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rVIII y IX
<br /> TABLD VI.-Coitmcriobls Folt Sas-CHoRDs AND LONG CHORDS. SLOPE REDUCTIONS.
<br /> FOR SUB-CHORDS ADD Ewen LONG CHORDS When distances are measured on a slope they may be reduced to
<br /> of are -- the equivalent horisontal distance by the following approximate rule:-
<br /> D 10 20 30 (40 50 60 70. SO 90 100 ft D 200 Soo 400 500 subtract from the slope distance the square of the rise divided by twice
<br /> I the-slepe distance. Thus for a slope distance of 250.3 ft. and a rise
<br /> V.00.00 .01 .01 .01 .01 ,01 .01 .00 0g 1199.99 299.97 399.92 499.85 of 15 ft. correction=154=2X250.3-.45 (by slide rule) or horizontal
<br /> 6 .00.O1 .01 02 ,02 ,02 0$$ .O1 O1 :Ob' !199.97 209.88 399.70 499.$9
<br /> s .O1 .O2 ,02 .08 .03 .03 :03 .02.01 .08' 3.199.93 299,73 399.82 498.83 eil�tanee250.3-•46=249.86. When vertical angle�Y.'A.is measured
<br /> 10 .01 .0 .03 .04 .05 .05 . .04-09 .18 4199.86299.51398.78497,67 horizontal distance-elope distance-slope distance (1-4Cos. V. A.).
<br /> 1! .02.04 .05 .08 .07'.07 .07 .05,03 .18 3 199.81 290.24 398,10 496.20 'thus for slope distance of 248.7 f t.and V.A.of 4°20'from Table VIII
<br /> 14 02,05 .07 .08 .09 .10 .09 .07.04 .25 $100
<br /> 298.90 397,26 494,53 Cos= .99714 and oorrection--1-.99714=.00286 per foot or total of.286X
<br /> 16 .03.06 .09 .11 .12 .12 .12 ,09.05 ,83 9 109.8833 288,511 396.28 492.57
<br /> 18 .04.08 .11 .14 .15 .16 .15 .12.07 .41 8 199.51 298.03 395.14 490.31 2Y2(neat enough)-.57 and horizontal distanoe==248.7--.57=248.13 ft.
<br /> 20 .05.10 .14 .17 .19 .20 .18 .15.09 .61 9 199.88 297,64 398.86 487.76
<br /> 22 .06 .12 .17 .21 .23 .24 .22 1g 10 .62 10 199.8 296,96 392.42 484,90
<br /> 24 .07 .14 .2 .25 .28 .28 ."c6 ,21 ,12 .74 12 198,90 295.63 389,1 478.34 Besflg.(s). TRIGONOMETRICAL FORMULAS.
<br /> 26 ,09 .17 ,24 ,29 .32 .33 .31 .25.15 .86 14 198-51294.06 385.22 470.65
<br /> 28 .10 .19 .27 .84 .37 .88 .88 .29.17 1.00 16198.05299.25380,78461.86 sin, A=.
<br /> 30 .11 .22 .31 .89 ,43 .44 .41 .33.19 1.16 18 197.&1290.21375.74 452.02 b ?o B B
<br /> 3! .13.25 .88 .44 .49 .60 .47 .38.22 1.81 20 196.96 287.94 370.17 441.15 COS. A=!
<br /> 34 .15.28 .40 .50 .5 .57 .63 ,43.25 1.48 U 196.82 285.44 364,06 429.30 a
<br /> 36 .17 .32 .45 .56 .62 .84 .59 .48.28 1.66 !4195. 292 71357.48 4 16.63 tan. A=j (a) b Q,.
<br /> 98 .18 .36 .51 .62 .70 .71 .66 .b3.31 88 6 194.8?279.76 350.80 402.89. b
<br /> 40 .21 .40 .66 .69 .77 .79 .73 .59.35 9.00 194,06 2'78.69 842.69 388.43 cot. A=a
<br /> 42 .23 .44 .62 .76 .85 .07 .81 .65 .88 2.28 3o 193.18 273.20 334.61 373.20 see. A= .4VP 'IJV
<br /> 44 .2 .68 .84 .9498 .89 .72.42 2.50 2 192.25 269.61 326.08 357.28
<br /> 46 .27 .52 .75 .92 1.02 f.05 .98 .78.46 2.74 34 191.26 X5.81 317.12 340.73 coseo. A=-! 1 t
<br /> 43 •30.57 .811.00 1.12 1.14 1.06 .86.50 2.99 190.21 281.80 307.77 323.61 s�as
<br /> 50 .32 .62 .89 1.09 1.211-24 1.15 .93,35 8.24 33 180.10 257.00 298.03 205.99 aZ
<br /> i! .a5 .67 .96 1.181.31 1.35 1.25 1. 18.62 40 187.04 258.21 287.94 287.94 FORMULA-Foil SOLVING TnIANGLES.
<br /> 64 .38 .73 1.04 1.28 1.42 1.461.85 1.09.64 8.60 43 168.72 248.63 277.51 209.64
<br /> 56 .41 .78 1.12 1.38 1.53 1.57 1.46 1.17 t 09 4l 185.44 243.87 266.78 260.85 Given sought. Right triangles. flee fig.(a).
<br /> 53 .44,84 1.20 1.48 1.65 1.69 1.57 1.26.74 4.40 46 184.I0 239.93 255.78 231.95 /
<br /> 60 .47.911.29 1.69 1.76 1.81 1.68185
<br /> 7$, 43 182.71 253.83 244.61 212.92 a,a A, B. b sin.A=a,cog.B=�, b=
<br /> NOTs.-When a chord of less than 100 ft.is used the,correction given in the above a,b A, B, c tan.A=j, cot.B=.-ab, c= --'+bs,
<br /> table should be added to the nominal length of chord to get the length which should bo
<br /> used in order that the 100 ft.pointe will check with those obtained by using the standard A,a B, b, c B=90°-A, b=a cot.A, a= d•
<br /> 100 ft.chord. Thus is looatmR a 14.curve by 25 ft.chorda measure 25 ,08 for each
<br /> chord. Lung chorda aro rnpaes�g
<br /> A, b B, a, c B=90° , a=b tan.A, c=�
<br /> Ad•
<br /> ( Tmmim VII.-MmDi iq OanngATEs R Rarr >N FxzT. A,c B, a, b B=90=-A, a=c sin.A, b=o cos.A
<br /> LENGTH OF RAILS LENGTH OF RAILS. ,B, Bought. Oblique triangles. Sea Sg..(o).
<br /> 8
<br /> A,B,a b b=s a(n.sin.A
<br /> Cu a 32 Ito 12s 124 124 122 120 cam. 32 so a 2e 24 22 20 A a b B sin.B=6 Mn,e
<br /> a,b,C A - B tan. (A-B)= -b)tae+6 (A+B)
<br /> 10 .022 .020.016 .013,011 .009.008 16° .856.818:273.286.200•170,139 •
<br /> 2 045.038.034 .029.026.021.017 19 .878.888.290•262 ,213.1 .148
<br /> 3 .067.659.051 .044.037.031 .026 . 18 .400.851 808.265.225.193.158 If s=%(a+b+c),sin.H A=�
<br /> 4 .089.079.089 .080.050.042.036 19 423 .871 .824. 238.201:l6b s(+�)
<br /> 5 .112.099 .088 .074 .088.Ob3.044 !0 445 .892.841 .996: 2 17 a,b,C A cos. A=�-�-,tan.%A= (' s) ,
<br /> 8 .134.117.102 .088 .0T6.084.052 466.410.857.809.982•222,182 (s--a)(a-b)(s-c) s
<br /> 9 .156.137.120 .104.088.074.061 !! ,375.32 37 .233•191 5111•A= e
<br /> 6 .179.158.137 .119.100.088.070 23 .509.4 38i• M43.199
<br /> 9 .201 .775.163 •133 ,112.096.078 !4 b3 489. 364, 263.208 ' , ' aa_s°sin.B sin.C-
<br /> t0 .223.196.171 .148.125.106,Q87 a :652:488•424,867.Eil.Mas.216 A B C a arca
<br /> 11 .246.218.188.183 .18 .119.098 !3 .673. 441 . 3 .M74.226 2 sin.A
<br /> 1! 288.236 •208 .179.ibl .128.1Qb . !7 .594.624.457.890. 284 .2,33
<br /> 13 .290.254 ,222 .192 .183.188.113 !4 .818.646 476.411, 294 .242 A,b,c area area= %b c sin-A
<br /> 14 .312 .M7 .239 .207.175.14 122 !9 838.684:491 .424.881 .503 .250 a,b,c area 8=1
<br /> 15 .334 .296 •257 .223.186.169 .131 90 600•588,508. 874.118, / (a+b+c),area= s(s-a)(s-b)(s=
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