|
VIII
<br />TABLE II.- Radii, Ordinates and Deflections: Chord= 100 It.
<br />Deg:
<br />di
<br />Raus
<br />&iid.
<br />Ord.
<br />Tan.
<br />Dist,
<br />I Def.
<br />Dist.
<br />Def.
<br />for
<br />1Ft.
<br />Deg.
<br />Radius
<br />I.
<br />Mid.
<br />Ord
<br />Tan,
<br />Dist.
<br />Def.
<br />Dist..
<br />Df.ef•
<br />1 Ft
<br />51
<br />t:
<br />ft.
<br />ft.
<br />ft.
<br />r
<br />43
<br />ft,
<br />ft.
<br />ft,
<br />ft.
<br />J9'
<br />0`10'.34377.
<br />25'
<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 />,5S2
<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 />.43G
<br />,573
<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 />8
<br />716.8
<br />1.746
<br />6.976
<br />13.95
<br />2.40
<br />1
<br />5729.6.218
<br />440
<br />.873
<br />1.745
<br />0.30
<br />20
<br />638.2
<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 />14.82
<br />2.55
<br />20
<br />•4297.3
<br />.291
<br />1.164
<br />2.327
<br />0.40
<br />40
<br />GGl.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 />7.84615.69
<br />52°
<br />2.70
<br />40
<br />3437.9
<br />.364
<br />1.454
<br />2.909
<br />0.50
<br />20
<br />G14.6
<br />2.037
<br />8.136
<br />16.27
<br />2.50
<br />50
<br />3125.4
<br />.400
<br />1.600
<br />3.200
<br />0.55
<br />30
<br />G03.8
<br />2.074.
<br />8.281
<br />16156
<br />2.85
<br />2
<br />2864.9
<br />.436
<br />1.745
<br />3:490.0.60
<br />44'
<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 />3.751
<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 />,
<br />30
<br />546.4
<br />2.292
<br />9. 150
<br />13;30
<br />3.15
<br />30
<br />2292.0
<br />.645
<br />2.181:
<br />4.363
<br />0.75
<br />11
<br />521.7
<br />2.402
<br />9.585
<br />19.1G
<br />3.30
<br />40
<br />2148.8
<br />.5S2
<br />2.327
<br />4.654
<br />0.80
<br />30
<br />499.4
<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 />20.1,1
<br />3.60
<br />8
<br />1910.1
<br />.655
<br />2.615
<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 />2.539
<br />11.32
<br />22.G4
<br />3.90
<br />20
<br />1719.1
<br />.727
<br />2.008
<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
<br />12.SS
<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 />39(3.2
<br />3.168
<br />12.G2
<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 />383:l
<br />3.277
<br />13.05
<br />26.11
<br />•1.50
<br />4
<br />1432.7
<br />.873
<br />3.490
<br />6.9S0
<br />1.20•
<br />BO
<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 />25.70
<br />4. 95
<br />30.
<br />1273.6
<br />.982
<br />3.926
<br />7.552
<br />1.35
<br />17
<br />338.3
<br />3.716
<br />t4.7S
<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 />302.9'4.155
<br />16.51'
<br />33.01
<br />5.70
<br />5
<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 />35.16
<br />6.60
<br />40
<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.S7
<br />G.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 />20.70
<br />41.58
<br />7.20
<br />50
<br />982.6
<br />1.273
<br />5.OSS
<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 .305._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 />1.85.
<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 />206.7.6.139
<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 />1 859.9
<br />1.455t5.814
<br />11.63
<br />2.00
<br />30
<br />193.2
<br />6.583
<br />25.55
<br />51.76
<br />9.00
<br />The middle ordinate in inches for anv cord of length (C) is equal to .0012 C'
<br />multiplied by the middle ordinate taken from the above table. Thud, 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 2,36 -inches,
<br />TABLE III. ,Deflections for Sub Chords for Short Radius Curves. ,
<br />Degree
<br />of
<br />Curve
<br />' Radius.
<br />50
<br />1� sub chord ,
<br />R =sin of : def. angle
<br />Length
<br />of arc
<br />for 100 ft.
<br />sin.'' def. ahg,
<br />12.5 Ft.
<br />15 Ft.
<br />20 Ft.
<br />25 Ft.
<br />30°
<br />193.18
<br />10
<br />51
<br />'°
<br />Ii
<br />^°
<br />581
<br />3°
<br />43
<br />;01.15
<br />32°
<br />181.39
<br />1°
<br />J9'
<br />2°
<br />25'
<br />3°
<br />lo'
<br />3°
<br />58'
<br />50;.33
<br />34°
<br />171.01
<br />2°
<br />o6'
<br />2°33
<br />4
<br />3°
<br />21'
<br />4°
<br />12'
<br />101,48
<br />36°
<br />161.80
<br />20
<br />13`
<br />2°41'
<br />.9000
<br />3°33'
<br />OS33
<br />4°26'
<br />.2500
<br />ioi.66
<br />380
<br />153.58
<br />2°
<br />20'
<br />?°49'
<br />'55
<br />3°
<br />44'.
<br />4°
<br />40'
<br />101.85
<br />40°
<br />146:19
<br />�°
<br />27'
<br />^-°
<br />57'
<br />3°
<br />55'
<br />4°
<br />54'
<br />io2.o6
<br />42'
<br />139.52
<br />2°
<br />34'
<br />3°
<br />05'
<br />4°
<br />07'•
<br />5°
<br />08'
<br />102.29
<br />440
<br />133 447
<br />2°
<br />41'
<br />3°
<br />13'
<br />4°
<br />18'
<br />5'
<br />22'
<br />102.53
<br />46°
<br />127.97
<br />2°48'
<br />29.4833
<br />3°21'
<br />39'
<br />4°29'
<br />49
<br />5°36'
<br />59
<br />102.76
<br />4S°
<br />122.92
<br />2°
<br />55'3°
<br />30
<br />29'
<br />4°
<br />40'
<br />5°
<br />50'.
<br />103.00
<br />50°
<br />IIS -3I
<br />3°02'
<br />.3°3S'
<br />4°5i'
<br />6°04'
<br />103.24
<br />52°
<br />114.06.
<br />3°
<br />09'
<br />•3°
<br />46'
<br />50
<br />02'
<br />6°
<br />17'
<br />103.54
<br />54°
<br />1lo.11
<br />3°
<br />16'
<br />3°
<br />J4'
<br />S°
<br />13'
<br />60
<br />31'
<br />I03.84
<br />56°
<br />io6.5o
<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 />l0'.
<br />5°
<br />34'
<br />.6°
<br />571,
<br />104.43
<br />60°
<br />loo.'oU
<br />3°
<br />35'
<br />. 4°
<br />t8'
<br />5°
<br />44'
<br />?°
<br />Il
<br />104-72
<br />Z�/Y ,y3'7�- �Z•s3
<br />=17j GiIRVE FORiVIL'LAS . .4-+ IX
<br />-7 C
<br />-?.74
<br />T = R tang & S" j. R = T'cot. 1,1 Chord clef. = chord2
<br />__ 5o tan I 1.Z 50 R
<br />T Sin. } ll l _
<br />qo R Sin. # D' I.
<br />Sin. i D = No, chords D
<br />R E= R ex. sec i I
<br />T_ 5o tan ; I
<br />Sin. D - ,1• E = T tan } I .Tan. def. chord def.
<br />The square of any distance, divided by twice 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 distance by .01745 (def. for 0 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 TRIAi;GLES. Square the altitude, divide by twice the
<br />base.._ Add quotient to base for hypotenuse.
<br />Given Base ioo,Alt. 10.102=200=.5. loo-.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, .00z; 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 />LEVELING. The correction for curvature and refraction, •in, feet
<br />and decimals of feet is equal to 0.574da, where d is.the distance in miles.
<br />The correction for curvature alone is closely, Jd2. The combined. cor-
<br />rection is. negative.
<br />PROBABLE ERROR. If d1, d,, d„ etc. are .the discrepancies of various
<br />results from the mean, and if fd2=the sum of the squares of these differ-
<br />ences and n=the number of observations, then the probable error of the
<br />mean= ± 0.6745 ids
<br />n (n-1)
<br />SOLAR EPHEIIERIs. 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 3x5 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 Iormulas; Natural andLogarithmic Functions;
<br />f and Logarithms of Numbers.
<br />TABLE IV. - Minutes in Decimals of a Degree.
<br />1'
<br />.0167
<br />11'
<br />.1833
<br />21'
<br />.3500
<br />31'
<br />.5167
<br />41'*
<br />GS33
<br />51'
<br />.8500
<br />2
<br />0333
<br />12
<br />.2000
<br />22
<br />.3667
<br />1
<br />32
<br />.5333
<br />42
<br />.7000
<br />52
<br />.8667
<br />3
<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 />.9167
<br />54
<br />.9000
<br />5
<br />OS33
<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 />36
<br />.6000
<br />46
<br />.7667
<br />56
<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 />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 />29.4833
<br />39'
<br />.6500
<br />49
<br />.8167
<br />59
<br />.9833
<br />10
<br />.1661
<br />20
<br />.3333
<br />30
<br />.5000
<br />40
<br />.0667
<br />50
<br />.8333
<br />60
<br />1,0000
<br />TABLE V. -
<br />Inches in Decimals of a Foot.
<br />1-1G
<br />3-32
<br />%
<br />3-1G
<br />5.16
<br />%
<br />0052
<br />.0078
<br />.010#
<br />.0156
<br />.0205
<br />.0260
<br />.0313
<br />.0417 .0521
<br />0 25
<br />6
<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 />1 .IGG7
<br />.2;,00
<br />.3333
<br />.4167
<br />.5000
<br />.5833•
<br />.6667' .7500
<br />.8333
<br />.9167
<br />
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