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 .03 .02 .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 .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 24 195.63 282.82 357.43 416.53 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 1.00 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 LENGTH OF RAILS 32 30 28 26 24 22 20 Deg. of Curve 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