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vua
<br />TABLE TL -- Radii, Ordinates and Deflections. Chord -100 f t.
<br />Deg,
<br />Radius
<br />Mid.
<br />Ord.
<br />Tau.
<br />Diet.
<br />Def.
<br />Dist.''
<br />Dor
<br />1 Ft.
<br />Deg.
<br />Radius
<br />Mid.
<br />Ord.
<br />Tan
<br />Dist.
<br />Def.
<br />Diet.
<br />beF.
<br />1 Ft,
<br />2° 58'
<br />t•
<br />I
<br />it.
<br />ft.
<br />i° 59`
<br />2' 25'
<br />ft. -
<br />3° 58'
<br />f t,
<br />Jt.
<br />171.01
<br />0'10'
<br />84377.
<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 />17t89.
<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 />1 .,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 />717:9,1.673
<br />4° 29
<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 />8
<br />716.8
<br />1.746
<br />.6.976
<br />13.95.2.40
<br />6004 1
<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 />2.10
<br />10
<br />4911.2
<br />.255
<br />1.018
<br />2.0360.35
<br />3° 22
<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 />t.892
<br />7.556
<br />15.11
<br />2. Go
<br />30
<br />3819.8
<br />.327
<br />1.301)
<br />2.6180.45
<br />9
<br />637.3
<br />1.965
<br />7.546
<br />15.69
<br />2.70
<br />40
<br />3137.9
<br />.364
<br />1.454
<br />2.909
<br />0.50
<br />20
<br />614.6
<br />2.037
<br />S.136
<br />16.27
<br />2.80
<br />50
<br />3125.4
<br />.400
<br />1.600
<br />3.20D
<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 />503.4
<br />2.110
<br />8.426
<br />16.85
<br />2.90
<br />10
<br />2614'.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 />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 />2149.S
<br />.582
<br />2.327
<br />4.654
<br />0.80
<br />30
<br />499.1
<br />2.51'1
<br />10.02
<br />20.04
<br />3.45
<br />60
<br />2022.4
<br />.618
<br />2.472
<br />4.945
<br />0.85
<br />12
<br />475.3
<br />2.620
<br />10.45
<br />20.91
<br />3.60
<br />8
<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 />1909.-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
<br />383.1
<br />3.277
<br />12.05
<br />26.11
<br />4:50
<br />4-
<br />1432.7
<br />.873
<br />3.490
<br />6.930
<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 />3.635
<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 />3.71.8
<br />7.561'1.30
<br />30
<br />348.5
<br />3.608
<br />14.35
<br />28.70
<br />4.95
<br />30
<br />1273.6
<br />.982
<br />3.920
<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 />3.935
<br />16.64
<br />31.29
<br />5.40
<br />50
<br />1185.8
<br />1.055
<br />4.217
<br />81.433
<br />1.45.
<br />19 .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 />27.1:4
<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 />35.16
<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.SS6
<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 />1.273
<br />5.088
<br />10.18'
<br />1.75
<br />25
<br />231.0
<br />6.476
<br />21.64
<br />43.28
<br />7.50
<br />d
<br />955.4
<br />1.309
<br />5.234
<br />10.47 .1.80
<br />26
<br />222.3
<br />5.697
<br />22.50
<br />44-99
<br />7.80
<br />30
<br />ON.6
<br />1.346
<br />5.379
<br />10.76
<br />1.85
<br />21 •
<br />214.2'
<br />.918
<br />23.35
<br />44.69
<br />8.10
<br />20
<br />905.1
<br />1.382,5:524
<br />11.05
<br />1.90
<br />28
<br />206.7
<br />.139
<br />24.19.
<br />48.38
<br />8:40
<br />30
<br />881:9
<br />1.418'5.669
<br />11.34
<br />LOS
<br />20
<br />199.7 16.360
<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 />193'216.583
<br />25.88
<br />51.76
<br />9.00
<br />tuo Tuame oruinate In Inc ties for any corn of long thL IV) I8 equal to UUIZ L'
<br />multiplied by the middle ordinate taken from the above table. .Thus, if it
<br />desired to bond 30 ft. rail to fit a 10 degree curve, its widdle 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 />50
<br />sin. Idef. ang.
<br />3i Bub chord def: angle
<br />R
<br />Length
<br />of arc
<br />for 100 ft.'
<br />12.5 Ft.
<br />IS 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 />i° 59`
<br />2' 25'
<br />3° lo'
<br />3° 58'
<br />101.33
<br />34°
<br />171.01
<br />2° 06'
<br />2' 33'
<br />3° 21'
<br />4° 12'
<br />101:48
<br />36°.
<br />161.80.
<br />z° 13`
<br />2° 41'
<br />3° 33`
<br />4° 26'-
<br />ioi.66
<br />36'
<br />153.58.
<br />20 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 />3° 55'4'
<br />54'
<br />lo2.o6.
<br />42°
<br />139.52 ..
<br />2° 34'
<br />3° 05'
<br />4° 07'
<br />5° 08
<br />102: 29.
<br />44°
<br />133.'47
<br />2° 41'
<br />3° 13'
<br />4°'18' '
<br />5° 22'
<br />]02.53
<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° 55�
<br />3° 29'
<br />4° 40
<br />5° 5o`
<br />103.00
<br />50°
<br />118.31
<br />3° 02'
<br />.3° 38'
<br />4° 51'
<br />6004 1
<br />103.24
<br />52'
<br />114.06
<br />3° 09'
<br />3' 46'
<br />S° Oz"
<br />6° 17"
<br />103.54
<br />54°
<br />110.11
<br />3° 16
<br />30 54'
<br />5° 13'6°
<br />31'
<br />103,84
<br />56'
<br />1o6.5o
<br />3° 22
<br />4° 02'
<br />5° 23'
<br />6° 44'
<br />10:1.. 14
<br />580
<br />J03. 14
<br />3° 29'
<br />4° Io'
<br />5' 34'
<br />60 57'
<br />104.43
<br />6o°
<br />100.00
<br />3' 35' 1
<br />4° 18
<br />5° 44
<br />7' 11
<br />I 104.72
<br />IX
<br />.0167
<br />CURVE FORMULAS
<br />.1833
<br />T
<br />So tan,I R - T 1Ot' ' f Chord def. = chorda
<br />.3500
<br />_
<br />T T Sin. s D H= 50
<br />Sin. '1
<br />.5167.
<br />Sin. 21 TJ = 5o
<br />No. chords = I
<br />c•
<br />R E R ex. sec I D
<br />1
<br />Sin. 2 D' -..So tai " I E = T tan } I Tan.def..= kchorddef.
<br />y
<br />.. The squaie of any distance, divided by twice the radius, 'will equal
<br />y•l
<br />the distance from tangent to curve, very nearly.
<br />;7
<br />To find angle for a given distance and deflection.
<br />.5333
<br />Rule I. Multiply the given distance by .01745 (def. for 1 ° for I ft..
<br />.7000
<br />see Table 11.), -and divide given deflection by the product.
<br />.8667
<br />)Rule z. "Multiply given deflection by 57.3, and divide the product by
<br />..0500
<br />the given distance.
<br />.2167
<br />To find deflection for a given angle and distance. Multiply the angle
<br />.3833
<br />by .oi745, and the product by. the distance.
<br />.5500
<br />GENERAL DATA.
<br />RIGHT ANGLE TRIANtiLES.- Square the altitude, divide by twice the
<br />base. Add quotient to base for hypotenuse.,
<br />Given Base too, Alt, lo-1o==2o0=.5. ioo+.5=1oo.5 hyo.
<br />Given Hyp. loo, Alt. 25.254-200=3.125. 106-3.125=96.873=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 />Lt-WEL1NG. 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, 02. The combined cor-
<br />rection is negative.
<br />PROBABLE ERROR. If d,, d2, da, etc. are the discrepancies of ,various
<br />results from the mean, and if Ed9=the sum of the squares of these differ=
<br />ences and n=the number of observations, then the probable error of the
<br />mean =. 1d 2
<br />-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 hooklet,.3gx6 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 />Tear F IV =Minutes in 17ecirnals of a Deoree.
<br />11
<br />.0167
<br />111
<br />.1833
<br />21'
<br />.3500
<br />3/1
<br />.5167.
<br />410
<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 />18
<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 />.0333
<br />7
<br />.11V
<br />17
<br />.2833
<br />27
<br />.4500
<br />37
<br />.0167
<br />47
<br />.7833
<br />57
<br />.9500
<br />8
<br />.1333
<br />to
<br />.3000
<br />28
<br />-4667
<br />38
<br />.0333
<br />48
<br />.8000
<br />58
<br />.9667
<br />9
<br />.1500
<br />l9
<br />.3167
<br />29
<br />-4833
<br />39
<br />.6500
<br />49
<br />.816759
<br />.9833
<br />10
<br />.1667
<br />20
<br />.3333
<br />30
<br />.5000
<br />40
<br />.6667
<br />50
<br />.8333
<br />60
<br />1.0000
<br />-1 A131,Fy.--Inches 1n 1)ecimais of a root.
<br />1-16
<br />3-32
<br />3-16%
<br />5-16
<br />%'-'.
<br />ss
<br />°/s
<br />3�
<br />0052
<br />.0078
<br />.0104
<br />f .0156
<br />.0208 I
<br />.0260
<br />.0313
<br />.0417
<br />.0521
<br />.0625
<br />.0729
<br />I
<br />1
<br />I
<br />�
<br />�
<br />. 4833
<br />.1667
<br />.2500
<br />I .3:333
<br />.41k67 I
<br />.:.U00
<br />..583:3
<br />.66G7.
<br />-7.5 00.
<br />..83:53
<br />Alti7 .
<br />
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