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VIII
<br />TADLE II. - Radii, Ordinates and Deflections. Chord=100 ft.
<br />Deg.
<br />Radius
<br />Mid.
<br />Ord.
<br />Tan.
<br />Dist.
<br />Def:
<br />Dist.
<br />Det.
<br />for
<br />I Ft.
<br />Deg.
<br />Radius
<br />Mid.
<br />Ord.
<br />', Tan:
<br />Dist.
<br />Def•
<br />Dist.
<br />Det.
<br />for
<br />1 Ft.
<br />2' 117'
<br />ft.
<br />ft.
<br />ft.
<br />it.
<br />i
<br />1° 59'
<br />--ft,
<br />, ft.
<br />ft,
<br />ft.
<br />34°
<br />0"10
<br />34377.
<br />•.036
<br />.145
<br />.201
<br />0.05
<br />7°
<br />519.0
<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 />G.540
<br />13.OS
<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 />6.655
<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 />6.076
<br />13.95
<br />2.40
<br />1
<br />5729:6
<br />.218
<br />.873
<br />1.745
<br />0.30
<br />20
<br />G3S.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 />G74.7
<br />1.855
<br />7,411
<br />11.82
<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 />3.309
<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 />.3G4
<br />1.454
<br />2.909
<br />0,50
<br />20
<br />614.6.2.037'
<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 />16.5G
<br />2.85
<br />2
<br />2804.9
<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 />3.7S1
<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'..545
<br />2.181
<br />4.363
<br />0.75
<br />it
<br />521.7
<br />2.402
<br />9.585
<br />19:16
<br />3.30
<br />{40
<br />2148.8
<br />.532
<br />2.327
<br />4.654
<br />0.80
<br />30
<br />499.1
<br />2.511
<br />10.02
<br />20.01
<br />3.45
<br />50
<br />2022.4
<br />.618
<br />2.472
<br />4.045
<br />0.85
<br />12
<br />478.3
<br />2,G20
<br />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 />22.61
<br />3.90
<br />120
<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 />•1.05
<br />.30
<br />.1637.3
<br />.764
<br />3.054
<br />6.105
<br />1.05
<br />14
<br />410.3
<br />3.058
<br />12.13
<br />24.37
<br />•1.20
<br />40
<br />1562.9
<br />.800
<br />3.199
<br />6.393
<br />1.10
<br />30
<br />396.2
<br />3.108
<br />12.62
<br />25.24
<br />4.35
<br />50
<br />1495.0
<br />.83G
<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 />!
<br />1432.7
<br />.873
<br />3.490
<br />6.980
<br />1.20.
<br />30
<br />370.8
<br />3.357
<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 />4.50
<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 />.032
<br />3.92G;
<br />7.852
<br />1.35
<br />17
<br />338.3
<br />3.716
<br />14.78
<br />29.56
<br />5.10
<br />1228.1
<br />1.018
<br />4.071
<br />8.143
<br />1.40
<br />1S
<br />319.6
<br />3.935
<br />15.64
<br />31.29
<br />5.40
<br />••40
<br />50
<br />1155.8
<br />1.055
<br />4.211
<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 />1140.3
<br />1.091
<br />4.362,8.724
<br />1.50
<br />20
<br />287.9
<br />4.374
<br />17.37
<br />34.73
<br />G.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 />3G.4.1
<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 />4.708
<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 />41.53
<br />7.20
<br />50
<br />OS2.6
<br />1.273
<br />5.083
<br />10.18
<br />1,75
<br />25
<br />231.0
<br />5.476
<br />21.64
<br />43.25
<br />7.50
<br />955.4
<br />1.309
<br />5.234
<br />IU178
<br />1.80
<br />26
<br />222.3
<br />5.697
<br />22.50
<br />44.09
<br />7.50
<br />-6
<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 />46.6,9
<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 />24.10
<br />48.35
<br />S.40
<br />30
<br />581.9
<br />1.418
<br />5.669'11.34
<br />1.95
<br />29
<br />199.7
<br />61.360
<br />25.04
<br />50.07
<br />S.70
<br />40
<br />1 859.9
<br />1.455
<br />5.314
<br />11.63
<br />2.00
<br />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 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 .0012X90OX2.183 or 2,3G inches.
<br />TNELE IIL- Deflections for Sub Chords for Short Radius Curves.
<br />Degree.
<br />of
<br />Curve
<br />Radius
<br />50
<br />M sub chord
<br />1t = sin of z def. angle
<br />of -Length L
<br />for 100 ft.
<br />sin-Idef.ang,
<br />12.5 Ft.
<br />15 Ft.
<br />20 Ft.
<br />25 Ft.
<br />30°.
<br />193-18
<br />1°• 5i'
<br />2' 117'
<br />2' S8' -
<br />3' 43'
<br />Ioi.15
<br />3z°
<br />181.39
<br />1° 59'
<br />2° 25
<br />3° lo'
<br />3° 58'
<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 />161.8o
<br />-2° 13,'-
<br />20 41'
<br />3° 33'
<br />4' 26'
<br />1oi.66
<br />38'
<br />153.58 -
<br />2° 20'
<br />2049 '
<br />3' 441
<br />: 4' 40'
<br />101.85
<br />40°
<br />146-19
<br />2° 27'
<br />2° 57'
<br />3° 55'•
<br />�4° 54'
<br />102.o6
<br />42
<br />139.52
<br />2° 34'
<br />3° 05
<br />4° 07'
<br />S' 08,
<br />102.29
<br />44°
<br />.,33.47
<br />2° 41
<br />.3 13'
<br />4° i8'
<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 />122.92
<br />2° 55'
<br />3° 29'
<br />4° 40'
<br />5° 50'
<br />103.00
<br />50°
<br />118.31
<br />3° 02'
<br />3° 38'
<br />4° 51'
<br />6° 04'
<br />103.2 }
<br />52o
<br />114,06
<br />3°09'
<br />3°46'
<br />5°02'
<br />6°17'
<br />103.54
<br />54
<br />110.11
<br />3° 16'
<br />3' S4
<br />?° i3'
<br />60 31'
<br />103.84
<br />560
<br />io6. 5o
<br />3° 22'
<br />4° 02
<br />5° 23'
<br />60 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 />100.00
<br />30 35'
<br />4° 18'
<br />50 44'
<br />7° 1 I'
<br />104.72
<br />IX
<br />CURVE FORMULAS
<br />T =, R tan 8 I r chordz
<br />50-tan+J-I' R.= T cot. z I Chord def: _
<br />T Sin. ll R 50 R
<br />`=
<br />.Sin. D = 50 Sin. 12 D 1`10, chords = D
<br />R E = R ex. sec' I .
<br />5o tan a I
<br />.Sin. D = q E = T tan I Tan. def. _ chord def:
<br />The square of any distance, divided by twice the radius, will equal
<br />the distance frorn 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 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. 10.102=200=.5. ioo+.5=ioo•5 hyp•
<br />Given Hyp. ioo,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 I I, and divide by 7-
<br />.. LEVELINc. The correction for curvature and refraction, in feet
<br />and decimals of feet is equal to 0.574 d', where d is the distance in miles.
<br />;The correction for curvature alone is closely, Ids. The combined cor-
<br />rection is negative.
<br />PROBABLE ERROR. If d; d„ d„ etc. are the discrepancies of various
<br />results from the mean, and if 7-d2=the sum of the squares of these differ-
<br />ences and n=the number of observations, then the probable error of tho
<br />mean=
<br />:I-- 0.6745v n (n-1)
<br />SOLAR EPHEMERIS. Attention is called to the Solar Ephemeris for
<br />the current year, published by Keuffel & Esser Co., and furnisbed free of
<br />charge upon request, which is 3;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 andLogarithmic Functions;
<br />and Logarithms of Numbers.
<br />TA13LF IV. - l linutes
<br />•
<br />in Decimals of a Degree.
<br />1'
<br />.0167
<br />11'
<br />1533
<br />21'
<br />.3500
<br />31'
<br />.5167
<br />41'
<br />.6S33
<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 />8
<br />.0500
<br />13
<br />.2167
<br />23
<br />.3833
<br />33
<br />.5500
<br />43
<br />.7107
<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 />OS33
<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 />IG
<br />.2667
<br />2G
<br />.4333
<br />3G
<br />.6000
<br />46
<br />.7667
<br />5G
<br />.9333
<br />7
<br />.1167.
<br />17
<br />.2833
<br />27
<br />.4500
<br />37
<br />GI67
<br />47
<br />.7833
<br />57
<br />.9500
<br />8
<br />.1333
<br />1S
<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 />.4833
<br />89
<br />.6500
<br />49
<br />.8167
<br />50
<br />.9833
<br />10
<br />.1G67 11
<br />20
<br />1 .3333 1130
<br />1 .5000
<br />11 40
<br />1 .0667
<br />j 50
<br />1 .83331,
<br />GO
<br />1.0000
<br />•
<br />TADLE V. -
<br />Inches in Decimals of a Foot.
<br />1-113
<br />3-32
<br />Y8
<br />3-18
<br />7(t
<br />5-16
<br />%
<br />Yys
<br />.0052
<br />.0078
<br />.0t01
<br />.0156
<br />.0209
<br />.0260
<br />.0313_
<br />.04]7 .0521
<br />0625
<br />.0729
<br />1
<br />2
<br />3
<br />4
<br />5
<br />6
<br />7
<br />8 9
<br />10
<br />11_
<br />.0833
<br />.1G67
<br />.2500
<br />.3333
<br />.4167
<br />.5000
<br />.5S33
<br />.6667 .7500
<br />.8333
<br />.9167
<br />
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