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Transcription
Table VI.—Corrections for Tangents and Externals.
These corrections are to be added to the approximate values, found by dividing
the tangent, or external, for a 1° curve (Table IV) by the degree of curve, in order
to obtain the true tangents, or externals. Intermediate values may be obtained by
interpolation.
FOR TANGENTS ADD
Central Angle DEGREE OF CURVE
5° 10° 15° 20° 25° 30° 35° 40° 45° 50° 55° 60° 65° 70°
10° .03 .06 .09 .13 .16 .19 .22 .25 .28 .31 .34 .38 .42 .46
15° .04 .10 .14 .19 .24 .29 .34 .39 .45 .51 .53 .58 .63 .68
20° .06 .13 .19 .26 .32 .39 .45 .51 .58 .65 .72 .79 .84 .90
25° .08 .16 .24 .33 .40 .49 .58 .67 .75 .83 .90 .99 1.06 1.14
30° .10 .19 .29 .39 .49 .59 .69 .79 .89 .99 1.09 1.20 1.29 1.39
35° .11 .22 .34 .47 .58 .69 .70 .81 .92 1.04 1.29 1.42 1.54 1.66
40° .13 .26 .40 .53 .67 .80 .93 1.06 1.20 1.34 1.49 1.64 1.79 1.94
45° .15 .30 .44 .60 .76 .91 1.06 1.21 1.37 1.52 1.70 1.87 2.04 2.21
50° .17 .34 .51 .68 .85 1.02 1.19 1.36 1.54 1.72 1.91 2.10 2.29 2.48
55° .19 .38 .57 .76 .95 1.14 1.32 1.52 1.72 1.92 2.14 2.35 2.56 2.77
60° .21 .42 .63 .84 1.05 1.27 1.49 1.71 1.94 2.17 2.38 2.60 2.83 3.07
65° .23 .46 .69 .93 1.16 1.40 1.64 1.88 2.13 2.38 2.63 2.88 3.13 3.39
70° .25 .51 .76 1.02 1.28 1.54 1.80 2.06 2.33 2.60 2.88 3.16 3.44 3.72
75° .27 .56 .83 1.12 1.40 1.69 1.98 2.27 2.57 2.87 3.16 3.47 3.78 4.09
80° .30 .61 .91 1.22 1.53 1.84 2.15 2.46 2.78 3.10 3.44 3.78 4.12 4.46
85° .33 .66 1.00 1.33 1.68 2.02 2.36 2.70 3.05 3.40 3.77 4.14 4.55 4.89
90° .36 .72 1.09 1.45 1.83 2.20 2.57 2.94 3.32 3.70 4.10 4.50 4.91 5.32
95° .39 .79 1.19 1.55 2.00 2.40 2.80 3.20 3.61 4.02 4.40 4.98 5.38 5.83
100° .43 .86 1.30 1.74 2.18 2.62 3.06 3.50 3.95 4.40 4.88 5.37 5.85 6.34
110° .51 1.03 1.56 2.08 2.61 3.14 3.67 4.21 4.76 5.31 5.86 6.43 7.01 7.60
120° .62 1.25 1.93 2.52 3.16 3.81 4.45 5.11 5.77 6.44 7.12 7.80 8.50 9.22
FOR EXTERNALS ADD
Central Angle DEGREE OF CURVE
5° 10° 15° 20° 25° 30° 35° 40° 45° 50° 55° 60° 65° 70°
10° .001 .003 .004 .006 .007 .008 .009 .011 .012 .014 .015 .017 .018 .020
15° .003 .007 .010 .014 .018 .023 .027 .029 .032 .035 .039 .043 .047 .051
20° .006 .011 .017 .022 .028 .034 .038 .045 .051 .057 .063 .070 .076 .083
25° .009 .018 .027 .036 .046 .056 .065 .074 .083 .093 .106 .120 .127 .135
30° .013 .025 .038 .051 .065 .078 .090 .103 .116 .129 .149 .170 .179 .188
35° .018 .035 .054 .072 .086 .109 .131 .153 .175 .197 .213 .230 .247 .264
40° .023 .046 .070 .093 .117 .141 .172 .203 .234 .265 .277 .298 .315 .341
45° .030 .060 .093 .119 .153 .184 .216 .254 .289 .325 .351 .370 .411 .445
50° .037 .075 .116 .151 .189 .227 .266 .305 .345 .384 .425 .467 .508 .550
55° .046 .093 .142 .188 .236 .283 .332 .381 .420 .479 .530 .582 .641 .700
60° .056 .112 .168 .225 .283 .340 .398 .457 .516 .575 .636 .697 .774 .851
65° .067 .135 .204 .273 .343 .412 .483 .554 .625 .697 .711 .845 .922 1.01
70° .080 .159 .240 .321 .403 .485 .568 .652 .735 .819 .906 .994 1.08 1.17
75° .095 .182 .286 .383 .480 .578 .678 .777 .877 .977 1.07 1.18 1.29 1.39
80° .110 .220 .332 .445 .558 .671 .787 .903 1.02 1.13 1.25 1.38 1.50 1.62
85° .128 .259 .391 .524 .657 .790 .926 1.06 1.20 1.34 1.47 1.62 1.76 1.91
90° .149 .299 .450 .603 .756 .910 1.07 1.22 1.38 1.54 1.70 1.87 2.03 2.20
95° .174 .350 .522 .706 .985 1.06 1.25 1.43 1.62 1.80 1.99 2.18 2.38 2.53
100° .200 .401 .604 .809 1.01 1.22 1.43 1.64 1.85 2.06 2.28 2.50 2.73 2.96
110° .268 .536 .806 1.08 1.35 1.63 1.91 2.20 2.48 2.76 3.05 3.35 3.66 3.96
120° .360 .721 1.08 1.45 1.82 2.19 2.57 2.95 3.33 3.72 4.11 4.50 4.91 5.32
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