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w
<br />VIII
<br />TABLE II. - Radii, Ordinates and Deflections. Chord =100 ft.
<br />Deg.
<br />1U9
<br />bfid.
<br />Ord.
<br />Tnn.
<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 />: f°,
<br />1 Ft.
<br />- 2° 17'
<br />ft,
<br />t.
<br />ft
<br />ft
<br />181.39
<br />1° 59'
<br />ft.
<br />ft.
<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 />1.073
<br />*•.291
<br />.582
<br />0.10
<br />20'
<br />781.8
<br />1.600
<br />6.305
<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 />1:037
<br />6:540
<br />13.08
<br />2:25
<br />40
<br />8594.4
<br />.145
<br />.552
<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;,6875.5
<br />122.92
<br />:182
<br />-.727
<br />1.454
<br />0.25
<br />8
<br />716.8
<br />1.746
<br />6.076
<br />13.95
<br />2.40
<br />1
<br />5720.6 .218
<br />52°
<br />.873
<br />1.745
<br />0.30
<br />20
<br />G8S.2
<br />1.819
<br />7.260
<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 />G74.7.1.855
<br />S° 23'
<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 />.3G4
<br />1.454
<br />2.909
<br />0.50
<br />20
<br />G14.6
<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 />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 />2.03G
<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
<br />0.85
<br />13
<br />478.3
<br />2:620
<br />10.45
<br />20.91
<br />3.GO
<br />S
<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 />1800.6
<br />:691
<br />2.763
<br />5.526
<br />0.95
<br />13
<br />441:7
<br />2.839
<br />11.32
<br />22.61
<br />3.00
<br />20.
<br />1719.1
<br />.727
<br />2.003
<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 />.7G4
<br />3.054
<br />6.1081.05'
<br />-14 •
<br />410.3
<br />3.058
<br />12.18
<br />24.37
<br />4.20
<br />40
<br />1562.0
<br />.800
<br />3.199
<br />6.393
<br />,1.10
<br />30
<br />356.2
<br />3.168
<br />12.62
<br />25.24
<br />4.35
<br />50
<br />1495.0'
<br />-.836
<br />3.345
<br />G.G89
<br />1.15
<br />15
<br />383.1
<br />3.277
<br />13.05
<br />26.11
<br />4.50
<br />.1432.7
<br />".873
<br />3:490
<br />G.9S0
<br />1.20
<br />30
<br />370.8
<br />3.387
<br />13.49 .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 />4.50
<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 />3.035
<br />15.64
<br />31.29
<br />5.40
<br />50
<br />1185.8
<br />1.055
<br />4.217
<br />8.433
<br />1.4.5
<br />19
<br />302.9
<br />4.155
<br />16.51
<br />33.01
<br />5.70
<br />b _
<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 />1074.7,1:164
<br />4:653
<br />'9.305
<br />1'.610
<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 />4.793
<br />9:596;
<br />1.615
<br />.23
<br />250.8
<br />5:035
<br />19.94
<br />39.87
<br />0.90
<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 />41.53
<br />7.20
<br />50
<br />982.G
<br />1.273
<br />5.088
<br />10.18
<br />1.75
<br />25
<br />231.0
<br />5.476
<br />21.61
<br />43.23
<br />7.50
<br />6 t•-
<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 />005.1
<br />1.382
<br />5.524
<br />11.05
<br />1.00
<br />28
<br />206.7
<br />6.13924.19
<br />48.35
<br />8.40
<br />30
<br />881.9
<br />1.418
<br />5.669
<br />11.34
<br />1.05
<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 />f 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 :0012X90OX2.183 or 2.36 inches.
<br />TABLE IIL . Deflections for Sub Chords for Short Radius Curves.
<br />Degree
<br />of
<br />Curve
<br />Radiub
<br />50
<br />�J sub chord
<br />It = sin of '� def. angle
<br />I ength
<br />of arc
<br />for.100 ft.
<br />sin. z def. ang.
<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° lo'
<br />3° 58'
<br />_101.33
<br />34°
<br />171.01
<br />2° o6'
<br />2':33'
<br />3° 21'
<br />4° I2',
<br />I01.48
<br />36°
<br />161.80
<br />2° 13
<br />,° 41'
<br />3° 33'
<br />4° 26'
<br />Io1.6G
<br />380
<br />153.58
<br />20 20'
<br />2°'49�
<br />3° 4,4'
<br />4° 40,
<br />101.85
<br />40°
<br />146.19
<br />2° 2'J'
<br />2° 57' '
<br />3* 55'
<br />4° 54
<br />1o2. o6
<br />42'
<br />139.52
<br />2° 34'
<br />3° 05',
<br />4° 07'
<br />S° 08
<br />102.29
<br />44°'
<br />133.47
<br />2° 41'3°
<br />13'
<br />4° 18'
<br />5° 22'
<br />102.53
<br />460
<br />127.97 .'
<br />2° 48'
<br />3° 21'
<br />4° 29'
<br />e 36'
<br />102.76
<br />48°
<br />122.92
<br />2° 55'
<br />3° 29'
<br />4° 4c'
<br />5° 50'
<br />103.00
<br />5o°
<br />I18.31
<br />3° 02'
<br />3° 38'
<br />4°.51'
<br />60 04'
<br />103.24
<br />52°
<br />114.o6
<br />3°09'
<br />3° 46' ..
<br />5° 02'
<br />6' f•7'
<br />103.54
<br />54°
<br />110. I I
<br />.3° 16'
<br />3° 54'
<br />S° 13'
<br />60 31'
<br />-103.84
<br />56°
<br />Io6. 50
<br />3' 22'
<br />4° 02'
<br />S° 23'
<br />6° 44'
<br />104-14
<br />58°
<br />103.14
<br />3° 29'
<br />4° 10'
<br />50 34'
<br />60 57"
<br />104.43
<br />60 °
<br />100.00
<br />3°35 '
<br />4°.18'
<br />5°44'
<br />7' 11.
<br />104.72
<br />IX
<br />'CURVE- FORMULAS
<br />T =• R tan IR= T cot ' 1 chord2
<br />5o tan- j I . • Chord def. _
<br />T - -Si ri'. I ll 50 R -
<br />R =
<br />Sin:.I D:= °° Sin. a D No. chords = I
<br />:R E = Res. sec l I D '
<br />_.50 tan ; I
<br />Sin: D - ,l, E = T`tan :'1.1 Tan. def.= a chord def.
<br />The square of any distance, divided Ly twice the radius, will equal
<br />the dlstance'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 .oi745, 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 ioo,Alt. Io.lo2=zoo=.5. ioo-i••.5=IOO.5 hyp.
<br />Given .. Hyp. I oo, Alt. 25.252-200=3.125- 100 -3.125 = 96.875 = Base.
<br />Error in first example, .002; In last, .645•
<br />To find Tons of Rail in one mile of track: multiply weight per yard
<br />by l i, and divide by 7. -
<br />LrVFLING. The correction for curvature and refraction, in feet
<br />and decimals of feet is equal to 0.574d2, A -here d is -the distance in miles.
<br />The'correction for curvature alone is closely, Jd2. The combined cor-
<br />rection is negative.
<br />PROBABLE ERROR. If d, , d„ da, ete. are the discrepancies of various
<br />results -f rom the mean, and if %de=the sum of the squares of these differ-
<br />" cnces and n=the number of observations, then the probable error of tho
<br />mein=(n
<br />0.6745 i1
<br />+ 1)
<br />SOLAR EPIIEUERls. Attention is•callcd 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 90 pages of data very
<br />useful to the Surveyor; such as the adjustments of transits, levels and
<br />solar attachments; directions andtablesfor 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 and Logarithmic 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 />.6533
<br />51'
<br />.8500
<br />2
<br />.0333
<br />12
<br />.2000
<br />22
<br />.3G67
<br />32
<br />.5333
<br />42
<br />.7000
<br />52
<br />.8667
<br />s
<br />.0500'
<br />13
<br />.2167
<br />23
<br />.3833
<br />33
<br />.5500
<br />43
<br />1.7167
<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 />OS33
<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 />7.1167
<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 />.•1667
<br />38
<br />.6333
<br />48.
<br />5000
<br />58
<br />.9667
<br />9
<br />.1500
<br />19
<br />.3167
<br />29
<br />.4833
<br />39
<br />.6500
<br />40
<br />.8167
<br />59
<br />.9833
<br />10
<br />.1667 11
<br />20
<br />1 .3333 1130
<br />1 .5000
<br />1, 40
<br />.6667
<br />50
<br />_93331,
<br />60
<br />1.0000
<br />TABLE 11. - Inches In _Uec finals of a Poot.
<br />1-16
<br />3-32
<br />Y
<br />3-16
<br />5-16
<br />.0052
<br />.0078
<br />.010-1
<br />.0156
<br />.020S
<br />.0260
<br />.0813
<br />.0417 .0521
<br />.0625
<br />0729
<br />1
<br />2
<br />3
<br />4
<br />5
<br />6
<br />7
<br />8 9
<br />10
<br />1
<br />11
<br />.0833
<br />.1667
<br />.2500
<br />.3333
<br />.4167
<br />.5000
<br />,5833
<br />:6667 .7500
<br />.8333
<br />.9167
<br />
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