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rill <br />Table VI. -Corrections for. TamTents and F.xtarnalc <br />These corrections are to be added to the approxiinate values, found by dividing <br />the tangent, or external, for a 19 (liable <br />curve I V).by the degree of curve, in,order <br />to obtain the true tangents, or externals. values may be obtained by <br />,Intermediate <br />interpolation. <br />FOR TANGENTS ADD- <br />Central <br />DEGREE OF CURVE <br />Angle <br />5° <br />100 <br />150 <br />201 <br />25° <br />'300 350 40° <br />45ff.31 <br />600 <br />650 <br />700 <br />100 <br />.03 <br />.04 <br />.06 <br />.10 <br />.09 <br />.14 <br />.13 <br />.19 <br />.16 <br />.24 <br />.19 <br />.29 <br />.22 <br />:34 <br />.25 <br />.39 <br />. <br />. <br />200 300 <br />.38 <br />.42 <br />.4615° <br />20° <br />26° <br />.06 <br />.08 <br />.13 <br />.16 <br />.19 <br />.24 <br />.26 <br />.33 <br />.32 <br />.40 <br />.39 <br />.49 <br />.45 <br />.58 <br />.51 <br />.67 <br />. <br />. <br />199.99 299.97 <br />.58 <br />.79 <br />'.99 <br />.63 <br />.84 <br />1.06 <br />.68 <br />.90 <br />1.14 <br />30° <br />350 <br />.10 <br />11 <br />.19 <br />.22 <br />.29 <br />.34 <br />.39 <br />.47 <br />.49 <br />.58 <br />.59 <br />.69 <br />.69 <br />.70 <br />.79 <br />.81 <br />.8.. <br />.92 <br />1.04 1.29 <br />1.20 <br />1.42 <br />1.29 <br />1.54 <br />1.39 <br />1.66 <br />40° <br />450 <br />.13 <br />.26 <br />.40 <br />.53 <br />.67 <br />',76 <br />•.80 <br />.93 <br />1.06 <br />'1.20 <br />1.34 1.49 <br />1.64 <br />1.79 <br />1.94 <br />.02 <br />.15 <br />.30 <br />.44 <br />.60 <br />-.05 <br />.91 <br />1.05 <br />1.21 <br />1.37 <br />1.52 1.70 <br />1.87 <br />2.04 <br />2.21 <br />500 <br />550 <br />17 <br />.34 <br />.51 <br />.68 <br />.85 <br />1.02 <br />1.19 <br />1.36' <br />1.54 <br />1.72 1.91 <br />2.10 <br />2.29 <br />2.48 <br />600 <br />.19 <br />.38 <br />.57 <br />.76 <br />-.84 <br />.95 <br />1.14 <br />1.32 <br />1.52 <br />1.72 <br />1.92 2.14 <br />2.35 <br />2.56 <br />2.77 <br />65° <br />.21 <br />.42 <br />.63 <br />.12 <br />1.05 <br />1.27 <br />1.49 <br />1.71 <br />1.94 <br />2.17 2.38 <br />2.60 <br />2.83 <br />3.07 <br />.08 <br />.23 <br />.46 <br />.69 <br />.93 <br />1.16 <br />1.40 <br />1.64 <br />1.88 <br />2.13 <br />2.38 2.63 <br />2.88 <br />3.13 <br />3.39 <br />70° <br />750 <br />.25 <br />.51 <br />.76 <br />1.02 <br />1.28 <br />1.54 <br />1.80 <br />2.06 <br />2.33 <br />2.60 2.88 <br />3.16 <br />3.44 <br />3.72 <br />800 <br />.27 <br />.56 <br />.83 <br />1.12 <br />1.40 <br />1.69 <br />1.98 <br />2.27 <br />2.57 <br />2:87 3.16 <br />3.47 <br />3.78 <br />4.09 <br />.14 <br />.30 <br />.61 <br />-.91 <br />1.22 <br />1.53 <br />1.84 <br />2.15 <br />2.46 <br />2.78 <br />3.10 3.44 <br />3.78 <br />4.12 <br />4.46 <br />850 <br />.33 <br />.66 <br />1.00 <br />1.33 <br />1.68 <br />2.02 <br />2.36 <br />2.70 <br />3.05 <br />3.40 3.77 <br />4.14 <br />4.55 <br />4.89 <br />900 <br />950 <br />.36 <br />.72 <br />1.09 <br />1.45 <br />1.83 <br />2.20 <br />2.57 <br />2.94 <br />3.32 <br />3.70 4.10 <br />4.50 <br />4.91 <br />5:32 <br />1000 <br />.39 <br />.79 <br />1.19 <br />1.55 <br />2.00 <br />2.40 <br />2.803.20 <br />1.15 <br />3.61 <br />4:02 4.40 <br />4.98 <br />5.38 <br />5.83 j <br />1100 <br />.43 <br />.86 <br />1.30 <br />1.74 <br />2.18 <br />2.62 <br />3.06 <br />3.50 <br />3.95 <br />4.40 4.88 <br />5.37 <br />5.85 <br />6.34 <br />.28 <br />..51 <br />1:03 <br />1.56 <br />2.08 <br />2.61 <br />3.14 <br />3.67 <br />4.21 <br />4.76 <br />5.31 5.86 <br />6.43 <br />7.01 <br />7.60 <br />1200 <br />.62 <br />1.25 <br />1.93 2.52 <br />.64 <br />3.16 <br />3.81 <br />4.45 <br />5.11 <br />5.77 <br />6.44 7.12 <br />7.80 <br />8.50 <br />9.22 <br />FOR. EXTERNALS ADD <br />Central <br />DEGREE OF CURVE - <br />Angle <br />5° <br />10° <br />151 <br />200 <br />250 <br />300 <br />350 <br />40° <br />450 <br />500 <br />550 <br />600 <br />65° <br />700 <br />100 <br />150 <br />001 <br />.003 <br />.003 <br />.007 <br />.004 <br />.010 <br />.006 <br />.014 <br />.007 <br />.018 <br />.008 <br />.023 <br />.009 <br />.027 <br />.011 <br />.029 <br />.012 <br />.014 <br />.015 <br />.017 <br />.018 <br />.020 <br />20° <br />250 <br />006 <br />.009 <br />.011 <br />.018 <br />.017 <br />.022 <br />.028 <br />.034 <br />.038 <br />,045 <br />.032 <br />.051 <br />.035 <br />.057 <br />.039 <br />.063 <br />.043 <br />.07U <br />.047 <br />.076 <br />.051.- <br />.083 <br />.72 <br />.42 <br />2.50 <br />,027 <br />.036 <br />.046 <br />.056 <br />•065 <br />:074 <br />.083 <br />•093 <br />.106 <br />.120 <br />.127 <br />.135 <br />300 <br />350 <br />400 <br />.013 <br />.018 <br />.025 <br />.035 <br />.038 <br />.054 <br />.051 <br />.072 <br />.065 <br />.086 <br />.078 <br />.109 <br />.090 <br />.131 <br />.103 <br />.153 <br />.116 <br />.175 <br />.129 <br />.197 <br />.149 <br />.213 <br />.170 <br />.230 <br />.179 <br />.188 <br />450 <br />.023 <br />.030 <br />.046 <br />.070 <br />.093 <br />.117 <br />.141 <br />.172 <br />.203 <br />.234 <br />.265 <br />.277 <br />.290 <br />.247 <br />.315 <br />.264 <br />.341' <br />38 <br />189.10 257.60 <br />.060 <br />.093 <br />.119 <br />.153 <br />.184 <br />.216 <br />.254 <br />.289 <br />:325 <br />.351 <br />.378 <br />.411 <br />.445 <br />50° <br />550 <br />600 <br />.037 <br />.046 <br />.075 <br />.093 <br />.116 <br />.142 <br />.151 <br />.188 <br />.189 <br />.236 <br />.227 <br />.283 <br />.266 <br />.332 <br />.305 <br />.381 <br />.345 <br />.420 <br />.384 <br />.479 <br />.425 <br />'530 <br />.467 <br />.508 <br />.550, <br />650 <br />.056 <br />067 <br />.112 <br />.135 <br />.168..225 <br />.204 <br />.273 <br />.283 <br />.343 <br />•340 <br />.412 <br />.398 <br />.483 <br />.457 <br />.554 <br />.516 <br />.625 <br />.575 <br />.697 <br />..636 <br />.711 <br />.582 <br />.697 <br />.845 <br />.641 <br />.774 <br />.922 <br />.700 <br />.851 <br />1.01 <br />700 <br />750 <br />800 <br />.080 <br />.095 <br />.159 <br />AK <br />.240 <br />.286 <br />.321 <br />.383 <br />,.403 <br />.480 <br />.485 <br />.578 <br />.568 <br />.678 <br />.652 <br />.777.877 <br />.735 <br />.819 <br />.977 <br />.906 <br />1.07 <br />.994 <br />1.18 <br />1.08 <br />1.29 <br />1.17 <br />1.39 <br />850 <br />.110 <br />.128 <br />.220 <br />.259 <br />.332 <br />.391 <br />.445 <br />.524 <br />.558 <br />.657 <br />.671 <br />.790 <br />.787 <br />.926 <br />.903 <br />1.06 <br />1.02 1.13 <br />1.20 1:34 <br />48 <br />1.25 <br />1.47 <br />1.38 <br />1.62 <br />1.50 <br />1.76 <br />1.62 <br />1.91 <br />90° <br />950 <br />.149 <br />.174 <br />.299.450 <br />.350 <br />.522 <br />•603 <br />.706 <br />•756 <br />.985 <br />.910 <br />1.06 <br />1.07 <br />1.25 <br />1.22 <br />1.43 <br />1.38 1.54 <br />1.62 1.80 <br />1.70 <br />1.99 2.18 <br />1.87 <br />2.03.2.20 <br />2.38 <br />100°.200 <br />110° <br />268 <br />.401 <br />.604 <br />.809 <br />1.01 <br />1.22 <br />1.43 <br />1.64 <br />1.85 2.06 <br />2.28 2.50 <br />2.73 <br />2.53 <br />2.96 <br />.536 <br />.806 <br />1.08 <br />1.35 <br />1.63 <br />1.91 <br />2.20 <br />2.48 2.76 <br />3.05 3.35 <br />3.66 <br />3.96 <br />1200 <br />.360 <br />.721 <br />1.08 <br />1.45 <br />1.82 <br />2.19 <br />2.57 <br />2.95 <br />3.33 3.72 <br />4.11 4.50 <br />4.91 <br />5.32 <br />8 <br />Table VII, -Corrections for Sub -Chords <br />and Long Chords. <br />FOR SUB -CHORDS ADD <br />Excess <br />of are <br />LONG CHORDS <br />LENGTH OF RAILS <br />D <br />10 <br />20 <br />30 <br />40 150 <br />28 <br />60 <br />70 <br />80 <br />90 <br />1er <br />00 ft. <br />D <br />200 300 <br />400 500 <br />4° <br />.00 <br />.00 <br />.01.01 <br />11 <br />.01 <br />.01 <br />.01 <br />.01 <br />.00 <br />.02 <br />1 <br />199.99 299.97 <br />399.92 499.85 <br />6 <br />.00 <br />.01 <br />.01 <br />.02 <br />.O2 <br />.02 <br />.02 <br />,01 <br />.01 <br />.O5 <br />2 <br />199.97 299.88 <br />399.70 499.39 <br />8 <br />.01 <br />.02 <br />.02 <br />.03 <br />.03 <br />.03 <br />.03 <br />.02 <br />.01 <br />.08 <br />3 <br />199.93 299.73 <br />399.32 498.63 <br />10 <br />.01 <br />.02 <br />.03 <br />.04 <br />.05 <br />.05 <br />-.05 <br />.04 <br />.02 <br />.13 <br />4 <br />199.88 299.51 <br />398.78 497.57 <br />12 <br />.02 <br />.04. <br />.05 <br />.06 <br />.07 <br />.07 <br />.07 <br />.05 <br />.03 <br />.18 <br />5 <br />199.81 299.24 <br />398.10 496.20 <br />14 <br />.02 <br />.05 <br />.07 <br />.08 <br />.09 <br />.10 <br />.09 <br />.07 <br />.04 <br />.25 <br />6 <br />199.73 298.90 <br />397.26 494.53 <br />16 <br />.03 <br />.06 <br />.09 <br />.11 <br />.12 <br />.12 <br />.12 <br />.09 <br />.05 <br />.33 <br />7 <br />199.63 298.51 <br />396.28 492.57 <br />18 <br />.04 <br />.08 <br />.11 <br />.14 <br />.15 <br />.16 <br />.15 <br />.12 <br />.07 <br />.41 <br />8 <br />199.51 298.05 <br />395.14 490.31 <br />20 <br />.05 <br />.10 <br />.14 <br />.17 <br />.19 <br />.20 <br />.18 <br />.15 <br />.09 <br />.51 <br />9 <br />199.38 297.54 <br />393.86 487.75 <br />22 <br />.06 <br />.-12 <br />.17 <br />.21 <br />.23 <br />.24 <br />.22 <br />.18 <br />.10 <br />.62 <br />10 <br />199.24 296.96 <br />392.42 484.90 <br />24 <br />.07 <br />.14 <br />..20 <br />.Z5 <br />.28 <br />.28 <br />.26 <br />.21 <br />A2 <br />.74 <br />12 <br />198.90 295.63 <br />389.12 478.34 <br />26 <br />.09 <br />.17 <br />.24 <br />.29 <br />.32 <br />.3.3 <br />.31 <br />.25 <br />.15 <br />.86 <br />14 <br />198.51"194.06 <br />385.22 470.65 <br />28.10 <br />.139 <br />.19 <br />.27 <br />.34 <br />.37 <br />.38 <br />.36 <br />.29 <br />.17 <br />1.00 <br />16 <br />198.05 '192.25 <br />380.76 461.86 <br />30 <br />.I1 <br />22 <br />.31 <br />.39 <br />.43 <br />.44 <br />.41 <br />.33 <br />.19 <br />1.15 <br />18 <br />197.54 290.21 <br />375.74 452.02 <br />32.13 <br />.290 <br />.25 <br />.36 <br />.44 <br />.49 <br />.50 <br />.47 <br />.38 <br />.22 <br />1.31 <br />20 <br />196.90 287.94 <br />370.17 441.15 <br />34 <br />.15 <br />.28 <br />.40 <br />.50 <br />.55 <br />.57 <br />,53 <br />.43 <br />.25 <br />1.48 <br />22 <br />196.32 285.44 <br />364.06 429.30 <br />36 <br />.17 <br />.32 <br />.45 <br />.56 <br />.62 <br />.64 <br />.59 <br />.48 <br />.28 <br />1.66 <br />24 <br />195.63 282.71 <br />357.43 416.53 <br />38.18 <br />.508 <br />.36 <br />.51 <br />.62 <br />.70 <br />.71 <br />.66 <br />.53 <br />.31 <br />1.86 <br />26 <br />194.87 279.76 <br />350.30 402.89 <br />40 <br />.21 <br />'40 <br />.56 <br />.69 <br />.77 <br />.79 <br />.73 <br />.59 <br />.35 <br />2.06 <br />28 <br />194.06 276.59 <br />342.69 388.42 <br />42 <br />.44 <br />.62 <br />.76 <br />.85 <br />.87 <br />.81 <br />.65 <br />.38 <br />2.28 <br />30 <br />193.18 273.20 <br />334.61 373.20 <br />44 <br />.23 <br />.25 <br />.48 <br />.68 <br />.84 <br />.94 <br />.96 <br />.89 <br />.72 <br />.42 <br />2.50 <br />32 <br />192.25 269.61 <br />326.08 357.28 <br />46 <br />.27 <br />.52 <br />.75 <br />.92 <br />1.02 <br />1.05 <br />.98 <br />.78 <br />.46 <br />2.74 <br />34 <br />191.26 265.81 <br />317.12 340.73 <br />48 <br />.30 <br />.57 <br />.81 <br />1.00 <br />1.12 <br />1.14 <br />1.06 <br />.86 <br />.50 <br />2.99 <br />36 <br />190.21 261.80 <br />307.77 323.61 <br />50 <br />.32 <br />.62 <br />.89 <br />1.09 <br />1.21 <br />1.24 <br />1.15 <br />.93 <br />.55 <br />3.24 <br />38 <br />189.10 257.60 <br />298.03 305.99 <br />52 <br />.35 <br />.67 <br />.96 <br />1.18 <br />1.31 <br />1.35 <br />1.25 <br />1.01 <br />.59 <br />3.52 <br />40 <br />187.94 253.21 <br />287.94 287.94 <br />54 <br />.38 <br />.73 <br />1.04 <br />1.28 <br />1.42 <br />1.46 <br />1.35 <br />1.09 <br />.64 <br />3.80 <br />42 <br />186.72 248.63 <br />'277.51 269.54 <br />56 <br />.41 <br />.78 <br />1.12 <br />1.38 <br />1.53 <br />1.57 <br />1.46 <br />1.17 <br />.69 <br />4.09 <br />44 <br />185.44 243.87 <br />266.78 250.85 <br />58 <br />.44 <br />.84 <br />1.20 <br />1.48 <br />1.65 <br />1.69 <br />1.57 <br />1.20 <br />.74 <br />4.40 <br />46 <br />184.10'239.93 <br />255.78 231.95 <br />60 <br />.47 <br />.91 <br />1.29 <br />1.59 <br />1.76 <br />1.81 <br />1.68 <br />1.35 <br />.80 <br />4.72 <br />48 <br />182.71 233.83 <br />244.51 212.92• <br />NOTE. -When a chord of less than 100 ft. is used the corrections given in the above <br />table should be added to the nominal length of chord to get the length which should <br />be used in order that the 100 ft. points will check with those obtained by using the <br />standard loo ft. chord. 'Thus in locating a 140 curve by Y5 ft. chords measure 251.011 <br />for each chord. Long chords are useful in passing obstacles. <br />Table VIII. -Middle Ordinates for Rails in Feet. <br />Deg. <br />of <br />LENGTH OF RAILS <br />Deg <br />of <br />LENGTH OF RAILS <br />Curve <br />32 <br />30 <br />28 <br />26 <br />24 <br />22 <br />20 <br />Curve <br />3230 <br />28 126 <br />24 <br />22 <br />20 <br />11 <br />.013 <br />.011 <br />.009 <br />.008 <br />160 <br />.356 <br />.313 <br />.273 <br />.236 <br />.200 <br />.170 <br />:139 <br />2 <br />.022 <br />.045 <br />.020 <br />.038 <br />.016 <br />.034 <br />.029 <br />.025 <br />.021 <br />.017 <br />17 <br />.378 <br />.333 <br />.290 <br />.252 <br />.213 <br />.180 <br />.148 <br />3 <br />.067 <br />.058 <br />.051 <br />.044 <br />.037 <br />.031 <br />.026 <br />18 <br />.400 <br />.351 <br />.306 <br />.265 <br />.225 <br />.190 <br />.156 <br />4 <br />.089 <br />.079 <br />.069 <br />.060 <br />.050 <br />.042 <br />.035 <br />19 <br />.423 <br />.371 <br />.324 <br />.280 <br />.238 <br />.201 <br />.165 <br />5 <br />.112 <br />.099 <br />.086 <br />.074 <br />.063 <br />.053 <br />.044 <br />20 <br />.445 <br />.392 <br />.341 <br />.296 <br />.250 <br />.212 <br />.174 <br />6 <br />.134 <br />.117 <br />.102 <br />.088 <br />.076 <br />.064 <br />.0.52 <br />21 <br />.466 <br />.410 <br />.357 <br />.309 <br />.262 <br />.222 <br />.182 <br />7 <br />.156 <br />.137 <br />.120 <br />.104 <br />.088 <br />.074 <br />.061 <br />22 <br />.487 <br />.430 <br />.375 <br />.325 <br />.275 <br />.233 <br />.191 <br />8 <br />.179 <br />.158 <br />.137 <br />.119 <br />.100 <br />.085 <br />.070 <br />23 <br />.509 <br />.450 <br />.390 <br />.338 <br />.287 <br />.243 <br />.199 <br />9 <br />.201 <br />.175 <br />.153 <br />.133 <br />.112 <br />.095 <br />.078 <br />24 <br />.531 <br />.469 <br />.408 <br />.354 <br />.299 <br />.253 <br />.208 <br />10 <br />.'223 <br />At <br />.171 <br />.148 <br />.125 <br />.106 <br />.087 <br />25 <br />.552 <br />.486 <br />.424 <br />.367 <br />.311 <br />.263 <br />.216 <br />11 <br />.'245 <br />.216 <br />.188 <br />.163 <br />.139 <br />.117 <br />.096 <br />26 <br />.573.506 <br />.441 <br />.382 <br />.323 <br />.274 <br />.225 <br />12 <br />.268 <br />.236 <br />.206 <br />.179 <br />.151 <br />.128 <br />.105 <br />27 <br />.594 <br />.524 <br />.457 <br />.396 <br />.335 <br />.284 <br />.233 <br />13 <br />.290 <br />.254 <br />.222 <br />.192 <br />.163 <br />.138 <br />.113 <br />28 <br />.618 <br />.545 <br />.475 <br />.411 <br />.348 <br />.294 <br />.242 <br />14 <br />.312 <br />.275 <br />.239 <br />.207 <br />.175 <br />.148 <br />.122 <br />29 <br />.638 <br />.564 <br />.491 <br />.424 <br />.361 <br />.303 <br />.250 <br />15 <br />.334 <br />.295 <br />.257 <br />.223 <br />.188 <br />.159 <br />.131 <br />30 <br />.660 <br />.583 <br />.508 <br />.438 <br />.374 <br />.313 <br />.259 <br />9 <br />