|
VITT__.
<br />TABLE I1. - Radii, Ordinates anal Deflections: Chord =100 ft.
<br />Deg:
<br />_ ._
<br />Ilndivs
<br />.
<br />Mid.
<br />I Ord,
<br />III
<br />Tan.
<br />IDis.
<br />Def,
<br />Dist.
<br />3)ef.{_
<br />for
<br />1 Ft.
<br />Deg.
<br />ltadius
<br />Mid.
<br />Ord.
<br />Tac.
<br />Dist,
<br />Def.
<br />Dist.
<br />Fcr
<br />L Ft.
<br />193.1$ -
<br />ft.
<br />ft.
<br />ft..
<br />.ft
<br />2'
<br />68'--
<br />ft,
<br />f�
<br />it,
<br />ft:
<br />181.34
<br />0°14;
<br />34377.
<br />030
<br />145
<br />,201',0.05,
<br />10'
<br />7°
<br />819.0
<br />1.528
<br />6.105
<br />12.21
<br />2,10
<br />20.17189
<br />2'.33
<br />073
<br />.241
<br />,.M
<br />0.10
<br />20'
<br />781.8
<br />1.600
<br />6.395
<br />12.70
<br />2,20
<br />30
<br />11159.
<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 />8094,4
<br />.145
<br />,582
<br />1.164
<br />0,20
<br />40
<br />747.9
<br />1.673
<br />6.085
<br />13.37
<br />2.30
<br />"50
<br />'6870.5
<br />182
<br />.737
<br />1.454
<br />0.25
<br />8
<br />710.8
<br />1.746
<br />6.976
<br />13.95
<br />2,40
<br />1`
<br />5729'.0
<br />.218
<br />.873
<br />1.74,5
<br />0.30
<br />20
<br />1338.2
<br />1.819
<br />7.266
<br />14.53
<br />2,50
<br />10
<br />4911.2
<br />.255
<br />1.018
<br />2.030
<br />0.35
<br />30
<br />074.7
<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 />3319.8
<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 />.361
<br />1.454
<br />2:909
<br />0.50
<br />20'614.6
<br />o2`
<br />2.037
<br />S. 13G
<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 />663.8
<br />2,074
<br />8.281.16.56
<br />56°
<br />2.85
<br />S
<br />2864.9.
<br />.4361
<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 />1.89L
<br />3,781
<br />0.65 '
<br />10
<br />573"7.
<br />2.183,'
<br />8.7LG
<br />17.43,3,00
<br />4°.
<br />20
<br />2455.7
<br />.509
<br />2.036
<br />4.072
<br />0.70
<br />30 .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 />4.303
<br />0.75
<br />11
<br />521.7
<br />2,40_
<br />9.585
<br />19.16
<br />3.30
<br />40
<br />2148.8',.582
<br />2.327
<br />4.054
<br />0.80 J
<br />30
<br />499.1
<br />2.511
<br />10.02
<br />20:0.1
<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 />2.620
<br />10.45
<br />20,91
<br />3.64
<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 />22.64
<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 />.76-1
<br />3.054
<br />6.108
<br />1.05
<br />14
<br />410.3
<br />3.058
<br />12.18
<br />24.37
<br />4.20
<br />40
<br />1562.3
<br />.800
<br />3.199
<br />6.398
<br />1.10
<br />30
<br />39G.2
<br />3.168
<br />12.62
<br />25.24
<br />4.35
<br />50
<br />1495.0
<br />.8361
<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 />V,
<br />1432.7
<br />.373
<br />3.400
<br />6.980
<br />1.24
<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 />3.715
<br />7.561
<br />1.30
<br />30
<br />348.5
<br />3.606
<br />14.35
<br />28.70
<br />4.05
<br />3o
<br />1273.6
<br />.982
<br />3:426
<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 />5.143
<br />1.40
<br />18
<br />319.6
<br />3,935
<br />15.64
<br />31.295.40
<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 />S
<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 />0.305
<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 />0.506
<br />1.65
<br />23 '
<br />250.6
<br />5,035
<br />19.94
<br />39.87
<br />6.00
<br />40
<br />'1011.5
<br />1.237
<br />4.943
<br />9.880
<br />1.70
<br />24
<br />240.5
<br />5.255
<br />20.79 .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 />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 />22.50.44.99
<br />7.84
<br />10
<br />929.6
<br />1.346
<br />5.37910.76
<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 />48.33
<br />8.40
<br />K
<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 />859.0
<br />1.405
<br />5.814
<br />11.63
<br />2.00
<br />30
<br />193.2
<br />P.5sl
<br />25.88
<br />51,76
<br />9.00
<br />Tho middle ordinate in inches for any cord of length (C) is equal to .0012 Cs
<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 .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 />11'
<br />i2 sub chord=
<br />R
<br />sin of z def. angle
<br />Length
<br />of arc
<br />for, 100 ft.
<br />sin,'' def. ang.
<br />12.5 Ft.
<br />15 Ft.
<br />20 Ft. _
<br />23 Ft.
<br />30°
<br />193.1$ -
<br />1'
<br />51'
<br />2°
<br />17'-
<br />2'
<br />68'--
<br />3°
<br />43'- -
<br />101-1.532°
<br />52
<br />181.34
<br />1,
<br />59
<br />2°
<br />251
<br />3°
<br />10'
<br />3°
<br />58'
<br />101.33
<br />0
<br />34
<br />171•oI
<br />0
<br />2
<br />1
<br />06
<br />2'.33
<br />I
<br />o
<br />� ,2I
<br />"-
<br />o
<br />�
<br />a
<br />I2.
<br />I0I,4.$
<br />360
<br />161.8o
<br />2°
<br />13'
<br />'°
<br />41'
<br />3°
<br />33`'
<br />4°
<br />26'
<br />101.66
<br />380
<br />153 58
<br />2°
<br />20`
<br />2°
<br />49
<br />3°
<br />44`
<br />4s
<br />40'- ,
<br />..101:85
<br />400146.29
<br />.0000
<br />2
<br />27:
<br />2
<br />57 '.
<br />3
<br />55
<br />4
<br />a4�
<br />E02.06
<br />42'
<br />139.52
<br />2°
<br />34'
<br />3°
<br />05'
<br />4°
<br />07'
<br />S°
<br />08
<br />102.29
<br />44°
<br />133.47
<br />2°
<br />41'
<br />30
<br />13
<br />4°
<br />18'
<br />5'
<br />22'
<br />102.53
<br />46°
<br />127.97
<br />2°
<br />48'
<br />3°
<br />21'
<br />4°
<br />29`
<br />5°
<br />36'
<br />102,76
<br />48°
<br />'122. 92
<br />2°
<br />55
<br />3°
<br />29'
<br />40
<br />40'.
<br />5°
<br />50'
<br />103.00
<br />so °
<br />118.31
<br />3°
<br />0z'
<br />3°
<br />33'
<br />4
<br />51'
<br />6°
<br />04'
<br />103.24
<br />520
<br />.114. o6
<br />3°
<br />09'
<br />3°
<br />46"
<br />5°
<br />o2`
<br />6°
<br />17'
<br />I03.54
<br />54°
<br />310.11
<br />3°
<br />16'
<br />3°
<br />54'•
<br />;°.13'
<br />6°
<br />311
<br />103,'84
<br />56°
<br />Io6.50
<br />3°
<br />22'
<br />4002
<br />5°
<br />23'
<br />6°
<br />44
<br />I04.14
<br />58°
<br />103.14
<br />3°
<br />29'
<br />4°
<br />10'
<br />5°
<br />34'
<br />6°
<br />57•
<br />104.43
<br />60°
<br />100. oo
<br />3,35
<br />4°.
<br />18'
<br />5°
<br />44'
<br />7'
<br />11'-'
<br />104.72
<br />Ih
<br />CURVE FORAIULAS
<br />'1' = R tan A- I chord2
<br />T - 50 tan s I P. = •T.cot. '2 I . Chord def. It
<br />Sin. f D R - 50
<br />? D, - 51° Sin. 2 D f 1
<br />Sin. .
<br />Na,.chords = �
<br />E = R ex. sec 1 i'
<br />"Sin: } D -' Sa t In z I E_= T tan 1 I . Tan. def.= a chord def.
<br />The square of any distance, didided by twice the radius, will equal
<br />the distance frons. -tangent to curve, very nearly.
<br />To find angle for a given distance and deflection.
<br />Rule 1. Multiply the given distance by ,01745 (def. for i° for 1 ft.
<br />see Table IL), 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:.o1745, 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. mo+.5,=ioo. hyp.--.
<br />Given Hyp, ioo, Alt, 25.252-' 200=3.125. loo-3.125=96.875=Base.
<br />Error in first example, :oat; In last, :045.
<br />To find Tons of Rail in ane -mile of tract.: multiply weight per yard
<br />-by Ii, 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, Id=. The combined cor-
<br />rection is negative.
<br />-PROBABLE ERROR. If d,, &, d2, etc, are the discrepancies of various
<br />results from the mean, and if W=the sum of the squares of these differ-
<br />enees and n=the number of observations; then the probable error of the
<br />2
<br />mean= 4-0.6745 1d
<br />n nn -1)
<br />SOLAR EPHEMERIS. Attention is called to the Solar Ephemeris for
<br />the current year, published by Kcuffel & Esser Co., and furnished free of
<br />charge upon, request, which is 3 Fx5j 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 />T4BLE IV. - 114inutes in Docimnls of n Dearee.
<br />V
<br />.0167
<br />11'
<br />.1833
<br />21'
<br />3500'
<br />31'
<br />.5107
<br />41'
<br />.6333
<br />51'
<br />.8500
<br />2 '
<br />.0333
<br />13
<br />,2000
<br />22
<br />,3667'
<br />32
<br />.5333
<br />42
<br />.0000
<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 />.7333
<br />54
<br />.9000
<br />5
<br />,0333
<br />15
<br />.2500
<br />25
<br />.4167
<br />35
<br />.5S33
<br />45
<br />.7500
<br />55
<br />.9167
<br />0
<br />,1000
<br />19
<br />,2667
<br />26
<br />.4333
<br />3G
<br />.0000
<br />46
<br />.7667
<br />56
<br />.9333
<br />7
<br />,1167
<br />17.
<br />.2S33
<br />27
<br />.4500
<br />31
<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 />4S
<br />.5000
<br />58
<br />.9667
<br />91
<br />,1500
<br />19
<br />.3167
<br />29
<br />.4333
<br />39
<br />.6500
<br />49
<br />.81G7
<br />59
<br />.9833
<br />10
<br />.1667
<br />20
<br />,3333
<br />30
<br />.5000 11
<br />40
<br />1 ,6667 11
<br />50
<br />1 8338
<br />1 60
<br />1 1.0000
<br />TABLE
<br />V. -
<br />Inches in Decimals of a. Foot.
<br />1-16
<br />3-32
<br />y
<br />3-16
<br />5-113
<br />%
<br />%
<br />Y,
<br />.0078
<br />.0104
<br />.0156
<br />.02U8
<br />.0200
<br />.0313
<br />_%
<br />.0417 .0521
<br />.0625
<br />_-0729
<br />_.0052
<br />1
<br />2
<br />3
<br />'1
<br />5
<br />6
<br />7
<br />8 9
<br />10
<br />11
<br />.0833
<br />.1667.
<br />,2500
<br />.3333
<br />,4167
<br />bDOD
<br />.6333
<br />:6607 7500
<br />•.S333
<br />1 .9167
<br />
|