864 67 1 2 2 3 4 23 0864 0872 0880 0888 0896 0904 0913 0921 0929 0938 0946 66 1 2 2 3 4 24 0946 0955 0963 0972 0981 0989 0998 1007 1016 1025 1034 65 1 2 3 3 4 25 1034 1043 1052 1061 1070 1079 1089 1098 1107 1117 1126 64 1 2 3 4 5 26 1126 1136 1145 1155 1164 1174 1184 1194 1203 1213 1223 63 1 2 3 4 5 27 1223 1233 1243 1253 1264 1274 1284 1294 1305 1315 1326 62 1 2 3 4 5 28 1326 1336 1347 1357 1368 1379 1390 1401 1412 1423 1434 61 1 2 3 4 5 29 1434 1445 1456 1467 1478 1490 1501 1512 1524 1535 1.1547 <8(Q>° 1 2 3 5 6 30° 1.1547 1559 1570 1582 1594 1606 1618 1630 1642 1654 1666 59 1 2 4 5 6 31 1666 1679 1691 1703 1716 1728 1741 1753 1766 1779 1792 58 1 3 4 5 6 32 1792 1805 1818 1831 1844 1857 1870 1883 1897 1910 1924 57 1 3 4 5 7 33 1924 1937 1951 1964 1978 1992 2006 2020 2034 2048 2062 56 1 3 4 6 7 34 2062 2076 2091 2105 2120 2134 2149 2163 2178 2193 2208 55 1 3 4 6 7 35 2208 2223 2238 2253 2268 2283 2299 2314 2329 2345 2361 54 2 3 5 6 8 36 2361 2376 2392 2408 2424 2440 2456 2472 2489 2505 2521 53 2 3 5 6 8 37 2521 2538 2554 2571 2588 2605 2622 2639 2656 2673 2690 52 2 3 5 7 8 38 2690 2708 2725 2742 2760 2778 2796 2813 2831 2849 2868 51 2 4 5 7 9 39 2868 2886 2904 2923 2941 2960 2978 2997 3016 3035 1.3054 50° 2 4 6 7 9 40° 1.3054 3073 3093 3112 3131 3151 3171 3190 3210 3230 3250 49 2 4 6 810 41 3250 3270 3291 3311 3331 3352 3373 3393 3414 3435 3456 48 2 4 6 810 42 3456 3478 3499 3520 3542 3563 3585 3607 3629 3651 3673 47 2 4 7 9 11 43 3673 3696 3718 3741 3763 3786 3809 3832 3855 3878 3902 46 2 5 7 911 44 3902 3925 3949 3972 3996 4020 4044 4069 4093 4118 1.4142 4B° 2 5 71012 45° 1.4142 (12) Secant Cosec&nafc ' JO J J© :t M M .4 .6 ,7 2 .1 .8 -9 1 JO 45° Tenths of the Tabular Differenca 12 3 4 5 2 .3 A .5 1.4142 45° 1.4142 4167 4192 4217 4242 4267 4293 4318 4344 4370 4396 44 3 5 8 1013 46 4396 4422 4448 4474 4501 4527 4554 4581 4608 4635 4663 43 3 5 8 1113 47 4663 4690 4718 4746 4774 4802 4830 4859 4887 4916 4945 42 3 6 8 1114 48 4945 4974 5003 5032 5062 5092 5121 5151 5182 5212 5243 41 3 6 9 12 15 49 5243 5273 5304 5335 5366 5398 5429 5461 5493 5525 1.5557 40° 3 6 9 13 16 50° 1.5557 5590 5622 5655 5688 5721 5755 5788 5822 5856 5890 39 3 710 13 17 51 5890 5925 5959 5994 6029 6064 6099 6135 6171 6207 6243 38 4 7 11 14 18 52 6243 6279 6316 6353 6390 6427 6464 6502 6540 6578 6616 37 4 7 11 15 19 53 6616 6655 6694 6733 6772 6812 6852 6892 6932 6972 7013 36 4 8 12 16 20 54 7013 7054 7095 7137 7179 7221 7263 7305 7348 7391 1.7434 35 4 8 13 17 21 55 1.7434 7478 7522 7566 7610 7655 7700 7745 7791 7837 7883 34 4 9 13 18 22 56 7883 7929 7976 8023 8070 8118 8166 8214 8263 8312 8361 33 5 10 14 19 24 57 8361 8410 8460 8510 8561 8612 8663 8714 8766 8818 8871 32 5 10 15 20 26 58 8871 8924 8977 9031 9084 9139 9194 9249 9304 9360 1.9416 31 5 1116 22 27 59 60° 1.9416 9473 9530 9587 9645 9703 9762 9821 9880 9940J 2.0000 3©° 29 6 12 18 23 29 2.000 2.006 2.012 2.018 2.025 2.031 2.037 2.043 2.050 2.056 2.063 112 3 3 61 2.063 2.069 2.076 2.082 2.089 2.096 2.103 2.109 2.116 2.123 2.130 28 112 3 3 62 2.130 2.137 2.144 2.151 2.158 2.166 2.173 2.180 2.188 2.195 2.203 27 112 3 4 63 2.203 2.210 2.218 2.226 2.233 2.241 2.249 2.257 2.265 2.273 2.281 26 12 2 3 4 64 2.281 2.289 2.298 2.306 2.314 2.323 2.331 2.340 2.349 2.357 2.366 25 12 3 3 4 65 2.366 2.375 2.384 2.393 2.402 2.411 2.421 2.430 2.439 2.449 2.459 24 12 3 4 5 66 2.459 2.468 2.478 2.488 2.498 2.508 2.518 2.528 2.538 2.549 2.559 23 12 3 4 5 67 2.559 2.570 2.581 2.591 2.602 2.613 2.624 2.635 2.647 2.658 2.669 22 12 3 4 6 68 2.669 2.681 2.693 2.705 2.716 2.729 2.741 2.753 2.765 2.778 2.790 21 12 4 5 6 69 2.790 2.803 2.816 2.829 2.842 2.855 2.869 2.882 2.896 2.910 2.924 20° 13 4 5 7 70° 2.924 2.938 2.952 2.967 2.981 2.996 3.011 3.026 3.041 3.056 3.072 19 13 4 6 7 71 3.072 3.087 3.103 3.119 3.135 3.152 3.168 3.185 3.202 3.219 3.236 18 2 3 5 7 8 72 3.236 3.254 3.271 3.289 3.307 3.326 3.344 3.363 3.382 3.401 3.420 17 2 4 6 7 9 73 3.420 3.440 3.460 3.480 3.500 3.521 3.542 3.563 3.584 3.606 3.628 16 2 4 6 8 10 74 3.628 3.650 3.673 3.695 3.719 3.742 3.766 3.790 3.814 3.839 3.864 15 2 5 7 9 12 75 3.864 3.889 3.915 3.941 3.967 3.994 4.021 4.049 4.077 4.105 4.134 14 3 5 8 11 13 76 77 4.134 4.445 4.163 4.479 4.192 4.514 4.222 4.549 4.253 4.584 4.284 4.620 4.315 4.657 4.347 4.694 4.379 4.412 4.732 4.771 4.445 4.810 13 12 3 6 9 12 16 «, 34—39 78 4.810 4.850 4.890 4.931 4.973 5.016 5.059 5.103 5.148 5.194 5.241 11 | 40-47 79 5.241 5.288 5.337 5.386 5.436 5.487 5.540 5.593 5.647 5.702 5.759 10° I 47-57 3= 80° 5.759 5.816 5.875 5.935 5.996 6.059 6.123 6.188 6.255 6.323 6.392 9 = 57—69 81 6.392 6.464 6.537 6.611 6.687 6.765 6.845 6.927 7.011 7.097 7.185 8 "2 72 ~ 88 82 7.185 7.276 7.368 7.463 7.561 7.661 7.764 7.870 7.979 8.091 8.206 7 | 91-115 83 84 8.206 9.567 8.324 9.728 8.446 9.895 8.571 10.068 8.700 10.248 8.834 10.433 8.971 10.626 9.113 10.826 9.259 9.411 11.034 11.249 9.567 11.474 6 5 °= 118—156 Interpolation 85 11.474 11.707 11.951 12.204 12.469 12.745 13.035 13.337 13.654 13.987 14.336 4 accurate, except 86 87 14.336 19.11 14.703 19.77 15.089 20.47 15.496 21.23 15.926 22.04 16.380 22.93 16.862 23.88 17.372 24.92 17.914 18.492 26.05 27.29 19.107 28.65 3 2 the last figure Interpolation not accurate 88 28.65 30.16 31.84 33.71 35.81 38.20 40.93 44.08 47.75 52.09 57.30 1 89 57.30 63.66 71.62 81.85 95.49 114.59 143.24 191.0 286.5 573.0 00 0° 90° 00 U3) ad « <5 c s c W r* ,e* V 1 5 t*2 sp *c ^ Log 1.00 1 3 3 4 5 6 7 8 9 10 0.0000 0004 0009 0013 0017 0022 0026 0030 0035 0039 0043 1.01 0043 0048 0052 0056 0060 0065 0069 0073 0077 0082 0086 1.02 0086 0090 0095 0099 0103 0107 0111 0116 0120 0124 0128 1.03 0128 0133 0137 0141 0145 0149 0154 0158 0162 0166 0170 1.04 0170 0175 0179 0183 0187 0191 0195 0199 0204 0208 0212 1.05 0212 0216 0220 0224 0228 0233 0237 0241 0245 0249 0253 1.06 0253 0257 0261 0265 0269 0273 0278 0282 0286 0290 0294 1.07 0294 0298 0302 0306 0310 0314 0318 0322 0326 0330 0334 1.08 0334 0338 0342 0346 0350 0354 0358 0362 0366 0370 0374 1.09 0374 0378 0382 0386 0390 0394 0398 0402 0406 0410 0414 1.10 0.0414 0418 0422 0426 0430 0434 0438 0441 0445 0449 0453 1.11 0453 0457 0461 0465 0469 0473 0477 0481 0484 0488 0492 1.12 0492 0496 0500 0504 0508 0512 0515 0519 0523 0527 0531 1.13 0531 0535 0538 0542 0546 0550 0554 0558 0561 0565 0569 1.14 0569 0573 0577 0580 0584 0588 0592 0596 0599 0603 0607 1.15 0607 0611 0615 0618 0622 0626 0630 0633 0637 0641 0645 1.16 0645 0648 0652 0656 0660 0663 0667 0671 0674 0678 0682 1.17 0682 0686 0689 0693 0697 0700 0704 0708 0711 0715 0719 1.18 0719 0722 0726 0730 0734 0737 0741 0745 0748 0752 0755 1.19 0755 0759 0763 0766 0770 0774 0777 0781 0785 0788 0792 1.20 0.0792 0795 0799 0803 0806 0810 0813 0817 0821 0824 0828 1.21 0828 0831 0835 0839 0842 0846 0849 0853 0856 0860 0864 1.22 0864 0867 0871 0874 0878 0881 0885 0888 0892 0896 0899 1.23 0899 0903 0906 0910 0913 0917 0920 0924 0927 0931 0934 1.24 0934 0938 0941 0945 0948 0952 0955 0959 0962 0966 0969 1.25 0969 0973 0976 0980 0983 0986 0990 0993 0997 1000 1004 1.26 1004 1007 1011 1014 1017 1021 1024 1028 1031 1035 1038 1.27 1038 1041 1045 1048 1052 1055 1059 1062 1065 1069 1072 1.28 1072 1075 1079 1082 1086 1089 1092 1096 1099 1103 1106 1.29 1106 1109 1113 1116 1119 1123 1126 1129 1133 1136 1139 1.30 0.1139 1143 1146 1149 1153 1156 1159 1163 1166 1169 1173 1.31 1173 1176 1179 1183 1186 1189 1193 1196 1199 1202 1206 1.32 1206 1209 1212 1216 1219 1222 1225 1229 1232 1235 1239 1.33 1239 1242 1245 1248 1252 1255 1258 1261 1265 1268 1271 1.34 1271 1274 1278 1281 1284 1287 1290 1294 1297 1300 1303 1.35 1303 1307 1310 1313 1316 1319 1323 1326 1329 1332 1335 1.36 1335 1339 1342 1345 1348 1351 1355 1358 1361 1364 1367 1.37 1367 1370 1374 1377 1380 1383 1386 1389 1392 1396 1399 1.38 1399 1402 1405 1408 1411 1414 1418 1421 1424 1427 1430 1.39 1430 1433 1436 1440 1443 1446 1449 1452 1455 1458 1461 1.40 0.1461 1464 1467 1471 1474 1477 1480 1483 1486 1489 1492 1.41 1492 1495 1498 1501 1504 1508 1511 1514 1517 1520 1523 1.42 1523 1526 1529 1532 1535 1538 1541 1544 1547 1550 1553 1.43 1553 1556 1559 1562 1565 1569 1572 1575 1578 1581 1584 1.44 1584 1587 1590 1593 1596 1599 1602 1605 1608 1611 1614 1.45 1614 1617 1620 1623 1626 1629 1632 1635 1638 1641 1644 1.46 1644 1647 1649 1652 1655 1658 1661 1664 1667 1670 1673 1.47 1673 1676 1679 1682 1685 1688 1691 1694 1697 1700 1703 1.48 1703 1706 1708 1711 1714 1717 1720 1723 1726 1729 1732 1.49 1732 1735 1738 1741 1744 1746 1749 1752 1755 1758 1761 (14) Log 1.50 1 2 3 4 5 6 7 8 9 10 0.1761 1764 1767 1770 1772 1775 1778 1781 1784 1787 1790 1.51 1790 1793 1796 1798 1801 1804 1807 1810 1813 1816 1818 1.52 1818 1821 1824 1827 1830 1833 1836 1838 1841 1844 1847 1.53 1847 1850 1853 1855 1858 1861 1864 1867 1870 1872 1875 1.54 1875 1878 1881 1884 1886 1889 1892 1895 1898 1901 1903 1.55 1903 1906 1909 1912 1915 1917 1920 1923 1926 1928 1931 1.56 1931 1934 1937 1940 1942 1945 1948 1951 1953 1956 1959 1.57 1959 1962 1965 1967 1970 1973 1976 1978 1981 1984 1987 1.58 1987 1989 1992 1995 1998 2000 2003 2006 2009 2011 2014 1.59 2014 2017 2019 2022 2025 2028 2030 2033 2036 2038 2041 1.60 0.2041 2044 2047 2049 2052 2055 2057 2060 2063 2066 2068 1.61 2068 2071 2074 2076 2079 2082 2084 2087 2090 2092 2095 1.62 2095 2098 2101 2103 2106 2109 2111 2114 2117 2119 2122 1.63 2122 2125 2127 2130 2133 2135 2138 2140 2143 2146 2148 1.64 2148 2151 2154 2156 2159 2162 2164 2167 2170 2172 2175 1.65 2175 2177 2180 2183 2185 .2188 2191 2193 2196 2198 2201 1.66 2201 2204 2206 2209 2212 2214 2217 2219 2222 2225 2227 1.67 2227 2230 2232 2235 2238 2240 2243 2245 2248 2251 2253 1.68 2253 2256 2258 2261 2263 2266 2269 2271 2274 2276 2279 1.69 2279 2281 2284 2287 2289 2292 2294 2297 2299 2302 2304 1.70 0.2304 2307 2310 2312 2315 2317 2320 2322 2325 2327 2330 1.71 2330 2333 2335 2338 2340 2343 2345 2348 2350 2353 2355 1.72 2355 2358 2360 2363 2365 2368 2370 2373 2375 2378 2380 1.73 2380 2383 2385 2388 2390 2393 2395 2398 2400 2403 2405 1.74 2405 2408 2410 2413 2415 2418 2420 2423 2425 2428 2430 1.75 2430 2433 2435 2438 2440 2443 2445 2448 2450 2453 2455 1.76 2455 2458 2460 2463 2465 2467 2470 2472 2475 2477 2480 1.77 2480 2482 2485 2487 2490 2492 2494 2497 2499 2502 2504 1.78 2504 2507 2509 2512 2514 2516 2519 2521 2524 2526 2529 1.79 2529 2531 2533 2536 2538 2541 2543 2545 2548 2550 2553 1.80 0.2553 2555 2558 2560 2562 2565 2567 2570 2572 2574 2577 1.81 2577 2579 2582 2584 2586 2589 2591 2594 2596 2598 2601 1.82 2601 2603 2605 2608 2610 2613 2615 2617 2620 2622 2625 1.83 2625 2627 2629 2632 2634 2636 2639 2641 2643 2646 2648 1.84 2648 2651 2653 2655 2658 2660 2662 2665 2667 2669 2672 1.85 2672 2674 2676 2679 2681 2683 2686 2688 2690 2693 2695 1.86 2695 2697 2700 2702 2704 2707 2709 2711 2714 2716 2718 1.87 2718 2721 2723 2725 2728 2730 2732 2735 2737 2739 2742 1.88 2742 2744 2746 2749 2751 2753 2755 2758 2760 2762 2765 1.89 2765 2767 2769 2772 2774 2776 2778 2781 2783 2785 2788 1.90 0.2788 2790 2792 2794 2797 2799 2801 2804 2806 2808 2810 1.91 2810 2813 2815 2817 2819 2822 2824 2826 2828 2831 2833 1.92 2833 2835 2838 2840 2842 2844 2847 2849 2851 2853 2856 1.93 2856 2858 2860 2862 2865 2867 2869 2871 2874 2876 2878 1.94 2878 2880 2882 2885 2887 2889 2891 2894 2896 2898 2900 1.95 2900 2903 2905 2907 2909 2911 2914 2916 2918 2920 2923 1.96 2923 2925 2927 2929 2931 2934 2936 2938 2940 2942 2945 1.97 2945 2947 2949 2951 2953 2956 2958 2960 2962 2964 2967 1.98 2967 2969 2971 2973 2975 2978 2980 2982 2984 2986 2989 1.99 2989 2991 2993 2995 2997 2999 3002 3004 3006 3008 3010 (15)-. & /Tog sin&Tog cos\ /log tan a log ctn\ M' 1$ These two pages give the common logarithms of numbers between 1 and 10, correct to four places. Moving the decimal point n places to the right (or left) in the number is equivalent to adding n (or — n) to the logarithm. Thus, log 0.017453 = 0.2419 — 2 [ = 2.2419 ]. M: For any Angle x, log (x in radians) = 2.2419 + log (x°) When x is between 0° and l°.l log sin x = 2.2419 + log (x°) log tan x = 2.2419 + log (x°) log cot x — 1.7581 — log (x°) When x is between 88°.9 and 90° log cos x = 2.2419 + log (90°— x°) log cot x = 2.2419 + log (90°— x°) log tan x = 1.7581 — log (90°—x°) Log it c 0* i* t<» rcC l>°° 1.0 1 3 3 4 5 6 7 8 9 10 0.0000 0043 0086 0128 0170 0212 0253 0294 0334 0374 0414 1.1 0414 0453 0492 0531 0569 0607 0645 0682 0719 0755 0792 1.2 0792 0828 0864 0899 0934 0969 1004 1038 i072 1106 1139 1.3 1139 1173 1206 1239 1271 1303 1335 1367 1399 1430 . 1461 1.4 1461 1492 1523 1553 1584 1614 1644 1673 1703 1732 1761 1.5 1761 1790 1818 1847 1875 1903 1931 1959 1987 2014 2041 1.6 2041 2068 2095 2122 2148 2175 2201 2227 2253 2279 2304 1.7 2304 2330 2355 2380 2405 2430 2455 2480 2504 2529 2553 1.8 2553 2577 2601 2625 2648 2672 2695 2718 2742 2765 2788 1.9 2788 2810 2833 2856 2878 2900 2923 2945 2967 2989 3010 2.0 0.3010 3032 3054 3075 3096 3118 3139 3160 3181 3201 3222 2.1 3222 3243 3263 3284 3304 3324 3345 3365 3385 3404 3424 2.2 3424 3444 3464 3483 3502 3522 3541 3560 3579 3598 3617 2.3 3617 3636 3655 3674 3692 3711 3729 3747 3766 3784 3802 2.4 3802 3820 3838 3856 3874 3892 3909 3927 3945 3962 3979 2.5 3979 3997 4014 4031 4048 4065 4082 4099 4116 4133 4150 2.6 4150 4166 4183 4200 4216 4232 4249 4265 4281 4298 4314 2.7 4314 4330 4346 4362 4378 4393 4409 4425 4440 4456 4472 2.8 4472 4487 4502 4518 4533 4548 4564 4579 4594 4609 4624 2.9 4624 4639 4654 4669 4683 4698 4713 4728 4742 4757 4771 3.0 0.4771 4786 4800 4814 4829 4843 4857 4871 4886 4900 4914 3.1 4914 4928 4942 4955 4969 4983 4997 5011 5024 5038 5051 3.2 5051 5065 5079 5092 5105 5119 5132 5145 5159 5172 5185 3.3 5185 5198 5211 5224 5237 5250 5263 5276 5289 5302 5315 3.4 5315 5328 5340 5353 5366 5378 5391 5403 5416 5428 5441 3.5 5441 5453 5465 5478 5490 5502 5514 5527 5539 5551 5563 3.6 5563 5575 5587 5599 5611 5623 5635 5647 5658 5670 5682 3.7 5682 5694 5705 5717 5729 5740 5752 5763 5775 5786 5798 3.8 5798 5809 5821 5832 5843 5855 5866 5877 5888 5899 5911 3.9 5911 5922 5933 5944 5955 5966 5977 5988 5999 6010 6021 4.0 0.6021 6031 6042 6053 6064 6075 6085 6096 6107 6117 6128 4.1 6128 6138 6149 6160 6170 6180 6191 6201 6212 6222 6232 4.2 6232 6243 6253 6263 6274 6284 6294 6304 6314 6325 6335 4.3 6335 6345 6355 6365 6375 6385 6^95 6405 6415 6425 6435 4.4 6435 6444 6454 6464 6474 6484 6493 6503 6513 6522 6532 4.5 6532 6542 6551 6561 6571 6580 6590 6599 6609 6618 6628 4.6 6628 6637 6646 6656 6665 6675 6684 6693 6702 6712 6721 4.7 6721 6730 6739 6749 6758 6767 6776 6785 6794 6803 6812 4.8 6812 6821 6830 6839 6848 6857 6866 6875 6884 6893 6902 4.9 6902 6911 6920 6928 6937 6946 6955 6964 6972 6981 6990 Tenths of the Tabular Difference 12 3 4 5 To avoid interpo- lation in the first ten lines, use the special table on the preceding page. 2 4 6 811 2 4 6 810 2 4 6 810 2 4 5 7 9 2 4 5 7 9 2 3 5 7 9 2 3 5 7 8 2 3 5 6 8 2 3 5 6 8 13 4 6 7 13 4 6 7 1 3 4 6 7 13 4 5 7 13 4 5 6 13 4 5 6 12 4 5 6 12 4 5 6 12 3 5 6 12 3 5 6 12 3 4 6 12 3 4 5 12 3 4 5 12 3 4 5 12 3 4 5 12 3 4 5 12 3 4 5 12 3 4 5 12 3 4 5 12 3 4 4 12 3 4 4 log tr = 0.4971 log e = 0.4343 log w/2== 0.1961 log IT 2 (16) ■■ 0.9943 log\AT= 0.2486 log (0.434^ =1.6378 Log 5.0 1 3 3 4 5 6 7 S 9 10 0.6990 6998 7007 7016 7024 7033 7042 7050 7059 7067 7076 5.1 7076 7084 7093 7101 7110 7118 7126 7135 7143 7152 7160 5.2 7160 7168 7177 7185 7193 7202 7210 7218 7226 7235 7243 5.3 7243 7251 7259 7267 7275 7284 7292 7300 7308 7316 7324 5.4 7324 7332 7340 7348 7356 7364 7372 7380 7388 7396 7404 5.5 7404 7412 7419 7427 7435 7443 7451 7459 7466 7474 7482 5.6 7482 7490 7497 7505 7513 7520 7528 7536 7543 7551 7559 5.7 7559 7566 7574 7582 7589 7597 7604 7612 7619 7627 7634 5.8 7634 7642 7649 7657 7664 7672 7679 7686 7694 7701 7709 5.9 7709 7716 7723 7731 7738 7745 7752 7760 7767 7774 7782 6.0 0.7782 7789 7796 7803 7810 7818 7825 7832 7839 7846 7853 6.1 7853 7860 7868 7875 7882 7889 7896 7903 7910 7917 7924 6.2 7924 7931 7938 7945 7952 7959 7966 7973 7980 7987 7993 6.3 7993 8000 8007 8014 8021 8028 8035 8041 8048 8055 8062 6.4 8062 8069 8075 8082 8089 8096 8102 8109 8116 8122 8129 6.5 8129 8136 8142 8149 8156 8162 8169 8176 8182 8189 8195 6.6 8195 8202 8209 8215 8222 8228 8235 8241 8248 8254 8261 6.7 8261 8267 8274 8280 8287 8293 8299 8306 8312 8319 8325 6.8 8325 8331 8338 8344 8351 8357 8363 8370 *8376 8382 8388 6.9 8388 8395 8401 8407 8414 8420 8426 8432 8439 8445 8451 7.0 0.8451 8457 8463 8470 8476 8482 8488 8494 8500 8506 8513 7.1 8513 8519 8525 8531 8537 8543 8549 8555 8561 8567 8573 7.2 8573 8579 8585 8591 8597 8603 8609 8615 8621 8627 8633 '7.3 8633 8639 8645 8651 8657 8663 8669 8675 8681 8686 8692 7.4 8692 8698 8704 8710 8716 8722 8727 8733 8739 8745 8751 7.5 8751 8756 8762 8768 8774 8779 8785 8791 8797 8802 8808 7.6 8808 8814 8820 8825 8831 8837 8842 8848 8854 8859 8865 7.7 8865 8871 8876 8882 8887 8893 8899 8904 8910 8915 8921 7.8 8921 8927 8932 8938 8943 8949 8954 8960 8965 8971 8976 7.9 8976 8982 8987 8993 8998 9004 9009 9015 9020 9025 9031 8.0 0.9031 9036 9042 9047 9053 9058 9063 9069 9074 9079 9085 8.1 9085 9090 9096 9101 9106 9112 9117 9122 9128 9133 9138 8.2 9138 9143 9149 9154 9159 9165 9170 9175 9180 9186 9191 8.3 9191 9196 9201 9206 9212 9217 9222 9227 9232 9238 9243 8.4 9243 9248 9253 9258 9263 9269 9274 9279 9284 9289 9294 8.5 9294 9299 9304 9309 9315 9320 9325 9330 9335 9340 9345 8.6 9345 9350 9355 9360 9365 9370 9375 9380 9385 9390 9395 8.7 9395 9400 9405 9410 9415 9420 9425 9430 9435 9440 9445 8.8 9445 9450 9455 9460 9465 9469 9474 9479 9484 9489 9494 8.9 9494 9499 9504 9509 9513 9518 9523 9528 9533 9538 9542 9.0 0.9542 9547 9552 9557 9562 9566 9571 9576 9581 9586 9590 9.1 9590 9595 9600 9605 9609 9614 9619 9624 9628 9633 9638 9.2 9638 9643 9647 9652 9657 9661 9666 9671 9675 9680 9685 9.3 9685 9689 9694 9699 9703 9708 9713 9717 9722 9727 9731 9.4 9731 9736 9741 9745 9750 9754 9759 9763 *768 9773 9777 9.5 9777 9782 9786 9791 9795 9800 9805 9809 9814 9818 9823 9.6 9823 9827 9832 9836 9841 9845 9850 9854 9859 9863 9868 9.7 9868 9872 9877 9881 9886 9890 9894 9899 9903 9908 9912 9.8 9912 9917 9921 9926 9930 9934 9939 9943 9948 9952 9956 9.9 9956 9961 9965 9969 9974 9978 9983 9987 9991 9996 Tenths of the abular Difference 2 3 4 5 2 3 3 4 2 3 3 4 2 2 3 4 2 2 3 4 2 2 3 4 2 2 3 4 2 2 3 4 2 2 3 4 12 3 4 12 3 4 12 3 4 12 3 4 12 3 3 12 3 3 12 3 3 12 3 3 12 3 3 12 3 3 12 3 3 12 3 3 12 2 3 12 2 3 12 2 3 12 2 3 12 2 3 12 2 3 12 2 3 12 2 3 12 2 3 12 2 3 12 2 3 12 2 3 12 2 3 12 2 3 12 2 3 12 2 3 1 2 '2 3 112 2 112 2 112 2 112 2 112 2 112 2 112 2 112 2 112 2 112 2 112 2 112 2 112 2 (17) > l #» ~3 >3 ^ /Tog sin & log cos\ BOSTON COLLEGE LIBRARY ioffcna'ioglffi^ HEX, MASl P o' , I' Log Sin * u u e j Log Cos r« 5 | JD © 11 (R ® 4 3 2 1 fO) Tenths of the Tabular Difference 1 2 3 4 o°.o o ■ 5 6 7 a St 12 3 4 5 -oo 4.2419 5429 7190 8439 9408 J 0200 0870 1450 1961 3.2419 89.9 0.1 3.2419 2833 3211 3558 3880 4180 4460 4723 4971 5206 5429 89.8 To avoid interpo- 0.2 5429 5641 5843 6036 6221 6398 6568 6732 6890 7043 7190 89.7 lation in the first c* 0.3 7190 7332 7470 7604 7734 7859 7982 8101 8217 8329 8439 89.6 eleven lines, usa | 0.4 8439 8547 8651 8753 8853 8951 9046 9140 9231 9321 3.9408 89.5 note.* 0.5 3.9408 9494 9579 9661 9743 9822 9901 9977 J 0053 0127 2.0200 89.4 0.6 2.0200 0272 0343 0412 0480 0548 0614 0679 0744 0807 0870 89.3 (Ordinary Inter- polation would not I s»5 0.7 0870 0931 0992 1052 1111 1169 1227 1284 1340 1395 1450 89.2 0.8 1450 1503 1557 1609 1661 1713 1764 1814 1863 1912 1961 89.1 be accurate in the C° 5 0.9 1961 2009 2056 2103 2150 2196 2241 2286 2331 2375 2.2419 89°.© first three lines.) r.o 2.2419 2462 2505 2547 2589 2630 2672 2712 2753 2793 2832 88.9 i.i 2832 2872 2911 2949 2988 3025 3063 3100 3137 3174 3210 88.8 4 8111519 1.2 3210 3246 3282 3317 3353 3388 3422 3456 3491 3524 3558 88.7 3 7 10 1417 1.3 3558 3591 3624 3657 3689 3722 3754 3786 3817 3848 3880 88.6 3 610 13 16 1.4 3880 3911 3941 3972 4002 4032 4062 4091 4121 4150 4179 88.5 3 6 9 12 15 1.5 4179 4208 4237 4265 4293 4322 4349 4377 4405 4432 4459 88.4 3 6 8 1114 1.6 4459 4486 4513 4540 4567 4593 4619 4645 4671 4697 4723 88.3 3 5 8 1113 K)<3 1.7 4723 4748 4773 4799 4824 4848 4873 4898 4922 4947 4971 88.2 2 5 710 12 1.8 4971 4995 5019 5043 5066 5090 5113 5136 5160 5183 5206 88.1 2 5 7 912 1.9 5206 5228 5251 5274 5296 5318 5340 5363 5385 5406 2.5428 gg .© 2 4 7 911 2°.0 2.5428 5450 5471 5493 5514 5535 5557 5578 5598 5619 5640 87.9 2 4 6 811 2.1 5640 5661 5681 5702 5722 5742 5762 5782 5802 5822 5842 87.8 2 4 6 810 2.2 5842 5862 5881 5901 5920 5939 5959 5978 5997 6016 6035 87.7 2 4 6 810 2.3 6035 6054 6072 6091 6110 6128 6147 6165 6183 6201 6220 87.6 2 4 6 7 9 2.4 6220 6238 6256 6274 6291 6309 6327 6344 6362 6379 6397 87.5 2 4 5 7 9 2.5 6397 6414 6431 6449 6466 6483 6500 6517 6534 6550 6567 87.4 2 3 5 7 9 2.6 6567 6584 6600 6617 6633 6650 6666 6682 6699 6715 6731 87.3 2 3 5 7 8 2.7 6731 6747 6763 6779 6795 6810 6826 6842 6858 6873 6889 87.2 2 3 5 6 8 2.8 6889 6904 6920 6935 6950 6965 6981 6996 7011 7026 7041 87.1 2 3 5 6 8 2.9 7041 7056 7071 7086 7100 7115 7130 7144 7159 7174 2.7188 87°.© 13 4 6 7 3°0 2.7188 7202 7217 7231 7245 7260 7274 7288 7302 7316 7330 86.9 13 4 6 7 3.1 7330 7344 7358 7372 7386 7400 7413 7427 7441 7454 7468 86.8 13 4 6 7 3.2 7468 7482 7495 7508 7522 7535 7549 7562 7575 7588 7602 86.7 13 4 5 7 3-3 7602 7615 7628 7641 7654 7667 7680 7693 7705 7718 7731 86.6 13 4 5 6 3.4 7731 7744 7756 7769 7782 7794 7807 7819 7832 7844 7857 86.5 13 4 5 6 3.5 7857 7869 7881 7894 7906 7918 7930 7943 7955 7967 7979 86.4 12 4 5 6 3.6 7979 7991 8003 8015 8027 8039 8051 8062 8074 8086 8098 86.3 12 4 5 6 3.7 8098 8109 8121 8133 8144 8156 8168 8179 8191 8202 8213 86.2 12 3 5 6 3.8 8213 8225 8236 8248 8259 8270 8281 8293 8304 8315 8326 86.1 12 3 5 6 3.9 8326 8337 8348 8359 8370 8381 8392 8403 8414 8425 2.8436 8(3°.© 12 3 4 5 4°.0 2.8436 8447 8457 8468 8479 8490 8500 8511 8522 8532 8543 85.9 12 3 4 5 4.1 8543 8553 8564 8575 8585 8595 8606 8616 8627 8637 8647 85.8 12 3 4 5 4.2 8647 8658 8668 8678 8688 8699 8709 8719 8729 8739 8749 85.7 12 3 4 5 4.3 8749 8759 8769 8780 8790 8799 8809 8819 8829 8839 8849 85.6 12 3 4 5 4.4 8849 8859 8869 8878 8888 8898 8908 8917 8927 8937 8946 85.5 12 3 4 5 4.5 8946 8956 8966 8975 8985 8994 9004 9013 9023 9032 9042 85.4 12 3 4 5 4.6 9042 9051 9060 9070 9079 9089 9098 9107 9116 9126 9135 85.3 12 3 4 5 4.7 9135 9144 9153 9162 9172 9181 9190 9199 9208 9217 9226 85.2 12 3 4 5 4.8 9226 9235 9244 9253 9262 9271 9280 9289 9298 9307 9315 85.1 12 3 4 4 4.9 9315 9324 9333 9342 9351 9359 9368 9377 9386 9394 2.9403 8S°.(Q 12 3 4 4 * When x is between 0° and l°.l . [See page 28] * When x is between 88°.9 and 90° iog sin * = log rad * (is) l°g cos * = lo S rad ( 90 ~ x * Log Sin 5°.0 5.1 5.2 5.3 5.4 5.5 5.6 5.7 5.8 5.9 6°0 6.1 6.2 6-3 6.4 8.5 8.6 8.7 8.8 8.9 9°0 9.1 9.2 9.3 9.4 9.5 9.6 9.7 9.8 9.9 2.9403 9412 9420 9429 9437 9446 9489 9497 9506 9514 9523 9531 9573 9581 9589 9598 9606 9614 9655 9664 9672 9680 9688 9696 9736 9744 9752 9760 9768 9776 9816 9824 9831 9839 9847 9855 9894 9901 9909 9917 9925 9932 2.9970 9978 9986 9993J0001 0008 1.0046 0053 0061 0068 0075 0083 0120 0127 0134 0142 0149 0156 1.0192 0200 0207 0214 0221 0228 0264 0271 0278 0285 0292 0299 0334 0341 0348 0355 0362 0369 0403 0410 0417 0424 0431 0438 0472 0478 0485 0492 0498 0505 6.5 0539 0545 0552 0558 0565 0572 6.6 0605 0611 0618 0624 0631 0637 6.7 0670 0676 0683 0689 0695 0702 6.8 0734 0740 0746 0753 0759 0765 6.9 0797 0803 0809 0816 0822 0828 7°.0 1.0859 0865 0871 0877 0884 0890 7.1 0920 0926 0932 0938 0945 0951 7.2 0981 0987 0993 0999 1005 1011 7.3 1040 1046 1052 1058 1064 1070 7.4 1099 1105 1111 1116 1122 1128 7.5 1157 1163 1168 1174 1180 1186 7.6 1214 1220 1226 1231 1237 1242 7.7 1271 1276 1282 1287 1293 1299 7.8 1326 1332 1337 1343 1348 1354 7.9 1381 1387 1392 1398 1403 1409 8°.0 1.1436 1441 1446 1452 1457 1462 8.1 1489 1494 1500 1505 1510 1516 8.2 1542 1547 1553 1558 1563 1568 8.3 1594 1600 1605 1610 1615 1620 8.4 1646 1651 1656 1661 1666 1672 1697 1702 1707 1712 1717 1722 1747 1752 1757 1762 1767 1772 1797 1802 1807 1812 1817 1822 1847 1851 1856 1861 1866 1871 1895 1900 1905 1910 191S 1919 1.1943 1948 1953 1958 1962 1967 1991 1996 2000 2005 2010 2015 2038 2043 2047 2052 2057 2061 2085 2089 2094 2098 2103 2108 2131 2135 2140 2144 2149 2153 2176 2181 2185 2190 2194 2199 2221 2226 2230 2235 2239 2243 2266 2270 2275 2279 2283 2288 2310 2314 2319 2323 2327 2332 2353 2358 2362 2367 2371 2375 9455 9463 9472 9480 2.9489 9539 9548 9556 9565 9573 9623 9631 9639 9647 9655 9704 9712 9720 9728 9736 9784 9792 9800 9808 9816 9863 9870 9878 9886 9894 9940 9948 9955 9963 2.9970 0016 0023 0031 0038 1.0046 0090 0098 0105 0112 0120 0163 0171 0178 0185 T.0192 0235 0243 0250 0257 0264 0306 0313 0320 0327 0334 0376 0383 0390 0397 0403 0444 0451 0458 0465 0472 0512 0519 0525 0532 0539 0578 0585 0591 0598 0605 0644 0650 0657 0663 0670 0708 0715 0721 0727 0734 0772 0778 0784 0790 0797 0834 0840 0847 0853 T.0859 0896 0902 0908 0914 0920 0957 0963 0969 0975 0981 1017 1022 1028 1034 1040 1076 1081 1087 1093 1099 1134 1140 1145 1151 1157 1191 1197 1203 1208 1214 1248 1254 1259 1265 1271 1304 1310 1315 1321 1326 1359 1365 1370 1376 1381 1414 1419 1425 1430 1.1436 1468 1473 1478 1484 1489 1521 1526 1532 1537 1542 1574 1579 1584 1589 1594 1625 1631 1636 1641 1646 1677 1682 1687 1692 1697 1727 1732 1737 1742 1747 1777 1782 1787 1792 1797 1827 1832 1837 1842 1847 1876 1881 1886 1890 1895 1924 1929 1934 1939 T.1943 1972 1977 1981 1986 1991 2019 2024 2029 2033 2038 2066 2071 2075 2080 2085 2112 2117 2121 2126 2131 2158 2162 2167 2172 2176 2203 2208 2212 2217 2221 2248 2252 2257 2261 2266 2292 2297 2301 2305 2310 2336 2340 2345 2349 2353 2379 2384 2388 2392 1.2397 84.9 84.8 84.7 84.6 84.5 84.4 84.3 84.2 84.1 M°.d 83.9 83.8 83.7 83.6 83.5 83.4 83.3 83.2 83.1 82.9 82.8 82.7 82.6 82.5 82.4 82.3 82.2 82.1 82°.0 81.9 81.8 81.7 81.6 81.5 81.4 81.3 81.2 81.1 ll°.C 80.9 80.8 80.7 80.6 80.5 80.4 80.3 80.2 80.1 Tenths of the Tabular Difference 12 3 4 5 12 3 3 4 12 3 3 4 12 2 3 4 12 2 3 4 12 2 3 4 12 2 3 4 12 2 3 4 12 2 3 4 112 3 4 112 3 4 112 3 4 112 3 4 112 3 3 112 3 3 112 3 3 112 3 3 112 3 3 112 3 3 112 3 3 112 2 3 112 2 3 112 2 3 112 2 3 112 2 3 112 2 3 112 2 3 112 2 3 112 2 3 112 2 3 112 2 3 112 2 3 112 2 3 112 2 3 112 2 3 112 2 3 112 2 3 112 2 112 2 112 2 112 2 112 2 112 2 112 2 112 2 112 2 112 2 112 2 112 2 112 2 112 2 ai (Xi •J ^ M 1* (19) IP** /r log sin & log cos\ /log tan & log ctn\ \ ...LOG / s Log Sin hog Cos ,0 L .© .1 .2 .7 3 4 .5 .4 .6 .7 .8 .! .9 ~ B §>©° - 00 0° — oo 3.2419 5429 7190 8439 9408 J 0200 0870 1450 1961 2.2419 89 1 2.2419 2832 3210 3558 3880 4179 4459 4723 4971 5206 5428 88 2 5428 5640 5842 6035 6220 6397 6567 6731 6889 7041 7188 87 3 7188 7330 7468 7602 7731 7857 7979 8098 8213 8326 8436 86 4 8436 8543 8647 8749 8849 8946 9042 9135 9226 9315 2.9403 85 5 2.9403 9489 9573 9655 9736 9816 9894 9970 J 0046 0120 1.0192 84 6 1.0192 0264 0334 0403 0472 0539 0605 0670 0734 0797 0859 83 7 0859 0920 0981 1040 1099 1157 1214 1271 1326 1381 1436 82 8 1436 1489 1542 1594 1646 1697 1747 1797 1847 1895 1943 81 9 1943 1991 2038 2085 2131 2176 2221 2266 2310 2353 1.2397 g(0>° 10° 1.2397 2439 2482 2524 2565 2606 2647 2687 2727 2767 2806 79 11 2806 2845 2883 2921 2959 2997 3034 3070 3107 3143 3179 78 12 3179 3214 3250 3284 3319 3353 3387 3421 3455 3488 3521 77 13 3521 3554 3586 3618 3650 3682 3713 3745 3775 3806 3837 76 14 3837 3867 3897 3927 3957 3986 4015 4044 4073 4102 4130 75 15 4130 4158 4186 4214 4242 4269 4296 4323 4350 4377 4403 74 16 4403 4430 4456 4482 4508 4533 4559 4584 4609 4634 4659 73 17 4659 4684 4709 4733 4757 4781 4805 4829 4853 4876 4900 72 18 4900 4923 4946 4969 4992 5015 5037 5060 5082 5104 5126 71 19 5126 5148 5170 5192 5213 5235 5256 5278 5299 5320 1.5341 70° 20° T.5341 5361 5382 5402 5423 5443 5463 5484 5504 5523 5543 69 21 5543 5563 5583 5602 5621 5641 5660 5679 5698 5717 5736 68 22 5736 5754 5773 5792 5810 5828 5847 5865 5883 5901 5919 67 23 5919 5937 5954 5972 5990 6007 6024 6042 6059 6076 6093 66 24 6093 6110 6127 6144 6161 6177 6194 6210 6227 6243 6259 65 25 6259 6276 6292 6308 6324 6340 6356 6371 6387 6403 6418 64 26 6418 6434 6449 6465 6480 6495 6510 6526 6541 6556 6570 63 27 6570 6585 6600 6615 6629 6644 6659 6673 6687 6702 6716 62 28 6716 6730 6744 6759 6773 6787 6801 6814 6828 6842 6856 61 29 6856 6869 6883 6896 6910 6923 6937 6950 6963 6977 1.6990 ° 30° 1.6990 7003 7016 7029 7042 7055 7068 7080 7093 7106 7118 59 31 7118 7131 7144 7156 7168 7181 7193 7205 7218 7230 7242 58 32 7242 7254 7266 7278 7290 7302 7314 7326 7338 7349 7361 57 33 7361 7373 7384 7396 7407 7419 7430 7442 7453 7464 7476 56 34 7476 7487 7498 7509 7520 7531 7542 7553 7564 7575 7586 55 35 7586 7597 7607 7618 7629 7640 7650 7661 7671 7682 7692 54 36 7692 7703 7713 7723 7734 7744 7754 7764 7774 7785 7795 53 37 7795 7805 7815 7825 7835 7844 7854 7864 7874 7884 7893 52 38 7893 7903 7913 7922 7932 7941 7951 7960 7970 7979 7989 51 39 7989 7998 8007 8017 8026 8035 8044 8053 8063 8072 1.8081 so° 40° 1.8081 8090 8099 8108 8117 8125 8134 8143 8152 8161 8169 49 41 8169 8178 8187 8195 8204 8213 8221 8230 8238 8247 8255 48 42 8255 8264 8272 8280 8289 8297 8305 8313 8322 8330 8338 47 43 8338 8346 8354 8362 8370 8378 8386 8394 8402 8410 8418 46 44 8418 8426 8433 8441 8449 8457 8464 8472 8480 8487 1.8495 45° 45° 1.8495 Tenths of the Tabular Difference 12 3 4 5 To avoid interpo- lation in the first ten lines, use the special table on the preceding page. (Ordinary inter- polation would not be accurate in the first three lines.) 4 8 12 16 20 4 7 11 15 19 3 710 1417 3 6 9 13 16 3 6 9 12 15 3 5 8 1114 3 5 8 1013 2 5 710 12 2 5 7 911 2 4 6 911 2 4 6 8 10 2 4 6 810 2 4 5 7 9 2 3 5 7 9 2 3 5 7 8 2 3 5 6 8 2 3 5 6 8 13 4 6 7 13 4 6 7 13 4 5 7 13 4 5 6 12 4 5 6 12 4 5 6 12 3 5 6 12 3 4 6 12 3 4 5 12 3 4 5 12 3 4 5 12 3 4 5 12 3 4 5 12 3 4 4 12 3 3 4 12 2 3 4 12 2 3 4 12 2 3 4 (20) Log Sin Log Cos 45° 46 47 48 49 50° 51 52 53 54 55 56 57 58 59 60° 61 62 63 64 65 66 67 68 69 70° 71 72 73 74 75 76 77 78 79 80° 81 82 83 84 85 86 87 88 89 90° 1.8495 8502 8510 8517 8525 8532 8569 8577 8584 8591 8598 8606 8641 8648 8655 8662 8669 8676 8711 8718 8724 8731 8738 8745 8778 8784 8791 8797 8804 8810 1.8843 8849 8855 8862 8868 8874 8905 8911 8917 8923 8929 8935 8965 8971 8977 8983 8989 8995 9023 9029 9035 9041 9046 9052 9080 9085 9091 9096 9101 9107 9134 9139 9144 9149 9155 9160 9186 9191 9196 9201 9206 9211 9236 9241 9246 9251 9255 9260 9284 9289 9294 9298 9303 9308 9331 9335 9340 9344 9349 9353 1.9375 9380 9384 9388 9393 9397 9418 9422 9427 9431 9435 9439 9459 9463 9467 9471 9475 9479 9499 9503 9506 9510 9514 9518 9537 9540 9544 9548 9551 9555 9573 9576 9580 9583 9587 9590 9607 9611 9614 9617 9621 9624 9640 9643 9647 9650 9653 9656 9672 9675 9678 9681 9684 9687 9702 9704 9707 9710 9713 9716 1.9730 9733 9735 9738 9741 9743 9757 9759 9762 9764 9767 9770 9782 9785 9787 9789 9792 9794 9806 9808 9811 9813 9815 9817 9828 9831 9833 9835 9837 9839 9849 9851 9853 9855 9857 9859 9869 9871 9873 9875 9876 9878 9887 9889 9891 9892 9894 9896 9904 9906 9907 9909 9910 9912 9919 9921 9922 9924 9925 9927 1.9934 9935 9936 9937 9939 9940 9946 9947 9949 9950 9951 9952 9958 9959 9960 9961 9962 9963 9968 9968 9969 9970 9971 9972 9976 9977 9978 9978 9979 9980 9983 9984 9985 9985 9986 9987 9989 9990 9990 9991 9991 9992 9994 9994 9995 9995 9996 9996 9997 9998 9998 9998 9998 9999 T.9999 9999J0000 0000 0000 0000 0.0000 8540 8547 8555 8562 8569 8613 8620 8627 8634 8641 8683 8690 8697 8704 8711 8751 8758 8765 8771 8778 8817 8823 8830 8836 1.8843 8880 8887 8893 8899 8905 8941 8947 8953 8959 8965 9000 9006 9012 9018 9023 9057 9063 9069 9074 9080 9112 9118 9123 9128 9134 9165 9170 9175 9181 9186 9216 9221 9226 9231 9236 9265 9270 9275 9279 9284 9312 9317 9322 9326 9331 9358 9362 9367 9371 T.9375 9401 9406 9410 9414 9418 9443 9447 9451 9455 9459 9483 9487 9491 9495 9499 9522 9525 9529 9533 9537 9558 9562 9566 9569 9573 9594 9597 9601 9604 9607 9627 9631 9634 9637 9640 9659 9662 9666 9669 9672 9690 9693 9696 9699 9702 9719 9722 9724 9727 1.9730 9746 9749 9751 9754 9757 9772 9775 9777 9780 9782 9797 9799 9801 9804 9806 9820 9822 9824 9826 9828 9841 9843 9845 9847 9849 9861 9863 9865 9867 9869 9880 9882 9884 9885 9887 9897 9899 9901 9902 9904 9913 9915 9916 9918 9919 9928 9929 9931 9932 1.9934 9941 9943 9944 9945 9946 9953 9954 9955 9956 9958 9964 9965 9966 9967 9968 9973 9974 9975 9975 9976 9981 9981 9982 9983 9983 9987 9988 9988 9989 9989 9992 9993 9993 9994 9994 9996 9996 9997 9997 9997 9999 9999 9999 9999 1-9999 0000 0000 0000 0000 0.0000 (21) 44 .43 42 41 4© c 39 38 37 36 35 34 33 32 31 3(0)° 29 28 27 26 25 24 23 22 21 2©° 19 18 17 16 15. 14 13 12 11 a©° 9 8 7 6 5 4 3 2 1 Tenths of the abular Difference 2 3 4 5 12 3 4 12 3 4 12 3 3 12 3 3 12 3 3 12 2 3 12 2 3 12 2 3 12 2 3 12 2 3 12 2 3 12 2 3 112 2 112 2 112 2 112 2 112 2 112 2 112 2 1112 1112 1112 1112 111 111 111 111 11 11 11 11 1 1 11 1 1 1 pa Q 2 I8K w t* v /log tana log ctn\ p 4 Log Tan Log C©tai o°.o 1 2 _%_ ® B ,4, g a 6*' 7 " 8~ ! © Tenths of the Tabular Difference 12 3 4 5 3 4 5* ~9 ' a f - °° 5.2419 5429 7190 8439 9408 J 0200 0870 1450 1961 3.2419 89.9 To avoid interpo- lation In the first eleven lines, use note.* 0.1 3.2419 2833 3211 3558 3880 4180 4460 4723 4972 5206 5429 89.8 0.2 5429 5641 5843 6036 6221 6398 6569 6732 6890 7043 7190 89.7 0.3 7190 7332 7470 7604 7734 7860 7982 8101 8217 8329 8439 89.6 0.4 8439 8547 8651 8754 8853 8951 9046 9140 9231 9321 3.9409 89.5 0.5 3.9409 9495 9579 9662 9743 9823 9901 9978J0053 0127 2.0200 89.4 0.6 0.7 2.0200 0870 0272 0932 0343 0992 0412 0481 1052 1111 0548 1170 0614 0680 0744 1227 1284 1340 0807 0870 1395 1450 89.3 89.2 (Ordinary inter- polation would not be accurate in the first three lines.) 0.8 0.9 1450 1962 1504 2010 1557 2057 1610 1662 2104 2150 1713 2196 1764 1814 1864 2242 2287 2331 1913 1962 2376 2.2419 89.1 gg)°.© 1°.0 2.2419 2462 2505 2548 2590 2631 2672 2713 2754 2794 2833 88.9 1.1 2833 2873 2912 2950 2988 3026 3064 3101 3138 3175 3211 88.8 4 8 11 15 19 1.2 3211 3247 3283 3318 3354 3389 3423 3458 3492 3525 3559 88.7 3 710 1417 1.3 3559 3592 3625 3658 3691 3723 3755 3787 3818 3850 3881 88.6 3 6 10 13 16 1.4 3881 3912 3943 3973 4003 4033 4063 4093 4122 4152 4181 88.5 3 6 9 12 15 1.5 4181 4210 4238 4267 4295 4323 4351 4379 4406 4434 4461 88.4 3 6 8 1114 1.6 4461 4488 4515 4542 4568 4595 4621 4647 4673 4699 4725 88.3 3 5 8 11 13 1.7 4725 4750 4775 4801 4826 4851 4875 4900 4924 4949 4973 88.2 2 5 710 12 1.8 4973 4997 5021 5045 5068 5092 5115 5139 5162 5185 5208 88.1 2 5 7 912 1.9 5208 5231 5253 5276 5298 5321 5343 5365 5387 5409 2.5431 m°m 2 4 7 911 2°.0 2.5431 5453 5474 5496 5517 5538 5559 5580 5601 5622 5643 87.9 2 4 6 811 2.1 5643 5664 5684 5705 5725 5745 5765 5785 5805 5825 5845 87.8 2 4 6 810 2.2 5845 5*865 5884 5904 5923 5943 5962 5981 6000 6019 6038 87.7 2 4 6 810 2.3 6038 6057 6076 6095 6113 6132 6150 6169 6187 6205 6223 87.6 2 4 6 7 9 2.4 6223 6242 6260 6277 6295 6313 6331 6348 6366 6384 6401 87.5 2 4 5 7 9 2.5 6401 6418 6436 6453 6470 6487 6504 6521 6538 6555 6571 87.4 2 3 5 7 9 2.6 6571 6588 6605 6621 6638 6654 6671 6687 6703 6719 6736 87.3 2 3 5 7 8 2.7 6736 6752 6768 6784 6800 6815 6831 6847 6863 6878 6894 87.2 2 3 5 6 8 2.8 6894 6909 6925 6940 6956 6971 6986 7001 7016 7031 7046 87.1 2 3 5 6 8 2.9 7046 7061 7076 7091 7106 7121 7136 7150 7165 7179 2.7194 87°.© 13 4 6 7 3°0 2-7194 7208 7223 7237 7252 7266 7280 7294 7308 7323 7337 86.9 13 4 6 7 3.1 7337 7351 7365 7379 7392 7406 7420 7434 7448 7461 7475 86.8 13 4 6 7 3.2 7475 7488 7502 7515 7529 7542 7556 7569 7582 7596 7609 86.7 13 4 5 7 3.3 7609 7622 7635 7648 7661 7674 7687 7700 7713 7726 7739 86.6 13 4 5 6 3.4 7739 7751 7764 7777 7790 7802 7815 7827 7840 7852 7865 86.5 13 4 5 6 3.5 7865 7877 7890 7902 7914 7927 7939 7951 7963 7975 7988 86.4 12 4 5 6 3.6 7988 8000 8012 8024 8036 8048 8059 8071 8083 8095 8107 86.3 12 4 5 6 3.7 8107 8119 8130 8142 8154 8165 8177 8188 8200 8212 8223 86.2 12 3 5 6 3.8 8223 8234 8246 8257 8269 8280 8291 8302 8314 8325 8336 86.1 12 3 5 6 3.9 8336 8347 8358 8370 8381 8392 8403 8414 8425 8436 2.8446 8S°.(D) 12 3 4 6 4°.0 2.8446 8457 8468 8479 8490 8501 8511 8522 8533 8543 8554 85.9 12 3 4 5 4.1 8554 8565 8575 8586 8596 8607 8617 8628 8638 8649 8659 85.8 12 3 4 5 4.2 8659 8669 8680 8690 8700 8711 8721 8731 8741 8751 8762 85.7 12 3 4 5 4.3 8762 8772 8782 8792 8802 8812 8822 8832 8842 8852 8862 85.6 12 3 4 5 4.4 8862 8872 8882 8891 8901 8911 8921 8931 8940 8950 8960 85.5 12 3 4 5 4.5 8960 8970 8979 8989 8998 9008 9018 9027 9037 9046 9056 85.4 12 3 4 5 4.6 9056 9065 9075 9084 9093 9103 9112 9122 9131 9140 9150 85.3 12 3 4 5 4.7 9150 9159 9168 9177 9186 9196 9205 9214 9223 9232 9241 85.2 12 3 4 5 4.8 9241 9250 9260 9269 9278 9287 9296 9305 9313 9322 9331 85.1 12 3 4 4 4.9 9331 9340 9349 9358 9367 9376 9384 9393 9402 9411 2.9420 @S°.(D 12 3 4 4 * When x is between 0° and l°.l log tan x = log rad x [See page 28] (22) .. * When x is between 88°.9 and 90° log ctn x — log rad (90°— x) Log Tan Log Coft&n 5°.0 g) _jr 1 hog Coftam 0*' ' ^ 5 .0 i .® -?a ^ 1 2 a M 4 5 .4 .6 .7 "T" J B ~ .9 1 90° Tenths of the Tabular Difference 12 3 4 5 — 00 c4V 0° 1 — 00 2.2419 3.2419 5429 2833 3211 7190 3559 8439 3881 9409 4181 J 0200 4461 0870 4725 1450 4973 1962 2.2419 5208 5431 89 88 To avoid interpo- lation in the first ten lines use the special table on tbe preceding page. 2 5431 5643 5845 6038 6223 6401 6571 6736 6894 7046 7194 87 3 7194 7337 7475 7609 7739 7865 7988 8107 8223 8336 8446 86 4 8446 8554 8659 8762 8862 8960 9056 9150 9241 9331 2.9420 85 5 2.9420 9506 9591 9674 9756 9836 9915 9992 J 0068 0143 1.0216 ; 84 (Ordinary inter- 6 1.0216 0289 0360 0430 0499 0567 0633 0699 0764 0828 0891 83 polation would not s»5 7 0891 0954 1015 1076 1135 1194 1252 1310 1367 1423 1478 82 be accurate in the 8 1478 1533 1587 1640 1693 1745 1797 1848 1898 1948 1997 81 first three lines.) 9 1997 2046 2094 2142 2189 2236 2282 2328 2374 2419 T.2463 80° r ~ 10° 1.2463 2507 2551 2594 2637 2680 2722 2764 2805 2846 2887 79 4 8 13 17 21 11 2887 2927 2967 3006 3046 3085 3123 3162 3200 3237 3275 78 4 8 12 16 19 12 3275 3312 3349 3385 3422 3458 3493 3529 3564 3599 3634 77 4 7111418 13 3634 3668 3702 3736 3770 3804 3837 3870 3903 3935 3968 76 3 710 13 17 14 3968 4000 4032 4064 4095 4127 4158 4189 4220 4250 4281 75 3 6 9 13 16 15 4281 4311 4341 4371 4400 4430 4459 4488 4517 4546 4575 74 3 6 9 1215 16 4575 4603 4632 4660 4688 4716 4744 4771 4799 4826 4853 73 3 6 8 1114 J,0 6 17 4853 4880 4907 4934 4961 4987 5014 5040 5066 5092 5118 72 3 5 8 1113 18 5118 5143 5169 5195 5220 5245 5270 5295 5320 5345 5370 71 3 5 8 10 13 19 5370 5394 5419 5443 5467 5491 5516 5539 5563 5587 1.5611 70° 2 5 710 12 s' 11 $* 20° 1.5611 5634 5658 5681 5704 5727 5750 5773 5796 5819 5842 69 2 5 710 12 21 5842 5864 5887 5909 5932 5954 5976 5998 6020 6042 6064 68 2 4 7 911 22 6064 6086 6108 6129 6151 6172 6194 6215 6236 6257 6279 67 2 4 6 911 23 6279 6300 6321 6341 6362 6383 6404 6424 6445 6465 6486 66 2 4 6 810 24 6486 6506 6527 6547 6567 6587 6607 6627 6647 6667 6687 65 2 4 6 810 25 6687 6706 6726 6746 6765 6785 6804 6824 6843 6863 6882 64 2 4 6 810 26 6882 6901 6920 6939 6958 6977 6996 7015 7034 7053 7072 63 2 4 6 8 9 27 7072 7090 7109 7128 7146 7165 7183 7202 7220 7238 7257 62 2 4 6 7 9 28 7257 7275 7293 7311 7330 7348 7366 7384 7402 7420 7438 61 2 4 5 7 9 29 7438 7455 7473 7491 7509 7526 7544 7562 7579 7597 1.7614 (SO 2 4 5 7 9 30° 1.7614 7632 7649 7667 7684 7701 7719 7736 7753 7771 7788 59 2 3 5 7 9 31 7788 7805 7822 7839 7856 7873 7890 7907 7924 7941 7958 58 2 3 5 7 9 32 7958 7975 7992 8008 8025 8042 8059 8075 8092 8109 8125 57 2 3 5 7 8 33 8125 8142 8158 8175 8191 8208 8224 8241 8257 8274 8290 56 2 3 5 7 8 34 8290 8306 8323 8339 8355 8371 8388 8404 8420 8436 8452 55 2 3 5 6 8 \ 35 8452 8468 8484 8501 8517 8533 8549 8565 8581 8597 8613 54 2 3 5 6 8 36 8613 8629 8644 8660 8676 8692 8708 8724 8740 8755 8771 53 2 3 5 6 8 37 8771 8787 8803 8818 8834 8850 8865 8881 8897 8912 8928 52 2 3 5 6 8 38 8928 8944 8959 8975 8990 9006 9022 9037 9053 9068 9084 51 2 3 5 6 8 39 9084 9099 9115 9130 9146 9161 9176 9192 9207 9223 1.9238 50° 2 3 5 6 8 40° 1.9238 9254 9269 9284 9300 9315 9330 9346 9361 9376 9392 49 2 3 5 6 8 41 9392 9407 9422 9438 9453 9468 9483 9499 9514 9529 9544 48 2 3 5 6 8 42 9544 9560 9575 9590 9605 9621 9636 9651 9666 9681 9697 47 2 3 5 6 8 43 9697 9712 9727 9742 9757 9772 9788 9803 9818 9833 1.9848 46 2 3 5 6 8 44 T.9848 9864 9879 9894 9909 9924 9939 9955 9970 9985J0.0000 4S° 2 3 5 6 8 45° 0.0000 (24) Log Tan Log Coftami JQ L * .$ .1 3 A 5 .4 .6 ~!*~ 1 M 45° 1 2 0.0000 45° 0.0000 0015 0030 0045 0061 0076 0091 0106 0121 0136 0152 44 46 0152 0167 0182 0197 0212 0228 0243 0258 0273 0288 0303 43 47 0303 0319 0334 0349 0364 0379 0395 0410 0425 0440 0456 42 48 0456 0471 0486 0501 0517 0532 0547 0562 0578 0593 0608 41 49 0608 0624 0639 0654 0670 0685 0700 0716 0731 0746 0.0762 4€)° 50° 0.0762 0777 0793 0808 0824 0839 0854 0870 0885 0901 0916 39 51 0916 0932 0947 0963 0978 0994 1010 1025 1041 1056 1072 38 52 1072 1088 1103 1119 1135 1150 1166 1182 1197 1213 1229 37 53 1229 1245 1260 1276 1292 1308 1324 1340 1356 1371 1387 36 54 1387 1403 1419 1435 1451 1467 1483 1499 1516 1532 1548 35 55 1548 1564 1580 1596 1612 1629 1645 1661 1677 1694 1710 34 56 1710 1726 1743 1759 1776 1792 1809 1825 1842 1858 1875 33 57 1875 1891 1908 1925 1941 1958 1975 1992 2008 2025 2042 32 58 2042 2059 2076 2093 2110 2127 2144 2161 2178 2195 2212 31 59 2212 2229 2247 2264 2281 2299 2316 2333 2351 2368 0.2386 3©° 60° 0.2386 2403 2421 2438 2456 2474 2491 2509 2527 2545 2562 29 61 2562 2580 2598 2616 2634 2652 2670 2689 2707 2725 2743 28 62 2743 2762 2780 2798 2817 2835 2854 2872 2891 2910 2928 27 63 2928 2947 2966 2985 3004 3023 3042 3061 3080 3099 3118 26 64 3118 3137 3157 3176 3196 3215 3235 3254 3274 3294 3313 25 65 3313 3333 3353 3373 3393 3413 3433 3453 3473 3494 3514 24 66 3514 3535 3555 3576 3596 3617 3638 3659 3679 3700 3721 23 67 3721 3743 3764 3785 3806 3828 3849 3871 3892 3914 3936 22 68 3936 3958 3980 4002 4024 4046 4068 4091 4113 4136 4158 21 69 4158 4181 4204 4227 4250 4273 4296 4319 4342 4366 0.4389 20° 70° 0.4389 4413 4437 4461 4484 4509 4533 4557 4581 4606 4630 19 71 4630 4655 4680 4705 4730 4755 4780 4805 4831 4857 4882 18 72 4882 4908 4934 4960 4986 5013 5039 5066 5093 5120 5147 17 73 5147 5174 5201 5229 5256 5284 5312 5340 5368 5397 5425 16 74 5425 5454 5483 5512 5541 5570 5600 5629 5659 5689 5719 15 75 5719 5750 5780 5811 5842 5873 5905 5936 5968 6000 6032 14 76 6032 6065 6097 6130 6163 6196 6230 6264 6298 6332 6366 13 77 6366 6401 6436 6471 6507 6542 6578 6615 6651 0688 6725 12 78 6725 6763 6800 6838 6877 6915 6954 6994 7033 7073 7113 11 79 7113 7154 7195 7236 7278 7320 7363 7406 7449 7493 0.7537 10° 80° 0.7537 7581 7626 7672 7718 7764 7811 7858 7906 7954 8003 9 81 8003 8052 8102 8152 8203 8255 8307 8360 8413 8467 8522 8 82 8522 8577 8633 8690 8748 8806 8865 8924 8985 9046 9109 7 83 9109 9172 9236 9301 9367 9433 9501 9570 9640 9711 0.9784 6 84 0.9784 9857 9932J0008 0085 0164 0244 0326 0409 0494 1.0580 5 85 1.0580 0669 0759 0850 0944 1040 1138 1238 1341 1446 1554 4 86 1554 1664 1777 1893 2012 2135 2261 2391 2525 2663 2806 3 87 2806 2954 3106 3264 3429 3599 3777 3962 4155 4357 4569 2 88 4569 4792 5027 5275 5539 5819 6119 6441 6789 7167 1.7581 1 89 1.7581 8038 8550 9130 9800J 2.0591 1561 2810 4571 7581 00 0° 90° oo (25) Tenths of the Tabular Difference 12 3 4 5 2 3 5 6 8 2 3 5 6 8 2 3 5 6 8 2 3 5 6 8 2 3 5 6 8 2 3 5 6 8 2 3 5 6 8 2 3 5 6 8 2 3 5 6 8 2 3 5 6 8 2 3 5 6 8 2 3 5 7 8 2 3 5 7 8 2 3 5 7 9 2 3 5 7 9 2 4 5 7 9 2 4 5 7 9 2 4 6 7 9 2 4 6 8 9 2 4 6 810 2 4 6 810 2 4 6 810 2 4 6 911 2 4 7 911 2 5 710 12 2 5 710 12 3 5 8 10 13 3 5 8 11 13 3 6 8 11 14 3 6 9 12 15 3 6 9 13 16 3 710 13 17 4 7 11 14 18 4 8 12 16 19 4 8 13 17 21 To avoid interpo- lation in the last ten lines, use the special table on the (Ordinary inter- polation would not be accurate in the last three lines.) a* &3 O w -J o o en 3 |o 12 4 5 6 %$L 13 4 5 6 &>3 13 4 5 6 13 4 5 7 i-4 13 4 6 7 m 4 13 4 6 7 13 4 2 3 5 6 6 7 8 -3 *• 2 3 5 6 8 O 2 2 3 5 7 8 53 &3 2 3 5 7 9 H» 2 4 5 7 9 CO rf 2 4 6 7 9 3 a 2 4 6 810 2 4 6 810 2 4 6 2 4 7 8 11 911 2 5 7 912 2 5 71012 3 5 81113 3 6 81114 3 6 912 15 3 6 10 13 16 3 710 1417 4 81115 19 To avoid interpo- lation in the last eleven lines, USB note.* M 1* These two pages give the common logarithms of " rad x " for angles x between 1° and 10°. Moving the decimal point n places to the right (or left) in the angle is equivalent to adding n (or — n) to the logarithm. Thus, log rad 0°.0002778 = 2.6856 — 4 = 0.6856 — 6. The abbreviation rad x means the radian measure of x, or the ratio of arc to radius. ,& When x is between 0° and l°.l When x is between 88°.9 and 90° For angles x log sin x = log rad x log cos x = log rad (90° — x°) near 0° or 90° : — log tan x = log rad x log ctn x = log rad (90° — x°) log ctn x — — log rad x log tan x = — log rad (90° — x°) Log Rad r.o 1 2 3 4 5 6 7 8 9 10 j 2.2419 2462 2505 2547 2589 2631 2672 2713 2753 2793 2.2833 .i 2833 2872 2911 2950 2988 3026 3063 3101 3138 3174 3211 .2 3211 3247 3282 3318 3353 3388 3422 3457 3491 3525 3558 .3 3558 3591 3625 3657 3690 3722 3754 3786 3818 3849 3880 .4 3880 3911 3942 3972 4002 4032 4062 4092 4121 4151 4180 1°.5 2.4180 4209 4237 4266 4294 4322 4350 4378 4405 4433 2.4460 •6 4460 4487 4514 4541 4567 4594 4620 4646 4672 4698 4723 .7 4723 4749 4774 4799 4824 4849 4874 4899 4923 4947 4971 .8 4971 4996 5019 5043 5067 5090 5114 5137 5160 5183 5206 •9 5206 5229 5252 5274 5297 5319 5341 5363 5385 5407 5429 2°.0 2.5429 5451 5472 5494 5515 5536 5557 5578 5599 5620 2.5641 .1 5641 5662 5682 5703 5723 5743 5763 5783 5803 5823 5843 .2 5843 5863 5882 5902 5921 5941 5960 5979 5998 6017 6036 .3 6036 6055 6074 6092 6111 6129 6148 6166 6185 6203 6221 .4 6221 6239 6257 6275 6293 6310 6328 6346 6363 6381 6398 2°. 5 2.6398 6416 6433 6450 6467 6484 6501 6518 6535 6552 2.6569 .6 6569 6585 6602 6618 6635 6651 6668 6684 6700 6716 6732 .7 6732 6748 6764 6780 6796 6812 6828 6844 6859 6875 6890 .8 6890 6906 6921 6937 6952 6967 6982 6998 7013 7028 7043 .9 7043 7058 7073 7087 7102 7117 7132 7146 7161 7175 7190 3°.0 2.7190 7204 7219 7233 7248 7262 7276 7290 7304 7318 2.7332 .1 7332 7346 7360 7374 7388 7402 7416 7429 7443 7457 7470 .2 7470 7484 7497 7511 7524 7538 7551 7564 7578 7591 7604 .3 7604 7617 7630 7643 7656 7669 7682 7695 7708 7721 7734 .4 7734 7746 7759 7772 7784 7797 7810 7822 7835 7847 7859 3°.5 2.7859 7872 7884 7897 7909 7921 7933 7945 7958 7970 2.7982 .6 7982 7994 8006 8018 8030 8042 8054 8065 8077 8089 8101 .7 8101 8113 8124 8136 8147 8159 8171 8182 8194 8205 8217 .8 8217 8228 8239 8251 8262 8273 8285 8296 8307 8318 8329 .9 8329 8341 8352 8363 8374 8385 8396 8407 8418 8429 8439 4°.0 2.8439 8450 8461 8472 8483 8493 8504 8515 8525 8536 2.8547 .1 8547 8557 8568 8578 8589 8599 8610 8620 8631 8641 8651 .2 8651 8662 8672 8682 8692 8703 8713 8723 8733 8743 8753 .3 8753 8764 8774 8784 8794 8804 8814 8824 8834 8843 8853 .4 8853 8863 8873 8883 8893 8902 8912 8922 8932 8941 8951 4° .5 2.8951 8961 8970 8980 8989 8999 9008 9018 9027 9037 2.9046 .6 9046 9056 9065 9075 9084 9093 9103 9112 9121 9131 9140 .7 9140 9149 9158 9167 9177 9186 9195 9204 9213 9222 9231 8 9231 9240 9249 9258 9267 9276 9285 9294 9303 9312 9321 .9 9321 9330 9338 9347 9356 9365 9374 9382 9391 9400 9408 Tenths of the Tabular Difference 12 3 4 5 4 8 12 17 21 4 8 11 15 19 3 710 14 17 3 6 10 13 16 3 6 9 12 15 3 6 8 1114 3 5 8 1113 2 5 7 1012 2 5 7 9 12 2 4 7 911 2 4 6 811 2 4 6 810 2 4 6 8 10 2 4 6 7 9 2 4 5 7 9 2 3 5 7 9 2 3 5 7 8 2 3 5 6 8 2 3 5 6 8 13 4 6 7 13 4 6 7 13 4 6 7 13 4 5 7 13 4 5 6 13 4 5 6 12 4 5 6 12 4 5 6 12 3 5 6 12 3 5 6 12 3 4 5 12 3 4 5 12 3 4 5 12 3 4 5 12 3 4 5 12 3 4 5 12 3 4 5 12 3 4 5 12 3 4 5 12 3 4 4 12 3 4 4 Note; log rad x log (number of degrees in x) + 0.2419 (28) Log Rad 5°.0 1 2 3 4 5 6 7 8 9 10 2.9408 9417 9426 9434 9443 9452 9460 9469 9477 9486 2.9494 .1 9494 9503 9511 9520 9528 9537 9545 9554 9562 9570 9579 .2 9579 9587 9595 9604 9612 9620 9629 9637 9645 9653 9662 .3 9662 9670 9678 9686 9694 9702 9710 9719 9727 9735 9743 A 9743 9751 9759 9767 9775 9783 9791 9799 9807 9814 9822 5°.5 2.9822 9830 9838 9846 9854 9862 9870 9877 9885 9893 9901 .6 9901 9908 9916 9924 9932 9939 9947 9955 9962 9970 2.9978 .7 29978 9985 9993 J 0000 0008 0015 0023 0031 0038 0046 1.0053 .8 1.0053 0061 0068 0075 0083 0090 0098 0105 0113 0120 0127 .9 0127 0135 0142 0149 0157 0164 0171 0179 0186 0193 0200 6°.0 1.0200 0208 0215 0222 0229 0236 0244 0251 0258 0265 1.0272 .1 0272 0279 0286 0293 0300 0308 0315 0322 0329 0336 0343 .2 0343 0350 0357 0364 0371 0378 0385 0391 0398 0405 0412 .3 0412 0419 0426 0433 0440 0447 0453 0460 0467 0474 0481 .4 0481 0487 0494 0501 0508 0514 0521 0528 0535 0541 0548 6°.5 1.0548 0555 0561 0568 0575 0581 0588 0594 0601 0608 1.0614 .6 0614 0621 0627 0634 0640 0647 0654 0660 0667 0673 0680 .7 0680 0686 0692 0699 0705 0712 0718 0725 0731 0737 0744 .8 0744 0750 0757 0763 0769 0776 0782 0788 0795 0801 0807 .9 0807 0814 0820 0826 0832 0839 0845 0851 0857 0864 0870 7°.0 1.0870 0876 0882 0888 0895 0901 0907 0913 0919 0925 1.0931 .1 0931 0937 0944 0950 0956 0962 0968 0974 0980 0986 0992 .2 0992 0998 1004 1010 1016 1022 1028 1034 1040 1046 1052 .3 1052 1058 1064 1070 1076 1082 1088 1093 1099 1105 1111 .4 1111 1117 1123 1129 1135 1140 1146 1152 1158 1164 1169 7°. 5 1.1169 1175 1181 1187 1192 1198 1204 1210 1215 1221 1.1227 .6 1227 1233 1238 1244 1250 1255 1261 1267 1272 1278 1284 .7 1284 1289 1295 1301 1306 1312 1317 1323 1329 1334 1340 .8 1340 1345 1351 1356 1362 1367 1373 1379 1384 1390 1395 .9 1395 1401 1406 1412 1417 1422 1428 1433 1439 1444 1450 8°.0 1.1450 1455 1461 1466 1471 1477 1482 1488 1493 1498 1.1504 .1 1504 1509 1514 1520 1525 1530 1536 1541 1546 1552 1557 .2 1557 1562 1567 1573 1578 1583 1589 1594 1599 1604 1610 .3 1610 1615 1620 1625 1630 1636 1641 1646 1651 1656 1662 .4 1662 1667 1672 1677 1682 1687 1692 1698 1703 1708 1713 8°.5 1.1713 1718 1723 1728 1733 1738 1744 1749 1754 1759 1.1764 .6 1764 1769 1774 1779 1784 1789 1794 1799 1804 1809 1814 .7 1814 1819 1824 1829 1834 1839 1844 1849 1854 1859 1864 .8 1864 1869 1873 1878 1883 1888 1893 1898 1903 1908 1913 .9 1913 1918 1922 1927 1932 1937 1942 1947 1952 1956 1961 9°.0 1.1961 1966 1971 1976 1980 1985 1990 1995 2000 2004 1.2009 .1 2009 2014 2019 2023 2028 2033 2038 2042 2047 2052 2057 .2 2057 2061 2066 2071 2075 2080 2085 2090 2094 2099 2104 .3 2104 2108 2113 2118 2122 2127 2132 2136 2141 2145 2150 .4 2150 2155 2159 2164 2168 2173 2178 2182 2187 2191 2196 9°.5 1.2196 2201 2205 2210 2214 2219 2223 2228 2232 2237 1.2241 .6 2241 2246 2251 2255 2260 2264 2269 2273 2278 2282 2286 .7 2286 2291 2295 2300 2304 2309 2313 2318 2322 2327 2331 .8 2331 2335 2340 2344 2349 2353 2358 2362 2366 2371 2375 .9 2375 2380 2384 2388 2393 2397 2401 2406 2410 2414 2419 Tenths of the abular Difference 2 3 4 5 2 3 3 4 2 3 3 4 2 2 3 4 2 2 3 4 2 2 3 4 2 2 3 4 2 2 3 4 2 2 3 4 12 3 4 12 34 12 3 4 12 3 4 12 3 3 12 3 3 12 3 3 12 3 3 12 3 3 12 3 3 12 3 3 12 2 3 12 2 3 12 2 3 12 2 3 12 2 3 12 2 3 12 2 3 12 2 3 12 2 3 12 2 3 12 2 3 12 2 3 12 2 3 12 2 3 12 2 3 12 2 3 12 2 3 12 2 3 112 2 112 2 112 2 112 2 112 2 112 2 112 2 112 2 112 2 112 2 112 2 112 2 112 2 a& ►J O O CO w r*« (29) , Exponentials ft* in s! 0° s in j K *a n YA <* 1 o< eft* l4 d n 0.00 .01 .02 .03 .04 0.05 .06 .07 .08 .09 0.10 .11 .12 .13 .14 0.15 .16 .17 .18 .19 0.20 .21 .22 .23 .24 0.25 .26 .27 .28 .29 0.30 .31 .32 .33 .34 0.35 .36 .37 .38 .39 0.40 .41 .42 .43 .44 0.45 .46 .47 .48 .49 0.50 1.000 1.010 1.020 1.030 1.041 1.051 1.062 1.073 1.083 1.094 1.105 1.116 1.127 1.139 1.150 1.162 1.174 1.185 1.197 1.209 1.221 1.234 1.246 1.259 1.271 1.284 1.297 1.310 1.323 1.336 1.350 1.363 1.377 1.391 1.405 1.419 1.433 1.448 1.462 1.477 1.492 1.507 1.522 1.537 1.553 1.568 1.584 1.600 1.616 1.632 1.649 0.50 .51 .52 .53 .54 0.55 .56 .57 .58 .59 0.60 .61 .62 .63 .64 0.65 .66 .67 .68 .69 0.70 .71 .72 .73 .74 0.75 .76 .77 .78 .79 0.80 .81 .82 .83 .84 0.85 .86 .87 .88 .89 0.90 .91 .92 .93 .94 0.95 .96 .97 .98 .99 1.00 1.649 1.665 1.682 1.699 1.716 1.733 1.751 1.768 1.786 1.804 1.822 1.840 1.859 1.878 1.896 1.916 1.935 1.954 1.974 1.994 2.014 2.034 2.054 2.075 2.096 2.117 2.138 2.160 2.181 2.203 2.226 2.248 2.270 2.293 2.316 2.340 2.363 2.387 2.411 2.435 2.460 2.484 2.509 2.535 2.560 2.586 2.612 2.638 2.664 2.691 2.718 16 17 17 17 17 18 17 18 18 18 18 19 19 18 20 19 19 20 20 20 20 20 21 21 21 21 22 21 22 23 22 22 23 23 24 23 24 24 24 25 24 25 26 25 26 26 26 26 27 27 n 1.0 .1 .2 .3 .4 1.5 .6 .7 .8 .9 2.0 .1 .2 .3 .4 2, 3 3, 3 4 4, 4 5, 6 6. 7, 8, 9, 9, 11, 2.5 12 .6 13, .7 14 .8 16 .9 18 3.0 20 .1 22, .2 24 .3 27 .4 29 3.5 33 .6 36 .7 40 .8 44 .9 49 4.0 54 .1 60 4.5 90 718* ,004 320 669 ,055 482 953 474 050 686 389 166 025 974 02 18 46 88 .44 17 ,09 20 ,53 11 96 12 60 45 70 40 60 34 69 70 45 02 148.4 403.4 1097. 2981. 8103. 22026. 4.810 23.14 111.3 535.5 2576. 12392. 59610. 5. 6. 7. 8. 9. 10. 7r/2 2tt/2 3tt/2 4tt/2 Stz/2 6tt/2 7tt/2 8tt/2 286751. n 0.00 .01 .02 .03 .04 0.05 .06 .07 .08 .09 0.10 .11 .12 .13 .14 0.15 .16 .17 .18 .19 0.20 .21 .22 .23 .24 0.25 .26 .27 .28 .29 0.30 .31 .32 .33 .34 0.35 .36 .37 .38 .39 0.40 .41 .42 .43 .44 0.45 .46 .47 .48 .49 0.50 „— n Sfc 1.000 0.990 ,-10 .980 .-10 .970 .-10 .961 -9 .951 .942 .932 .923 .914 .905 .896 .887 .878 .869 .861 .852 .844 .835 .827 .819 .811 .803 .795 .787 .779 .771 .763 .756 .748 .741 .733 .726 .719 .712 .705 .698 .691 .684 .677 .670 .664 .657 .651 .644 .638 .631 .625 .619 .613 0.607 -10 -9 .-10 -9 -9 -9 -9 -9 -9 -9 -8 -9 -9 -8 -7 -7 -7 -7 -7 -7 -7 -7 -6 -7 -6 -6 -6 n 0.50 .51 .52 .53 .54 0.55 .56 .57 .58 .59 0.60 .61 .62 .63 .64 0.65 .66 .67 .68 .69 0.70 .71 .72 .73 .74 0.75 .76 .77 .78 .79 0.80 .81 .82 .83 .84 0.85 .86 .87 .88 .89 0.90 .91 .92 .93 .94 0.95 .96 .97 .98 .99 1.00 .607 .600 .595 .589 .583 .577 .571 .566 .560 .554 .549 .543 .538 .533 .527 .522 .517 .512 .507 .502 .497 .492 .487 .482 .477 .472 .468 .463 .458 .454 .449 .445 .440 .436 .432 .427 .423 .419 .415 .411 .407 .403 .399 .395 .391 .387 .383 .379 .375 .372 .368 -7 -5 -6 -6 -6 -6 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -4 -5 -5 -4 -5 -4 -5 -4 -4 -5 -4 -4 -4 -4 -4 -4 -4 -4 -4 -4 -4 -4 -3 -4 n 1.0 .368* .1 .333 .2 .301 .3 .273 .4 .247 1.5 .223 .6 .202 .7 .183 .8 .165 .9 .150 2.0 .135 .1 .122 .2 .111 .3 .100 .4 .0907 2.5 .0821 .6 .0743 .7 .0672 .8 .0608 .9 .0550 3.0 .0498 .1 .0450 .2 .0408 .3 .0369 .4 .0334 3.5 .0302 .6 .0273 .7 .0247 .8 .0224 .9 .0202 4.0 .0183 .1 .0166 .2 .0150 .3 .0136 .4 .0123 4.5 .0111 5. .00674 6. .00248 7. .000912 8. .000335 9. .000123 10. .000045 tt/2 .208 2tt/2 .0432 3tt/2 .00898 4tt/2 .00187 5tt/2 .000388 67T/2 .000081 7tt/2 .000017 87T/2 .000003 * Note : Do not interpolate in third and sixth columns. e=2.71828 l/e=0.367879 log Io e=0.4343 sinhx=i(e*-e-*) cosh x=i{e'+e~ x ) log IO (0.4343)= 1.6378 (30) l/(0.4343)=2.3026 log IO (e w )=n(0.4343) Moving the decimal point & places to the right (or left) in the number is equivalent to adding fc times 2.30259 (or — h, times 2.30259) to the logarithm. k log e (10k) 5 6 7 8 9 11.51293 13.81551 16.11810 18.42068 20.72327 1 2 3 4 2.30259 4.60517 6.90776 9.21034 Log e (Base e= =2.71828+) Tenths of the 1 2 3 4 5 6 7 8 9 10 Tabular Difference .i 12 3 4 5 -2.303 - -2.207 - 2.120 -: 2.040- 1.966 - -1.897 - -1.833 -1.772 -1.715 -1.661 - -1.609 2 96—52 .2 -1.609 • -1.561 - 1.514 - 1.470 - 1.427 • -1.386 - -1.347 -1.309 -1.273 -1.238 • -1.204 £ 48—34 .3 -1.204 - -1.171 - L.139 - L.109 -: L.079 - -1.050 - -1.022 -0.994 -0.968 -0.942 • -0.916 £ 33—26 .4 -.9163 -.8916 - -.8675 - -.8440- -.8210 -.7985 -.7765 -.7550 -.7340 -.7133 -.6931 ig 247—202 .5 -.6931 -.6733 - -.6539 - -.6349 - -.6162 -.5978 -.5798 -.5621 -.5447 -.5276 -.5108 2 198—168 .6 -.5108 -.4943 - -.4780 - -.4620 - -.4463 -.4308 -.4155 -.4005 -.3857 -.3711 -.3567 ^o 165—144 .7 -.3567 -.3425 - -.3285 - -.3147 - -.3011 -.2877 _.2744 -.2614 -.2485 -.2357 -.2231 & 142-126 .8 -.2231 -.2107 - -.1985 - -.1863 - -.1744 -.1625 -.1508 -.1393 -.1278 -.1165 -.1054 9 124—111 .9 -.10536 -.09431 -.08338 -.07257 -.06188 -.05129 -.04082-.03046-.02020-.01005 .00000 g 1105—1005 1.00 .00000 .00100 .00200 .00300 .00399 .00499 .00598 .00698 .00797 .00896 .00995 10 20 30 40 50 1.01 .00995 .01094 .01193 .01292 .01390 .01489 .01587 .01686 .01784 .01882 .01980 10 20 30 39 49 1.02 .01980 .02078 .02176 .02274 .02372 .02469 .02567 .02664 .02762 .02859 .02956 10 20 29 39 49 1.03 .02956 .03053 .03150 .03247 .03343 .03440 .03537 .03633 .03730 .03826 .03922 10 19 29 39 48 1.04 .03922 .04018 .04114 .04210 .04306 .04402 .04497 .04593 .04688 .04784 .04879 10 19 29 38 48 1.05 .04879 .04974 .05069 .05164 .05259 .05354 .05449 .05543 .05638 .05733 .05827 9 19 28 38 47 1.06 .05827 .05921 .06015 .06110 .06204 .06297 .06391 .06485 .06579 .06672 .06766 9 19 28 38 47 1.07 .06766 .06859 .06953 .07046 .07139 .07232 .07325 .07418 .07511 .07603 .07696 9 19 28 37 47 1.08 .07696 .07789 .07881 .07973 .08066 .08158 .08250 .08342 .08434 .08526 .08618 9 18 28 37 46 1.09 .08618 .08709 .08801 .08893 .08984 .09075 .09167 .09258 .09349 .09440 .09531 9 18 27 37 46 1.1 .0953 .1044 .1133 .1222 .1310 .1398 .1398 .1484 .1570 .1655 .1740 .1823 9 18 27 36 44 9 17 26 34 43 1.2 .1823 .1906 .1989 .2070 .2151 .2231 .2231 .2311 .2390 .2469 .2546 .2624 8 16 24 33 41 8 16 24 31 39 1.3 .2624 .2700 .2776 .2852 .2927 .3001 .3075 .3148 .3221 .3293 .3365 7 15 22 30 37 1.4 .3365 .3436 .3507 .3577 .3646 .3716 .3784 .3853 .3920 .3988 .4055 7 14 21 28 34 1.5 .4055 .4121 .4187 .4253 .4318 .4383 .4447 .4511 .4574 .4637 .4700 6 13 19 26 32 1.6 .4700 .4762 .4824 .4886 .4947 .5008 .5068 .5128 .5188 .5247 .5306 6 12 18 24 30 1.7 .5306 .5365 .5423 .5481 .5539 .5596 .5653 .5710 .5766 .5822 .5878 6 11 17 23 29 1.8 .5878 .5933 .5988 .6043 .6098 .6152 .6206 .6259 .6313 .6366 .6419 5 11 16 22 27 1.9 .6419 .6471 .6523 .6575 .6627 .6678 .6729 .6780 .6831 .6881 .6931 5 10 15 21 26 2.0 .6931 .6981 .7031 .7080 .7129 .7178 .7227 .7275 .7324 .7372 .7419 5 10 15 20 24 2.1 .7419 .7467 .7514 .7561 .7608 .7655 .7701 .7747 .7793 .7839 .7885 5 9 14 19 23 2.2 .7885 .7930 .7975 .8020 .8065 .8109 .8154 .8198 .8242 .8286 .8329 4 9 13 18 22 2.3 .8329 .8372 .8416 .8459 .8502 .8544 .8587 .8629 .8671 .8713 .8755 4 9 13 17 21 2.4 .8755 .8796 .8838 .8879 .8920 .8961 .9002 .9042 .9083 .9123 .9163 4 8 12 16 20 2.5 .9163 .9203 .9243 .9282 .9322 .9361 .9400 .9439 .9478 .9517 .9555 4 8 12 16 20 2.6 .9555 .9594 0.9632 0.9670 0.9708 0.9746 0.9783 0.9821 0.9858 0.9895 0.9933 4 8 11 15 19 2.7 0.9933 0.9969 1.0006 1.0043 1.0080 1.0116 1.0152 1.0188 1.0225 1.0260 1.0296 4 7 11 15 18 2.8 1.0296 1.0332 1.0367 1.0403 1.0438 1.0473 1.0508 1.0543 1.0578 1.0613 1.0647 4 7 11 14 18 2.9 1.0647 1.0682 1.0716 1.0750 1.0784 1.0818 1.0852 1.0886 1.0919 1.0953 1.0986 3 7 10 14 17 3. 1.099 1.131 1.163 1.194 1.224 1.253 1.253 1.281 1.308 1.335 1.361 1.386 3 6 9 12 15 3 5 8 11 13 4. 1.386 1.411 1.435 1.459 1.482 1.504 1.504 1.526 1.548 1.569 1.589 1.609 2 5 7 9 12 2 4 6 8 11 5. 1.609 1.629 1.649 1.668 1.686 1.705 1.723 1.740 1.758 1.775 1.792 2 4 5 7 9 6. 1.792 1.808 1.825 1.841 1.856 1.872 1.887 1.902 1.917 1.932 1.946 2 3 5 6 8 7. 1.946 1.960 1.974 1.988 2.001 2.015 2.028 2.041 2.054 2.067 2.079 13 4 5 7 8. 2.079 2.092 2.104 2.116 2.128 2.140 2.152 2.163 2.175 2.186 2.197 12 4 5 6 9. 2.197 2.208 2.219 2.230 2.241 2.251 2.262 2.272 2.282 2.293 2.303 12 3 4 5 3d tf> &3 jj 8U O O 2 log e 10=2.3025851 log e x= (2.3026) log IO x (31) log IO e=0.4342944S log IO *=(0.4343)log e x w I Radians From Radians into Degrees 7 8 9 10° 1 2 3 4 15 6 7 8 9 20° 1 2 3 4 25 6 7 8 9 30° 1 2 3 4 35 6 7 8 9 40° 1 2 3 4 45 6 7 8 9 .0000 .0175 .0349 .0524 .0698 .0873 6 .1047 .1222 .1396 .1571 .1745 .1920 .2094 .2269 .2443 .2618 .2793 .2967 .3142 .3316 .3491 .3665 .3840 .4014 .4189 .4363 .4538 .4712 .4887 .5061 .5236 .5411 .5585 .5760 .5934 .6109 .6283 .6458 .6632 .6807 .6981 .7156 .7330 .7505 .7679 .7854 .8029 .8203 .8378 .8552 50° .8727 50° 1 2 3 4 55 6 7 8 9 60° 1 2 3 4 65 6 7 8 9 70° 1 2 3 4 75 6 7 8 9 80° 1 2 3 4 85 6 7 8 9 90° 1 2 3 4 95 6 7 8 9 100° 0.8727 .8901 .9076 .9250 .9425 .9599 .9774 0.9948 1.0123 1.0297 1.0472 1.0647 1.0821 1.0996 1.1170 1.1345 1.1519 1.1694 1.1868 1.2043 1.2217 1.2392 1.2566 1.2741 1.2915 1.3090 1.3265 1.3439 1.3614 1.3788 1.3963 1.4137 1.4312 1.4486 1.4661 1.4835 1.5010 1.5184 1.5359 1.5533 1.5708 1.5882 1.6057 1.6232 1.6406 1.6581 1.6755 1.6930 1.7104 1.7279 1.7453 0°.l .0017 .2 .0035 .3 .0052 .4 .0070 .5 .0087 .6 .0105 .7 .0122 .8 .0140 .9 .0157 0°.01 .0002 .02 .0003 .03 .0005 .04 .0007 .05 .0009 .06 .0010 .07 .0012 .08 .0014 .09 .0016 30° 0.5236= n/6 45° 0.7854= 7r/4 60° 1.0472= tc/3 90° 100 110 120° 130 135° 140 150° 160 170 180° 190 200 210° 220 225° 230 240° 250 260 270° 280 290 300° 310 315° 320 330° 340 350 360° 1.5708 1.7453 1.9199 2.0944 2.2689 2.3562 2.4435 2.6180 2.7925 2.9671 3.1416 3.3161 3.4907 3.6652 3.8397 3.9270 4.0143 4.1888 4.3633 4.5379 4.7124 4.8869 5.0615 5.2360 5.4105 5.4978 5.5851 5.7596 5.9341 6.1087 6.2832 tt/2 2tt/3 3tt/4 57T/6 77T/6 57T/4 4tt/3 = 3tt/2 : 5tt/3 = 77T/4 :ll7T/6 = 2tt Multiples of 360° or 27T radians 360° 720° 1080° 1440° 1800° 2160° 2520° 8 2880° 9 3240° 10 3600° 6.28319 12.56637 18.84956 25.13274 31.41593 37.69911 43.98230 50.26548 56.54867 62.83185 1 radian = 180°/7T = 57°.29578 l°=7r/180 = 0.0174533 radians. log (x in radians) = log (x in degrees) + 0.2419 — 2 0.00 .01 .02 .03 .04 0.05 .06 .07 .08 .09 0.10 .11 .12 .13 .14 0.15 .16 .17 .18 .19 0.20 .21 .22 .23 .24 0.25 .26 .27 .28 .29 0.30 .31 .32 .33 .34 0.35 .36 .37 .38 .39 0.40 .41 .42 .43 .44 0.45 .46 .47 .48 .49 0.50 o°.oo 0°.57 1°.15 1°.72 2°.29 2°. 86 3°.44 4°.01 4°.58 5°. 16 5°.73 6°.30 6°. 88 7°.45 8°.02 8°.59 9°. 17 9°.74 10°. 31 10°. 89 11°.46 12°.03 12°.61 13°.18 13°.75 14°.32 14°.90 15°.47 16°.04 16°.62 17°. 19 17°.76 18°.33 18°.91 19°.48 20°.05 20°. 63 21°.20 21°.77 22°.35 22°.92 23°.49 24°.06 24°.64 25°.21 25°.78 26°.35 26°. 93 27°.50 28°.07 28°.65 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 57°.30 114°.59 171°. 89 229°. 18 286°.48 343°.77 401°.07 458°.37 515°.66 572°.96 0.001 .002 .003 .004 .005 .006 .007 .008 .009 0°.06 °.ll °.17 °.23 °.29 °.34 °.40 °.46 °.52 0.50 .51 .52 .53 .54 0.55 .56 .57 .58 .59 0.60 .61 .62 .63 .64 0.65 .66 .67 .68 .69 0.70 .71 .72 .73 .74 0.75 .76 .77 .78 .79 0.80 .81 .82 .83 .84 0.85 .86 .87 .88 .89 0.90 .91 .92 .93 .94 0.95 .96 .97 .98 .99 1.00 28°.65 29°.22 29°.79 30°.37 30°.94 31°.51 32°.09 32°.66 33°.23 33°.80 34°.38 34°.95 35°.52 36°. 10 36°.67 37°.24 37°.82 38°.39 38°.96 39°.53 40°. 11 40°.68 41°.25 41°. 83 42°.40 42°.97 43°. 5 4 44°. 12 44°. 69 45°.26 45°. 84 46°. 41 46°.98 47°. 5 6 48°. 13 48°.70 49°.27 49°. 85 50°.42 50°.99 51°.57 52°. 14 5 2°. 70 53°.29 53°.86 5 4°. 43 55°.00 55°.58 56°.15 56°.72 57°.30 0.0001 .0002 .0003 .0004 .0005 .0006 .0007 .0008 .0009 °.01 °.01 °.02 °.02 °.03 °.03 °.04 °.05 °.05 1.00 .01 .02 .03 .04 1.05 .06 .07 .08 .09 1.10 .11 .12 .13 .14 1.15 .16 .17 .18 .19 1.20 .21 .22 .23 .24 1.25 .26 .27 .28 .29 1.30 .31 .32 .33 .34 1.35 .36 .37 .38 .39 1.40 .41 .42 .43 .44 1.45 .46 .47 .48 .49 1.50 .51 .52 .53 .54 1.55 .56 1.57 1.5708 90° 3.1416 180° 4.7124 270° 6.2832 360 c log (x in degrees)=log {x in radians) +1.7581 (32) Conden sed T able of Tngoi lometnc J -•unctions Constants rad ^ sin tan sec vers covers esc ctn cos ir=3.14159265 ■ ia e=2.71828183 ^^^^^™ 0.0000 0° 0.0000 0.0000 1.000 0.0000 1.000 oo oo 1.000 9©° 1.571 1 mile=5280 ft. oH5 .0175 1 .0175 .0175 1.000 .0002 0.983 57.30* 57.29* 1.000 89 1.553 ^ i .0349 2 .0349 .0349 1.001 .0006 .965 28.65* 28.64* 0.999 88 1.536 30 mi. per hr. ~~ m .0524 3 .0523 .0524 1.001 .0014 .948 19.11* 19.08* .999 87 1.518 =44 ft. per sec. o =| .0698 4 0.0873 5° .0698 0.0872 .0699 0.0875 1.002 .0024 1.004 0.0038 .930 14.34* 0.913 11.47* 14.30* .998 11.43* 0.996 86 1.501 85° 1.484 1 nautical mile =6080.3 ft. iy =~ t| ^==5 c .1047 6 .1045 .1051 1.006 .0055 .895 9.57* 9.51* .995 84 1.466 =1.1516 mi. 'id 1 .1222 7 .1219 .1228 1.008 .0075 .878 8.21* 8.14* .993 83 1.449 CJ — t-H .1396 8 .1392 .1405 1.010 .0097 .861 7.19* 7.12* .990 82 1.431 1 rod=16J ft. en j II t-i .1571 9 .1564 .1584 1.012 .0123 .844 6.39* 6.31* .988 81 1.414 r\Ji^ ™ " m a-. o 0.1745 10° .1920 11 .2094 12 0.1736 .1908 .2079 0.1763 .1944 .2126 1.015 0.0152 1.019 .0184 1.022 .0219 0.826 5.76* .809 5.24 .792 4.81 5.67* 0.985 5.14 .982 4.70 .978 80° 1.396 79 1.379 78 1.361 1 acre =160 sq. rods =43560 sq. ft. 1X3 u H .2269 13 .2250 .2309 1-026 .0256 .775 4.45 4.33 .974 77 1.344 1 sq. mile / =640 acres to .2443 14 .2419 .2493 1.031 .0297 .758 4.13 4.01 .970 76 1.326 T 0.262 15° 0.259 0.268 1.035 0.0341 0.741 3.86 3.73 0.966 75° 1.309 t-H || .279 16 .276 .287 1.040 .0387 .724 3.63 3.49 .961 74 1.292 1 bushel (U. S.) ' H .297 17 .292 .306 1.046 .0437 .708 3.42 3.27 .956 73 1.274 =2150.42 cu. in. .314 18 .309 .325 1.051 .0489 .691 3.24 3.08 .951 72 1.257 1 gallon (U. S.) =231 cu. in. f .332 19 .326 .344 1.058 .0545 .674 3.07 2.90 .946 71 1.239 > .419 24 0.436 25° .407 0.423 .445 0.466 1.095 .0865 1.103 0.0937 .593 2.46 0.577 2.37 2.25 .914 2.14 0.906 66 1.152 65° 1.134 a! £ .454 26 .438 .488 1.113 .1012 .562 2.28 2.050 .899 64 1.117 £. .471 27 .454 .510 1.122 .1090 .546 2.20 1.963 .891 63 1.100 mercury=13.6 .489 28 .469 .532 1.133 .1171 .531 2.13 1.881 .883 62 1.082 1 £ s 13 .506 29 .485 .554 1.143 .1254 .515 2.06 1.804 .875 61 1.065 1 cu. ft. of water a! 0.524 30° 0.500 0.577 1.155 0.1340 0.500 2.00 1.732 0.866 (B©° 1.047 weighs 62.4 lbs. 1 cu. ft. dry air (32° F„ 30 in.) weighs .0807 lbs. S to .541 31 .515 .601 1.167 .1428 .485 1.942 1.664 .857 59 1.030 g .559 32 .530 .625 1.179 .1520 .470 1.887 1.600 .848 58 1.012 "S P. .576 33 .545 .649 1.192 .1613 .4o5 i.836 1.540 .839 57 0.995 .593 34 .559 .675 1.206 .1710 .441 1.788 1.483 .829 56 .977 c 0.611 35° 0.574 0.700 1.221 0.1808 0.426 1.743 1.428 0.819 55° 0.960 Veloc. of sound .628 36 .646 37 .588 .602 .727 .754 1.236 .1910 1.252 .2014 .412 1.701 .398 1.662 1.376 .809 1.327 .799 54 .942 53 .925 in air =1090 ft./sec. B. .663 38 .616 .781 1.269 .2120 .384 1.624 1.280 .788 52 .908 Veloc. of li°"ht C .681 39 .629 .810 1.287 .2229 .371 1.589 1.235 .777 51 .890 in vacuum= 0.698 40° 0.643 0.839 1.305 0.234 0.357 1.556 1.192 0.766 50° 0.873 186 000 mi./sec. i .716 41 .656 .869 1.325 .245 .344 1.524 1.150 .755 49 .855 1 .733 42 .669 .900 1.346 .257 .331 1.494 1.111 .743 48 .838 Earth's radii : .750 43 .682 .933 1.367 .269 .318 1.466 1.072 .731 47 .820 3963mi.,3950mi. .768 44 .695 0.966 1.390 .281 .305 1.440 1.036 .719 46 .803 Earth's density (water=l)=5.5 Diameter of 0.785 45° 0.707 1.000 1.414 0.293 0.293 1.414 1.000 0.707 45° 0.785 C©S eta csc covers veirs sec tela snira M md fc=3 Sun, 866 000 mi., Moon, 2163 mi. 1 meter=39.37 in. =3.2808 ft. I inch=2.5400 cm. 1 ft.=0.3048 m. 1 kilometer=0.62137 mi. L mile=1.60935 kilometers Mass 1 hectare=10000 sq. meters=2.471 acres L acre=0.4047 hectares (Earth=l): Sun, 334 000; 1 cu. meter=1.3079 cu. yds L cu. yd.=0.76456 cu. meters 1 liter=1000 cu. cm.=0.2642 gal. (U. S.) 1 gallon (U. S.) =3.785 liters Moon, 0.0123 1 kg.=2.2046 lbs. 1 gm .=15.432 grains L lb.=0.4536 kg 1 erain=0.0648 gm. 1 kg./sq. cm.=14.22 lbs./sq. in.= 0.968 atmos L lb./sq. in.=0.0703 kg./sq. cm.=0.680 atm ds Distance of (1 atmo=1.033 kg./sq. cm. =760 mm. of Hg) 1 atmo=14.70 lbs./sq. in.=29.92 in. of Hg ) Sun, 1 kilogram meter=7.233 ft. lbs. L ft. lb. =0.1383 kilogram meters 93 000 000 mi., 1 kilowatt=1.341 horse-power L H. P.=550 ft. Ibs7sec.=746 watts Moon, SM 81 cm./sec. z = =977.99+5.22 sin 2 flat.) 7=322 ft./sec. 2 =32.087+0J71 sin 2 (lat.) 240 000 mi. 1$