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VIII
<br />TABLE IL - Radii, Ordinates and Deflections. Chord =100 ft.
<br />i Deg.
<br />Radius
<br />Mid •Tan.
<br />Ord.
<br />Dist.
<br />Def.
<br />Dist.
<br />Def.
<br />forI
<br />( 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 />z° 17'
<br />t,
<br />ft.
<br />t.
<br />ft.
<br />181.39
<br />1° 59'
<br />it.
<br />it.
<br />it.
<br />ft.
<br />34°
<br />0°10'
<br />34377.
<br />om
<br />.145
<br />'.291
<br />0.65
<br />7"
<br />819.0
<br />1.528
<br />6.105
<br />12.21
<br />2.10
<br />20
<br />17189.
<br />073
<br />.29L
<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..109
<br />102.06
<br />.436
<br />.873
<br />0.15
<br />30
<br />764.5
<br />1.637
<br />6.540
<br />13.OS
<br />2.25
<br />40
<br />5594.4
<br />.145
<br />.582
<br />1.164
<br />0.20
<br />.40
<br />747.9
<br />1.673
<br />6.655
<br />13.37
<br />2.30
<br />50
<br />6375.5
<br />.182
<br />.727
<br />1:454
<br />0.25
<br />S.
<br />716.8
<br />1.746
<br />6.976
<br />13.95
<br />2.40
<br />1
<br />5729.6
<br />.218
<br />.873
<br />1.745
<br />0.30
<br />20
<br />685.2
<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 />2.327.0.40
<br />104.43
<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 />2.618
<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
<br />.304
<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 />2
<br />2864.9
<br />.436
<br />1.745
<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 />_3.490
<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 />2.131
<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 />U
<br />478.3
<br />2.G20
<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 />3.05S
<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. 27 7
<br />13.05
<br />26.11
<br />4.50
<br />4'
<br />1432.7
<br />.873.3.490
<br />6.950
<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 />3.035
<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 />S
<br />1146.3
<br />1,091
<br />4.362
<br />8.724
<br />1.50
<br />20
<br />257.9
<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 />4.653
<br />9:305
<br />1.60
<br />22
<br />262.0
<br />4.814
<br />10.08
<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 />48.33
<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 />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 to .0012 C2
<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 />4 sub chord
<br />R = sin of II def. angle
<br />of arch
<br />for 100 ft.
<br />sin. i def. ang.
<br />12.5. Ft.
<br />1 15 Ft:
<br />20 Ft.
<br />25 Ft.
<br />30°
<br />193.18
<br />I° 51'
<br />z° 17'
<br />2° 58'
<br />3° 43'
<br />I01.15
<br />32°
<br />181.39
<br />1° 59'
<br />2°25'
<br />3°l0'
<br />3°58'
<br />101.33
<br />34°
<br />171.01
<br />2°° o6'
<br />2° 33'
<br />3° 2i'
<br />4° 12'
<br />101.4.8
<br />360
<br />161.80
<br />2 13'
<br />2° 41'
<br />3° 33'" '
<br />4' 26'
<br />'101.66
<br />38°
<br />153.58
<br />2° 20'
<br />20 49'
<br />3° 44'
<br />40 40'
<br />101.85.
<br />40°
<br />146.19
<br />2°27
<br />2°57'
<br />3°55'
<br />4°54'
<br />102.06
<br />420
<br />139.52
<br />z°34'
<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 />4029
<br />S° g6'
<br />102.76
<br />48°
<br />122.92.
<br />2° 55'
<br />3° 29'
<br />4° 40'
<br />5° 50'
<br />103.00
<br />50°'
<br />118.31
<br />3002 1
<br />3° 38'
<br />40 51'
<br />6° 04'
<br />103.24
<br />52°
<br />114..06
<br />3° o9'
<br />3° 46'
<br />5° 02'
<br />6° 17'
<br />103.54
<br />54°
<br />110. I I
<br />3° 16'
<br />3° 54
<br />S° 13 .
<br />6° 3L'
<br />103.84
<br />5b°
<br />106.50
<br />3022 1
<br />4° 02'
<br />5° 23'
<br />6° 44
<br />104.14
<br />58°
<br />103.14
<br />3° 29'
<br />4° l0'
<br />5° 3.4'
<br />60 57'
<br />104.43
<br />• 60°
<br />.100.00 .
<br />• 3° 35'
<br />4° 18'
<br />5° 44'
<br />7° 11'
<br />104.72
<br />CURVE FORMULAS
<br />LX
<br />T o tan f I R= T_ cot. z I Chord def. =chord'
<br />T = Sin. J D R. 50 R
<br />50 Sin. , D L
<br />Sin. } D = 'R No, chords = -
<br />E= R ex. sec I I D
<br />Sin. j D =, 50 tan ; 1, E = T tan I Tan, def.= s 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 I. Multiply the given distance by -01745 (def. for I° for I 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 />the given distance.
<br />To find deflection for a given angle and distance. Multiply the angle
<br />by .01745, and the product by the distance.
<br />GENERAL DATA
<br />RIGHT ANGLE TRIANGLES. Square the altitude, divide by twice the
<br />base. Add quotient to base for hypotenuse.
<br />Given Base loo, Alt. Io.i02=200=.5. 100-{-.5=100.5 hyp.
<br />Given Hyp. loo, 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 track: multiply weight per yard
<br />by 1s, and divide by 7 -
<br />LEVELING. The correction for curvature and refraction,! in feet
<br />and decimals of feet is equal to 0.574dn, where d is the distance in miles.
<br />The,correction for curvature alone is closely; Jde. _ The combined cor-
<br />rection is negative.
<br />PROBABLE ERROR. If dl, d�, da, etc. are the discrepancies of various
<br />results from the mean, and if 7_&=the sum of the squares of these differ,.
<br />enees and n -the number of observations, then the probable error of the
<br />mean= ±0.6745 ids
<br />n (n -l)
<br />SOLAR EPHEMERIS. Attention is called to the Solar Ephemeris for
<br />the current year, published by'Keuffel & Esser Co., and furnished free of
<br />charge upon request, which is 8x5j 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 f ormulas; Natural andLogarithmic Functions;
<br />and Logarithms of Numbers.
<br />TABLE IV. ' Minutes
<br />in Decimals of a Dcgree.
<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 />a
<br />0500
<br />13.2167
<br />6
<br />23
<br />.3833'
<br />33
<br />.5500
<br />43
<br />7167
<br />53
<br />.8533
<br />4
<br />.0667
<br />14
<br />.2333
<br />24
<br />.4000
<br />34
<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 />.5833
<br />45
<br />.7500
<br />55
<br />.9167
<br />6
<br />.1000
<br />16
<br />.2667
<br />26•
<br />.4333.
<br />36.
<br />.6,000
<br />46
<br />.7607
<br />56
<br />.9333
<br />7
<br />.1167
<br />17
<br />.2833
<br />27.
<br />.4500,
<br />37
<br />.6167
<br />47
<br />.7333
<br />57
<br />"58
<br />.9500
<br />8
<br />.1333
<br />18
<br />.3000
<br />28
<br />.4667
<br />38'
<br />.6333
<br />48
<br />.5000
<br />.9667
<br />9
<br />.1500
<br />19
<br />.3167
<br />29
<br />.4833
<br />39
<br />" .6500
<br />49
<br />.8167
<br />59
<br />.9533
<br />10
<br />1 .1667 1
<br />20
<br />.3333
<br />30
<br />.5000
<br />11 40'
<br />1 .6667 11
<br />50
<br />1 .S333 11
<br />60
<br />1.0000
<br />'N
<br />TABLE V. - Inches in Decimals of a root.
<br />1.16
<br />3-32
<br />3-16
<br />5-16
<br />%
<br />73
<br />0052
<br />.0078
<br />.0104
<br />.01561
<br />.0203
<br />.0260
<br />.0313
<br />.0417 .0521
<br />0625
<br />.0729
<br />1
<br />2--F
<br />3
<br />4
<br />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 />.8333
<br />.9167
<br />'N
<br />
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