|
..�. 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 />i for--
<br />1 Ft.
<br />Deg:
<br />Radius
<br />Mid..
<br />-Ord;'
<br />Tan.
<br />- Dist.
<br />Def..
<br />`Dist.
<br />llef.
<br />for
<br />1 Ftw
<br />2° 17
<br />ft._
<br />ft.
<br />ft.
<br />lt.
<br />. !
<br />1 59
<br />It. ,
<br />IL
<br />It...
<br />It.
<br />i
<br />0'10'
<br />34377:
<br />'.036
<br />:145
<br />, .
<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 />17159.
<br />.073
<br />.291
<br />:582.0.10"
<br />3° 44' . -
<br />20'
<br />751.8
<br />1.600
<br />6.395
<br />12.79'2.20
<br />2° 57'
<br />3D
<br />11459..
<br />109
<br />.430
<br />:'873
<br />0.15
<br />30
<br />764.5
<br />1.637
<br />6.540
<br />13.03
<br />2.25
<br />" 40
<br />`-8594.4
<br />•.145
<br />.582
<br />I.1G4
<br />0120
<br />_
<br />40
<br />747.9
<br />1.673
<br />6.G35
<br />13.37
<br />2.30
<br />50
<br />. 6875.5
<br />,182
<br />.727
<br />4°4o'
<br />5°50
<br />'8
<br />716.8
<br />1.746
<br />6.97G
<br />13195
<br />240
<br />1-
<br />5729.6
<br />.218
<br />.873
<br />_1:454,0.25
<br />1.745
<br />0.30
<br />20
<br />688.2
<br />1.519
<br />7.266
<br />•14.53
<br />2..50
<br />.10
<br />4911.2
<br />.255
<br />1.018
<br />2.030
<br />0.35
<br />30
<br />674.7
<br />1.855
<br />7.411
<br />19.52
<br />2.55
<br />20
<br />4297.3
<br />-.291
<br />1.1G4
<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 />0145
<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 />16.2.
<br />50
<br />, 3125.4
<br />..400
<br />1.600
<br />3.200
<br />0.55
<br />30
<br />GO3.8
<br />2.074
<br />8.291
<br />16.56.2.85
<br />2
<br />2864:9
<br />.436
<br />1.745
<br />3.490
<br />O.GO.
<br />40
<br />593.4
<br />2.110
<br />8.426
<br />16.85.2.90
<br />30
<br />2644.6
<br />.473
<br />1.591
<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 />2.030
<br />4.072
<br />0.70
<br />30
<br />546.4
<br />2.292
<br />9.150
<br />18.30
<br />3.15
<br />10
<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 />'-09.1
<br />2.511
<br />10.02
<br />20.0-1
<br />3.45
<br />50
<br />'2022:4
<br />3.613
<br />2.472
<br />4.%45
<br />0.55
<br />12 ' .
<br />478.3
<br />2.G20
<br />10.45
<br />'20.91
<br />3.60
<br />a".
<br />1910.1
<br />-.655
<br />2.615
<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 />22.6-4
<br />3.90
<br />20
<br />1719.1
<br />•727
<br />2.908
<br />5.517
<br />1.00
<br />30
<br />425.4
<br />2.049
<br />11.75
<br />23.51
<br />4.05
<br />.30
<br />1637.3
<br />.7G4
<br />3:05.1
<br />6.108
<br />1.05
<br />14.
<br />410.3
<br />3. WS
<br />12.18
<br />24.37
<br />4.20
<br />40
<br />'1562.9
<br />.SOO
<br />3.190
<br />G.398
<br />1.10
<br />30
<br />396.2
<br />3.163
<br />12.62
<br />25.24
<br />4.35
<br />50
<br />1495.0
<br />.336
<br />3.345
<br />6.689
<br />1.15
<br />15
<br />383.1
<br />3.277.13.05
<br />26.11
<br />4.50
<br />4
<br />1432.7
<br />.873
<br />3.490
<br />6.080
<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.SO
<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.G
<br />3.935
<br />15.64
<br />31.29
<br />55.40
<br />50
<br />1185.8
<br />1.055
<br />4.217
<br />5.433
<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 />5.724
<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 />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 />41.53
<br />7.20
<br />50
<br />982.6
<br />1.273
<br />5.088
<br />10.15
<br />1.75
<br />25
<br />231.0
<br />5.47G
<br />21,64
<br />43.23
<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 />10
<br />'929.6
<br />1.346
<br />5.379
<br />10.76
<br />1.8527
<br />214.2
<br />5.91S
<br />23.35
<br />5.10
<br />20
<br />905.1
<br />1.332
<br />5.524
<br />11.05
<br />1.90
<br />28
<br />206.7
<br />6.139
<br />24.19
<br />48.38
<br />SAO
<br />30
<br />851.9
<br />1.418
<br />5.669
<br />11.34
<br />1.95
<br />29
<br />199'.7
<br />6.360
<br />25.04
<br />146,19
<br />50.07
<br />S.70
<br />40
<br />859.9
<br />1.455
<br />15.814'11.63
<br />2.00
<br />30
<br />193.2
<br />6.5S3
<br />25.85
<br />51.76
<br />9.00
<br />The iiddlo ordinate in inches for any cord of length (C) is equal to .0012 C=
<br />multiplied by the middle-ordinnte taken from the above table. Thus, if it
<br />desired to bend a 30 ft. rail to fit 1.0 degree curve, its middle ordinate should
<br />be-.0012X000X2.183 or 2.36 inches.
<br />TAR'LE III. 'Deflections for Sub Chords for Short Radius Curves.
<br />Degree
<br />of
<br />Curve
<br />Radius
<br />5D
<br />M. sub chord , 7
<br />It = sin of def. angle
<br />Lengtki
<br />a arc
<br />for 100 ft.
<br />sin.; def. ang.12.5
<br />Ft.
<br />15 Ft.
<br />20 Ft.
<br />25 Ft.
<br />30° -
<br />.1.93, i8
<br />I° 51_
<br />2° 17
<br />2' 58'
<br />3° 43
<br />IOI. 15
<br />32
<br />181.39
<br />1 59
<br />-' 25
<br />3 10
<br />3 58
<br />101.33
<br />340
<br />171,02
<br />2° o6'
<br />2° 33'
<br />3° 21'
<br />4° 12
<br />I01.48
<br />36°
<br />= 161.80'.
<br />o ,
<br />2 13
<br />o ,
<br />2 41
<br />o. „ ,.
<br />3 03
<br />o r
<br />4 26
<br />ioi.66
<br />3S°
<br />..153.58
<br />2° 20'
<br />2° 49'
<br />3° 44' . -
<br />4°.40'
<br />-101.85
<br />40°
<br />146. 19
<br />2° 27'
<br />2° 57'
<br />3° 55'•
<br />4° 54
<br />102.06
<br />42°
<br />139.52
<br />2° 34'
<br />3° 05'
<br />4° 07'
<br />5° 08'
<br />1 102.29
<br />44
<br />133.47
<br />2° 41'
<br />30 13'
<br />4° IS'
<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 />122.9'
<br />2°55
<br />3°29
<br />4°4o'
<br />5°50
<br />103.00
<br />50°
<br />I18.3f
<br />3° 02`
<br />3° 38'
<br />4° 51'
<br />6° 04
<br />103.24
<br />52°
<br />114. c6
<br />3° 09'
<br />3° 4.6'
<br />5' oz'
<br />6° 17
<br />103.54
<br />54°
<br />Ito. ii
<br />3° 16'
<br />3° J4'
<br />.5° 13'
<br />6° 31'
<br />103.84
<br />56°
<br />1o6.50
<br />3° 22
<br />4°. 02'
<br />5° 23'
<br />6° 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 />C•o°
<br />100.000i
<br />3° 35'
<br />4° 18
<br />5° 44'
<br />7° 11'
<br />I4.7z.
<br />IX
<br />".. CURVE; FORMULAS
<br />T = R tan I. R = T cot. I „Chord def. chord2
<br />5o tan.i I • - R . .
<br />T Sin. 4 D -, 50 . ..
<br />5o P Sin. a D I:
<br />D = 'R \ o. chords = -
<br />E = R:ex. sec i D
<br />50 tan ; I -
<br />Sin.. i D = 1, - E = T tan f 1 Tan. def. _ chord def:
<br />The, sgdare of any distance, divided by • tivice 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 distancc,by .oi745 (def. for'1° 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 A\GLE 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=1oo•5 -hyp•
<br />-Given Hyp. Too, Alt. 25252=200=3.125. TOO-3.125=96.875=Base.
<br />Error in first examle, .002; In last, .045•
<br />To find Tons of Rail in one -mile of track: multiply weight peryard
<br />by iI, and divide by 7.
<br />D&VELRRG. .The correction for curvature and refraction, in feet
<br />and decimals of feet is equal to 6.574d9, where d is the distance -in miles.'
<br />The correction for curvature alone is closely, Jd2:. The combined cor-
<br />rection is negative.
<br />PROBABLr ERROR. If'dt; d2; d3; etc: are the discrepancies of various
<br />results from the mean; and if Edz=the sum.of the squares of these differ-
<br />ences and n=the number of observations, then the probable error.of-the
<br />mean'= _f 7-d
<br />± O.Gi45 -
<br />V n (n-1)
<br />SOLAR ErnEMERIS. Attention is called to -the Solar Ephemeris for
<br />the current year, published by Keuffcl &Esser Co., and -furnished free -of
<br />charge upon request, which is 31x51 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 deelinatio:i; arithmetic constants; English and Metric
<br />conversions; trigonometric formulas; Natural andLogarithmic Functions;
<br />-and Logarithms of 13umbers.
<br />TA13LE IV. - Minutes in Dreimals of a Degree:
<br />1'
<br />.0167
<br />11'
<br />.1833
<br />21'
<br />.3500
<br />31'
<br />.5167
<br />41'
<br />.6333
<br />51'
<br />.8500
<br />2
<br />.0333
<br />12
<br />.2000
<br />2'1
<br />.366667
<br />32
<br />5333
<br />42
<br />17000
<br />52
<br />.5667
<br />3
<br />.0500
<br />13
<br />.2167
<br />%3
<br />.35331
<br />13
<br />.5500
<br />43
<br />.7161
<br />53
<br />.8833
<br />4
<br />OG67
<br />14
<br />.2333
<br />24
<br />:4000
<br />31
<br />.5GG7
<br />44
<br />.7333
<br />54
<br />9000
<br />5
<br />.0533
<br />15
<br />.2500
<br />25
<br />.4167•
<br />35
<br />.5533
<br />45
<br />.7500
<br />55
<br />.9167
<br />G
<br />•.1000
<br />16
<br />.2067
<br />2G
<br />.4333
<br />3G
<br />.6000
<br />40
<br />.7667.
<br />56
<br />.9333
<br />7
<br />.1167
<br />17
<br />.2533,
<br />27
<br />.4500.
<br />37
<br />G167
<br />44
<br />.7;33
<br />57
<br />.9500
<br />8-
<br />.1333
<br />1S
<br />3000
<br />2S
<br />.4667.
<br />38
<br />0333
<br />48
<br />.3000
<br />58
<br />.9667
<br />9
<br />.1500
<br />19
<br />,3167
<br />29
<br />.4333
<br />39
<br />.0500
<br />49
<br />-•167
<br />59
<br />.9S33'
<br />10
<br />.1667
<br />20
<br />,3333 1110
<br />1 .5000 11
<br />41)
<br />, -6667
<br />50
<br />x333 11
<br />G0
<br />1.0000
<br />• -
<br />TABLE V. -
<br />Inches in Decimals of a Foot.
<br />1-16 1
<br />3-32
<br />38
<br />3-16
<br />/
<br />5-16
<br />',&
<br />:� %s
<br />Y4
<br />l
<br />.0059
<br />.0075
<br />.0104
<br />.0156
<br />.0205
<br />.0260
<br />.0313
<br />.0617 .0521
<br />0625
<br />.07X9
<br />1
<br />2
<br />3
<br />4
<br />5
<br />G
<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 />.5333
<br />.9167
<br />
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