|
VIII
<br />TABLE IL:m- Radii, Ordinates and Deflections. Chord =100. f t.
<br />:Deg.
<br />Radius
<br />Md.
<br />Ord.
<br />Tan.
<br />Diet.
<br />,Dei.
<br />Dist.
<br />for
<br />1 Ft
<br />Deg.
<br />.Radios
<br />Mid.
<br />�'
<br />Tan
<br />Dist.
<br />Def,
<br />Dom'
<br />Def.
<br />for
<br />I Ft.
<br />2° 17'
<br />20 58'
<br />30 43'I01.15
<br />-
<br />22
<br />.3667
<br />32
<br />:.20. 25
<br />t.
<br />f t.
<br />f t.
<br />340
<br />0'10!.34377.
<br />20 o6'
<br />036
<br />'.145
<br />291
<br />0.05
<br />V
<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.;8594.4
<br />o -I r
<br />3 •: 3
<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 />5 b0'
<br />6875:5
<br />2os ', .
<br />.727
<br />•1.454
<br />0.25
<br />8 .
<br />716.8
<br />1.746
<br />6.976
<br />13.95
<br />2.40
<br />1
<br />5729.6
<br />,.182'
<br />1.218
<br />.873
<br />'1.745
<br />0.30
<br />20
<br />688.2
<br />1:819
<br />7.266
<br />14.53.2.50
<br />-3° 16'
<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 />,:.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 />r 30
<br />'3819:8
<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 />2.70
<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-.:3125.4
<br />.400
<br />1.600
<br />3.2000.55
<br />30-
<br />603.8
<br />2.074
<br />8.281
<br />16.56
<br />2.85
<br />2
<br />' 2864.9.436
<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 />.473'1.891
<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 />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 />44..'2148:8
<br />=.582
<br />2.327
<br />4.654
<br />0.80
<br />30
<br />499:1
<br />2.511.10.02
<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 />2.618
<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 />1809.6
<br />.691
<br />2.763
<br />5.526
<br />0.95.
<br />13 ,
<br />441.7.839,
<br />11.32
<br />22.64
<br />3.90
<br />t.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 />1637.3.764
<br />3.054
<br />6.108
<br />1.05.
<br />.
<br />410.3
<br />3.058
<br />12.19
<br />24.37
<br />4.20
<br />40
<br />1562.9
<br />.800
<br />3.199
<br />6.398
<br />1.10
<br />.14
<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 />.277
<br />13.05
<br />26.11
<br />4:50
<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
<br />26.97
<br />4.65
<br />1375.4
<br />.909
<br />3.635
<br />.7.271
<br />1.25'
<br />16359.3
<br />.496
<br />13.92
<br />27.84
<br />4..80
<br />20•
<br />1322.5
<br />_'.945'3.718
<br />7.561
<br />1:30
<br />30.
<br />348:5
<br />.606
<br />14.35.
<br />28.70
<br />4.95
<br />30`-1273.6
<br />.982
<br />3.926
<br />7.852
<br />1.35
<br />17
<br />338.3
<br />3.716
<br />14.78-'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 /><' 60
<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 />41.58
<br />7.20
<br />'50
<br />982:6
<br />1.2735.088
<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 />.234
<br />5.234110.47.
<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 />.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
<br />middle ordinate
<br />in inches for any cord of.length (0) is'erl to .0012 0'
<br />multinlied'bv
<br />the middle
<br />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 />SU
<br />sub*chord
<br />= sin of I def. angle
<br />R
<br />Length
<br />of arc
<br />for 100 ft.
<br />sin. I def. ang.
<br />12.5'Ft.
<br />15 Ft.
<br />20 Ft.
<br />25, Ft.
<br />30°
<br />193.18
<br />I° 51'
<br />2° 17'
<br />20 58'
<br />30 43'I01.15
<br />-
<br />22
<br />.3667
<br />32
<br />:.20. 25
<br />3' io'
<br />,3° 58' ..
<br />101:33
<br />340
<br />171.01
<br />20 o6'
<br />2° 33'
<br />3° 21
<br />4° 12'
<br />I01.48
<br />36°
<br />,16v,80.:
<br />. 2° 13',...
<br />,2° 41'
<br />;, 39 33'
<br />4° 26'
<br />ioi.66
<br />380
<br />153.88
<br />20 20'
<br />io 49'
<br />3° 44`
<br />4° 40'
<br />for. 85
<br />4Q
<br />146.;�9.._
<br />. 2 27
<br />2 '.57•
<br />55
<br />4 54
<br />102.06
<br />,;w
<br />42°'
<br />139.52:
<br />2°'34'•
<br />30.05,
<br />.3
<br />40 07,
<br />�° 08
<br />102.29
<br />44 : ::-
<br />_1
<br />. 33" 47.
<br />Zo 1,.
<br />4
<br />o -I r
<br />3 •: 3
<br />o I$/
<br />4
<br />5 ° 22'
<br />.IO2. 53
<br />.4333
<br />36
<br />z°`48�:.
<br />3° 2I'
<br />40.29,
<br />50 36'
<br />102..76
<br />7
<br />:L�x:92.
<br />2os ', .
<br />3° 29''
<br />4' 40'
<br />S° 50'
<br />103:00
<br />o°
<br />.1'18%3i' :
<br />' 3°02'.:,
<br />3°38,,
<br />.40,51,
<br />6°iO4'
<br />103.24
<br />52° `
<br />114..06 '.
<br />30 09,
<br />30; 46�.
<br />5° 02,
<br />6° 17'
<br />103-54
<br />34° ;.
<br />IIO II
<br />-3° 16'
<br />3° 54'
<br />5°-13'
<br />6°.31'
<br />103:84
<br />56`: ;
<br />Io6.. so ' :.:
<br />3° 22' '
<br />:.4'' 02'
<br />5° 2.1 ..
<br />6°_44`
<br />10.4. 14
<br />_,580'._:..103
<br />14''
<br />30;291
<br />40:16' ..•
<br />5034'.
<br />.
<br />' V -5i,
<br />.104.43.
<br />60 ; -'
<br />• 100:00 ' :
<br />• 3 35
<br />4.18'_:..
<br />.. 5 ;4'4
<br />I I
<br />104:72: .
<br />�a
<br />IX
<br />CURVE FORMULAS
<br />T= R tan aI = T cot. Z I chord'
<br />__ 5o tan 1,1 Chord def. _
<br />T Sin. ; D R 50 R
<br />=
<br />Sin. 2' D = 50 Sin. I D No. chords = I
<br />R E= R ex. sec 3 I D
<br />Sin. z D 50't T 2 I E. = T tan } I
<br />Tan. def. = 8 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. 10.10==200=.5. 100+.5=ioo.5 hyp.
<br />Given Hyp. ioo, Alt. 25.254=200=3.125. 100-3.125=96.875 =Base.
<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 I I, and divide by 7.
<br />LEVELING. The correction for curvature and . refraction, in feet
<br />and decimals of feet is equal to 0.574d4, where d is the distance in miles.
<br />The correction for curvature alone is closely, .5ds. The combined cor-
<br />rection is negative.
<br />PROBABLE ERROR. If d,, d2; d3, etc. are the discrepancies of various
<br />results from the mean, and if Edo='the sum of the squares of ,these differ-
<br />ences and n=the number of observations, then the probable error of the
<br />meanXd2
<br />t 0.6745 n(n_1)
<br />SOLAR EPHEMERIS. 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, 38x6 in., has about 190 pages of data very
<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 />1t
<br />.0167
<br />111
<br />.1833
<br />211
<br />.3500
<br />311
<br />.5167
<br />411
<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 />62
<br />.8667
<br />-3
<br />.0500
<br />13
<br />.2167
<br />23
<br />.3833
<br />33
<br />.5.500
<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 />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 />.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 />.1667 11
<br />20-
<br />.3333
<br />30
<br />.5000
<br />40
<br />1 .6667
<br />50
<br />1 .8333 11
<br />60
<br />11.0000
<br />.- . -
<br />;. TA13LE V.
<br />-Inches in Decimals of a Foot.
<br />1-16 3-32
<br />3-16
<br />11
<br />5-16
<br />%
<br />'�z
<br />%
<br />%
<br />'�.0052
<br />.0078
<br />.31
<br />.0203
<br />.0260
<br />.0313
<br />.0417
<br />.0521
<br />.0625
<br />0729
<br />I
<br />�121�
<br />�.2a00 I
<br />I
<br />1..5833
<br />I
<br />0833 .1667
<br />3333
<br />4167
<br />.5000
<br />.6667
<br />.7500
<br />.8333
<br />.9167
<br />
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