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VIII
<br />TA13LE IL - Radii, Ordinates and Deflections. Chord= 100 ft,
<br />Deg.
<br />Radios
<br />Mid.
<br />Ord.
<br />Tan.
<br />Dist.
<br />Def.
<br />Dist.
<br />Det
<br />fpr
<br />1 Ff.
<br />Deg.
<br />Radius
<br />Mid,
<br />0rd,
<br />Tan
<br />Dist.
<br />Def..
<br />Dist.
<br />ist
<br />Def.
<br />fpr
<br />1 Ft.
<br />20 17'2'
<br />ft.
<br />fL
<br />ft.,
<br />ft.
<br />181.38
<br />1° 59'
<br />ft,
<br />ft.
<br />ft,
<br />ft.
<br />r
<br />8'10'
<br />34377.
<br />03E
<br />.145
<br />. 291
<br />0.05
<br />7°
<br />8100
<br />t.528
<br />6.105
<br />12.21
<br />2.10
<br />20
<br />17189.
<br />.073
<br />.291
<br />.582
<br />0,.10
<br />20'
<br />781..8
<br />1.600
<br />6.395
<br />12.79
<br />2:20
<br />30
<br />11459.
<br />.109
<br />.4,6
<br />.873
<br />0.15
<br />30
<br />764.5
<br />1.637
<br />6.540
<br />13.08
<br />2.25
<br />40
<br />8594.4
<br />.145
<br />.582.
<br />•1:164
<br />0.20
<br />40
<br />747.9
<br />1.673
<br />G.685
<br />13.37
<br />2.30
<br />50
<br />6875.5.182
<br />2° 55`
<br />.727
<br />454
<br />1.745
<br />0.25
<br />S
<br />71.6.8
<br />1.746
<br />6.976
<br />13.95
<br />2.40
<br />1
<br />5729.6
<br />.218
<br />-.873
<br />3° 09'
<br />0.30
<br />20
<br />688.2
<br />1.819
<br />'7.266
<br />14.53
<br />2.50
<br />10
<br />4911.2
<br />.255
<br />1.018
<br />2.036
<br />0.35
<br />30
<br />074.7
<br />1.855
<br />7.411
<br />14.82
<br />2.55
<br />20
<br />4297.3
<br />.291
<br />1.164
<br />2.327
<br />0.40
<br />40
<br />661.7
<br />1.892
<br />7.556
<br />15.11
<br />2.60
<br />30
<br />3819.8
<br />.327
<br />1.309
<br />2.613
<br />0,45
<br />9
<br />637.3
<br />1.965
<br />7.846
<br />15.69
<br />2.70
<br />40
<br />3437.9
<br />.364
<br />1.454
<br />2.909
<br />0.50
<br />20
<br />G14.6
<br />2.037
<br />8.136
<br />16.27
<br />1.80
<br />'50
<br />3125:4
<br />.400
<br />1.600
<br />3.200
<br />0.55
<br />30
<br />003.8
<br />2.074
<br />8.281
<br />16.56
<br />2.85
<br />2
<br />2864.9
<br />.436
<br />1.745
<br />3.490
<br />0.60
<br />40
<br />593.4
<br />2.110
<br />8.426
<br />16:85
<br />2.90
<br />10
<br />2644.6
<br />.473
<br />1.891
<br />3.781
<br />0.65
<br />10
<br />573.7
<br />2.133
<br />8.71.6
<br />17.43
<br />3.00
<br />20
<br />2455.7
<br />.509
<br />2.030
<br />4.072
<br />0:70
<br />30
<br />546.4
<br />2.292
<br />9.150
<br />13.30
<br />3.15
<br />30
<br />2292,0
<br />.545
<br />2.181
<br />4.363
<br />0.75
<br />11 -
<br />521.7
<br />2.402
<br />9.585
<br />19.16
<br />3.30
<br />40
<br />2148.8
<br />.582
<br />2.327
<br />4.654
<br />0.80
<br />30
<br />499.1
<br />2.511
<br />10.02
<br />20.04
<br />3.45
<br />50
<br />2022.4
<br />.618
<br />2.472
<br />4.945
<br />0.85
<br />13
<br />478.3
<br />2.620
<br />10.45
<br />20 91
<br />3.60
<br />a
<br />1910.1
<br />.655
<br />2.618
<br />5.235
<br />0.90
<br />30
<br />459.3
<br />2.730
<br />10.89
<br />.21.77
<br />3.75
<br />10
<br />1809.6
<br />.691
<br />2.763
<br />5.526
<br />0.95
<br />13
<br />441.7
<br />2.839
<br />11.32
<br />22.64
<br />3.90
<br />20
<br />1719.1
<br />'.727
<br />2.908
<br />5.817
<br />1.00
<br />30
<br />425.4
<br />2.949
<br />11.75
<br />23.51
<br />4.05
<br />30
<br />1637.3
<br />.764
<br />3.054
<br />6.108
<br />1.05
<br />14
<br />410.3
<br />3.058
<br />12.18
<br />24.37
<br />4.20
<br />40
<br />1562.9
<br />.800
<br />3.199
<br />6.393
<br />1.10
<br />30
<br />396.2
<br />3.168
<br />12.62
<br />25:24
<br />4.35
<br />50
<br />1495.0
<br />.836
<br />3.345
<br />6.689
<br />1.15
<br />15
<br />383.1
<br />3.277
<br />13.05
<br />2611
<br />4,50
<br />4
<br />1432.7
<br />.873
<br />3.490
<br />6.980
<br />1.20
<br />30
<br />370.8
<br />3.387
<br />13.49
<br />26.97
<br />4.65
<br />10
<br />1375.4
<br />.909
<br />3,635
<br />7.271
<br />1.25
<br />16
<br />359.3
<br />3.496
<br />13.92
<br />27.84
<br />4.S0
<br />20
<br />1322.5
<br />.945
<br />3.718
<br />7.561
<br />1.30
<br />30
<br />348.5
<br />3.606
<br />14.35
<br />28.70
<br />4,95
<br />30
<br />. 1273.6
<br />.932
<br />3.926
<br />7.852
<br />1.35
<br />17
<br />338.3
<br />3.716
<br />14.78
<br />29.56
<br />5.10
<br />40
<br />. 1228.1
<br />1.018
<br />4.071
<br />8.143
<br />1.40
<br />IS
<br />319.6
<br />3.935
<br />15.64
<br />31.29
<br />5.40
<br />5U
<br />1185.3
<br />1.055
<br />4.217
<br />8.433
<br />1.45
<br />19
<br />302.9
<br />4.155
<br />16.51
<br />33.01
<br />5.70
<br />5
<br />1146,3
<br />1.091
<br />4.862
<br />8.724
<br />1.50
<br />20
<br />287.9
<br />4.374
<br />17.37
<br />34.73
<br />6.00
<br />10
<br />1109.3
<br />1.127
<br />4.507
<br />9:014
<br />1.55
<br />21
<br />274.4
<br />4.594
<br />18.22
<br />36.44
<br />6.30
<br />20
<br />1074.7
<br />1.164
<br />4.053
<br />9.305
<br />1,60
<br />22
<br />262.0
<br />4.814
<br />19.08
<br />38.16
<br />6.60
<br />30
<br />.1042:1
<br />1.200
<br />4-798
<br />9.596
<br />1,65
<br />23
<br />250.8
<br />5.035
<br />19.94
<br />39.87
<br />6.90
<br />40
<br />1011.5
<br />1.237
<br />4.943
<br />9.886
<br />1,70
<br />24
<br />240.5
<br />5.255
<br />20.79
<br />41.58
<br />7.20
<br />50
<br />982.6
<br />1,273
<br />5.088
<br />10.18
<br />1.75
<br />25
<br />231.0
<br />5.476
<br />21.64
<br />43.28
<br />7.50
<br />6 :
<br />955.4
<br />1.309
<br />5.234
<br />10.47
<br />1.80
<br />26
<br />222.3
<br />5.697
<br />22.50
<br />44.99
<br />7.S0
<br />10
<br />929.6
<br />1.346
<br />5.379
<br />10.76
<br />1.85
<br />27
<br />214.2
<br />5.918
<br />23.35
<br />46.69
<br />8.10
<br />20
<br />905.1
<br />1.382
<br />5,524
<br />11.05
<br />1.90
<br />28
<br />206.7
<br />6.139
<br />24.19
<br />48.38
<br />8.40
<br />30
<br />881.9
<br />1.418
<br />5.669
<br />11.34
<br />1.95
<br />29
<br />199.7
<br />6.360
<br />25.04
<br />50.07
<br />8.70
<br />40
<br />1 859.0
<br />1.455
<br />5.814
<br />11.63
<br />12.00
<br />1 30
<br />193.2
<br />6.583
<br />25.88
<br />51.76
<br />9.00
<br />The middle ordinate in inches for any cord of length (C) is equal to0012 C'
<br />mnitiplied by the middle ordinate taken from the above table. Thus. if it
<br />desired to bend a 30 ft. rail to fit 10 degree curve, its middle ordinate should
<br />be, .0012X900X2.183 or 2.36 inches.
<br />TABLE III. Deflections for Sub Chords for Short Radius Curves.
<br />Degree
<br />of
<br />Carve
<br />Radius
<br />so
<br />Y2 sub chord _ sin of i def. angle
<br />R
<br />Length
<br />of arc
<br />for 100 ft.
<br />sin. 1, def. ang;
<br />12.5 Ft.
<br />15 rt.
<br />20 Ft.
<br />25 Ft.
<br />30e
<br />193.1$
<br />I° 51'
<br />20 17'2'
<br />58'
<br />3° 43'
<br />101.15
<br />32
<br />181.38
<br />1° 59'
<br />2° 25
<br />3° 10
<br />30 58'
<br />101.33
<br />340
<br />171.01
<br />2° 06'
<br />2° 33'3°
<br />21'
<br />4° 12'
<br />101.48
<br />360
<br />161. So
<br />2° 13
<br />2° 411
<br />3° 33
<br />4° 26"
<br />ao1.6G
<br />38°
<br />153.58
<br />z° 201
<br />20 49 -
<br />3° 44`
<br />4 40'
<br />1o1. 8'S
<br />40°
<br />146.ig
<br />2127,
<br />2° 57'
<br />3° 55`
<br />4° 54'
<br />io2.o6
<br />42°
<br />139.52
<br />2° 34r
<br />3° 05
<br />4° 07'
<br />5° 08'
<br />102.29
<br />44°
<br />133.47
<br />2° 41'
<br />3° 13
<br />4° 18'
<br />5° 22'
<br />102.53
<br />46°
<br />127.97
<br />2° 48'
<br />3° 21'
<br />4°29
<br />5° 36'
<br />102,76
<br />48°
<br />122.42
<br />2° 55`
<br />3° 29`
<br />4° 40
<br />S° 50
<br />I03.00
<br />50°
<br />118.31
<br />3° 02
<br />3° 38`
<br />4 51'
<br />6-04
<br />103.24
<br />52°
<br />114,c6 `
<br />3° 09'
<br />3° 46' -
<br />5°02'
<br />6° 17'
<br />103.54
<br />54°
<br />lIo.Il
<br />3° 1b'
<br />30 54'
<br />S° 13'
<br />60 31'
<br />303.84
<br />56
<br />106.5o
<br />3° 22'
<br />4° 02
<br />S° 23
<br />6° 4'
<br />104.14
<br />58.103.
<br />14
<br />3° 29'
<br />4° lo'
<br />5° 34'
<br />60 57'
<br />104.43
<br />60°
<br />100.00
<br />3° 35'
<br />4° l8'
<br />L5° 44'
<br />7° I1'
<br />1 104-72
<br />19-.
<br />IX
<br />CURVE FORMULAS
<br />T = Rtan I R = T cat. 1 Chord def. = chord2
<br />T = 54 R
<br />Sin. D R =
<br />5o Sin. a D I .
<br />Sin. D ' o. chords = -
<br />R E= R ex. sec I D
<br />.Sin. D = 5o tan a I E = T tan.'J I Tan. def.= z chord def.
<br />The square of any distance, divided by twice the radius, will equal.
<br />the distance from tangent to curve, very nearly.
<br />To find angle for a given distance and deflection.
<br />Rule 1. Multiply the given distance by .01745 (clef. for I° for l ft.
<br />see Table IL), and divide given deflection by the product. -
<br />Rule 2. Multiply given deflection by 57.3, and divide the product by
<br />thegiven. distance.
<br />To find deflection for a given angle and distance, Multiply the angle
<br />by .01743, and the product by the distance.
<br />GENERAL DATA
<br />RLGHT ANGLE TRI UNGLES. Square the altitude, divide by twice the
<br />base. Add quotient to base for hypotenuse.
<br />.Given Base Ioo, Alt. 10.102' 200=.5. 100-x-.5=.100.5 'bYP-
<br />Given Hyp. 1od, Alt. 25.252=200=3.125. 100-3.125 =o6.875 =Base.
<br />Error in first example, .002; in last, .045•
<br />To find `]'ons of Rail in one mile of track: multiply weight per yard
<br />by i r, and divide by 7.
<br />LEVELING. The correction for curvature and refraction, in feet
<br />and decimals of feet is equal to 0.574 d2, where d is the distance in miles.
<br />The correction for curvature alone is closely, X12. The combined cor-
<br />rection is negative. I -
<br />PROBABLE ERROR. If dl, d.,, da; etc, are the discrepancies of various
<br />results from the mean, and if 7_d2=the sum of the squares of these diff or-
<br />ences and n=the number of observations, then the probable error of the
<br />mean -
<br />0.6_745d
<br />Yd
<br />n (n-1)
<br />SOLAR EPHEMERIS. Attention is called to the Solar Ephemeris -for
<br />the current year, published by Keuffel & Esser Col, and furnished free of
<br />charge upon request, which is 8}x6.l in., with about 90 pages of data very
<br />useful to the Surveyor; such as the adjustments of transits, levels and
<br />solar attachments; directions and tables for determining the meridian
<br />and the latitude from observations on the sun and Polaris; stadia meas-
<br />urements; magnetic declination; arithmetic constants; English and Metric .
<br />conversions; trigonometric formulas; Natural and Logarithmic Functions;
<br />and Logarithms of Numbers.
<br />TABLE IV. - Minutes
<br />in Decimals of a Degree. -
<br />1'
<br />.0167
<br />11'
<br />.1823
<br />21'
<br />.3500
<br />31'
<br />.51 G7
<br />41'
<br />.6833
<br />G1'
<br />.8500
<br />2
<br />.0333
<br />12.2000
<br />.0156
<br />22
<br />3667
<br />32
<br />.iW3
<br />42
<br />.7000
<br />52
<br />.6667
<br />3
<br />.0500
<br />13
<br />.2167
<br />23:3833
<br />3
<br />.3833
<br />33
<br />.5500
<br />43
<br />.7167
<br />53
<br />.8833
<br />4
<br />.0667
<br />14
<br />.2333
<br />24
<br />.4000
<br />31
<br />.5667
<br />44
<br />.7333
<br />54
<br />.9000
<br />5
<br />.0833
<br />15
<br />.2500
<br />25
<br />.4167
<br />.35
<br />.5853
<br />45
<br />.7500
<br />55
<br />.91G7
<br />6
<br />.1000
<br />16 ,
<br />.2667
<br />26
<br />.4333
<br />36
<br />.6000
<br />46
<br />.7667
<br />56
<br />.9333
<br />7
<br />.1167
<br />17
<br />.2833
<br />27
<br />.1500
<br />37
<br />.6167
<br />47
<br />.7833
<br />57
<br />.9500
<br />8
<br />.1333
<br />1s
<br />.3000
<br />28
<br />.4667
<br />38
<br />.G333
<br />48
<br />.8000
<br />58
<br />.9667
<br />9
<br />.1500
<br />19
<br />.3107
<br />20
<br />.4833
<br />39
<br />.6500
<br />49
<br />.8167
<br />59
<br />.9833
<br />10
<br />1 1667
<br />20
<br />1 .3333
<br />30
<br />1 .5000
<br />11 40
<br />1 8667
<br />11 50
<br />1 8333
<br />60
<br />11.0000
<br />TABLE V. -- Inches in Decimals of a Foot.
<br />1-10
<br />3-32
<br />%
<br />3-16
<br />5.10
<br />as
<br />3a %
<br />V
<br />.0052
<br />.0078
<br />.0104
<br />.0156
<br />.0203
<br />.0260
<br />,0313
<br />.0617 .0531
<br />.0625
<br />.0729
<br />1
<br />2
<br />3
<br />4
<br />5
<br />G'
<br />7
<br />S9
<br />10
<br />11
<br />0833
<br />.1667
<br />.2500
<br />,3333
<br />.4107
<br />,5000
<br />.5833
<br />.GGf;7 .7500
<br />.8333 .9167
<br />
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