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Q'IYY
<br />TABLE If- Radii, Ordinates and Deflections. Chord =100 ft.
<br />Deg'
<br />Radius
<br />Mid..
<br />Ord.
<br />Tan..
<br />Diet..:
<br />Def..
<br />Diet.
<br />Def.
<br />for
<br />1 Ft-
<br />Deg.
<br />Rediae
<br />Mid.-
<br />Ord.
<br />Tan
<br />:Diet.
<br />Def.
<br />Dist.
<br />Def.
<br />for
<br />1 Ft.
<br />i'5i'
<br />t.
<br />f t.
<br />it.
<br />ft.
<br />I -
<br />.2000'
<br />ft,
<br />ft..
<br />ft._
<br />ft.
<br />i
<br />0"10'
<br />34377.
<br />-.036
<br />.145
<br />.291
<br />0.05
<br />7° .
<br />819.0
<br />1.528
<br />6.165
<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 />3.0
<br />11459.
<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 />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 />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 />2.036
<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 />2.60
<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 />7.846
<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 />2.80
<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 />4°
<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 />1.;30
<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 />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 />,4.945.0.85"
<br />12
<br />478.3
<br />2.620
<br />10.45'
<br />20.91
<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..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 />•.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 />383.1
<br />3.277
<br />13.05
<br />26.11
<br />4.50
<br />4'.
<br />1432:7
<br />.873
<br />3.490
<br />6:980
<br />1.20
<br />- 30.370.8
<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 />3.718
<br />7.561
<br />,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 />8.143
<br />1.40
<br />18,
<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 />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 />4.814,19.08
<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..39.87
<br />6.90
<br />'40
<br />1011.5
<br />1.237
<br />4.943
<br />9.886
<br />1.70
<br />2C
<br />240.5
<br />5.255
<br />20:79.
<br />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 />0.
<br />955.4
<br />1.3095.234
<br />10.47
<br />1.80,
<br />26
<br />222.3
<br />5.697.22.50
<br />44.99
<br />7.80
<br />10
<br />929.8
<br />1.346
<br />5.379.
<br />10.76
<br />1.85
<br />_
<br />27.
<br />214.2
<br />5.918
<br />23.35
<br />45.69
<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 />48.38
<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 />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 />51.76
<br />9.00
<br />The middle ordinate in inches for any cord of length (0) is equal to .0012 C'
<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 />50
<br />in Decimals of a Degree.
<br />A suti chord - sin of I def. angle
<br />R
<br />Length
<br />of arc
<br />for 100 ft.
<br />sin. } def. ang.12.5
<br />Ft.
<br />15 Ft.
<br />20 Ft..'
<br />25 Ft.
<br />.5167
<br />193. 18_
<br />i'5i'
<br />51'
<br />z°.17'_
<br />2°.58'
<br />0333
<br />3°43'-
<br />.2000'
<br />101.15
<br />3z°
<br />181.39
<br />1059'
<br />42
<br />2°25'
<br />52
<br />3°
<br />Io'
<br />3°
<br />58'
<br />101.33
<br />34°
<br />171.01
<br />2°
<br />o6'
<br />20
<br />33'
<br />30
<br />21'
<br />40
<br />12'
<br />101.48
<br />360
<br />:i61. 86,
<br />20.
<br />13'
<br />2.41'
<br />_
<br />30
<br />33'
<br />40
<br />26'
<br />:`ioI.66
<br />38°
<br />153.5$
<br />2°
<br />20'.
<br />2°
<br />49'
<br />3°
<br />44'
<br />40
<br />o
<br />40,.
<br />1
<br />101.85
<br />40o.
<br />146.19
<br />0-
<br />:2.27
<br />'
<br />o
<br />2'57
<br />r
<br />o
<br />3
<br />r
<br />55
<br />4
<br />54
<br />102. o6
<br />420
<br />139.52
<br />-20
<br />34'
<br />3°
<br />05'4°
<br />37
<br />07'
<br />5°08'
<br />. 102.29
<br />44' ,
<br />133.47.
<br />2'
<br />411.
<br />3°
<br />131
<br />4°
<br />18'
<br />50
<br />22'
<br />--102.53
<br />46°
<br />127.97
<br />20481
<br />.1500
<br />30211
<br />.3167
<br />40291
<br />.4833
<br />5°36'
<br />.6500
<br />102.76
<br />48°,
<br />122.92
<br />20
<br />55'
<br />30
<br />29'•
<br />4'
<br />40'
<br />50
<br />50'
<br />103.00
<br />- 50°
<br />I I&. i
<br />3`
<br />oz'
<br />3°
<br />38'
<br />4°
<br />51'
<br />6°
<br />04
<br />I03.24
<br />52° `
<br />t
<br />l Ig.o6
<br />"3°
<br />09'
<br />3°
<br />46'
<br />S°
<br />02'
<br />6°
<br />17'
<br />103 -54
<br />54°
<br />I Io. I I '
<br />3°
<br />T6'
<br />3°
<br />54' .
<br />5°
<br />13'
<br />6°
<br />31'
<br />103.84
<br />56°
<br />1'o6 5o
<br />3°
<br />22'
<br />4°
<br />02'
<br />5°
<br />231
<br />6°
<br />441
<br />104.14
<br />580•
<br />103.14
<br />3°29'
<br />4°
<br />10'
<br />5°34'
<br />6°
<br />57'
<br />104.43
<br />600
<br />100.00
<br />3°35'
<br />4°
<br />18'
<br />5°44'
<br />7°
<br />II'
<br />104.72
<br />a►_
<br />rr
<br />.CURVE 'FORMULAS
<br />a.'_
<br />T = R tan I/ R = T cot. 2
<br />I _ go tan I Chord def. = R
<br />Sin. J D _ -_ _ 60
<br />Sin. j D = 50 R Sin: D No, chords =
<br />R 'E ='R ex. sec ; I
<br />Sin. JD = 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 from tangent to curve, very nearly.
<br />To find angle for a given distance and deflection.
<br />Rule I. Multiply -'the giveri distance by .01745 (def. for I° 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 gives 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 basefor hypotenuse.
<br />Given Base ioo, Alt. 10,.102-200 =.5. 100+-5 = Ioo.5 hyp•
<br />Given Hyp. Ioo, Ali. 25.252-. 100=3.125=96.875=Base.
<br />Error in.first example, .002; In last, -045-
<br />*,To. 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 Ifor 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, •Jda." The combined, cor-
<br />rection',is negative..
<br />. PROBABLE ERROR. If d%, de, da, etc. are the discrepancies of various
<br />results from the mean; -and if %da=the sum of the squares of these dif or-
<br />ences and n=the number of observations, then the probable error 0f the,
<br />mean'= + 0.6746 Id
<br />a
<br />n (n-1)
<br />SOLAR EPHEMERIS. Attention is called to the Solar Ephemeras -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 f ormulas; Natural andLogarithmic Functions;
<br />and Logarithms of Numbers.
<br />TABLE IV.'- Minutes
<br />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 />.8667
<br />a
<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 />.5833
<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 />47:7833
<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 />.1500
<br />19
<br />.3167
<br />29
<br />.4833
<br />39
<br />.6500
<br />49
<br />.8167
<br />59
<br />.9833
<br />" 10
<br />.1667
<br />20
<br />.3333
<br />30
<br />.5000
<br />1, 40
<br />.6667
<br />50
<br />:8333
<br />60
<br />1.0000
<br />-
<br />TASLn
<br />V. --Inches in Decimals of a Foot.
<br />1-16
<br />3-32
<br />H/3-18
<br />5-16
<br />j,
<br />.0052
<br />.0078
<br />..0104
<br />,0156
<br />.:0208
<br />.0260 .0313
<br />.0417 .0521
<br />.0625
<br />0729
<br />1
<br />2
<br />3
<br />4
<br />5
<br />6 7
<br />8 9
<br />10
<br />11
<br />.0833
<br />.1667
<br />.2500
<br />..3333,
<br />.4167
<br />.5000 .58a3
<br />.6667 .7500
<br />.8333.
<br />.9167
<br />
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