Table VII.—Corrections for Sub-Chords and Long Chords. FOR SUB-CHORDS ADD Excess of arc per 100 ft. LONG CHORDS D | 10 | 20 | 30 | 40 | 50 | 60 | 70 | 80 | 90 | D | 200 | 300 | 400 | 500 4°. .00 .00 .01 .01 .01 .01 .01 .01 .00 .02 | 1 | 199.99 | 299.97 | 399.92 | 499.85 6 .00 .01 .01 .02 .02 .02 .02 .01 .01 .05 | 2 | 199.97 | 299.88 | 399.70 | 499.39 8 .01 .02 .02 .03 .03 .03 .02 .01 .01 .08 | 3 | 199.93 | 299.73 | 399.32 | 498.63 10 .01 .02 .03 .04 .05 .05 .05 .04 .02 .13 | 4 | 199.88 | 299.51 | 398.78 | 497.57 12 .02 .04 .05 .06 .07 .07 .07 .05 .03 .18 | 5 | 199.81 | 299.24 | 398.10 | 496.20 14 .02 .05 .07 .08 .09 .10 .09 .07 .04 .25 | 6 | 199.73 | 298.90 | 397.26 | 494.53 16 .03 .06 .09 .11 .12 .12 .12 .09 .05 .33 | 7 | 199.63 | 298.51 | 396.28 | 492.57 18 .04 .08 .11 .14 .15 .16 .15 .12 .07 .41 | 8 | 199.51 | 298.05 | 395.14 | 490.31 20 .05 .10 .14 .17 .19 .20 .18 .15 .09 .51 | 9 | 199.38 | 297.54 | 393.86 | 487.75 22 .06 .12 .17 .21 .23 .24 .22 .18 .10 .62 | 10 | 199.24 | 296.96 | 392.42 | 484.90 24 .07 .14 .20 .25 .28 .28 .26 .21 .12 .74 | 12 | 198.90 | 295.63 | 389.12 | 478.34 26 .09 .17 .24 .29 .32 .33 .31 .25 .15 .86 | 14 | 198.51 | 294.06 | 385.22 | 470.65 28 .10 .19 .27 .34 .37 .38 .36 .29 .17 1.00 | 16 | 198.05 | 292.25 | 380.76 | 461.86 30 .11 .22 .31 .39 .43 .44 .41 .33 .19 1.15 | 18 | 197.54 | 290.21 | 375.74 | 452.02 32 .13 .25 .36 .44 .49 .50 .47 .38 .22 1.31 | 20 | 196.90 | 287.94 | 370.17 | 441.15 34 .15 .28 .40 .50 .55 .57 .53 .43 .25 1.48 | 22 | 196.32 | 285.44 | 364.06 | 429.30 36 .17 .32 .45 .56 .62 .64 .59 .48 .28 1.66 | 24 | 195.63 | 282.71 | 357.43 | 416.53 38 .18 .36 .51 .62 .70 .71 .66 .53 .31 1.86 | 26 | 194.87 | 279.76 | 350.30 | 402.89 40 .21 .40 .56 .69 .77 .79 .73 .59 .35 2.06 | 28 | 194.06 | 276.59 | 342.69 | 388.42 42 .23 .44 .62 .76 .85 .87 .81 .65 .38 2.28 | 30 | 193.18 | 273.20 | 334.61 | 373.20 44 .25 .48 .68 .84 .94 .96 .89 .72 .42 2.50 | 32 | 192.25 | 269.61 | 326.08 | 357.28 46 .27 .52 .75 .92 1.02 1.05 .98 .78 .46 2.74 | 34 | 191.26 | 265.81 | 317.12 | 340.73 48 .30 .57 .81 1.09 1.12 1.14 1.06 .86 .50 2.99 | 36 | 190.21 | 261.80 | 307.77 | 323.61 50 .32 .62 .89 1.09 1.21 1.24 1.15 .93 .55 3.24 | 38 | 189.10 | 257.60 | 298.03 | 305.99 52 .35 .67 .96 1.18 1.31 1.35 1.25 1.01 .59 3.52 | 40 | 187.94 | 253.21 | 287.94 | 287.94 54 .38 .73 1.04 1.28 1.42 1.46 1.35 1.09 .64 3.80 | 42 | 186.72 | 248.63 | 277.51 | 269.54 56 .41 .78 1.12 1.38 1.53 1.57 1.46 1.17 .69 4.09 | 44 | 185.44 | 243.87 | 266.78 | 250.85 58 .44 .84 1.20 1.48 1.65 1.69 1.57 1.20 .74 4.40 | 46 | 184.10 | 239.93 | 255.78 | 231.95 60 .47 .91 1.29 1.59 1.76 1.81 1.68 1.35 .80 4.72 | 48 | 182.71 | 233.83 | 244.51 | 212.92 NOTE.—When a chord of less than 100 ft. is used the corrections given in the above table should be added to the nominal length of chord to get the length which should be used in order that the 100 ft. points will check with those obtained by using the standard 100 ft. chord. Thus in locating a 14° curve by 25 ft. chords measure 25'.06 for each chord. Long chords are useful in passing obstacles. Table VIII.—Middle Ordinates for Rails in Feet. LENGTH OF RAILS Deg. of Curve | 32 | 30 | 28 | 26 | 24 | 22 | 20 | Deg. of Curve | LENGTH OF RAILS | | | | | | | | | 32 | 30 | 28 | 26 | 24 | 22 | 20 1°. .022 .020 .016 .013 .011 .009 .008 | 16°. .356 .313 .273 .236 .200 .170 .139 2 .045 .038 .034 .029 .025 .021 .017 | 17 .378 .333 .290 .252 .213 .180 .148 3 .067 .058 .051 .044 .037 .031 .026 | 18 .400 .351 .306 .265 .225 .190 .156 4 .089 .079 .069 .060 .050 .042 .035 | 19 .423 .371 .324 .280 .238 .201 .165 5 .112 .099 .086 .074 .063 .053 .044 | 20 .445 .392 .341 .296 .250 .212 .174 6 .134 .117 .102 .088 .076 .064 .052 | 21 .466 .410 .357 .309 .262 .222 .182 7 .156 .137 .120 .104 .088 .074 .061 | 22 .487 .430 .375 .325 .275 .233 .191 8 .179 .158 .137 .119 .100 .085 .070 | 23 .509 .450 .390 .338 .287 .243 .199 9 .201 .175 .153 .133 .112 .095 .078 | 24 .531 .469 .408 .354 .299 .253 .208 10 .223 .196 .171 .148 .125 .106 .087 | 25 .552 .486 .424 .367 .311 .263 .216 11 .245 .216 .188 .163 .139 .117 .096 | 26 .573 .506 .441 .382 .323 .274 .225 12 .268 .236 .206 .179 .151 .128 .105 | 27 .594 .524 .457 .396 .335 .284 .233 13 .290 .254 .222 .192 .163 .138 .113 | 28 .618 .545 .475 .411 .348 .294 .242 14 .312 .275 .239 .207 .175 .148 .122 | 29 .638 .564 .491 .424 .361 .303 .250 15 .334 .295 .257 .223 .188 .159 .131 | 30 .660 .583 .508 .438 .374 .313 .259 9