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VIII
<br />TALE 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 />for
<br />I FL
<br />Deg.
<br />Radius
<br />Mid.
<br />Ord.
<br />Tan.
<br />Dist,
<br />. Def.
<br />Dist.
<br />Def.
<br />for
<br />1 Ft.
<br />1°
<br />t.
<br />rt-
<br />17`
<br />it.
<br />I
<br />3°43'
<br />ft.
<br />ft.
<br />ft.
<br />it.
<br />10
<br />0°10'
<br />34377,
<br />'.036
<br />.145
<br />.291
<br />0.05
<br />7°
<br />519.0
<br />1,525
<br />6.105
<br />12.21
<br />2.10
<br />20
<br />17189.
<br />.073
<br />.291
<br />.552
<br />0.10'
<br />20'
<br />751.8
<br />1.600
<br />6.395
<br />12.79
<br />2.20
<br />30
<br />11459.
<br />.109
<br />.436
<br />.873
<br />6.15
<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 />.552
<br />1.164
<br />0.20
<br />40
<br />747.0
<br />1.673
<br />G.GS5
<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 />1
<br />5729.6
<br />'.218
<br />.873
<br />1.745
<br />0.30
<br />20
<br />G88.2
<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 />1.555
<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 />1.592
<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 />G37.3
<br />1.96:;
<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 />014.6
<br />2.037
<br />8.136
<br />36.27
<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 />8.251
<br />161.56
<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 />1.591
<br />3.781
<br />0.65
<br />10
<br />573.7
<br />2.153
<br />8.7;63
<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 />2.202
<br />9.150
<br />18.20
<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 />2,4C2
<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 />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 />3 -
<br />1910.1
<br />.655
<br />2.618
<br />5.235
<br />0.90
<br />30
<br />459.3
<br />2.730
<br />10,59
<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.S39
<br />11.32
<br />22.64
<br />3.90
<br />20
<br />1710.1
<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 />6.103
<br />1.05
<br />14
<br />410.3
<br />3.058
<br />12.1S
<br />24.37
<br />4.20
<br />40
<br />1562.0
<br />.800
<br />3.199
<br />6.398
<br />1.10
<br />30
<br />390.2
<br />3.165
<br />12.62
<br />25.24
<br />4.35
<br />50
<br />1495.0
<br />.836
<br />3.345
<br />6.659
<br />1.15
<br />15
<br />3S3.1
<br />3.277
<br />13.05
<br />26.11
<br />4.50
<br />a
<br />1432.7
<br />.S73
<br />3.490
<br />6.950
<br />1.20
<br />30:
<br />370.8
<br />3:357
<br />13.49
<br />2G.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 />3.406
<br />13.02
<br />27.54
<br />4.80
<br />20
<br />1322.5
<br />.945
<br />3.71S
<br />7.561
<br />1.30
<br />30
<br />345.5
<br />3.60G
<br />14.35
<br />25.70
<br />4.95
<br />30
<br />1273.6
<br />.0S2
<br />3.92G
<br />7.852
<br />1.35
<br />17
<br />338.3
<br />3.716
<br />14.75
<br />29.50
<br />5.10
<br />40
<br />1223.1
<br />1.018
<br />4.071
<br />5.143
<br />1.40
<br />18
<br />319.6
<br />3.035
<br />15.6.1
<br />31.20
<br />5.40
<br />50
<br />1IS5.8
<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 />5
<br />1146.3
<br />1.091
<br />4.362
<br />5.724
<br />1.50
<br />20
<br />2S7.9
<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 />3G.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 />4.793
<br />9,596
<br />1.65
<br />23
<br />250.8
<br />5.035
<br />10.04
<br />39.57
<br />6.90
<br />40
<br />1011.5
<br />1.237
<br />4.943
<br />9.8SG
<br />1.70
<br />24
<br />240.5
<br />5.255
<br />20.79
<br />41.55
<br />7.20
<br />50
<br />932.6
<br />1.273
<br />5. OSS
<br />10.15
<br />1.75
<br />25
<br />231.0
<br />5.476
<br />21.64
<br />43.25
<br />7.50
<br />6
<br />955.4
<br />1.309
<br />5.2234
<br />10.47
<br />1.80
<br />26
<br />222.3
<br />5.697
<br />22.50
<br />44.99
<br />7.S0
<br />10
<br />929.6
<br />1.346
<br />5.379
<br />10.76
<br />1.85
<br />27
<br />214.2
<br />5,915
<br />23.35
<br />46.69
<br />S.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 />559.9
<br />1.455
<br />5.814
<br />11.63
<br />2.00
<br />30
<br />193.2
<br />6.583
<br />25.58
<br />51.76
<br />9.00
<br />The middle ordinate in inches for any cord of length (C) is equal to .0012 G'
<br />multiplied by the middle ordinate talien from the above table. Thus, if it
<br />desired to bend a 30 ft, rail to fit a, 10 degree tune, its middle ordinate should
<br />be .0012X90OX2.183 or 236 inches.
<br />TABLEIII. Deflections for Sub.Chords for Short Radius Curves.
<br />Degree
<br />of
<br />Curve
<br />50
<br />Radi7anng.
<br />36 sub chord.
<br />It
<br />in of def. angi
<br />h
<br />Length
<br />of arc
<br />for 100 fl
<br />sin. a def
<br />12.5 Ft.
<br />15 Ft.
<br />20 Ft. 1,
<br />25 Ft.
<br />30°193.18
<br />.8500
<br />1°
<br />51'
<br />2°
<br />17`
<br />2°58'
<br />.3667
<br />3°43'
<br />.5333
<br />I01.1
<br />320
<br />181.J9
<br />10
<br />59'
<br />2°
<br />25
<br />3°.l0'
<br />23
<br />3°
<br />55'
<br />I0I.3�
<br />34
<br />171.0I
<br />2
<br />06
<br />'
<br />33
<br />3
<br />2I
<br />4
<br />I2
<br />I0I,4
<br />360
<br />161.86
<br />2°
<br />�3,
<br />2°
<br />41'
<br />3°
<br />33,
<br />4°
<br />26'
<br />iol.6(
<br />38°
<br />153.58
<br />2°
<br />20'
<br />2°
<br />49'
<br />3°
<br />44'
<br />16
<br />40'
<br />101.8;
<br />40°
<br />W. r9
<br />'-°
<br />27-'
<br />20
<br />57�
<br />3 °
<br />55
<br />4°
<br />54'
<br />102. of
<br />42°
<br />139.52
<br />2°
<br />34'
<br />30
<br />05�
<br />4°
<br />07'
<br />5°
<br />08'-
<br />102.25
<br />44°
<br />133.47
<br />2°
<br />41'
<br />3°
<br />13'
<br />4°
<br />r8'
<br />5°
<br />22'
<br />102.5?
<br />460
<br />127.97
<br />2°
<br />48'
<br />3°
<br />21`
<br />40
<br />29'
<br />5',36'
<br />.0833
<br />102.7E
<br />4S°
<br />122.92
<br />2°
<br />55'
<br />3°.29'
<br />40
<br />4°
<br />40'
<br />5°
<br />50'
<br />103.0(
<br />50°
<br />118.31
<br />3'
<br />02,
<br />3°
<br />38,
<br />4°
<br />51,
<br />6°
<br />04'
<br />103.24
<br />103.24
<br />52°
<br />114-o6
<br />3°
<br />09'
<br />3°
<br />46'
<br />S°
<br />02'
<br />6°
<br />17'
<br />103.5
<br />54°
<br />II0,11
<br />3°
<br />16'
<br />3°
<br />54�
<br />5°
<br />13'
<br />6°
<br />31%
<br />103.8
<br />560
<br />1o6.5o
<br />3°
<br />22'
<br />4°
<br />02`
<br />5°
<br />23'
<br />6°
<br />44'
<br />'1()4 . I"
<br />58°
<br />103.14
<br />3°29'
<br />4°l0'
<br />5*
<br />34
<br />6°57'
<br />104.4
<br />6o°
<br />100.00
<br />30
<br />35'
<br />4°
<br />18
<br />5°
<br />44'
<br />7°
<br />11,
<br />104.7
<br />4
<br />4.` '
<br />3.
<br />2
<br />IX
<br />CURVE FORMULAS
<br />T= R tan - I / P= T cot.: I chord-*
<br />T _ 50 tan :4 I Chord def. = R
<br />Sin. I D 50
<br />R = �
<br />Sin. D ='90 Sin. 2 D No. chords = I
<br />R E=R ex.secI D
<br />Sin. ?I D = 5O tan 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 frons tangent to curve, very nearly."
<br />To find anile 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. illultiply 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 ANGLi TRIANGLES. Square the altitude, divide by twice the
<br />base. Add quotient to base for hypotenuse.
<br />Given Base Ioo,Alt.'r0.102=200=.5. Ioo-i-.5=1oo.5 hyp.
<br />Given Hyp. ioo, Alt- 25.252-zoo=3.125; roo-3.125=96.878=Base.
<br />Error in fist example, .002; in last -..045 -
<br />To find Tons of Rail in one mile of track: multiply weight per yard
<br />by li, 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, 3d-. The combined cor-
<br />rection is negative.
<br />PROIIAeLE ERROR. If d„ &, ds, etc. are the discrepancies of various
<br />results from the mean, and if fd`=the sum of the squares of these differ-
<br />ences and n=the number of observations, then the probable error. of the
<br />mean= 0.63745 7d3
<br />1 n (n-1)
<br />SOLAR ErnrMERis. 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 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 />TABLE W. - 14inutes 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 />.5667
<br />3
<br />.0500
<br />13
<br />.2167
<br />23
<br />.3833
<br />33
<br />.5500
<br />43
<br />.7167
<br />53
<br />.5833
<br />4
<br />.0667
<br />14
<br />.2333
<br />24
<br />.4000
<br />34
<br />.5667
<br />44
<br />.7333
<br />64
<br />.9000
<br />5
<br />.0533
<br />15
<br />.2500
<br />25
<br />.4167
<br />.35
<br />.5333
<br />45
<br />.7500
<br />55
<br />.9167
<br />6
<br />.1000
<br />16
<br />.2667
<br />26
<br />.4333
<br />3G
<br />G000
<br />46
<br />.7667
<br />66
<br />.9333
<br />7
<br />.1167
<br />17
<br />.2833
<br />27
<br />.4500
<br />37
<br />.6167
<br />47
<br />.7533
<br />57
<br />'.9500
<br />8
<br />.1333
<br />18
<br />.3000
<br />28
<br />.4667
<br />38
<br />.6333
<br />48
<br />.5000
<br />58
<br />9667
<br />9
<br />.1500
<br />"19 "
<br />.3167
<br />29
<br />.4533
<br />39
<br />.6500
<br />49
<br />S167
<br />59
<br />.0833
<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 />1
<br />TABLE V. -
<br />Inches in Decimals of a Foot,
<br />1 -IG
<br />3-32
<br />!g 3-163
<br />%
<br />5-1G
<br />e
<br />'$
<br />0052
<br />.0075
<br />.0104 .0156
<br />.0205
<br />.0260
<br />13613
<br />.0313
<br />.0417 .0521
<br />.0625
<br />.0729
<br />1
<br />°
<br />3 4
<br />5
<br />67
<br />S fl
<br />10
<br />11
<br />,OS33
<br />.1GG7
<br />.2.500 .3333
<br />.4167
<br />.5000
<br />.5833
<br />.6667 .7500
<br />.5333
<br />.9167
<br />1
<br />
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