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TABLE IL - Radii, Ordinates and Deflections. Chord =100 ft.
<br />Deg'
<br />Radius"
<br />Mid.
<br />Ord.
<br />Tan. "
<br />Dist.
<br />. Def.
<br />Dist.
<br />Def.
<br />Radius
<br />If Ft
<br />Deg.
<br />15 Ft.
<br />Mid.
<br />Ord.
<br />Tan
<br />Dist.
<br />Def.
<br />Dist.
<br />Def.
<br />1 r t.
<br />I°
<br />t.
<br />t.
<br />t.
<br />ft
<br />1
<br />3°
<br />ft,
<br />it.
<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 />204
<br />781.8
<br />1.600
<br />6.395
<br />12.70
<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 />1.454
<br />0.25
<br />6 •
<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 />688.2
<br />1.819
<br />7.266
<br />14.53
<br />2.50
<br />20
<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 />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 />S.
<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 />3.7810.65.
<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 />5.0
<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
<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 />3.058.12.18
<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 />L
<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 />1S
<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 />d
<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 />0
<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 />1.346,5.379
<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 />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 6.30 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 />3 e sub chord = sin of } def, angle
<br />R
<br />Length
<br />of arc
<br />for 100 ft.
<br />sin. $ 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 />2°
<br />17'
<br />2°
<br />581
<br />3°
<br />431
<br />101.15
<br />32°
<br />181.39
<br />1°
<br />59'
<br />2°
<br />25'
<br />3°
<br />lo'-
<br />30
<br />58'
<br />I01.33
<br />34°
<br />171.01
<br />2°
<br />o6'
<br />2°
<br />33'
<br />3°
<br />21'
<br />4°
<br />12'
<br />I01.48
<br />360
<br />161.8o .
<br />2°
<br />13'
<br />2°
<br />41'.
<br />3°.33'
<br />.9000
<br />4°
<br />26'
<br />Ioi.66
<br />380
<br />153.58
<br />2°20'
<br />_
<br />2°49'
<br />45
<br />3'441
<br />b
<br />4°40'
<br />6
<br />Io1.85
<br />400
<br />146.19
<br />20
<br />27'
<br />2°
<br />57'
<br />3°
<br />55
<br />4°
<br />54'
<br />02. o6
<br />42'
<br />139.52
<br />2'34'
<br />27
<br />3'
<br />05,
<br />4°07'
<br />47
<br />5°08'
<br />57
<br />102.29
<br />44°
<br />133.47
<br />20
<br />41'
<br />30
<br />13'
<br />4°
<br />18'
<br />5°.22'
<br />.8000
<br />102.53
<br />46'
<br />127.97
<br />2°
<br />48f
<br />30
<br />21,
<br />40
<br />29
<br />5°
<br />36'
<br />102.76
<br />48°
<br />122.92
<br />2°
<br />55'
<br />3°291
<br />.3333
<br />4°4O,
<br />.5000
<br />5'
<br />50'
<br />103.00
<br />-50°"
<br />118.31
<br />3°02'
<br />3°38'
<br />4°51'
<br />6°04'
<br />1103.24
<br />52°
<br />114.06
<br />3009
<br />1
<br />3°
<br />46'
<br />5°
<br />02'
<br />60
<br />17'
<br />103:54
<br />-54° .
<br />110..11
<br />3°
<br />16'
<br />3054
<br />1
<br />5°13'
<br />60
<br />31'
<br />iO3.84
<br />56°
<br />106.50
<br />3°
<br />22'
<br />4°
<br />02'
<br />5°
<br />23'
<br />6°
<br />44'
<br />104.14 .
<br />58°
<br />103.14
<br />3'
<br />29
<br />4'
<br />10,1
<br />50
<br />34"
<br />60571
<br />104.43
<br />600
<br />100.00
<br />3°
<br />35'
<br />40
<br />18'
<br />50
<br />44'
<br />70.1I�
<br />104:72
<br />CURVE FORMULAS.
<br />T= R tan j I R= T cot, z Ch
<br />I cord$
<br />50 tan f I • ord def. = R
<br />T - Sin.J D R = 60
<br />Sin. D = 50 Sin. $ D No. chords = I
<br />R E= R ex. sec 1,I D
<br />Sin. D = 5o tan + I E =T tan } I Tan. def. =1, chord def.
<br />The square of any distance, divided by twice the radius, will equal
<br />il 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 />i 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. ()O+.5 =100.5 hyp.
<br />Given Hyp. loo, Alt. 15.252+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'fi, and divide by 7.
<br />LEVELING. The correction for curvature and" refraction, in feet
<br />and decimals of feet is equal to 0.574 de, where d is the distance in miles.
<br />The correction for curvature alone is closely, jda. The combined cor-
<br />rection is negative.
<br />PROBABLE ERROR. If d;, d, da, etc, are the discrepancies of various
<br />results from the mean, and if fid°=the sum of the squares of these differ-
<br />ences and n=the number of observations, then the probable. error of the,
<br />mean=.:h 0.6745
<br />SOLAR EPHEMERIS. ttention is called to the Solar Ephemefis for,
<br />the current year, published by Keuffel &Esser Co., and furnished free of
<br />charge upon request, which is 3}x5� 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 deteiznining 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 a, Logarithm a Functions;
<br />and Logarithms of Numbers.
<br />TABLE IV. - 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 />a
<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 />.7167
<br />53
<br />.8833
<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 />b
<br />.0833
<br />15
<br />.2500
<br />25
<br />.4167
<br />35
<br />.5833
<br />45
<br />.7500
<br />b
<br />.9167
<br />6
<br />.1000
<br />16
<br />.2667
<br />26
<br />.4333
<br />36
<br />.6000
<br />46
<br />7667•
<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 />6
<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 />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 />J
<br />TABLE V. -Inches in Decimals of a Foot.
<br />lab
<br />342
<br />"
<br />3-16
<br />� 5-16
<br />%
<br />34 %
<br />X '
<br />0052
<br />.0078
<br />.0104
<br />.0158
<br />.0208 .0260
<br />.0313
<br />.0417 . b21
<br />.0625 .0
<br />1
<br />23
<br />4
<br />. 5 6
<br />7
<br />8 9
<br />10 11
<br />.am.
<br />.1667
<br />.2500
<br />.3333
<br />.4167 .50 00
<br />.5833
<br />.6687 1 .7500
<br />.8333 .9267
<br />J
<br />
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