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7M
<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 />Dor'
<br />1 or
<br />-Deg:
<br />Radius
<br />Mid.
<br />Ord.
<br />Tan.
<br />Dist.
<br />. Def.
<br />Dist. -
<br />Dor• •
<br />1 r t.
<br />51'
<br />ft.
<br />ft.ft.
<br />.8500
<br />ft.
<br />/
<br />43' ;
<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 />_
<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 />.436
<br />:873
<br />0.15
<br />30
<br />764.5
<br />1.6376.540
<br />2°
<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 />13.372.30
<br />55'
<br />50
<br />6875.5
<br />.182
<br />.727
<br />1.454
<br />0.25
<br />a
<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 />2,150
<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 />2.155
<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 />7.656
<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 />2170
<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 />S
<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 />3.7810.65
<br />104.43
<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 />2.327
<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 />Ib
<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 />3.058.12.18.
<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 />4.38
<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 />L'-.
<br />1432.7
<br />.873
<br />3.490
<br />6.980
<br />1.20
<br />30
<br />370.8
<br />3.387.13.49
<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
<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 />41.59
<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,
<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 />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 />48.38
<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 (C) 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 />341 sub chord
<br />R = sin of 'r def. angle
<br />Length
<br />of arc
<br />for 100 ft.
<br />sin.'r def. ang.
<br />12.5 Ft.
<br />15 Ft.
<br />20 Ft.
<br />25 Ft.
<br />_30°
<br />193.18
<br />1°
<br />51'
<br />2°
<br />17'2°
<br />.8500
<br />58'
<br />3'
<br />43' ;
<br />101.15.
<br />32°
<br />181.39
<br />1°59'
<br />.5333
<br />2°25'
<br />.7000
<br />3'
<br />10'
<br />3°58'
<br />.0500
<br />101.33
<br />34°
<br />171.01
<br />20
<br />o6'
<br />2°.33'
<br />43
<br />3°
<br />21'
<br />4°
<br />12'
<br />101.4.8
<br />360
<br />161.80
<br />2°
<br />13'
<br />2'
<br />41'
<br />3'
<br />33'
<br />4°.26'
<br />.9000
<br />`io1.66
<br />38°
<br />153.58
<br />2020,
<br />25
<br />2°
<br />49'
<br />3°
<br />44'
<br />4'
<br />40'
<br />101.85
<br />40°
<br />146.19
<br />2°
<br />27'
<br />2'
<br />57'
<br />30
<br />55'
<br />4'
<br />54'
<br />102.o6
<br />42'
<br />139.52
<br />2'
<br />34'
<br />3005
<br />27
<br />4°
<br />07'
<br />S'
<br />08'
<br />102.29
<br />440
<br />133.47
<br />z°41'
<br />.1333
<br />3°13'
<br />4'18'
<br />.4667
<br />-5°22'
<br />.6333
<br />.102.53
<br />460
<br />127.97
<br />2°
<br />48'
<br />3021
<br />19
<br />4'
<br />29'
<br />-5s.
<br />36'
<br />102.76
<br />48°
<br />122.92
<br />z°55'
<br />.9833
<br />3'29,
<br />.166711
<br />4°40'
<br />1 .3333 1130
<br />5'50'
<br />•.5000
<br />103.00
<br />50.°-
<br />118.31
<br />3°.02'
<br />60
<br />3°
<br />38'
<br />4°
<br />51'
<br />6°
<br />04'
<br />103.24
<br />52°
<br />I14. o6
<br />.3'
<br />09'
<br />3°
<br />46'
<br />5'
<br />02'
<br />60.17'
<br />163.54
<br />54°
<br />I IO. I I
<br />30
<br />16'
<br />3°
<br />54'
<br />5'
<br />13'
<br />60
<br />31'
<br />103.84
<br />56°
<br />1o6.50
<br />3022'.
<br />4'
<br />O2'
<br />50
<br />�3'
<br />6°
<br />44'
<br />104.14
<br />58°
<br />103.14
<br />30
<br />29'
<br />40
<br />10'
<br />5'
<br />34'
<br />.60
<br />57'
<br />104.43
<br />600
<br />100.00
<br />3035
<br />4'
<br />18'
<br />5'
<br />44'
<br />7°-r1'
<br />104.72
<br />1E
<br />CURVE FORMULAS
<br />T= R tan I R= T cot. 12 I chords
<br />T _ 50.tan I Chord def. = R
<br />Sin. DR50
<br />=
<br />Sin, J D = :50 Sin. sj D No. chords = I
<br />R E= R ex. sec 8 I D
<br />So tan I
<br />' Sin. � 'D = ,r E = T tan J 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 .01745 (def. for I° for 1 ft.
<br />see, Table II.), and divide glveri 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 .oi745, an& 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. 100-}-.5=100.5 'hyp,
<br />Given Hyp. Ioo,Alt. 25.252=200=3.125. 100 -3.125 =96.875 =.Base.
<br />Error 1n first example, .002; In last,".045•
<br />.To find Tons of Rail in one. mile of. track: 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 da, where d is the distance in miles.
<br />The.correction for curvature alone is closely, I&. The combined cor-
<br />rection is negative.
<br />PROBABLE ERROR. If d; , d2, da, etc. are. the discrepancies of various
<br />results from the mean, and if Y-d2=the sum of the squares of these diff0r-
<br />ences and n=the.number of observations, then the probable error of the,
<br />mean=fid$
<br />.1 0.6745 n (n-1)
<br />SOLAR EPHEMERIS,:Attention is called to the Solar Ephemefb for
<br />the current year, published by Keuffel & Esser Co., and furnished free of
<br />charge upon request, which is 34x5} 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 />TABLE 1V. - Minutes
<br />TABLE V. - Inches in Decimals off -a Foot.
<br />in Decimals
<br />of a Degree. ' -_
<br />" 1'
<br />.0167
<br />'11'
<br />.1833
<br />21'
<br />.3500
<br />31'
<br />.5167
<br />41''.6833
<br />.0104
<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 />8
<br />.0500
<br />13
<br />.2167
<br />23
<br />.3833
<br />33
<br />.5500
<br />43
<br />7167
<br />53
<br />:.8833-
<br />A
<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 />554�
<br />.9167
<br />6
<br />:3000
<br />16
<br />.2667
<br />26
<br />.4333
<br />36.
<br />.6000
<br />46
<br />.7667
<br />50
<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 />1S-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 />.166711
<br />20
<br />1 .3333 1130
<br />•.5000
<br />40
<br />1 .666711
<br />50
<br />1 8333 11
<br />60
<br />1.0000
<br />TABLE V. - Inches in Decimals off -a Foot.
<br />1-16 3-32
<br />H
<br />3-16
<br />YL 5-16
<br />%
<br />%
<br />Y4
<br />9
<br />.0052' .0078
<br />.0104
<br />.0156
<br />.0208 .0260
<br />.0313
<br />.0417 .0521
<br />.06 5
<br />.07
<br />1 2
<br />3
<br />4
<br />b 6
<br />7
<br />8 9
<br />10
<br />11
<br />,0833 .1867
<br />.2500
<br />.3333
<br />,4167 ..5000 1
<br />.5833 1
<br />.6667 .7500
<br />1-.8333
<br />1.9167
<br />
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