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VM
<br />TAsim It- Radii, Ordinates and'Deflections. Chord=100 ft.
<br />The middle ordinate in inches for any cord 0 .length (C) is equal to .0012 C'
<br />multiplied by the middle ordinate; taken from the above table. Thus, iP it
<br />desired to bend a 30 ft. rail to fit a 10 degree curve, its middle ordI te:shodld'
<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 />Mid. •
<br />Ord..
<br />Tan. '
<br />Diet.
<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 />foi
<br />1 Ft.
<br />51' .
<br />t.
<br />ft.
<br />ft.
<br />ft.
<br />/
<br />101. 15
<br />ft.•
<br />ft.
<br />ft.
<br />ft.
<br />,
<br />0°:10'
<br />34377.:
<br />.036
<br />.145
<br />1 :291
<br />0.05
<br />V
<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 />764.5
<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 />6.685
<br />13.37
<br />2.30
<br />50
<br />6875.5
<br />.182
<br />.727,
<br />A.454
<br />0.25,
<br />8
<br />716.8
<br />1.746.
<br />6.976
<br />13.95
<br />2.40
<br />I.
<br />5729.6
<br />,.218
<br />.873
<br />-1.745
<br />0.30
<br />20
<br />688.2
<br />1.819
<br />7:26614.53
<br />22'
<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
<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 />r. 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 />6.55
<br />;30'
<br />603.8
<br />2.074
<br />8.281.16.56
<br />22'
<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 />:3.781'0.65
<br />6o°
<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 />130-
<br />546.4
<br />2.292
<br />9:150
<br />18130
<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 '20.04
<br />3.45
<br />50
<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 />6 ..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 />43 ;
<br />441.7
<br />2.839
<br />11.32 '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 />1.16,
<br />15`
<br />383.1
<br />3.277.
<br />13.05
<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 />.26.11
<br />13:49''26.97
<br />4.65
<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=.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 />1228.1'1.018
<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 />S
<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.: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 />39.16
<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 />5.036
<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 />7.80
<br />10929.8
<br />1.346
<br />5.379
<br />10.76
<br />1.85
<br />271
<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 />206.7-6.139
<br />24.19
<br />48.38
<br />8.40
<br />30
<br />;881.911.418
<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 />:859.911.455
<br />5.814
<br />11.63
<br />2.00
<br />30;
<br />1193.216.-583M.88
<br />51'.76
<br />9.00
<br />The middle ordinate in inches for any cord 0 .length (C) is equal to .0012 C'
<br />multiplied by the middle ordinate; taken from the above table. Thus, iP it
<br />desired to bend a 30 ft. rail to fit a 10 degree curve, its middle ordI te:shodld'
<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 />SU
<br />35 sub -chord =sin of } de[. angle '
<br />R
<br />Length
<br />of arc
<br />for 100 ft.
<br />sin.1 def. ang.
<br />12.5. Ft.
<br />15 Ft.
<br />20 Ft.
<br />25 Ft.
<br />3°°..-
<br />...193; 18_
<br />I°
<br />51' .
<br />2°°17 2°
<br />.8500
<br />58,
<br />3°
<br />43'
<br />101. 15
<br />320
<br />181.39
<br />1°
<br />89'
<br />2'
<br />25'
<br />30
<br />10'
<br />30
<br />58'
<br />101.33
<br />34°
<br />171.01
<br />20
<br />06'
<br />2°
<br />33'3°
<br />.7167
<br />21'
<br />Q.°
<br />12'
<br />101.48
<br />360
<br />:i61.8o
<br />20
<br />13'
<br />2°
<br />41.
<br />30
<br />33'
<br />40
<br />26'
<br />Iol.66
<br />380
<br />153.58.
<br />2020,
<br />25
<br />2°
<br />49'
<br />3°
<br />4.4'
<br />4°
<br />40'.
<br />101.85 .
<br />40°'
<br />146.19
<br />2°
<br />27'
<br />2057'
<br />.4333
<br />.3°
<br />55'
<br />4°
<br />54'
<br />102.o6
<br />42'
<br />139.52
<br />2°
<br />34';
<br />30
<br />65'
<br />40
<br />07'
<br />50
<br />08'
<br />io2:z9
<br />440
<br />3
<br />1347
<br />2°
<br />41,
<br />3°
<br />13'
<br />4°
<br />18'
<br />50
<br />22'
<br />102.53
<br />460
<br />127.97
<br />2°
<br />48'.
<br />3°
<br />21'
<br />4°
<br />291_
<br />50
<br />36'
<br />102.76
<br />48°
<br />:122.92
<br />20
<br />55'.
<br />30
<br />29'
<br />40
<br />40'
<br />5°,50'
<br />.5000
<br />103:°0
<br />- 5o°:
<br />118.31
<br />3°
<br />oz'
<br />3°.38'
<br />' 4°
<br />51
<br />6004
<br />1
<br />103.24.
<br />52°<
<br />114.0.6 ..
<br />3°
<br />09'
<br />30
<br />46,
<br />5°
<br />O2'
<br />6'
<br />17,
<br />103.54
<br />- 54°'
<br />13'
<br />IIO.II
<br />30
<br />W.
<br />30
<br />54'
<br />S°
<br />6°
<br />3i'
<br />"103.84
<br />560
<br />106.50
<br />30
<br />22'
<br />40
<br />02'
<br />5°
<br />23'
<br />6°.44''
<br />104.14
<br />580
<br />103.14
<br />30
<br />29'
<br />4°
<br />10'
<br />5°
<br />34'
<br />60
<br />57'
<br />104.43
<br />6o°
<br />100.00
<br />30
<br />35
<br />4°
<br />18`
<br />5°
<br />44'
<br />70
<br />11'
<br />104.72
<br />xx
<br />CURVE FORMULAS
<br />T =` R tan j "I chord'
<br />R=Tcot.�I
<br />_ 50 tan }.I . Chord def.
<br />T Sin. J 1) R- b0 R
<br />Sin. D = 50 Sin., D. No. chords I
<br />R. 'E = R ex: sec JJ D
<br />Sin. J D =`5° tT ' I E =T tan I I Tan. def. _ }chord def.
<br />The square of any distance, divided'by.twice the radius, will equal
<br />the distance from tangent tocurve, very nearly:
<br />To find angle for a given distance and deflection.
<br />Rule 1. Multiply 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 *loo, Alt. 10.102._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'fii•st example, .002; In last, .045•'
<br />To find' Tons of • Rail in one mile of track: multiply weight per yard'
<br />by 'i i, and divide by 7.
<br />Litvti 1md._ The correction jor curvature and refraction, in feet
<br />and decimals of feet is equal to 0.57449, where d.is the.distance in miles.
<br />Thecorrection for vurvature alone is closely,''Id.2. The combined cor-
<br />rection is negative.
<br />PROBABLE ERROR. If dk, de; da, etc. are, the discrepancies of various
<br />iesults.from the mean; and 1f 7-da=the sum of the squares of these diftor-
<br />ences and n=the numbei of observations, then the probable error of the.
<br />mean=
<br />j=-0.6745 • n (n 1) _
<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 34x5] 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 />TASLD
<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 />a -
<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 />.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 />.6000
<br />46
<br />.7667
<br />56
<br />.9333
<br />7
<br />.1167
<br />Y7.
<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 />b8
<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 />9833
<br />10.
<br />.1667
<br />20
<br />'.3333
<br />30
<br />.5000
<br />40
<br />.6667
<br />50
<br />.8333
<br />60
<br />1.0000
<br />TASLD
<br />V. -Inches in Decimals of a Foot.
<br />1-16 3-32
<br />',4
<br />3-16
<br />b-16
<br />%
<br />M
<br />.0052_._-•0078
<br />..0104.
<br />-0156-
<br />.0208
<br />.0260
<br />..0313
<br />.0417 .C521
<br />.0625
<br />.07
<br />1 2
<br />3
<br />4
<br />b
<br />6
<br />7
<br />8 9
<br />10
<br />11
<br />0833 .1667
<br />.25,00
<br />.3333
<br />.4167
<br />.5000
<br />.b833
<br />_.8667 .750D
<br />.8333
<br />.9167
<br />
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