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VIII
<br />TABLE IL - Radii, Ordinates and Deflections. Chord -100 ft.
<br />Deg,
<br />Radius
<br />Ivfid
<br />Ord.
<br />Taa.
<br />Dist.
<br />Def.
<br />Diet.
<br />D r _
<br />1 Ft.
<br />.Deg.
<br />Radial
<br />'
<br />Mid.
<br />Ord
<br />Ten,
<br />Disk
<br />Dd.
<br />D
<br />Diet.
<br />lfor
<br />1 Ft.
<br />2° 58'
<br />t.
<br />t.
<br />32°
<br />181.39.
<br />1° 59'
<br />2° 25'
<br />t .
<br />t.
<br />14
<br />ft, -
<br />171.01
<br />0°10''34377.
<br />2° 33'
<br />.036
<br />.145
<br />.291
<br />0.05
<br />7'
<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 />.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 />7-17.9
<br />1.6736.685
<br />5° 36'
<br />13.37
<br />2.30
<br />50
<br />6875.5
<br />.185
<br />.727
<br />.1.454
<br />0.25
<br />S
<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.G0
<br />10
<br />4911.2
<br />.255
<br />1.Ot8
<br />2.036
<br />0.35
<br />.30
<br />674.7
<br />1.855
<br />7.411
<br />14.82
<br />2.53
<br />20
<br />4297.3
<br />;291
<br />1364
<br />2.327
<br />0.40
<br />40
<br />601.7
<br />1.892
<br />7.556
<br />15.11
<br />2. GO
<br />30
<br />3839.8
<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 />2.710
<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 />8.136
<br />1G. 27
<br />2.80
<br />50
<br />3125.4
<br />.400
<br />1.600
<br />3.200
<br />0.55
<br />30
<br />603.8.2.074
<br />8.281.16.56
<br />2.85
<br />2
<br />2864.9
<br />,4301.745
<br />3.490
<br />0. GO
<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 />516.4
<br />2.292
<br />9.150
<br />18.30
<br />3,la
<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 />_214818
<br />.592
<br />2.327
<br />4.654
<br />0.80
<br />30
<br />409.1
<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 />O.S5
<br />12
<br />478.3
<br />2.620
<br />10.45
<br />20.91
<br />3.60
<br />E
<br />1910.1
<br />.655
<br />2.818
<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 />12.18
<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 .383.1
<br />3.277
<br />13.05
<br />26,11
<br />4,50
<br />4
<br />1132.7
<br />.873
<br />3.490
<br />6.980
<br />1.20
<br />30
<br />370.8
<br />3.367
<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 />30,348.5
<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 />319.673.935
<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 />302.9'4.155
<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 />9.305.1.60
<br />22
<br />262:0
<br />4.914
<br />19.08 '3S.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 />1011.51.237
<br />4.943
<br />9.886
<br />1.70
<br />24-
<br />340.5
<br />5.255
<br />20.79
<br />41.58
<br />7.20
<br />50
<br />082.6
<br />1.273
<br />5.088
<br />10.18
<br />1.75
<br />25
<br />231.0
<br />5.476
<br />2t.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 />5.607
<br />22.50
<br />44.99
<br />7.SO
<br />10
<br />929.6
<br />1.346
<br />5.379
<br />10.76
<br />1.85
<br />27
<br />214.2
<br />b.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 />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 />0.360
<br />25.04
<br />50.07
<br />8.70
<br />40
<br />859.9
<br />1.455
<br />5.814
<br />11.83
<br />2.00
<br />30
<br />16,139
<br />193.2
<br />0.583
<br />25.88
<br />51.76
<br />9.00
<br />The middle ordinato'n ine hes for any cord of length (C) is equal to .0012 C'
<br />multiplied by the mild e 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 />Curve
<br />Radius
<br />50
<br />sin, idef.ang.
<br />sub chord = sin of def. angle
<br />R '
<br />Lengt'•r
<br />of are
<br />Far _111011.
<br />12.5 Ft.
<br />15 Ft,
<br />20 Ft.
<br />25 Ft.
<br />30°
<br />193.18
<br />1° 51
<br />2° 17'
<br />2° 58'
<br />3° 43'
<br />101.15
<br />32°
<br />181.39.
<br />1° 59'
<br />2° 25'
<br />3° 10'
<br />3° 58'
<br />101.33
<br />3.40
<br />171.01
<br />2° 06'
<br />2° 33'
<br />3° 21'
<br />4° 12'
<br />101.48
<br />36°
<br />.161. S0
<br />2° 13'
<br />2° 411
<br />3° 331
<br />26'
<br />1o1.6G
<br />38°
<br />153-58
<br />2020
<br />2° 491
<br />3° 44`
<br />4° 40`
<br />IDI.8,i
<br />40`
<br />146.19
<br />2° 27
<br />2° 57'
<br />3° 55
<br />4° 54
<br />102.06
<br />42°
<br />139.52
<br />2° 34'
<br />3° 05'
<br />4° 07'
<br />08
<br />102.29
<br />44°`
<br />733.47
<br />z° 41'
<br />3° 13'
<br />4° 18'
<br />S° 22'
<br />102.53
<br />46°•
<br />127,97
<br />2° 48
<br />30 21'
<br />4° 29'
<br />5° 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
<br />3° 38'
<br />4° 51'
<br />6-04
<br />103.24
<br />5i°
<br />114. o6
<br />3.09
<br />3° 46'
<br />5° oz'
<br />6° 17
<br />103.54
<br />54°
<br />110. 11
<br />3° 1.6'
<br />3° 54'.
<br />5° 13'
<br />60 32'
<br />103.84
<br />56°
<br />106.5o
<br />3° 22
<br />40 02'
<br />y° 23'
<br />6° 44'
<br />104.14
<br />58°
<br />103.14
<br />3°29'
<br />4' 10'
<br />5° 34'
<br />6° 57'
<br />104.43
<br />60°
<br />100.00
<br />3°35'
<br />4° 1?'
<br />5°44'
<br />7° 11'
<br />104.72
<br />rx
<br />CURVE FORMULAS
<br />T_ R tan 211 R= T cat. -'1 I chord'
<br />1 5o tan I I 50 Chord def. _
<br />Sin. ll R
<br />.
<br />,
<br />Sin. s D = 5° Sin. p No. chords = 1
<br />R E= R ex. see 1 I D
<br />Sin. ; D = ,o tan 4 E 'Plan}I
<br />Tan. def. _ ; chord def.
<br />.I. =
<br />The square of any distance, divided by twice the radius, will equal
<br />the distance frons -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 I ft.
<br />see Table, 11.), 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 fora given angle and distance. Multiply the angle
<br />by .01745, and the product by the distance.
<br />GENERAL DATA
<br />RIGHT ANGLE TRIANGLFs5. Square the altitude, divide by twice the
<br />base. Add quotient to base for hypotenuse.
<br />Given Base too, Alt. 10.102=200=.,,5. loo+- 5=Ioo.5 hyp.
<br />Given Hyp. too, Alt. 25.25x-200=3.125. 100 -3.125=96.875 -Base.
<br />Error in first example, .002; in last, .o45.
<br />To find Tons of Rail in one mile of track: multiply weight per yard
<br />by I I, and divide by 7.
<br />LFVIkLINC. The correction for curvature and refraction, in feet
<br />anddecimals of feet is equal to 0.574d2, where d is the distance in miles.
<br />1'hc correction for curvature alone is closely, 3d2. The combined -cor-
<br />rection is negative.
<br />PROBABLF. ERROR. If di, d2, da, 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 />mean Zdx i
<br />X0.6745 n(n-1)
<br />SOLAR ErimMERls. 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, 35x6 in., has about 190 pages of data eery
<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 />N
<br />.0167
<br />111
<br />.1833
<br />211
<br />.3500
<br />311
<br />.5167
<br />411
<br />.6833
<br />511
<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 />16
<br />.2667
<br />.26
<br />.4333
<br />36
<br />.6000
<br />46
<br />.7667
<br />56
<br />.9333
<br />7
<br />.1167
<br />1.7
<br />.2833
<br />27
<br />.4500
<br />37
<br />.6167
<br />47
<br />7833
<br />57
<br />9300
<br />8
<br />.1333
<br />Is
<br />.3000
<br />28
<br />.4667
<br />38
<br />.6333
<br />48
<br />.8400
<br />58
<br />9667
<br />9
<br />.1500
<br />I9
<br />_3167
<br />29
<br />.4633
<br />39
<br />.6500
<br />49
<br />.8167
<br />59
<br />.9833
<br />10
<br />.1667 11
<br />20
<br />1 _3333
<br />38
<br />1 .5000 11
<br />40
<br />.6667 11
<br />50
<br />1 .8333 11
<br />60
<br />11.0000
<br />"TABLE \'.--Inches
<br />in Decimals of a Foot.
<br />1-163-32
<br />3-16
<br />.0052
<br />.0078
<br />.0104
<br />.0136
<br />.0208
<br />.0260
<br />.0313
<br />.0417
<br />.05 21
<br />.06 2.5
<br />0729
<br />1
<br />2
<br />I
<br />3
<br />4
<br />5
<br />ti
<br />7
<br />8
<br />9
<br />10
<br />11
<br />.0833
<br />.1667
<br />.2500
<br />.3333
<br />.4167
<br />.5000
<br />. ;833
<br />.66G7
<br />.7500
<br />. S333
<br />.9167
<br />
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