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VIII
<br />TABLE IL - Radii, Ordinates and Deflections. Chord =100 f t.
<br />Deg.
<br />-Radius
<br />Mid.
<br />Or&,
<br />Tan.
<br />Dist.:
<br />Def..
<br />Dist
<br />Def.
<br />for -
<br />1 Ft.
<br />Deg.
<br />Radius
<br />Mid
<br />Ord.
<br />Tan
<br />Dist.
<br />Def.
<br />Dist.
<br />Def.
<br />for
<br />I Ft.
<br />2° 172°
<br />58'
<br />t
<br />101-15
<br />,.3i'
<br />-181-.39 ..
<br />1°"59'.._.
<br />t.
<br />t.
<br />t.
<br />t.
<br />340171.01
<br />0°10'
<br />34377.
<br />.036
<br />.145
<br />.291
<br />0.05
<br />7°
<br />819.0.1.528
<br />20 13'
<br />6.105
<br />12.21.2.10
<br />4o261
<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 />6.54013.08
<br />44°
<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 />5720.6
<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 />1.300
<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 />.304
<br />1.454
<br />2.909
<br />0.50
<br />20
<br />614.6
<br />2.037
<br />8136
<br />16.27
<br />2.80
<br />50
<br />3125.4
<br />.400
<br />1.600
<br />3.2000.55
<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 />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.a27
<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 />3
<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 />.764
<br />3.054
<br />6.108
<br />1.05
<br />14
<br />410.3
<br />3.058
<br />12.15
<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
<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 />13.02
<br />27:84
<br />4.80
<br />20
<br />1322.5
<br />.945
<br />3.718'7.561
<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
<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 />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 />41.58
<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 />7.80
<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 />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 />.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 />'I'ne mlddl9 orMnate . n inches for any cold of length (0) 1s equal to .0012 U -
<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 Choi -as for Short Radius Curves.
<br />Degree
<br />of
<br />Curve
<br />Radius
<br />50
<br />Y2 sub chord = sin of 1 def. angle
<br />Length
<br />of arc
<br />for 100 ft.
<br />sin. Is def. ang.
<br />12.5 Ft.
<br />15 Ft.
<br />20 Ft._R
<br />25 Ft.,
<br />-300
<br />(93.18
<br />1° Si'
<br />2° 172°
<br />58'
<br />3' 43'
<br />101-15
<br />,.3i'
<br />-181-.39 ..
<br />1°"59'.._.
<br />20 25, ..,.
<br />3°-10'
<br />30.58,-...
<br />101.33"
<br />340171.01
<br />;3
<br />2°'o6'
<br />2° 33'
<br />3° 21'
<br />4° 12'
<br />101.48
<br />36°
<br />161 ;8o
<br />20 13'
<br />z° 41'
<br />3° 33' "
<br />4o261
<br />Ioi.66
<br />38°.
<br />153.58
<br />2° 20'
<br />20 49'
<br />3° 44'
<br />4° 46'
<br />Ioi .8..5
<br />40°
<br />146.19
<br />2o -27
<br />57'
<br />2'
<br />_
<br />3° 55"
<br />4° 54'
<br />Ioz:o6
<br />420
<br />1'39.52
<br />20 34'
<br />30 05'
<br />4' 4' 07'
<br />50 08
<br />`102.29 .
<br />44°
<br />133.47_ .
<br />2° 41
<br />3° 13
<br />40 18'.
<br />5° 22'- :.
<br />162.53
<br />46°
<br />127 •.9T .
<br />2° 48'
<br />3° 21
<br />4`.29'
<br />5`36' ::
<br />102..76 .
<br />480
<br />122.92:
<br />2° 55'
<br />3o29,
<br />4o 401
<br />5o 50,
<br />103.00
<br />_500.
<br />118:31
<br />3°.02'
<br />3° 38'
<br />4' Si'.
<br />6° 04'•
<br />103.24
<br />52°
<br />114. o6'
<br />30 09,
<br />30 46,
<br />:50 02'
<br />60 17'
<br />1103,54
<br />54° r
<br />IIO.II
<br />3°16
<br />3°.54,_
<br />5o_�3,
<br />6031
<br />Ioi 84
<br />56° J
<br />Io6. 5o.
<br />3° 22'
<br />4° 02'
<br />S°.23'
<br />6° 44',-
<br />io4. 14
<br />58° i
<br />103. 14
<br />3° 29'
<br />4° 10'.
<br />5° 34'
<br />6° 57'
<br />104.43.
<br />60°
<br />Ioo.00
<br />3° 35'
<br />4° 18
<br />5° 44'
<br />70 11'
<br />Io4.72
<br />IX
<br />CURVE FORMULAS
<br />T= Rtan 1I , _
<br />T _ 5 1` 12 = T cot. 2 I Chord def. =chord
<br />o tan , I R
<br />Sin. 12 D R = 50
<br />a
<br />Sin. z D = 50 Sin. 2_D No. chords = I
<br />R E= R ex. sec 2' I D
<br />Sin, 12 D = 5o taT ; I E- T tan } I Tan. def. = 2 chord def.
<br />The square of any distance, divided by twice the radius, will equal
<br />-the distance frorn'tangent to curve, very nearly.
<br />To find angle for a given distance and deflection.
<br />Rule I. M ultiply;the given distance by .01743 (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 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 loo, Alt. 10:102=200=.5. 1oo+.5=1oo.5 hyp.
<br />Given Hyp. ioo, 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 0.574d2,'where d is the distance in miles.
<br />The correction for curvature alone is closely, 3d2. The combined cor-
<br />rection is negative.
<br />PROBABLE ERROR. If d,, d2, ds; etc. are the discrepancies of various
<br />results from the mean, and if 2;d2=the sum of the squares of these differ-
<br />ences and n=the number of observations, then the probable error of the
<br />meand2
<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, -38x6 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 />TART.F. iV -Minutes in Decimals of a Degree.
<br />1'.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 />;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 />.5833
<br />45
<br />.7500_
<br />55
<br />.9167
<br />6
<br />.1000
<br />.36
<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 />.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 />40
<br />1 1667
<br />20
<br />1 .3333 11
<br />30
<br />1 .5000 11
<br />40
<br />1 .6667 11
<br />50
<br />1 .8333 11
<br />60
<br />11.0000
<br />1ABLE V.
<br />-Inches in Uecimals of a root.
<br />1-183-32
<br />Y
<br />3-16
<br />Y
<br />5-16
<br />%
<br />11
<br />%
<br />%
<br />?�
<br />I I
<br />4
<br />5I
<br />I
<br />I
<br />I 900
<br />I
<br />.0833
<br />.10667
<br />.2500
<br />.3333
<br />.4167I
<br />..05000
<br />..05833
<br />.6667
<br />.07
<br />.8333
<br />.9167
<br />
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