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VIII
<br />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 1 Ft
<br />Deg -Radius
<br />20 Ft.
<br />Mid.
<br />Ord.
<br />Tan.
<br />Dist.
<br />Dal.
<br />Dist.
<br />Def.
<br />for Ft.
<br />2° 17'
<br />ft.
<br />t.
<br />ft.,
<br />;ft.
<br />I
<br />1° 59'
<br />-ft.
<br />- It.
<br />ft.
<br />ft.
<br />34°
<br />0'10'
<br />34377.:
<br />.03G
<br />.145
<br />.291
<br />0.05
<br />7
<br />819.0
<br />1.525
<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 />.436
<br />.873
<br />0.15
<br />'30
<br />764.5
<br />1:637
<br />6.540
<br />13.05
<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
<br />.218
<br />.873
<br />1.745
<br />0.30
<br />.
<br />20
<br />688.2
<br />1.819
<br />7.266
<br />14.53
<br />2.50
<br />10
<br />4911.2
<br />.255
<br />1.018
<br />2.03G
<br />0.35
<br />30
<br />G74.7
<br />1.855
<br />7.411
<br />14.52
<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 />7.55G
<br />15.11
<br />2.60
<br />30
<br />3819.8
<br />.327
<br />1.309
<br />2.613
<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 />'.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 />2.50
<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 />2.55
<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 />2.636
<br />4.072
<br />0.70
<br />130
<br />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 />4.363
<br />0.75
<br />11
<br />521.7
<br />2.402
<br />0.585
<br />19.1G
<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 />20.01
<br />3.60
<br />a
<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 />.6
<br />.91
<br />2.763,
<br />5.526
<br />0.95
<br />13
<br />441.7
<br />2.&^,9
<br />11.32
<br />22.64
<br />3.90
<br />.20
<br />1719.1
<br />.727
<br />2.903
<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 />.765
<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 />.600
<br />3:199
<br />a 6.393
<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 />383.1
<br />3.277
<br />13.05
<br />26.11
<br />4.50
<br />1432.7
<br />.873
<br />3.490
<br />0.980
<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 />3.6:15
<br />7.271
<br />1.25
<br />16
<br />359.3
<br />3.496
<br />13.92.
<br />27.81
<br />4.SO
<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 />3.026
<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 />319.6
<br />3.93.5
<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 />6
<br />114G.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 />6,1.90
<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.OS8
<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 />055.4
<br />1.309
<br />5. T14
<br />10.47
<br />1.80
<br />26
<br />222.3
<br />5.697
<br />22.50
<br />.99
<br />7.80
<br />10
<br />929.6
<br />1.34G
<br />5.379
<br />10.76
<br />1.85
<br />27
<br />214.2
<br />5.918
<br />,44
<br />23.35
<br />46.69
<br />2:10
<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 />30'
<br />S31.9
<br />1418
<br />5.GG9
<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 />859.9
<br />11.:455,5.814,11.63
<br />2.07)
<br />30
<br />193:2
<br />G-.5-83-12-55,88
<br />51.76
<br />9.00
<br />The middle ordinate in inches for any cord of length (C) is equal to .0012 C2
<br />multiplied by the middle ordinate taken from the above table. Thus, if it
<br />desired to Lend a 30 ft, rail to fit a 10 degree curve, its middle ordinate should
<br />be .0012X900X2.183 or 2.3G inches.
<br />TABLE III. Deflections for Sub Chords for Short Radius Curves.
<br />Degree
<br />of
<br />Curve
<br />Radius.
<br />50
<br />A sub chord = sin of ( def. angle
<br />R
<br />Length
<br />of arc
<br />for 100 ft.
<br />sin, l def. ang.
<br />12.5 Ft.
<br />15 Ft.
<br />20 Ft.
<br />1 25 Ft.
<br />30'
<br />19.3.18
<br />1° 51'
<br />2° 17'
<br />1..5 81
<br />3° 1 43�
<br />101.15
<br />32°
<br />181.J9
<br />1° 59'
<br />�° 25'
<br />3° 1o'
<br />;° 58'
<br />101.33
<br />34°
<br />171.01
<br />2°.06
<br />2° 33'
<br />S 21'
<br />4° 12'
<br />IOI.49
<br />36°
<br />161.8o
<br />2° 13'
<br />2° 41'
<br />3° 33'4
<br />26'
<br />Io1.66
<br />- 38°
<br />153.58
<br />20 20'
<br />2° 49'
<br />3' 44'
<br />4° 40'
<br />Io1.85
<br />0
<br />40
<br />146.19
<br />0 )
<br />2 27
<br />o )
<br />2 57
<br />o - -,-
<br />3 »
<br />0-
<br />4 54
<br />IO2.o6
<br />42'
<br />139.52
<br />20 34'
<br />3°05'
<br />4°07'
<br />5°o8'
<br />102.29
<br />44°
<br />133.47
<br />2° 41'
<br />3° 13
<br />4° 18'
<br />5° 22'
<br />io2.5J
<br />460
<br />127.97
<br />2°48'
<br />3°2i'
<br />4°29'
<br />S°36'
<br />102.76
<br />48°
<br />122.92
<br />2°55'
<br />3°29'
<br />4°40'
<br />5°50'
<br />103.00
<br />50°
<br />118.31
<br />3° 02'3°
<br />38'
<br />4° 51'
<br />6004 . 103.24
<br />.1333
<br />52°
<br />114.o6
<br />3° 09'
<br />3° 46'
<br />5° 02'
<br />6° 17'
<br />103.54
<br />54°
<br />110.11
<br />3° 16'
<br />3° 54'
<br />S0 13'
<br />6031 1
<br />103.84
<br />56°
<br />106.50
<br />103.14
<br />3° 22'
<br />4° 02'°
<br />gz3'
<br />60 44'
<br />60 '
<br />104.14
<br />58°
<br />6o0
<br />100.00.
<br />3° 29'
<br />3' 35
<br />4° 10'
<br />4° 18'
<br />5' 34'
<br />5° 44'
<br />51'
<br />7° i 1'
<br />104.43
<br />104.72
<br />•_ IX
<br />CURVE FORMULAS
<br />T = R tan # IP. =:T cot.:' I chordz
<br />5o tan J I ' Chord def. _ -R
<br />R
<br />T Sin. J 1) 50
<br />=
<br />Sin. 2L D = 50 Sin. -z D No, chords = I
<br />R E=R ex. see ;'l D
<br />r;i.-. D _ 5' tT a I L = T tan I I Tan. clef. _ "� chord def.
<br />The "square of any distance; divided by twice the radius, will'egtial
<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 .or745 (def, for I° for i 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 .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 too, Alt. 10.102-* 200 100-{-.5=100.5 hy-p.
<br />Given .Hyp. 100, 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 11, and divide by 7.
<br />LEVELING. The correction for curvature and' refraction, in feet
<br />and decimals of feet is equal to 0.574 d', where d is the distance in miles.
<br />The correction for curvature alone is closely, yd2. The combined cor-
<br />rection is negative.
<br />PROBABLE ERROR. If d,, ds, d„ etc. are the discrepancies of various
<br />f results from the mean, and if 7-de=the sum of the squares of these differ-
<br />ences.and n=the•number of observations; then the probable error of the
<br />mean= fid''
<br />SOLAR EPHEDIERIS. 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'�x5y in., with about 190 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 />i and the latitude from observations on the sun and Polaris; stadia meas-
<br />urements; magnetic declination; arithmetic constants; English and Metric
<br />conversions; trigonometric f ormulas; Natural and Logarithmic Functions;
<br />t .. and Logarithms of Numbers.
<br />TABLE IV. - Minutes in Decimals of a Degree.
<br />t,
<br />1' .0167 11' .1333 21! .3500 31' .51G7I 11' .0833 51' .8500
<br />2 .0333 12 2000 22 .3667 32 .5333 4': 7000 52 .8667
<br />3 A500 13- .2167 23 .3833 33 .5500 43 .7167 63 .8833
<br />4 .0667 14 2333 24 .4000 34 .5667 4t
<br />TABLE V. - Inches in Decimals of a Foot..
<br />1-1G
<br />3-32
<br />§
<br />3-16
<br />;t
<br />%iYS
<br />0052
<br />.0078
<br />.0104
<br />.01!,16
<br />.0208
<br />.0260
<br />.0313
<br />.0417 .05^1
<br />.0625
<br />.0729
<br />1
<br />2
<br />3
<br />4
<br />5
<br />6
<br />7'
<br />5 9
<br />10
<br />11
<br />0833
<br />.1667
<br />.2500 1
<br />.3333
<br />.4167
<br />1 .5000
<br />.5533 I
<br />.666,1 7500
<br />.5333
<br />.9167
<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 />.7100
<br />55
<br />.9167
<br />6
<br />.1000
<br />1G
<br />.2667
<br />26
<br />.4333
<br />36
<br />.6000
<br />46
<br />.7667
<br />56
<br />.9333
<br />7
<br />.1167
<br />11
<br />.2833
<br />27
<br />.4500
<br />37
<br />.6167
<br />47
<br />.7333
<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 />0
<br />.1500
<br />19
<br />.3167
<br />29
<br />.4$33
<br />39
<br />.omo
<br />49
<br />.8167
<br />59
<br />.9833
<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 />TABLE V. - Inches in Decimals of a Foot..
<br />1-1G
<br />3-32
<br />§
<br />3-16
<br />;t
<br />%iYS
<br />0052
<br />.0078
<br />.0104
<br />.01!,16
<br />.0208
<br />.0260
<br />.0313
<br />.0417 .05^1
<br />.0625
<br />.0729
<br />1
<br />2
<br />3
<br />4
<br />5
<br />6
<br />7'
<br />5 9
<br />10
<br />11
<br />0833
<br />.1667
<br />.2500 1
<br />.3333
<br />.4167
<br />1 .5000
<br />.5533 I
<br />.666,1 7500
<br />.5333
<br />.9167
<br />
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