|
VIII
<br />T"ix II. - Radii, Ordinates and Deflections. Chord =100 it.
<br />Deg. •
<br />132, ,Mid:
<br />Ord.
<br />Tan.
<br />Dist,
<br />Def.
<br />Dista
<br />Def.
<br />for
<br />1 Ft.
<br />Des.
<br />Ssdiva
<br />Mid.
<br />Ord.
<br />Ten.
<br />Dist.
<br />Def.
<br />t
<br />Dist.
<br />Def.
<br />for '
<br />I Ft.
<br />'° 17
<br />it.t.
<br />3° 43`
<br />t.
<br />t.
<br />'
<br />1°59'
<br />[t,
<br />t
<br />1t..
<br />ft.
<br />340
<br />0'10'
<br />34377.
<br />.OUG
<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 />.582.0.10-
<br />44'
<br />20'
<br />781.8
<br />1.000
<br />6.395
<br />12.79
<br />2.29
<br />30
<br />11459.
<br />.109
<br />.4n6
<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 />.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 />1 6875.5
<br />.182
<br />..727
<br />1.454
<br />0.25
<br />8
<br />716.8
<br />1.745
<br />6.976
<br />13.95.2.40
<br />4° 5i`
<br />1
<br />5729.6
<br />'.218
<br />:873
<br />1:745.0.30"
<br />3° 46,
<br />20
<br />638.2
<br />1.319
<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 />.201
<br />1.164
<br />2.327
<br />0.40
<br />40
<br />601.7
<br />1.892
<br />7.556
<br />15.,11
<br />2.60
<br />30
<br />3819.8
<br />.327
<br />1.309
<br />2.61.8
<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 />.364
<br />1.454
<br />2.909
<br />0.50
<br />20
<br />61.4.6
<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 />8.4.26
<br />16. ET
<br />'L.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 />8.716'17.43
<br />3.00
<br />20
<br />2455.7
<br />.509'2.030
<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 />10.03
<br />20.04
<br />3.45
<br />50
<br />2622.4
<br />.018
<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 />a
<br />1910.1
<br />..655
<br />2.618
<br />5.`235
<br />0.90
<br />30
<br />439.3
<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 />18
<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 />5.81,7
<br />1.00
<br />30
<br />425.4
<br />2.949
<br />11.75
<br />23.51
<br />4.05
<br />30
<br />1837.3
<br />.704
<br />3.054
<br />6.103
<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 />GO
<br />1495:0
<br />.830
<br />3.845
<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 .26.97
<br />4.65
<br />10
<br />1375.4
<br />.909
<br />3.035
<br />7.271
<br />1.25
<br />10
<br />359.3
<br />3.496
<br />13.92.
<br />27.84
<br />9.80
<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 />1273.0
<br />.982
<br />3.926
<br />7.852
<br />1.33
<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 />1140.3
<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 />G.DO
<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 />36.44.6.30
<br />20
<br />1074.7
<br />1.164
<br />4.553
<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 />4.708.
<br />9.696
<br />1.65
<br />23
<br />250.4
<br />5.035
<br />19.94
<br />39.87
<br />6.00
<br />40
<br />3011.5
<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 />60
<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 />935.4
<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 />5.379.10.76
<br />1.8ci
<br />27
<br />214.2
<br />5.918
<br />23.35
<br />0.69
<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 />6.199
<br />24.19
<br />48.38
<br />8.90
<br />30
<br />-881.9
<br />1.418
<br />5.669'11.34
<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 />1.466
<br />5.81411.63
<br />2.00
<br />1 SO.
<br />193.2
<br />0.683
<br />26.88
<br />51.75
<br />9.00
<br />The middle ordinate in inches for any cord of length (C) is a nal to .0012 C'
<br />multiplied by the middle ordinato. taken from the above table• Thug, if it
<br />desired to bend a 30 ft, rail to fit 1.0 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 />`50R
<br />A sub chord
<br />= sin of i def. angle
<br />of age
<br />for 100 ft.
<br />sia. z def. ails,
<br />12.5 Ft.
<br />15 Ft.
<br />26 Ft.
<br />25 Ft.
<br />:6833
<br />.193.18.
<br />1° 51`
<br />'° 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 />340
<br />171.01
<br />2° o6' .
<br />2° 33
<br />3° 21'
<br />4. 12'
<br />I0I.48
<br />36°
<br />161.8o
<br />2° 13'
<br />2° 41'
<br />3° 33'
<br />4° 26'
<br />161.66
<br />38°,.153.53
<br />1,5
<br />2° 20'
<br />2° 49'3°
<br />44'
<br />4° 40'''
<br />101.85
<br />40°
<br />146. ig
<br />2° 27'
<br />2° 57'
<br />• 37 55'
<br />4° 54'
<br />102.o6
<br />42°
<br />139.52
<br />2° 34'3°
<br />05'
<br />4° 07'
<br />S° 08'
<br />102-29
<br />44°
<br />133.47
<br />2° 41'
<br />3° 13'
<br />4° 18'
<br />5° 22'•
<br />102.53
<br />46"
<br />-127-97-
<br />20 48'
<br />3° 21'
<br />4° 29`
<br />51 . 36'
<br />102.76
<br />48°
<br />122.92
<br />2° 55
<br />3° 2g'
<br />4° 40`
<br />5° 50'
<br />103.00
<br />500
<br />118:31
<br />.3° 02'
<br />3° 38'
<br />4° 5i`
<br />6° 04'
<br />103.24
<br />52°.
<br />114.o6
<br />31>0 91
<br />3° 46,
<br />5° 02'
<br />6° 17'
<br />103.54
<br />54°.
<br />11o.11
<br />3° 16'
<br />3° 54'
<br />5.'13
<br />6-31,
<br />103.84
<br />56°
<br />106'.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 />5034
<br />6° 47'
<br />104.43
<br />600
<br />100.00
<br />3° 35
<br />4° 18
<br />5744
<br />7° 11'
<br />104.']2
<br />IX
<br />CURVE 'FORMULAS
<br />T= R tan Q I R= T cot. 1. I chord2
<br />_ 5o tan I Chord def. = R
<br />T Sin. D. R 60
<br />Sin. J D '= 50 Stn. 2 D. . -,No. chords = I
<br />R E= Res. scc z 1 D
<br />_ tan I
<br />. Sin. � D - 5o ,I, P: = T tea J I Tan. def. chord def.
<br />The.square of any distance, divided by twice t.:e radius, will equal
<br />the distance from tangent to curve, very nearly.
<br />To find angle for a given.distance and deflection.
<br />Rule J. Nlultiply the given distance by ,01745 (def. for L° for 1 ft.
<br />see Table If.), 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 10o,Alt. Lo.io2-* 2oo=.5. loo+.5=1oo.5 hyp.
<br />Given Hyp. loo, Alt. 25.252=200=3.125.100 3.125=96.875=Base.
<br />Error in first example, ,cot; in last, .oq.5.
<br />To find Tons of Rail in one mile of trach: multiply v;cight 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 0.874 da, where d is the distance in miles.
<br />The correction for curvature alone is closely, �d2. The combined cor-
<br />rection is negative.
<br />PROBABLE ERROR. If d1, d„ da, etc. are the discrepancies of various
<br />results from the mean, and if Md the sum of the squares bf these differ-
<br />ences and n=the number of observations, then the probable error of the
<br />s
<br />mean= -I- 6.6745
<br />SOLAR EPIIFMERLS: Attention is called to the Solar Ephemeris for
<br />the current year, published by Keu(Iel & Esser Co., and furnished free of
<br />charge upon request, wl11c11 is 3aa,5g 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 />it TABLE IV. - Minutes in Dreimsle of s DRPFP.f .
<br />1'
<br />.0167
<br />11'
<br />.1833
<br />21'
<br />.3500
<br />31'
<br />.5167
<br />41'
<br />:6833
<br />51'
<br />Swo
<br />2
<br />.0333
<br />12.2000
<br />22
<br />.3667
<br />32
<br />.5333
<br />t2
<br />.7000
<br />52
<br />.8667
<br />3
<br />.0500
<br />13
<br />.2167
<br />23
<br />.3833
<br />33
<br />.5500
<br />t3
<br />.7167
<br />53 '
<br />.8833
<br />4
<br />.0667
<br />1,5
<br />.2333
<br />24
<br />.4000
<br />34
<br />.5667
<br />#4
<br />.7333
<br />54
<br />.9000
<br />5
<br />.0333
<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 />IG
<br />.2667
<br />24
<br />.4333
<br />26
<br />.0900
<br />40
<br />.7667
<br />50
<br />.9333
<br />7
<br />.1167
<br />17
<br />.2533
<br />27
<br />.4500
<br />37
<br />.0167
<br />47
<br />.7833
<br />57
<br />.9500
<br />8
<br />.1333
<br />13
<br />.3000
<br />28
<br />.4067
<br />38
<br />G333
<br />48
<br />WN
<br />58
<br />.9667
<br />9
<br />.1500
<br />19
<br />.3167
<br />29
<br />.4833
<br />"
<br />.6500
<br />40
<br />"167
<br />59
<br />.9833
<br />10
<br />.IG67 11
<br />_
<br />203
<br />1 .3333 11
<br />20
<br />1 .5000
<br />11 49 -
<br />,5667
<br />50
<br />.8333 11
<br />60
<br />1.0000
<br />TABLE V. - Inches in Decimals of a Foot.
<br />1-10 5-32 3 -LG 5 -IG J 71
<br />.0052 .0078 .0104 .0150 .0208 .0260 .0313 '.0117 .0521 .0625 .0729
<br />1 2 3. 4 5 fi 7 8 9 10 11
<br />.0833 .1667 .2.5 .3333 .4167 .5000 .5833 6667 ..7500 .8333 .9167
<br />
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