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VIII .
<br />TABLE IL - Radii, Ordinates and Deflections. Chord �' 100 f t.
<br />Deg.
<br />RadiusMid
<br />Ord.
<br />Tan
<br />Dist.
<br />Def:'
<br />Dist.
<br />for
<br />1 Ft.
<br />Deg.
<br />Radius
<br />Mid.
<br />Ord.
<br />Tan.
<br />Dist.
<br />Det.
<br />Dist.
<br />Dor
<br />1 Ft.
<br />193.18
<br />1° 51'
<br />2° 17'
<br />2° 58'
<br />3° 43'
<br />161.15
<br />32°
<br />t.
<br />ft.
<br />ft.
<br />I=
<br />3° 58'
<br />O'10'
<br />34377.
<br />.036
<br />.145
<br />.291
<br />0.05
<br />V
<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 />20'
<br />781.8
<br />1.600
<br />6.395
<br />12.79
<br />2.20
<br />30-
<br />11459.
<br />.109
<br />..430
<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 />.682
<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
<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.W
<br />10
<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'. GO
<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. G9
<br />2.70
<br />40
<br />3137.9
<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 />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 />1.891
<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 />2.036
<br />4.072
<br />0.70
<br />30
<br />546.4
<br />2.292
<br />0.150
<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 />0.585
<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 />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 />1 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 />12.18
<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 />333.1
<br />3.277
<br />13.05 -26.11
<br />4.50
<br />L
<br />1132.7
<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 />7.2711.25
<br />10.
<br />359.3
<br />4.496
<br />13.92
<br />27.84
<br />4.80
<br />20
<br />1322.5
<br />.945
<br />3.718
<br />7.561'1.30
<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 />8.1431.40
<br />19
<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 />8
<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 />1.237
<br />4.943
<br />9.886
<br />1.70
<br />24
<br />240.5
<br />5.255
<br />20.79
<br />41.68
<br />7.20
<br />50
<br />_1011.5
<br />982.6
<br />1.273
<br />5.088
<br />10.18
<br />1.75
<br />25
<br />231.0
<br />6.476
<br />21.64
<br />43.28
<br />7.50
<br />e.
<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 />1.85
<br />27
<br />214.2
<br />:918
<br />23.35
<br />40,60
<br />8.10
<br />20
<br />005.1
<br />1.382
<br />5.524
<br />11.05
<br />1.90
<br />28
<br />206.7
<br />.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.?
<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 />51.78
<br />9.00
<br />The middle ordinate* n inches for any cord of length (0) is equal to .0012 C'
<br />multiplied by the snidW.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 .0012X90OX2.183 or 2.36 inches.
<br />TABLE III. Deflections for Sub Chords for Short Radius Curves.
<br />Degree
<br />of
<br />Radius
<br />50
<br />'X sub chord
<br />R = sin of If def. angle
<br />Len th
<br />a arc
<br />Curve
<br />sin. i def. ang.
<br />12.5 Ft.
<br />15 Ft.
<br />20 Ft.
<br />25 Ft.
<br />for 100 ft.
<br />300
<br />193.18
<br />1° 51'
<br />2° 17'
<br />2° 58'
<br />3° 43'
<br />161.15
<br />32°
<br />181.39
<br />1° 59'
<br />2° 25'
<br />3° 10'
<br />3° 58'
<br />101.33
<br />34°
<br />171.01
<br />2° 06'
<br />2° 33'
<br />3° 21'
<br />4° 12'
<br />101.48
<br />36°
<br />161.80
<br />2° 13'
<br />z° 41'
<br />3° 33'
<br />4° 26'
<br />loi.66
<br />38°
<br />153.58
<br />2' 20'
<br />2° 49'
<br />3° 44'
<br />4° 4a'
<br />1o1.85
<br />40°•-
<br />. 146.19
<br />2° 27'
<br />2° 57
<br />3' 55'
<br />4° 54'
<br />102.o6 .
<br />42°
<br />139.5?
<br />2° 34' .
<br />30 05'
<br />4007
<br />5° 08
<br />102.29
<br />44-9,
<br />133:• 47
<br />2° 41
<br />3°. 13'
<br />4° 18
<br />5°'-2'
<br />102.53'
<br />46°
<br />127-97
<br />2° 48
<br />3° 21'
<br />4° 29'.
<br />50 36'
<br />102.76
<br />48°
<br />122.92
<br />2° 55'
<br />3°.29,
<br />40 40,
<br />5' 5o,
<br />-103.00
<br />500-
<br />)'18'.31
<br />3° 02
<br />3° 38'
<br />4° 51'
<br />6° o4'
<br />103.24
<br />52°
<br />114.o6
<br />3° og'
<br />3° 46' .
<br />5° 02'
<br />6° 17' -
<br />103.54
<br />54'
<br />110..1 i
<br />3° 16'
<br />30.54'
<br />5° 13'
<br />6° 31'
<br />103.84
<br />56°
<br />1o6.5o
<br />3° 22'
<br />4° 02'.
<br />5° 23'
<br />6° 44'
<br />104-14
<br />.58°
<br />103 1:4
<br />3° 29'
<br />4° 10'
<br />5° 34
<br />6° 57'
<br />104.43
<br />60°
<br />Igo. we
<br />3° 35'
<br />4° 18'
<br />5° 44'. 1
<br />7° 11'
<br />104.72
<br />Ix
<br />CURVE FORMULAS
<br />T= R tan -2 I R= T cot. 12 1 chord'
<br />I = 5o tan # I R
<br />50 Chord def. =
<br />Sin. 1 1)
<br />R =
<br />Sin. 1, D = 5o Sin. a , D No. chords = I
<br />R E= R ex. sec A,, I D
<br />Sin. 1. D = 5o tan
<br />. " 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 .o1745 (def. for I° for t 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 TRIANGLES. Square the altitude, divide by twice the
<br />base. Add quotient to base for hypotenuse.
<br />Given Base Ion, Alt. 10.10'_200=.5. 100+-5=100.5 hyp.
<br />Given Hyp. too, Alt. 25.252-200=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 I I, and divide by 7.
<br />LEVELING. The correction for curvature and refraction, in feet
<br />and decimals of feet is equal to 0.574d', where d is the distance in miles.
<br />The, correction for curvature alone is closely, d'. The combined cor-
<br />rection is negative.
<br />PROBABLE ERROR. If di, d,, da, etc. are the discrepancies of various
<br />results from the mean, and if Ed' =the sum of the squares of these differ-
<br />ences and n=the number of observations, then the probable error of the
<br />mean= Zd2
<br />-0.6745 n(n-1)
<br />SOLAR EPHEMERIS. Attention is called to the Solar Ephemeris for
<br />the current year, published by Keuffel & Esser Co., and furnished upon
<br />request. This handy booklet, I'M in., has about 190 pages of data very
<br />useful to. the Surveyor; such as the adjustments of transits, -levels and solar
<br />attachments; directions and tables for determining the meridian and the
<br />latitude from observations on the sun and Polaris; stadia measurements;
<br />magnetic declination; arithmetic constants, etc..
<br />TABLE IV. -Minutes in Decimals -of a Degree.
<br />1t
<br />.0167
<br />IIP
<br />.1833
<br />21F
<br />.3500
<br />31P
<br />.5167
<br />411
<br />.6833
<br />51'
<br />.8500
<br />2
<br />.0333
<br />t2
<br />.2000
<br />22
<br />.3667
<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 />.7333
<br />54
<br />.9000
<br />5
<br />,0833
<br />15
<br />.2500
<br />25-
<br />.4167
<br />35
<br />.58.33
<br />45
<br />.7600
<br />55
<br />.9167
<br />6
<br />'.1000
<br />16
<br />.2667
<br />26
<br />.4333
<br />.6000
<br />46
<br />.7667
<br />56
<br />.9333
<br />7
<br />.1167
<br />17
<br />.2833
<br />27
<br />.4500
<br />.36
<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 />.8000
<br />58
<br />.9667
<br />9
<br />.1.500
<br />19
<br />.3167
<br />29
<br />.4833
<br />39
<br />.6500
<br />49
<br />.8167
<br />59
<br />.9833
<br />10
<br />.1667 11
<br />20
<br />1 .3333 11
<br />30
<br />1 .5000
<br />40
<br />1 .6667 11
<br />50
<br />1 .8333 11
<br />60 11.0000
<br />TABLE V. --inches
<br />in Decimals
<br />of a.Foot,.
<br />-
<br />1-16 3-32
<br />le
<br />3-16
<br />�;
<br />5-16
<br />%-
<br />%
<br />4'a
<br />%
<br />',c
<br />0052 .0078
<br />.0104
<br />.0156 I
<br />.0208
<br />.0260
<br />.0313
<br />I .0417 I
<br />.0521
<br />.0625
<br />.0729
<br />1 2
<br />I I
<br />3
<br />4
<br />I
<br />5
<br />I
<br />6
<br />I
<br />7
<br />1 8
<br />9
<br />10
<br />11
<br />.0833 .1667
<br />.2500
<br />.3333
<br />.4167
<br />.5000
<br />.5833
<br />. f,667
<br />I`
<br />.7 500
<br />.8333
<br />.9167
<br />
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