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<br />TABLE IL - Radii, Ordinates and Deflections. Chord' --'100 ft.
<br />Deg'
<br />•. -
<br />Radius
<br />Mid.
<br />Ord.
<br />Tan.
<br />Dist.
<br />Def. -
<br />Dist.
<br />Def.
<br />lfor
<br />Deg.
<br />Radius
<br />Mid.
<br />Ord-
<br />Tan
<br />Dist.
<br />Def.
<br />Dist.-
<br />Def.
<br />1 r
<br />2° 17'
<br />t.
<br />ft.
<br />ft.
<br />ft.
<br />t
<br />1° 59'
<br />ft..
<br />ft.
<br />ft,
<br />ft.
<br />i
<br />0'10'
<br />34377.
<br />.036
<br />.145
<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.
<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 />.436
<br />.873
<br />0.15
<br />30..
<br />764.6
<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 />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 />it .' '
<br />5729.6
<br />.218
<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 />130
<br />674.7
<br />1.855
<br />7.411
<br />14.82
<br />2.55
<br />20
<br />4297.3.291
<br />4° 10'. -
<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 />2.618
<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 />.364
<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 />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 />10
<br />2644.6
<br />.473
<br />1.891
<br />3.7810.65
<br />10
<br />573.7
<br />2.183.
<br />8.716'17.43
<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:'30.3.15
<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 />2.511.10:02.
<br />20.04
<br />3.45
<br />b0
<br />2022.4
<br />.618
<br />2.472
<br />4.945
<br />0.85"
<br />12
<br />478.3
<br />2.620.10.45
<br />20.91
<br />3.60
<br />8•
<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 />80
<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 />6
<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 />8
<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 />1.55
<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 />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 />44.99'7.80
<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 />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 />5176
<br />9.00
<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'shonld
<br />be .0012X900X2.183 or 2.36 inches..
<br />TABLE III.: Deflections for Sub Chords for Short Radius Curbes.
<br />Degree
<br />of
<br />Curve
<br />Radius
<br />50
<br />A sub chord =sin of $ def. angle
<br />R
<br />Length
<br />of arc
<br />for 100 ft.
<br />sin. i def. ang.
<br />12.5. Ft.
<br />15 Ft.
<br />20 Ft.
<br />25 Ft.
<br />30°
<br />193.18
<br />1° 51'
<br />2° 17'
<br />2° 58'
<br />30 43'
<br />101.15 -
<br />32°
<br />181.39
<br />1° 59'
<br />2° 25,
<br />3° IV
<br />3° 581
<br />101.33
<br />34°
<br />171.01
<br />2° o6'
<br />2° 33'
<br />3° 21'
<br />4° 12'
<br />101.48
<br />360
<br />,f61.8o
<br />2° 13'
<br />2° 41'
<br />3° 33'
<br />, : 40 26'...
<br />: •'1oI.66
<br />380
<br />153.58.
<br />_
<br />2°20'
<br />2°49'
<br />3°44'
<br />4° 40'
<br />I0I.85
<br />40°
<br />146.19
<br />2° 27'
<br />?` 57'3°
<br />55'
<br />40 54'
<br />lo2.06
<br />42°.
<br />139.52
<br />20 34':
<br />3° 05'
<br />4° 07''
<br />5° o8'
<br />'IO2.29
<br />440.
<br />133.47.
<br />2° 41'
<br />3° 13'
<br />4° i8'.
<br />5°.z2' .
<br />102.53
<br />46°
<br />' 127.97
<br />2° 48'
<br />30 21'
<br />4° 29'
<br />5° 361-
<br />102.76
<br />48°
<br />122.92
<br />2°'55'
<br />3° 29'
<br />4° 40'
<br />S° 50'
<br />103.00
<br />50°.
<br />118..31
<br />3° 02.
<br />3° 38'
<br />40 51'
<br />6° 04'
<br />I03.24
<br />520
<br />114.06
<br />30 09'-
<br />3' 46'
<br />5° o2'
<br />6°17'
<br />103 54 .
<br />54°..
<br />IIO.II
<br />3016
<br />3° 54'
<br />S° 13".
<br />6° 31,.
<br />103 84
<br />569-1
<br />1o6.56
<br />3022
<br />• 4° O2'
<br />50 23'6'
<br />44'
<br />.104-.14.
<br />"58'
<br />103.14
<br />3° 29'
<br />4° 10'. -
<br />5° 34.
<br />6°'57'
<br />104.43.
<br />6o°
<br />Ioo.00
<br />30 35'
<br />4° 18"
<br />5° 44'
<br />�° iI'
<br />104:72
<br />. " CURVE FORMULAS
<br />T RtanjI
<br />__ 5o tan I R = T cot. 11 Chord def. =.chord$ `
<br />T Sin. J D R =
<br />50 R
<br />Sin. j D = 5o Sin: D No, chords = I
<br />R " E� R ex. sec #-I D
<br />5o tan l}•I - a
<br />Sin. J D -= T E= T tan j I Tan. def. = 2 chord def.
<br />The square of any distance, divided by twice the radius, will e4ual
<br />the', distance from tangent to curve, very nearly. '
<br />To find angle'for a given distance and deflection.
<br />Rule'1. Mtiltiply the given distance•by -01745 (def. for I'. for I ft.
<br />see. Table II.), 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.Ioo,Alt. IO.Io2=200=-5. 100--.5=100.5 hyp
<br />Given Hyp. 100, 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 m1le of track: multiply weight per yard
<br />`by'1',, 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, Ida:-, The combined cor-
<br />rection is negative. .
<br />PROBABLE ERROR. If 'dk, d9, da, etc. are. the discrepancies of various
<br />results from the mean, and 1f;7:da=the sum of the squares of these'diffor-
<br />ences and n=the number of observations, then the probable error of the,
<br />mean= 0.6746 ri (n 1)
<br />SOLAR EPHEMERIS., Attention is called't0 the Solar Ephemefis fo-F
<br />the current year; published by Keuffel & Esser Co., and furnished free of
<br />charge upon request, which is 3jx5j 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'1V. - Minutes
<br />TasLE V. -'Inches in Decimals of a Foot.
<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 />Z<
<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 />..0667
<br />14
<br />.2333
<br />24 .
<br />.4060
<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 />54
<br />.9167
<br />0
<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 />8.1500
<br />19
<br />3167
<br />29
<br />.4833
<br />39
<br />.6500_
<br />49
<br />.8167
<br />59
<br />.9833
<br />10
<br />1667jj
<br />20
<br />.3333 1130
<br />1 .5000
<br />11 40
<br />1 .66671,
<br />50
<br />1 .833311
<br />60 '1.0000
<br />TasLE V. -'Inches in Decimals of a Foot.
<br />04
<br />08
<br />5-16
<br />0052 0078
<br />10
<br />•.0156 - .023-16
<br />.0260
<br />313
<br />.0417 .0521
<br />.0625 .0729
<br />1 2
<br />3
<br />.4 5t6
<br />7
<br />8 9
<br />10 11
<br />-...)838..1667
<br />_.2500
<br />..3330 ,4167
<br />_.5000
<br />1 .5833_
<br />.6667 -.7600_
<br />.8333 .9167.
<br />
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