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<br /> TAes.R VI.-COMMOrmxa roa SUB-CHORDS AND LONG C»oans. SLOPE REDUCTIONS.
<br /> FOR SUB-CHORDS ADD Ezoees LONG CHORDS When distances are measured on a slope they may be reduced to
<br /> of arc the equivalent horizontal distance by the following approximate rule:-
<br /> D 1 11 10 20 go 140 b0 I eo 70 s0 90 100 ft D 200 I goo 1400 1500 subtract from the slope distance the square of the rise divided by twice
<br /> the slope distance. Thus for a slope distance of 250.3 ft. and a rise
<br /> 4°.00.00 .0011 .01 .01 .01 .0011 .01.00 .02 1 199.99 299.97 399.92 499,85 of 15 ft. correction--152+2X250.3=.45 (by slide rule) or horizontal
<br /> b ,00:01 .0011 .02 ,02 .02 ,02 .01 01 .05 1 199.97 299.88 399.70 499.39 distantx�250 3-.45=249.85. When vertical angle---V.A.is measured
<br /> 6 .001.02 :02 03 .03 .03 .02.01 .08 3199.93 299.73 399.32 498.63
<br /> 10 .001.02 .03 .06 .05 .05 .05 .04.02 .13 4 199.88 299.51 398.78 497.57 horizontal distance lope distance---slope distance (1--Cos. V. A.).
<br /> it .003.04 .06 .006 .07 .07 .07 .05.03 .I8 5 199.81 299.24 398.10 496.20 Thus for slope distance of 248.7 f t.and V.A.of 4°20"from Table VIII
<br /> 14 .07 .08 .09 .110 .09 .07.04 .25 199.73 298.90 397.26 494.63 99714 and correction=1-.99714=.00286 per foot or total of.286 X
<br /> 16 .08.08 .11 .12 .12 .12 .09,05 ,33 199.63 298.51 396.28 492.57
<br /> 16 .04.08 .11 .14 .18 .10 .15 .12.07 .41 8 199.51 298.05 395.14 490.81 2%(near enOugh�.57 and horizontal distance---248.7-.57-24&13 ft.
<br /> >A ,1 .14 .17 .19 .20 .18 .115.09 .al 9 199.38 297.64 383.86 487.75
<br /> !! .12 .17 .21 .28 .24 .22 .18.10 .62 10 199.24 296.96 392.42 484.90
<br /> 26 .07.14 .25 .28 .28 .26 .21 .12 .74 19 198.90 295.63 380.12 478.84 See gt,W.' TRIGONOMETRICAL. FORMULAS.
<br /> 16 .09 .17 .24 .29 .32 .83 .31 .25.15 .86 14 198.51 294.06 385.22 470.65 _
<br /> 26 .1 .19 .27 .84 .87 .38 .86 .29.17 1.00 16 198.05 292.25 380.76 461.86 �a
<br /> M .11.22 .31 .39 .43 .44 .41 .33.19 11.15 18197.54 290.21375.74 452.02 sin. A=-! B
<br /> 3t .13 .25 .36 .44 .49 .50 .47 .38.22 1.81 20 196.96 287.94 370.17 441.15 mss• A'e S x
<br /> 34 .15 .28 .4 .50 .55 .57 .53 .43.25 1.48 n 196.82 285.44 364.06 429.30 a
<br /> 3i .17 .32 .4 W .62 .64 .59 .48.28 1.66 24 195.63 282.71357.43 416.53 'tan. A=a (a)
<br /> 36 . .18 .61 .62 .70 .71 .66 .53.31 1.80 96 194.87 279.76 350.80 402.89 a
<br /> 40 ,21 .40 .56 :69 .77 .79 .73 .59 .35 2.06 28 194.05 276.59 342.69 388.43 cot. A=! ,
<br /> 42 .23.44 .62 .76 .85 .87 .81 .65 .88 2.28 30 193.18 273.20 334.61 378.20 sec. A=% A
<br /> M .2 .48 .68 .84 .94 .96 .89 .72.42 2.50 33 192.25 269.61 326.08 3 7.28 C
<br /> M .27 .62 .75 .92 1.02 1.05 .98 .78.46 2.74 34 191.26 285.81317.12 340.73 cosec. A=a j
<br /> Y .57 .811.00 1.12 1.14 1.08 .86.b0 2.99 36 190.21 261.80 307.77 323.61
<br /> s0 .82,62 .89 1.09 1.21 1.21 1.15 .93.65 8.24 36189.10 257.00 298.03 305.99
<br /> 52 .35.67 .96 1.18 1.31 1.35 1.251.01 .59 8.52 40 187.94 253.21 287.94 287.94 FORMULA BOH SoLvma THIANGLEs.
<br /> 66 .38.73 1.04 1.28 1.42 1.46 1.85 1.09.64 8.89 41 186.72 248.63 277.51269.54
<br /> 66 .41 .78 1.12 1.88 1.63 1.57 1.46 1.17 .69 4.09 K 185.44 243.87 266.78 250.85 Given Bought. Right triangle See fla.(a).
<br /> 66 .44 .84 1.20 1.48 1.65 1.69 1.57 1.26.74 #,40 46 184.10 239.93 255.78 231.95
<br /> 60 .47.91 1.29 1.69 1.76 1.81 1,68 1.35,80 j4.72 46 182.71 233.83 244.•1 212.92 a,c A, B. b blue A=�,008.B=�, b�.�(o+a)
<br /> Norm. When a chord of lees than 100 ft.Is used the corrections given in the above a,b. A, B, c tan.A= , cot.B=i,
<br /> table should be added to the nominal length of chord to get the length which should be a
<br /> used in order that the 100 ft.points will check with those obtained by using the standard A a B b c B=900-A, b=a cot.A, a=�A.
<br /> 100 ft.chord. Thus In locating a 14°curve by 25 it.chords measure 25 1.06 for each , ' '
<br /> chord. Long chords ars useful is passing obetsclee. , A,b B, a, c B=90=A, a=b tisn.A, c=,p&A.
<br /> TAwA VII.-MmDLi4 OHDutATzs Bou PtArw of Mwr.. Aa c B, g, b 8=90=A, a=c sin.A, b=c cos.A
<br /> Given Bought. Oblique triangles. See As.(b).
<br /> LENGTH OF RAILS LENGTH OF RAILS. a stn.B
<br /> c o A,B,a b b=aa,A.;
<br /> Curve 81 80 28 126 114 122 20 Curve 82 30 ( 28 26 24 22 120 •B=b nn.A
<br /> A,a,b B a
<br /> 1• .022.020 .016 .018.011 .009.008 16 .356 .313.273.23 .200 .170.139
<br /> a,b,C A - B tan. 31(A-B)=(a--b)tan+b(A+B)
<br /> ,045.038•034 •029.025.021 .017 17 .378.833 .290 .252 .213.180.148 � r a
<br /> 3 .067.058.051 .044.037.031 .026 16 .400 .351,806 .265.225.190.156 If a= (a'}b{c),Sia• A=tir- be'
<br /> 4 .089.079 .069 .060.050.042.035 19 .423.871.324 .280.238.201 .165 1 (s-D)
<br /> a .112.099 .086 .074 .063.053. 10 .445 .392.341 . 3,.250.212.174 b C A cos. A=v-S�r tan. A= ,
<br /> i
<br /> 134 117.102 .088 .076.064.052 11 ,466.41 .357.309 .262.222.182 a, ,
<br /> Y .156.137.120 .104 .088.074.061 11 .487.480.875.325 .27 .233.191 2 VW--Y( )
<br /> a .179.158.137 .119 .100.685.07 13 .609.4b•.890.388.287 .243 .199 �'A- �o
<br /> 9 .201.175.163 .133.112.095 .078 14 .531 .469.4 .854 .299.253.208
<br /> 1• 228.196,171 .148.125.106.087 16 [550542:94
<br /> ,424,887 .811 .263.218 as cin.B sine C
<br /> 11 .245.210.188.163.139.117.096 26 573 .441. .323 .274.228 A,B,C,a ares area=as
<br /> sin.A
<br /> 12 .288.238.208 .179.151 .128 .105 17 487 .8911 .335.284.233
<br /> is .290 .254 .222 .192 .163.138.113 16 618.545.475.411 .848.294.242 A,b,c area area= %b c sin-A14 .812 .275 .239 .207 .175 .148 .122 19 638 .564 ,491 .424 .361 .303 .250
<br /> 15 .834 .298.257 .223.188 .159 .131 30 660.588.508.488.374 .313 .259 a,b,c area a=3j (a+b+c),area=Vra(a-a)(a-b)(s---c)
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