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TABLE Y — Sllddle Ordinates for Ralls <br />Deg <br />LENGTH <br />OF <br />RAILS <br />peg <br />10 <br />61T9 <br />OF <br />RAILS <br />r <br />of <br />Curve <br />of <br />9urv0 <br />32 <br />130 <br />28 <br />26 <br />24 <br />22 <br />20 <br />32 <br />30 <br />23 <br />1 28 <br />.24 <br />22 <br />120 1 <br />1° <br />022 <br />020 <br />017 <br />01a <br />013 <br />011 <br />049 <br />160 <br />356 <br />913 <br />273 <br />236 <br />0W <br />170 <br />1391 <br />2 <br />045 <br />039 <br />034 <br />030 <br />02a <br />021 <br />017 <br />17 <br />378 <br />dd3 <br />290 <br />252 <br />213 <br />160 <br />148 <br />3 <br />W-, <br />0x9 <br />0,1 <br />044 <br />038 <br />032 <br />026 <br />1S <br />400 <br />351 <br />950 <br />2bo <br />225 <br />NO <br />156 <br />4 <br />069 <br />079 <br />068 <br />Ov9 <br />Oso <br />042 <br />035 <br />19 <br />423 <br />371 <br />324 <br />280 <br />138 <br />201 <br />16 <br />6 <br />112 <br />098 <br />ON <br />074 <br />0631 <br />053 <br />044 <br />20 <br />44a <br />392 <br />341 <br />296 <br />250 <br />212 <br />174 <br />O <br />134 <br />118 <br />103 <br />086 <br />075 <br />063 <br />052 <br />21 <br />409 <br />410 <br />357 <br />3014 <br />262 <br />222 <br />182 <br />7 <br />156 <br />137 <br />120 <br />103 <br />088 <br />044 <br />061 <br />22 <br />497 <br />430 <br />375 <br />825 <br />275 <br />288 <br />191 <br />8 <br />159 <br />157 <br />134 <br />118 <br />100 <br />084 <br />cA <br />24 <br />509 <br />450 <br />390 <br />338 <br />287 <br />245 <br />199 <br />9 <br />201 <br />177 <br />154 <br />193 <br />113 <br />055 <br />048 <br />?# <br />531 <br />459 <br />408 <br />3�4 <br />&,) <br />253 <br />208 <br />10 <br />223 <br />196 <br />171 <br />147 <br />126 <br />105 <br />08" <br />25 <br />x59 <br />486 <br />424 <br />367 <br />311 <br />269 <br />016 <br />11 <br />245 <br />216 <br />188 <br />162 <br />148 <br />116 <br />096 <br />26 <br />573 <br />506 <br />441 <br />382 <br />9213 <br />274 <br />22e <br />112 <br />269 <br />235 <br />20o <br />177 <br />151 <br />127 <br />10 <br />27 <br />594 <br />024 <br />457 <br />990 <br />330 <br />284 <br />233' <br />14 <br />290 <br />2x4 <br />222 <br />192 <br />163 <br />138 <br />113 <br />28 <br />618 <br />545 <br />475 <br />11I <br />348 <br />204 <br />242 <br />14 <br />312 <br />27�> <br />290 <br />207 <br />lis <br />148 <br />122 <br />29 <br />638 <br />n64 <br />491 <br />4214 <br />461 <br />803 <br />250 <br />13 <br />334 <br />290 <br />257 <br />223 <br />188 <br />108 <br />131 <br />d0 <br />660 <br />683 <br />508 <br />498 <br />374 <br />813 <br />2o9i <br />CURVE FORMUL.d <br />T= R tan I <br />U— <br />T cot1 I <br />$ <br />Chord def = <br />chord2 <br />T = <br />50 <br />tan <br />I <br />Sin D <br />R = <br />50 <br />Sin <br />D = <br />50 <br />Sm D <br />No <br />chords <br />= g <br />I <br />E= R ex <br />see <br />B I <br />1 <br />Sin D= 50R an <br />I <br />T <br />�E = <br />T tan f I <br />Tan def =J, chard <br />def <br />The square of any distance, divided by twice the radius, iiill equal the�l <br />distance from tangent to curve, very nearl} <br />Table IV contains Tangents and Externals to a 10 curve Tan and Eat <br />to any other radius may be found, netirly enough, bti dividing the Tan or <br />Eat oliposlte the gn en central angle by the given degree cf carve <br />To flnd Deg of Curve, having the Central Anglo and Tangent Dn lde <br />Tan opposite the given Central Angle by the given Tangent <br />To find Deg of Curve, having the Central Angle and External Divide , <br />Est opposite the giyq Central Angle by the given External <br />To $nd Nat Tan and Nat Ea Sec for any angle by Table IV Tan <br />or Eat of twice the given angle divided by the radius of a 10 curve nilI be+ <br />the Nat Tau or Nat Ex Sec <br />To find angle for a given distance and deflection <br />Rule 1 Irlultlply the given distance by 01745 (def for 10 for 1 ft), and <br />divide given deflection by the product <br />ICule 2 Multiply given deflection by 57 3, and divide the product by k <br />the given distance < <br />To find deflection far a green angle and distance Kultiply the angle 1 <br />by 01745, and the product by the distance <br />DIGHT AAGLE T'RTANGLLS — SquarP the altitude, divide by twico the base s <br />Odd quotient to base for hvpothenuse 1 <br />G1%ea Base 100, Alt 10 102-200= 5 100 { 5=700 5 hyp ' <br />Given Hyp 100, Alt 25 252— 200=3 125 100-3 125=96 875=Base <br />Error in first example, 002, in last, 045 <br />To find Tons of Rail in one mile of trach multiply weight pei yard <br />bti 11, and dnide by 7 ya r <br />s, <br />- I- <br />t;- <br />_I - <br />T 7,4 <br />�Yo <br />W1 �J <br />