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-
<br />TA131M IL - Radii, Ordinates and Deflection. Chord ®100 ft.
<br />---
<br />D°6•
<br />-
<br />Iiadwe
<br />--
<br />Mid
<br />Ord.'
<br />Tan
<br />Dist.
<br />Def.
<br />Dist.-,'ifFt.
<br />,15 Ft.
<br />Wig.,
<br />Radius..
<br />Mid
<br />Ord.
<br />Tsn
<br />Dist,.
<br />Def.
<br />Diet.
<br />Def.
<br />I(or
<br />Ft.
<br />2° 58'
<br />3° 43'....
<br />io1.15
<br />32
<br />181.39
<br />1 59
<br />2 25
<br />t.
<br />ft.
<br />ft..
<br />-ft.
<br />L 1.01
<br />7
<br />0.10,
<br />34 377.
<br />'.036
<br />.1'45
<br />.291
<br />0.05
<br />0'
<br />819.0
<br />1.528
<br />,6:105
<br />12.21
<br />2.10
<br />20"17181
<br />153•_58
<br />'.073:436',
<br />291
<br />.,.582
<br />0.10
<br />20,
<br />781.8
<br />1.800'
<br />6.395'12.79
<br />2°-57'
<br />2.20
<br />:'30
<br />11459.
<br />.109
<br />.436.873
<br />2° 34',-
<br />0.15
<br />30
<br />764.5
<br />1.637
<br />.;6.540
<br />13.08
<br />2.25
<br />'40 i
<br />8591.4
<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 />6875.5
<br />:.188'
<br />.727
<br />1.454
<br />0.25
<br />8716.8
<br />118.31
<br />L.746
<br />6.976
<br />13.95
<br />2.40
<br />1 '
<br />5729.6
<br />' .218
<br />.873
<br />1.745
<br />0.30
<br />20
<br />688.2,1.819
<br />54°
<br />7:266
<br />14.53
<br />2.M
<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 />4.411
<br />14.82
<br />2.55
<br />20
<br />"4297:3;`.291
<br />5° 34
<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 />1.300
<br />2.618
<br />0.45
<br />9 -
<br />637.3
<br />1.965
<br />:7:846
<br />15:69
<br />2.70
<br />90
<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
<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 />.435
<br />1.745
<br />0.60
<br />40
<br />593-4
<br />2.110
<br />8.426
<br />16.85
<br />2.90
<br />.10
<br />2G44:6
<br />.473
<br />1.891
<br />,3:490
<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 />2.03 6
<br />4.072
<br />0'.70
<br />30
<br />546.4
<br />2',292
<br />9.150
<br />18.30
<br />3.1.1
<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 />0.85
<br />'.30
<br />499:1
<br />2,511
<br />10:02 .20.04
<br />3.45
<br />50'
<br />2022.4,
<br />.618
<br />2.472
<br />4.945
<br />0.85:
<br />.12 ' .478.3
<br />2:620'10:45
<br />.20.91
<br />3.60
<br />31910.1
<br />.655
<br />2.618
<br />'5.235
<br />0.00'
<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 />0.05
<br />13 °
<br />441.7,2.839
<br />11.32.
<br />22.64
<br />3.00
<br />20-
<br />1719.1
<br />.727
<br />2.908
<br />5.817
<br />1.00
<br />30
<br />42554,2.949
<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 />.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 />396.21.594
<br />.168
<br />12.62
<br />25.24
<br />4.35
<br />60
<br />1495:0
<br />;.836
<br />3.345
<br />6.689'1'.15
<br />15
<br />383.1.277
<br />13.05 '26.11
<br />4.50
<br />4...
<br />1432.7
<br />.873
<br />3.490
<br />6.980
<br />1.20
<br />30
<br />370:8.387
<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 />10' ';
<br />359.3A96
<br />13,92.'27.84
<br />4.80
<br />20,
<br />1322.5
<br />.945
<br />3:718
<br />7..561
<br />1.30--
<br />30.348.5:606
<br />14.35
<br />28.70
<br />4.95
<br />`30--1273.6'
<br />.982
<br />3.926
<br />7.852
<br />1.85
<br />'17
<br />338`.3.716
<br />14:78 .29.56
<br />5.10
<br />40'
<br />1228.1
<br />1.0184.071
<br />8.143
<br />1.40
<br />18 `
<br />319.6.935
<br />15:64
<br />31.29
<br />5.40
<br />50'
<br />1185.8
<br />1.055.4.217.
<br />8.433
<br />1.45-
<br />18
<br />302.9.155
<br />16.51-
<br />33:01
<br />5,70
<br />8
<br />1146,3
<br />1.091
<br />4.362
<br />8.724
<br />1.50
<br />20
<br />287.9.374
<br />17.37'
<br />34.73
<br />6.00
<br />10;!•1109.3
<br />1.127
<br />4.507
<br />9.014
<br />1.55
<br />21
<br />27.1.4
<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 r
<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 />1.237.4:043
<br />0.886
<br />1:70
<br />.24
<br />240.5
<br />5.255
<br />20.'79 -
<br />41.58
<br />7.1'0
<br />50
<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 />.955.-4
<br />1:309
<br />5.234
<br />10,47
<br />1.80
<br />26 r
<br />222.3
<br />5.697
<br />22.50
<br />44:99
<br />7.80
<br />10
<br />.929.6
<br />1,346
<br />5.879
<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 />24.19
<br />48.38
<br />8.40
<br />30
<br />881.91.418
<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 />859.9'1:455
<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 />Thomiddle ordinate 'n inches for nay cord of length (0) is equal to .0012 W
<br />multiplied by the midd a ordinate taken, from the above table. Thus, if it
<br />desired to bends 30 ft. rail to fits 20 degree curve, its middle ordinate should
<br />be .0012X900X2.183 or 2.36 inlehes.
<br />Tmii E TIL "Deflections for Sub Chords for Short Radius Curves.
<br />Degree
<br />of
<br />Curve
<br />; Radius
<br />50
<br />sin.; def. ang.
<br />M sub chord - sin of z defangle
<br />R .
<br />-Length
<br />of arc
<br />for 100 it.
<br />, 123 Ft.
<br />,15 Ft.
<br />20 Ft..
<br />23 Ft.
<br />30°
<br />193.18
<br />1° 51r
<br />2° 17'
<br />2° 58'
<br />3° 43'....
<br />io1.15
<br />32
<br />181.39
<br />1 59
<br />2 25
<br />3 Iol-
<br />58'.
<br />101. 33
<br />°
<br />34
<br />L 1.01
<br />7
<br />2° 06'
<br />2° '
<br />33
<br />o '
<br />3 z1
<br />o ,
<br />¢,1z
<br />101.48
<br />36°
<br />"161.80
<br />.z°13'-.
<br />z�41',
<br />3°33''
<br />- 4°:26'..-:
<br />Joi.66
<br />380'_
<br />153•_58
<br />2° 20'--2`
<br />49± --
<br />--3°-44'x
<br />4° 40
<br />.101.85
<br />40° .
<br />146: iq
<br />2° 27
<br />2°-57'
<br />30 55'
<br />4° 51
<br />io2:o6
<br />-42°
<br />_ 139.52 .
<br />2° 34',-
<br />3° 65' .
<br />4° 07'
<br />S° 08;
<br />162:29
<br />44`.
<br />',133-:47 .
<br />2° 41'
<br />3' 13'
<br />4° 18'
<br />S° 22'-
<br />102.53
<br />46° '
<br />t27, 97
<br />2° 48'
<br />3° 21'
<br />4° 29
<br />5° 36'
<br />102.76
<br />148°
<br />122.92
<br />2° 55'
<br />3° 29'
<br />0'
<br />4° 40'-
<br />5° so'_,
<br />r03.00
<br />500.
<br />118.31
<br />3° 02'
<br />3° 38'
<br />4° 51'
<br />6° 04'
<br />10
<br />103.24
<br />52°
<br />114.o6)
<br />3° 09'
<br />3° 46'
<br />5° 02
<br />6° 17'
<br />1b3-54
<br />54°
<br />110. I I; .
<br />. 3° 16'
<br />3° 54'
<br />5° 13' ,
<br />6° 31'
<br />,103.84
<br />56°
<br />io6. 501
<br />3° 22'
<br />4° 02'
<br />5° 23
<br />6° 44
<br />104.1'4
<br />58°
<br />k13: 14
<br />3° 29'
<br />40 lo',
<br />5° 34
<br />6° 57'
<br />104-43
<br />60°
<br />100.00.
<br />3°35''
<br />4°1s'
<br />S' 44'
<br />7°i1'
<br />)04.72
<br />CURVE'FORMULAS. Ix
<br />T- R tan 2 i R=_ T cots f, chord;
<br />T - .So tan x i 50 Chord def.•= R
<br />R=
<br />5
<br />Sin 1"D - Sin. 7D0. I
<br />° R E'= R ex.'sec 1 No. chords =.D
<br />go tan
<br />Sin: ' I
<br />S. D - 1, E = T tan I I Tan. def. = ; 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 .0r745 .(def. for 1° for 1 ft.
<br />see,Table 1I.), and divide given deflection. by the product.
<br />Rule 2: . Multiply given deflection by 57.3, and-divide'the prgduct by
<br />the given distance.
<br />To find defleetion_for a given angle and disiance.''Mu'Itiply.fhe angle
<br />•by .oi.745, and. the product by the distance.
<br />GENERAL DATA
<br />RIGLIT ANGLE TRIANGLES. Square the altitude,'divide.by--twice the
<br />base. Add gliotient.to.base for hypotenuse.
<br />,Given'Base 1oo,.Alt. 10.102=200-.5. 100-•.5=10M. .11y1) -
<br />Given -Hyp.
<br />hyl1.Given-Hyp. too, Alt. .25.252=2010=3.125. 100.-3.12 96:875=13ase.
<br />Error in first .example, .hoz; in Iasi, :045:
<br />To find Tons of- Rail in one mile of track: niultiply. weight' lier. yard
<br />by' 1 i, and divide by 7:. `
<br />'LEVELING. The correction -for .curvature ands refraction, in feet
<br />and decimals of feet is equal to 0.574d2, where d.is the distance in'niiles.
<br />The correction for curvature -alone is closely, 2d?. The combined cor-
<br />-rection.is negative.
<br />-' PROSABLP, ERROR.- If d1,.d2, da, etc. are the discrepancies' of various
<br />results, from the mean, and if Eda=the sum of the squares of these differ-
<br />ehces and n --the number of observations, then the probable,error of the
<br />meant =. I:d 2
<br />X0.6745 7(n-1)
<br />SOLAR EPHEMERIS. Attention is called to the Solar Ephemeris for
<br />the current year, published by Keuffel & F..sser Co.,.and furnished upon
<br />request.: This handy booklet; 3ax6 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 Dearee.
<br />1f
<br />.0167
<br />.11t,.--.1833
<br />21/-.-.3500
<br />1-16 3-32
<br />31t.
<br />.5167
<br />41f
<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 />.9000
<br />5
<br />.0833
<br />15
<br />.2500
<br />25
<br />.4167
<br />35
<br />.6833
<br />45-
<br />.7300
<br />55
<br />.0167
<br />'6
<br />,1000
<br />16.2667
<br />26
<br />.4333
<br />36
<br />.6000
<br />46
<br />.7667
<br />56
<br />.9333
<br />"7-
<br />.116 7
<br />. 17
<br />.2833.
<br />27 -
<br />AMO
<br />37
<br />.6167'
<br />47
<br />.7833
<br />" 57
<br />.9500-
<br />6
<br />.I333
<br />19
<br />.3000
<br />28
<br />'.4667
<br />38
<br />.6333
<br />48
<br />SOOO
<br />59
<br />9667
<br />91500
<br />i9 •
<br />.3I67
<br />29 .
<br />.4833
<br />39
<br />.6500
<br />49
<br />,8167
<br />59
<br />.9833
<br />10
<br />.1667
<br />20
<br />.3333
<br />30
<br />.5000
<br />40.
<br />-6667
<br />60
<br />.8333
<br />60
<br />LOOM)
<br />-- -i-
<br />-TAR1•F i',
<br />Inches in Decimals of a Foot.
<br />}
<br />1-16 3-32
<br />3=16'
<br />�•j
<br />5-16
<br />36
<br />%
<br />se
<br />:n
<br />'b
<br />.0052 0078
<br />.0104
<br />I ,01,6
<br />,0208
<br />.0260
<br />0313
<br />0417
<br />.0:121
<br />0625
<br />.0729
<br />1 3
<br />3 1
<br />4
<br />5
<br />6
<br />7
<br />L
<br />3
<br />9
<br />lU
<br />11
<br />_.0833. ..tfi67
<br />.2500
<br />3333
<br />'.4167
<br />.3000...3833.
<br />.61167
<br />.7500
<br />.83$3
<br />9167 - i
<br />
|