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VIII
<br />TABLE II. - Radii, Ordinates and Deflections. Chord =100 ft.
<br />Deg.
<br />I P•uiius
<br />I Mid.
<br />Ord.:
<br />Tan.
<br />Dd.
<br />Dist.
<br />for
<br />1 rt.
<br />Deg.
<br />Radius
<br />1lid.
<br />Ord.
<br />Tan,
<br />Dist.
<br />Def.
<br />Dist.
<br />for
<br />Dist.
<br />1 Ft
<br />2° 17,
<br />ft.
<br />ft.
<br />ft.
<br />IL
<br />.3667
<br />10591
<br />ft.
<br />it.
<br />ft.
<br />ft.
<br />34'
<br />0".10,
<br />34377.
<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 />.552
<br />0.10
<br />20'
<br />781.S
<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 />747.9
<br />1.67,^,
<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 />S
<br />716.8
<br />1.746
<br />6.976
<br />13.95
<br />2.40
<br />1
<br />5729.G
<br />.218
<br />.S73
<br />1.745
<br />0.30
<br />20
<br />688.2
<br />1.819
<br />7.2GG
<br />14.53
<br />2.50
<br />10
<br />4911.2
<br />.255
<br />1.01S
<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 />7.550
<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 />1.665
<br />7.846
<br />15.69,2.70
<br />40
<br />3437.9
<br />.361
<br />1.454
<br />2.909
<br />0.50
<br />20
<br />G14.6
<br />2.037
<br />8.130
<br />16.27
<br />2.80
<br />50
<br />312.5.4
<br />.400
<br />1.600
<br />3:200
<br />0.55
<br />603.8
<br />2.074
<br />.8.281
<br />16.56
<br />2.85
<br />2
<br />28G4.9
<br />.430
<br />1.745
<br />3.490
<br />0.60
<br />,30
<br />40
<br />;93.4
<br />2.110
<br />8.426
<br />16.85.2.90
<br />10
<br />264.1.6
<br />.473
<br />1.561
<br />3.751
<br />0.65
<br />10
<br />573.7
<br />2.183
<br />8.716
<br />17.43
<br />3.00
<br />20
<br />2155.7
<br />,509
<br />2.036
<br />4.072
<br />0.70
<br />30
<br />54G.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 />it
<br />521.7
<br />2.402
<br />0.585
<br />19.10
<br />3.30
<br />40
<br />2149.8
<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 />3
<br />1910.1
<br />.655
<br />2.613
<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 />1500.6
<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 />6.393
<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 />4
<br />1432.7.
<br />.873
<br />3.490
<br />6.990
<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 />3.035
<br />7.271
<br />1.25
<br />16
<br />359.3
<br />3.400
<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 />318.5
<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 />1.36
<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 />11S5.8
<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 />0.00
<br />10
<br />1109.3
<br />1.127
<br />4.507
<br />0.014
<br />1.55
<br />21
<br />274.4
<br />4.594
<br />18.22
<br />30.44
<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 />4.799
<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 />41,55
<br />7.20
<br />50
<br />932.6
<br />1.273
<br />5.088
<br />10.18
<br />1.7.5
<br />25
<br />231.0
<br />5.476
<br />21.64
<br />43.23
<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 />7.80
<br />110
<br />929.6
<br />1.340
<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 />24.10
<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 />559.9
<br />1.455
<br />5.814
<br />11.63
<br />2.00
<br />30
<br />193.2
<br />6.583
<br />25.83
<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 muddle ordinate taken frmn the above table. Thus, if it
<br />desired to bend y 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 />80
<br />3z sub chordLength
<br />- R =sin of z, def. angle
<br />of arc
<br />for 100 ft.
<br />sin, $ def. mg.
<br />12.5 Ft.
<br />15 Ft'.
<br />20 Ft.
<br />25 Ft.
<br />30°
<br />193-18
<br />1' 511
<br />2° 17,
<br />,° 581.
<br />3° 43'
<br />I01.15
<br />320.181.39
<br />.3667
<br />10591
<br />2° 25
<br />3° 10'
<br />3° 58'
<br />101.33
<br />34'
<br />171.01
<br />2°o6'
<br />2° 33'
<br />3°2I'
<br />4°12'
<br />101.45
<br />36'
<br />161.8o
<br />2°13'
<br />2°41
<br />3°33'
<br />4° 26'
<br />ioi.66
<br />3$°
<br />I'a3.58
<br />2° 20'
<br />2° 411'
<br />30 44'
<br />4° 40'
<br />101::85 .
<br />40°
<br />146.19
<br />2027'
<br />2° 57'
<br />3° 551
<br />.
<br />4°54'
<br />102.o6
<br />42
<br />139.52
<br />2° 34
<br />3° o5'
<br />4° 07'
<br />S° 08
<br />IO2.29
<br />440
<br />133-47
<br />2° 41'
<br />30 13'
<br />40 18'
<br />5° 22 •
<br />102.53
<br />46'
<br />127.97
<br />2° 48
<br />3°21'
<br />4°29'
<br />5°36'
<br />102.76
<br />48°
<br />122.92
<br />2°55t
<br />3'29
<br />4°40'
<br />5°50'
<br />103.00
<br />So°
<br />118.31
<br />3 02'
<br />30 38'
<br />4° 51'.
<br />6° 04
<br />103.24
<br />52°
<br />114.06,
<br />3°09'
<br />3°46'
<br />5°oa'
<br />6°17'
<br />103.54
<br />54°
<br />110.11
<br />3° 16'
<br />3° 54'
<br />1' 13'
<br />6-31,
<br />103.84
<br />56°
<br />1o6.5o
<br />3°22'
<br />4°02'
<br />5°23'
<br />6°44'
<br />104.14
<br />58°
<br />103.14
<br />3° 29'
<br />4° 10'
<br />5° 341
<br />69,57'
<br />104.43
<br />6o°
<br />Ioo. oo
<br />3° 35'
<br />4' 18'
<br />1 5° 44'
<br />79 11'
<br />104.72
<br />IX
<br />CURVE. FORMULAS
<br />T= R tan U1 I R= T co. r, I. Chchord2
<br />,r _ So tan ,L I t-ord def. = H
<br />Sin. ll ' R 50
<br />=
<br />50 Sin. a D I
<br />Sin. � D ='R:.. , No. chords= -
<br />E=Rex. see 4I D
<br />Sin. } D = 5° tT I E = T tan J.1 Tan. def. = a 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 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. zoo+.5=1oo.5 hyp.
<br />Given Hyp, loo, Alt. 25.252_200=3.125. 100-3.125=96.875=13ase.
<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 0.574d', where d is the distance in miles.
<br />The "correction for curvature alone is closely, 3d'. The combined cor-
<br />rection is negative.
<br />PROBABLE ERROR. If dl, d„ d3', etc. are the discrepancies of various
<br />results from the mean, and if Y-d'=the sum of the squares of these differ-
<br />ences and n=the number of observations, then the probable error of the
<br />mean 0.6745 2.dx'
<br />x,11 (n-1)
<br />SOLAR EPHEBIERis. Attention is called to the Solar Ephemeris for
<br />the current year, published by Keuffel & Esser Co., and furnished free of
<br />charge upon request, which is 3;;x5 in., with about 9.0 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 IV. - Minutes in Decimals of a Deuce.
<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 />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 />.0000
<br />5
<br />OS33
<br />15
<br />.2500
<br />25
<br />.4167
<br />35
<br />5333
<br />45
<br />.7500
<br />55
<br />.9167
<br />6
<br />.1000
<br />16
<br />.2667
<br />2G
<br />.4333
<br />36
<br />.6000
<br />46
<br />.7667
<br />66
<br />.9333
<br />7
<br />.1167
<br />17
<br />.2333
<br />27
<br />.4500
<br />37
<br />.6167
<br />47
<br />.7833
<br />57
<br />.9500
<br />8
<br />.1333
<br />13
<br />.3000
<br />28
<br />.4607
<br />33
<br />.6333
<br />48
<br />.5000
<br />5S
<br />.9667
<br />9
<br />.1500
<br />19
<br />.3167
<br />29
<br />.4533
<br />39
<br />.6500
<br />49
<br />.8167
<br />59
<br />.9333
<br />10
<br />.1667 11
<br />20
<br />.3333 Ij
<br />33
<br />.5000
<br />40
<br />.6661
<br />50
<br />.8333
<br />60
<br />1.0000
<br />TABLE V. -
<br />Inches in Decimals of a foot,
<br />1. 1W
<br />3-32
<br />11
<br />3-16
<br />Y.,
<br />5 -IG %
<br />0052
<br />.0078
<br />.0101
<br />.0156
<br />.0203
<br />.0260 .0313
<br />..n417 .0sz1
<br />0625
<br />_.°729
<br />1
<br />2
<br />3
<br />4
<br />5
<br />G i
<br />8 9
<br />10
<br />11
<br />1
<br />.0833
<br />.1667
<br />.2500
<br />.3333
<br />.41617 f
<br />.5000 .58.33
<br />.6667 .7500
<br />.6333
<br />.9167
<br />
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