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'9YYY -
<br />TABLE IL - Radii; Ordinates and Deflections. Chord =100 ft.
<br />Deg.
<br />�
<br />Mid
<br />Ord.,-
<br />Tan. ,
<br />Dist. >
<br />Def...
<br />Dist.-
<br />"Def.
<br />for"-.
<br />1 Ft.
<br />Deg.
<br />Radius
<br />Mid
<br />Ord.
<br />"Tan
<br />Dist.
<br />Def.
<br />Dist.
<br />Def.
<br />for
<br />1 Ft.
<br />I°
<br />t.
<br />ft.
<br />ft.
<br />ft.
<br />I
<br />3°.43'-.
<br />ft,
<br />ft.
<br />ft. -
<br />ft.
<br />o
<br />159
<br />0"10'
<br />34377.
<br />.036.145
<br />0
<br />3
<br />.291
<br />0.05
<br />7'
<br />819.0
<br />1.528
<br />6.105
<br />12.21
<br />2.10
<br />20
<br />17189..t.073
<br />3°
<br />.291
<br />.5S2
<br />0.10
<br />20'
<br />781.8
<br />1.600.
<br />6.395
<br />12.79
<br />2.20
<br />30
<br />11459:'.:.109
<br />'..
<br />.436
<br />.873
<br />0.15
<br />30
<br />764.5
<br />1.637
<br />6.540
<br />13.082.25
<br />49'
<br />40
<br />8594:4
<br />'.145
<br />.582
<br />1:164
<br />0.20
<br />.40
<br />747.9
<br />1:673
<br />6.685
<br />13.37
<br />2.30
<br />50
<br />-6875:5
<br />.182
<br />.727
<br />'1:454
<br />0.25
<br />8
<br />716.8
<br />1:746
<br />•6.976
<br />13.95
<br />2.40
<br />1 _
<br />5729F6:r.218
<br />102.29
<br />.873
<br />1.745
<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 />674.7
<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 />47.556
<br />15.11
<br />2.60
<br />30
<br />3819:8
<br />..327
<br />1.309
<br />2.618
<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.:.364
<br />09'.
<br />1.454
<br />-2:909
<br />0.50
<br />20
<br />614.6
<br />2:037
<br />8.136
<br />16.27
<br />2.80
<br />50-:
<br />3125.4
<br />.400
<br />1.600
<br />3.200
<br />0.55.
<br />30
<br />603.8
<br />2.074
<br />8.281
<br />16:56
<br />2.85
<br />22'1.
<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 />16.85'2.90
<br />29'
<br />10
<br />2644.6
<br />.473
<br />1.891
<br />3:781
<br />0.65
<br />10
<br />573.7
<br />2:183
<br />8.716
<br />17.43
<br />3.00
<br />20
<br />2455.7
<br />.509
<br />2.036
<br />4.072
<br />0.70
<br />30
<br />546.4
<br />2.292
<br />9:150
<br />18.30
<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 />`•60
<br />2022.4
<br />.618
<br />2.472
<br />4.945
<br />0.85
<br />12
<br />478.3
<br />2.620
<br />10.45
<br />20.91
<br />3.60
<br />3 ,.
<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 />6.398
<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 />26.11
<br />4.50
<br />A
<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 />4.80
<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 />-.982
<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 />18
<br />319.6
<br />3.935
<br />15.64
<br />31.29
<br />5.40
<br />50
<br />1185.8
<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 />6
<br />1146.3
<br />1.091
<br />4.362
<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 />1.65
<br />21
<br />274.4
<br />4.594,18.22
<br />36.44
<br />6.30
<br />20`
<br />1074.7
<br />1.164
<br />4.653
<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 />10.8 ,1
<br />1.75
<br />25
<br />231.0
<br />5.476
<br />21.64
<br />43.23
<br />7.60
<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 />7.80
<br />10''
<br />929'.6
<br />1.346
<br />6.379
<br />10.76
<br />1:85
<br />27
<br />214.2
<br />5.918
<br />23.35 '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 />859.9
<br />1.455
<br />5.814
<br />11.63
<br />2.00
<br />30
<br />193.2
<br />6.583
<br />25.88
<br />51'.7619.00
<br />The middle ordinate in inches for any cord of length (C) is equal to .0012 C'
<br />multiplied by the middle ordinate taken from the above table. Thus, if it
<br />desired to bend a 30 ft. rail to fit a 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 />Curve
<br />Radius
<br />50 '
<br />in Decimals of a Degree.
<br />M sub chordLength
<br />R = sin of $def. angle
<br />of arc
<br />for 100 ft.
<br />sin. 22 def. ang.
<br />12.5 Ft.
<br />15 Ft.
<br />20 Ft. ',
<br />25 Ft.
<br />30°
<br />193.18
<br />I°
<br />51'
<br />20
<br />17'
<br />2°
<br />58'
<br />3°.43'-.
<br />22
<br />101.15
<br />o--
<br />'"3z
<br />--
<br />181.39
<br />o
<br />159
<br />,
<br />o
<br />i
<br />,
<br />25
<br />0
<br />3
<br />10 r
<br />- 30-581
<br />101.33
<br />34°
<br />171.01
<br />2°
<br />o6'
<br />2°
<br />33'
<br />3°
<br />21'
<br />4°
<br />12,
<br />101.48
<br />360
<br />161.80
<br />2°
<br />13'
<br />20
<br />41'`.3033
<br />54
<br />'..
<br />; 4°-26'--'
<br />0833
<br />. 1o1.66
<br />38°
<br />_
<br />153-F58_
<br />2'
<br />20'
<br />z°
<br />49'
<br />3°
<br />44'
<br />4°
<br />4Q'
<br />iof .85
<br />'o•-
<br />`40
<br />-
<br />. `146.19
<br />o
<br />'.z
<br />27'.
<br />o
<br />2
<br />r
<br />57
<br />o
<br />3
<br />r
<br />55
<br />- o
<br />.4
<br />i
<br />54 ..
<br />102.06..
<br />.1167
<br />139' 52'
<br />2°
<br />341
<br />3°
<br />051
<br />4°
<br />07'
<br />S°.o8'
<br />-
<br />102.29
<br />_42°
<br />440.
<br />-
<br />133.47
<br />2°
<br />41'
<br />3°
<br />13'
<br />4°
<br />18' _
<br />.5°
<br />22'
<br />-102.53
<br />46° =
<br />' 127.97 .-.
<br />-20
<br />48�
<br />30
<br />21'
<br />4°
<br />29'
<br />5°
<br />36'.
<br />IO2.76
<br />480
<br />12Z. 9?
<br />2°
<br />55'
<br />30
<br />29'
<br />40
<br />401
<br />50:50'
<br />.6500
<br />1 .6667 11
<br />103.00
<br />-50.°• y
<br />118.'31•
<br />3°
<br />02
<br />3°
<br />38'
<br />4°
<br />51'
<br />6°
<br />04'-
<br />- 103.24
<br />5i°
<br />�- 114.06
<br />3°
<br />09'.
<br />3°
<br />46'
<br />5°.02'
<br />6°
<br />1.7.
<br />103.54
<br />-54° "
<br />110': I I`..
<br />T 3°
<br />16'
<br />3°
<br />54'
<br />S°
<br />13'
<br />6031'
<br />103. $4
<br />56' • .
<br />1 106.50
<br />3°
<br />22'1.
<br />4°
<br />02'
<br />S°
<br />23'
<br />60-44'
<br />,_104.14
<br />58°
<br />103.14-
<br />3°
<br />29'
<br />4°
<br />10'
<br />`5°
<br />34'
<br />60
<br />57'
<br />104.43
<br />60°'
<br />i0o.00
<br />3035
<br />4018
<br />X50
<br />44'
<br />.70.11'
<br />< 104.72
<br />CURVE FORMULAS -
<br />T= R tan j I R= T cot. 3 I chord'
<br />50 tan I- z -Chord def. _ R
<br />T Sin.. D_60
<br />R =
<br />Sin. ,} D = 5o Sin. i} D No. chords = I
<br />R E =Rex. sec ; I D
<br />50 tan $ I
<br />Sin. D = ,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 tangefit to curve, very nearly.
<br />To find angle for a given distance and deflection.
<br />Rule I. Multiply the given distance by -01745 (def. for O for I ft.
<br />see =Table II.), and divide given deflection by the product. 'I
<br />Rule 2. Multiply given deflection by 57.3, and divide the product by
<br />the •given -distance.
<br />To find deflection for a given angle and distance. Multiply the angle
<br />by .o1748, and the product by -the distance.:
<br />GENERAL DATA -
<br />RIGHT ANGLE TRIANGLES.' Square, the altitude, divide by twice the
<br />j base. Add -quotient to base•for hypotenuse.
<br />Given Base loo, Alt: 10:102_200=.5. 1oo+.5=100.5 hyp.
<br />Given Hyp, loo, A1t.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 track: multiply weight per yard
<br />by 1I, and divide by 7.;'
<br />LEVELING. The correction for curvature and refraction, in feet
<br />and -decimals of feet is equal to 0.574d2,where d is the distance in miles.
<br />The correction for curvature alone'is closely, jd2. -The .combined cor-
<br />rection is negative.
<br />PROBABLE ERROR. If d,, da, da, etc. are the discrepancies of various
<br />results from the mean, and if 7-d2=the sum of the squares of these diffor-
<br />ences and n=the number of observations, then the probable error of the.
<br />mean= ± 0.6745 oda
<br />SOLAR EPHEMERIS. Attention is. called to the Solar "'Ephemelvs for'
<br />the current year, published by. Keuffel & Esser Co., and furnished free of
<br />charge upon request, which is, 3j -x58 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 W. - Minutes
<br />in Decimals of a Degree.
<br />1'
<br />.0167
<br />11'
<br />.1833
<br />21'
<br />.3500
<br />31'
<br />.5167
<br />41'
<br />.6833
<br />51'
<br />.8500
<br />2
<br />.0333
<br />12
<br />:2000
<br />22
<br />.3667
<br />32
<br />.5333
<br />42
<br />.7000
<br />52
<br />.8667
<br />3.
<br />.0500
<br />13
<br />.2167
<br />23
<br />.3833
<br />33
<br />.5500
<br />43
<br />.7167
<br />53
<br />.8833
<br />4
<br />6
<br />.0667
<br />14
<br />.2333
<br />24
<br />.4000
<br />34
<br />.5667
<br />44
<br />.7333
<br />54
<br />.9000
<br />8
<br />0833
<br />15
<br />.2500
<br />25
<br />.4167
<br />35
<br />.5833
<br />45
<br />.7500
<br />0
<br />.9167
<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 />.4500
<br />37
<br />.6167
<br />47
<br />.7833
<br />57
<br />.9500
<br />8
<br />.1333
<br />18
<br />.3000
<br />28
<br />.4667
<br />38
<br />.6333
<br />48
<br />.8000
<br />58
<br />.9667
<br />9
<br />..1500
<br />19
<br />.3167
<br />29
<br />39
<br />49
<br />.8167
<br />59
<br />.9833
<br />10
<br />-.1667
<br />20
<br />.3333 1130
<br />.4833
<br />1 .5000
<br />11 40
<br />.6500
<br />1 .6667 11
<br />50
<br />.8333
<br />60
<br />11.0000
<br />-
<br />TABLE V. - Inches in Decimals of a Foot.
<br />1-16
<br />3-32
<br />X
<br />3-16
<br />X
<br />5-16
<br />%
<br />34 %
<br />%
<br />?�
<br />.0052
<br />.0078
<br />.0104
<br />.0156
<br />:0208
<br />.0260
<br />.0313
<br />.0417 .0521
<br />.0625
<br />.0729
<br />1
<br />2
<br />3.
<br />4
<br />1 5
<br />6
<br />7
<br />8 9
<br />10
<br />11
<br />0833
<br />.1667
<br />.2500
<br />.3333
<br />:4167
<br />.5000
<br />.5833
<br />..6667 .7500
<br />.8338
<br />.9167
<br />
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