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i XII 3-39 XIII 3 j j TABLE VIIL-NATURAL TRIGONOMETRICAL FUNCTIONS. TABLE IX.-CALCULATION OF EARTHWORK. 3 d` 4 e_f Angle Sine. Tan. Cots. Cosin. Angle Sine. Tan. Cots. Cosies. HF,IGHT d� .d Of Of 1 2 8 4 b i y 8 1 9 10 11 12 13 14 15 32 .5289 .6249 1.600 .81806 58 30 .6225 .7954 1.257 .78261 30 1 .02 .04 .06 .07 .09 11 .I3 .15 .17 .18 .20 .22 .24 .26 28 10 .5324 .6289 1.590 .84660 50 40 AM .800E 1.250 .78079 20 2 ..04 .07 .11 .15 .18 .22 .26 .30 .33 .37 .41 .44 .48. .52 .56 20 .5346 .6330 1.580 .84M5 40 50 .6271 :8060 1.242 .77897 10 3 .06 .11 .17 :22 ,28 .33 .39 .44 .50 .56 .61 .67 .72 .78 .83 30 .5373 .8371 1.570 .84339 30 f 4 .07 .15 .22 .30 .37 .14 .52 .59 .67 .74 .81 89 .96 1.04 1.11 40 .6396 .6412 1.560 .84182 20 39 .6293 .8088 1.235 .77715 51 b .09 .19 .28 .37 .46 .56 .65 .74 .83 .93 1.02 L 11 1.20 1.30 . 50 Mn. .6153 1.550 .84025 10 10 .6316 .8146 1.228 .77531 50 1.39 20 .6338 .8195 1.220 .77347 40 8 .11 .22 .33 .44 .56 .67 .78 .89 1.00 1.11 1.22 1.33 1.44 1.55 1.67 33 5446 .6494 1.540 .83887 57 30 .6361 .82{3 1.213 .77162 10 .5471 .6638 1.530 :83708 50 40 .&983 AM 1.206 .70977 20 � .13 .26 •39 •52 .65 .78 .91 1.04 1.16 1.30 1.42 L 55 1.68 1.81 1.94 20 .5495 .6677 1.520 .83549 40 50 .6406 .8342 1.199 .76791 10 .15 .30 .44 3.59 .74 .89 1.64 1.19 1.33 1.48 1.63 L78 1.92 2.08 2.22 30 .5519 .8619 1.511 .83389 30 8 .17 33 .50 .67 .83 1:00 1.17 1.33 1.50 1.67 1.83 2.00 2.17 2.33 2.50 9 10 .18 .37 ..56 .74 .93 1.11 1.38 1.48 1.67 1.85 2.04 2.22 2.41 2.59 2.78 40 .5514 .6661 1.501 .83228 20 40 .6428 .8391 1.192 .?6604 b0 , 50 .5568 .6703 1.492 .89066 10 10 .6460 .8441 1.185 .76417 50 11 .20 .41 .61 .82 1.02 1.22 1,43 1.63 1.832.04 2.24 2.44 2:65 2.85 3.06 20 .6472 .8491 1.178 .76229 40 1$ :-22 22 .44 .67 .a9 1.11 1.33 1.86 1.78 2.00 2.22 2.44 167 2.89 3.11 3.33 34 .5592 .6745 1.483 .8M be 30 .6494 .8541 1,171 .76041 30 4$ !8 .72 ,96 1.10 1.44 1.61 1.92 2.16 2.41 2.65 188 3.13. 3.37 3.61 w' 10 .5616 .6787 1.473 .82941 50 40 .6517 .8591 1.164 .7586I 20 .52 .78 1.01 1.30 1.55 1.81 2.06 2.33 2.59 2.85 3.11 3.37 •3.63 20 .5840 .8630 1.464 .82577 40 50 .� .8842 1.157 .75661 10 lb .28 .56 .83 1.11 1.39 1.67 1.94 2.22 2.50 2.78 3.06 3.33 3.61 3.89 4.17 30 .5664 .6873 1.455 .82413 30 40 ..5688 :6016 1446 .82248 ZO 41 .6561 .8693 1.150 .75471 49 16 .30 .59 .89-1.18 1.48 178 2.07 2.37.2.67 2.96 3.26 3.56 3.86 4.15 4.44 50 .5712 .6959 1.437 .82082 10 10 .6583 .8744 1.144 .75280 50 17 .31 .63 .94 1.26 1.57 1.88 2.20 2.52 2.83 3:15 3.46 3.78 4.09 4.41 4.72 20 .66041 .8796 1.137' .75088 40 11 18 .33 .67 1.00 1.33 1.67 2.00 2.33 2.67 3.00 333 3.67 4.00 4.33 4.67 5.00 35 .5736 .7002 1.428 .81915 bb 30 .6626 .8847 1.130 .74896 30 i 18 :35 .70 1.08 1.41 1.76 2.11 2.46 2.82 3.17 3.52 3.87 4.22 4.57 4.9E 5.26 10 .5780 .7046 1.419' .81748 50 40 .6648 1.8889 1.124 .74703 20 20 .37 .74 1.11 1.48 1.85 2.22 2.59 2.96 3.33 370 4.07 4.44 4.81 5.18 5.56 C 20 .5783 .7088 1.411 .81580 40 50 .6670 .8852 1.117 .74509 10 40 .5807 .7133 1.402 .81412 30 $$1 .39 .78 1.17 1.565 1.94 2.33 2.72 3.11 3.50 3.89 4.28 C67 5.06 5.44 5.83 40 .5831 .7177 1.393 .81242 20 42 .6691 .9004 1.111 ,74314 48 $8 .41 :81 1.22 1.63 2.04 2.44 2.85 3.76 3.67 4.07 4.48 4.89 5.30 5.70 6.11 50 .5854 .7221 1:386 .81072 10 10 .6713 .9057 1.104 .74120 50 3 .43 .86 1.28 1.70 2.13 E.56 2.98 3.41 3.83 4.26 4.66 5.11 5.54 5.96 6.39 20 .6734 .9110 1.098 .73924 40 .44 .89 1.33 1.78 2.22 2.67 3.11 3.56 4.00 4.44 4.89 5.33 5.78 6.22 6.67 36 .5878 .7265 1.376 .80802 54 30 .6756 .9163 1.091 .73728 30 Sb .46 .92 1.39 1.86 2.31 2. 3.24 3.711 4.17 4.63 5.� 5.56 6.02 8.48 6.94 10 .5901 .7310 1.368 .WM) 50 40 .6777 .9217 1.085 .73531 20 20 .5925 .7355 1.360 .80658 40 50 .6799 .9271 1.079 .73333 10 t .48 .96 1.44 1.92 2.41 2.89 3.37 3.86 4.33 4.82 5.30 5.78 6.26 6.74 7.24 30 .5848 .7400 1.351 .80386 30 .50 1.00 1.50 2.00 2.50 3.00 3. 400 4.50 5.00 5.50 &00 6.50 .7.00 7.50 40 .5972 .7445 1.343 .88E12 20 48 .6820 AW5 1.072 .73135 47 2 .52 1.04 1.55 2.07 2.59 3.11 3.63 415 4.67 5.18 5.70 6.22 6.74 7.26 7.78 50 .5995 .7490 1.335 :80036 10 10 -.6841 .9380 1.066 .72937 50 .54 1.07 1.61 2.15 2.68 3.22 3.76 4.30 4.83 5:37 5.91 &" 6.98 7.52 8.06 20 .6862 .9435 1.060 .72737 40 .56 1.11 1.67 2.22 2.78 3.33 3.89 4.44 5.00>5.55 6.11 6.67 7.22 7.78 8.33 37 .6018 .7536 1.327 .79864 53 30 .6884 .9490 1.054 .72537 30 10 ,6046 .7581 1.319 .79688 50 40 .6906 ,9545 1.048 .72337 20 81 .57 1.15 1.72 2.30 2.87 3.44 4.02 4.59 5.17 5.74 6.32 &89 7.46 8.04 8.61 20 .6066 .7622 1.311 .79512 40 50 .8826 ,9601 1.042 .72136 10 .59 1.18 1.78 2.37 2.96 306 4,15 4.74 5.33 592 6.52 7.11 7.70 8.30 8.89 30 .6068 .7673 1.304 .793.95 30 3 .61 1.22 1.83 2.44 3.05 167 4.28 4.88 5.60 6.11 6.72 7.33 7.94 8.55 9.17 40 .6111 .7720 1.295 .79158 20 44 .6947 .9657 1.036 .71934 46 .63 1. 1.89 2.52 3.15 3.78 4.40 504 5.67 629 6.93 7.56 8.18 8.81 9.44 50 .6134 .7766 1.280 .78960 10 10 .6867 .9713 1.000 .71732 50 33300D .66 1. 1.94 2.59 3.24 3.89 4.53 5.18 5.83 6.48 7.13 7.78 8.42 9.08 9.72 20 .6988 _9770 1.024 .71529 40 y 88 .6157 .7813 L 280 .78601 53 30 .7068 .9827 1.018 .71325 30 gg8 .67 1.33 2.00 2.67 3.33 4.00 4.66 5.33 6.00 6.67 7.33 &00 8.67 9.33 10.00 10 .6180 .7860 1.272 .78822 50 40 .7030 ,9884 1.012 .71121 20 37 .68 1.37 2.06 2.74 3.42 4,11 4.79 5.49 6.17 6.85 7.54 &22 8.91 9.59 10.28 20 .6202 .7907 1.265 .78442 40 50 •7050 .9942 1.006 .70916 10 3 .70 1.41 2.11L2.82 3.0e52 4.2E 4.95 66.63 6.33 7.04 7.74 844 9.�15g 9.86L10.83 .7071 .1 1. .70711 45 4 7 2 4 1.48 2.22 .70 4.44 3:18 5.92 6.67 7.41 78 6.50.7.22 B.15 &89 9.63 10.37 Of Table gives cu.yds,in I ft.oft ttiangle of given width and height. Corrections for tenths of width are one tenth the values found under each height considering Cesin. Cott. Tan. Sipe. Ang Cosip. Cots. Tan. Sine. Angle the widths from Ito Was tenths and similarly the corrections ter tenths of height are one tenth the figura opposite width considering the heights from 2 to 9 An tenths. Thus ifwd16 2andh-6.3,cu.yds.s1.48}.018}.089_1.5Wcu.ydaorpmeUcally159 cu.Yda per 100 ft. It exceeds ft;,use one half and multiPlY result by 2,it both wand ham large.ase one halt of esch and multiplY result by 4. Any cromp4metion 4 may be divided.inte ttlangles by the following rule. To the triangle of thie sum of the outside cub(or Alis)-h,and M the roadbed-w add n the.tr` •\ .� '•'ty „ angles fse'med by p R F I 1 taking the distance out to each break in turn(=w's)by the ditseremee between the cuts(or Hlle)on each side of it(sh's)always subtracting the outer from the,.inner.