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VIII
<br />TABLE II. - Radii, Ordinates and•Deflmtions. Chord =100 ft.
<br />Deg.
<br />Radius
<br />Mid
<br />Qrd.
<br />Tan.
<br />Dist,
<br />- Dd,
<br />Dist.
<br />(or
<br />I Pt
<br />Deg.
<br />Radius
<br />Itifid.
<br />Ord.
<br />Tan•
<br />Dist,
<br />Dd. ,
<br />Dist,
<br />Deet,
<br />1 pt.
<br />=° 17
<br />ft.
<br />ft.
<br />it.
<br />it.
<br />!
<br />1°59'
<br />1t,
<br />It:
<br />It,
<br />ft.
<br />340
<br />0°10
<br />34377.
<br />.036
<br />.145
<br />.291
<br />0.05
<br />- 7'
<br />819.0
<br />1.528
<br />fi.105
<br />12.21
<br />2.10
<br />20
<br />17189.
<br />.073
<br />.291
<br />.582
<br />0.1.0
<br />20'
<br />781.8
<br />1.600
<br />6.395
<br />12,79
<br />2.20
<br />-30
<br />11459.
<br />.I09
<br />.436.
<br />,873
<br />0,15
<br />30
<br />764.5
<br />1.6.37
<br />0,540
<br />13,03
<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 />_6875.5
<br />.182_.727
<br />3° 29'
<br />,1,454
<br />0.25
<br />8
<br />71G.8,1.746
<br />118,31
<br />6.076
<br />13.95
<br />2.40
<br />1
<br />5729.6
<br />.218
<br />,873
<br />A. 745
<br />0.30
<br />20
<br />G38.2
<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
<br />1.855
<br />7,411
<br />14.82
<br />2.555
<br />20
<br />4297.3'
<br />.291
<br />1.164
<br />2.327
<br />0.40
<br />- 40
<br />G61.7,1.892
<br />3° 31
<br />7.556
<br />15.11
<br />2.60
<br />30
<br />3819.8
<br />.327
<br />1.309
<br />-2.6118
<br />0.40
<br />9
<br />637.3
<br />1.965
<br />7.846
<br />15.69
<br />2.70
<br />40
<br />3437.9
<br />,30t
<br />1,454
<br />2.900
<br />MO.
<br />20
<br />614. 111
<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 />o.55
<br />30'603.8
<br />2.074
<br />8.281
<br />16.56
<br />2.85
<br />8
<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.G
<br />.473
<br />1.891
<br />.3.781
<br />0.65
<br />10
<br />573.7
<br />2.183
<br />6.716
<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 />13.30
<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 />4.651
<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 />11,
<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 />-1:;9:3
<br />2.730
<br />10.89
<br />21.77
<br />3.75
<br />10.
<br />1802.6
<br />.691
<br />2.763
<br />5.526
<br />0.95
<br />'13
<br />441.7
<br />2:839
<br />11.32
<br />22. G3
<br />3.90
<br />20
<br />17(9.1
<br />:727
<br />2.903
<br />5.817
<br />1,00
<br />30
<br />425.4
<br />2.949
<br />11.75
<br />23.514.05
<br />30
<br />1637:3
<br />.704
<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 />306.2
<br />3.168
<br />12.62
<br />27.24
<br />4.35
<br />50
<br />1495.0.836
<br />3,343
<br />6.689
<br />1.15
<br />15
<br />383.1
<br />3.277
<br />1.3.05
<br />20.11
<br />4.50
<br />IL '-1432.7
<br />,873
<br />3.490
<br />6.980
<br />1.20
<br />30
<br />370.8.3.387
<br />'13.49
<br />26.97
<br />1,65
<br />I0
<br />1375.4
<br />.909
<br />3.635
<br />7.271
<br />1.25
<br />16
<br />359.3
<br />3,406
<br />13.92
<br />27.84
<br />4.80
<br />.20
<br />.1322.0
<br />,945
<br />3,713
<br />'7.561
<br />1.3030
<br />348,5
<br />3-606
<br />14.35
<br />28.70
<br />-1.95
<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 />29.55
<br />:1.10
<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 />1.70
<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 />30.73
<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 />1S.22 .30.44
<br />6.30
<br />,20
<br />1074:7
<br />1.164'4.653
<br />9.305
<br />1.60.
<br />22
<br />'262.0
<br />4.814
<br />19.OS
<br />38.16
<br />61.60
<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 />I011.5
<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 />_982.6
<br />1,273'5.088
<br />10.18
<br />1.75
<br />25
<br />231.0
<br />5.476
<br />21.64
<br />43,23
<br />7.50
<br />6 • -
<br />955.4
<br />1.309
<br />5.234
<br />10.47
<br />1.80
<br />20
<br />222.3
<br />5.697
<br />22.50
<br />44.99
<br />7 -SO
<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 />23.3.5
<br />40.69
<br />S.10
<br />20
<br />905,1
<br />1,382
<br />5.524
<br />11.05.
<br />1.90
<br />26
<br />206.7.6.139
<br />24.19
<br />48.35
<br />S.40
<br />30
<br />881.9
<br />1.418
<br />5.669
<br />11.34
<br />L 9:5
<br />29
<br />199.7'6.360
<br />25.04
<br />50.07
<br />S.
<br />40
<br />1 859.9
<br />1.455
<br />5,814.11,63
<br />2.00
<br />30
<br />193.2
<br />6.583
<br />25.88
<br />5.76
<br />9.00
<br />The middle ordinate in inches for any cord of length QC) is equal to .0013 W
<br />multiplied by the middla ordinate taken fromtho above table. Thee, if it
<br />desired to bend -a 30 ft. rail to fit a 10 degree curve, its middle ordinate should
<br />be .0012X000X2.183 or 2,36 inches.
<br />TABLE III, Deflections for Sub Chords for Short Radius Curves.
<br />Degree
<br />of -
<br />Curve
<br />liadius
<br />59
<br />y§ sub chord_ sin Of, def,.angle
<br />R
<br />Length
<br />of arc
<br />for 100 ft.
<br />sin, ; def. ang.
<br />12.5 Ft.
<br />15 Ft.
<br />20 -Ft.--]-25
<br />Ft.
<br />3o!,-
<br />193•`18
<br />- i° 51'
<br />=° 17
<br />2° 55`
<br />3. 43`
<br />101.15
<br />32°
<br />181.39
<br />1°59'
<br />20.25
<br />3°l0'
<br />3° 58'
<br />101,33
<br />340
<br />171:01_
<br />2° 06`
<br />2° 33'
<br />3° 21
<br />4° Iz'
<br />101,48
<br />u-36°
<br />161. So
<br />2° 13
<br />2° 41'
<br />3 •33':
<br />40 26`
<br />1oi.66
<br />-38-
<br />153-.58
<br />2° 20'.
<br />2° 49'
<br />3e 44'
<br />4° 40'
<br />101,85
<br />40°
<br />146.19.
<br />2° 27'
<br />2° 571•
<br />3° 55'
<br />4° 54"
<br />Io2. o6
<br />42'
<br />139.52
<br />'°'34'
<br />3° 05':
<br />4' 07'
<br />5° 08'
<br />102.24
<br />44'
<br />133.47
<br />20 41'
<br />3° 13
<br />4° is,
<br />S° 22'
<br />IO2.53
<br />46°
<br />1127:97
<br />2° 48'
<br />3° 21'
<br />4° 29'
<br />S° 36'
<br />102.76
<br />48°
<br />122.92
<br />2° 556
<br />3° 29'
<br />4° 40'
<br />5° 50'
<br />103.00
<br />5o°
<br />118,31
<br />3° 02'
<br />3° 38'
<br />4° 51'
<br />6° 04'
<br />103.24
<br />52°
<br />114.06
<br />3° 09
<br />30 46'
<br />5° 02'
<br />6° 11
<br />103.54
<br />54°
<br />110.11
<br />3° 16'
<br />3° 54'
<br />S° 13'
<br />61 31
<br />103-84
<br />56°
<br />106.50
<br />3° z2'
<br />4° 02'
<br />5° z3'
<br />6° t4'
<br />501.14
<br />58°
<br />103.14
<br />3° 29`
<br />4° lo'
<br />5° 34'
<br />6' 57'
<br />104.43 c..
<br />60°
<br />100.00
<br />3° 31
<br />4° 18'
<br />5° 44`
<br />7° 11'
<br />104.7.2.
<br />IX}
<br />CURVE- FbRMULAS
<br />T = R tan 8 I chord'
<br />5o tan>J'I- ' : - -R = T cot. -s I Chord def. = R
<br />T _ Sin: ll
<br />1
<br />Sir... 8'D. = 5o Sm. , D No. chords I
<br />R E= R eN:, sec t I, D
<br />5o tan ; I
<br />Sia: 11). = ` T E = T tan 8 I Tan. def.= z chord def.
<br />The square of 'any distance, divided by tivice the radius,' will equal
<br />the distance from tangent to curve, very nearly..
<br />To find angle for a given distance and deflection,
<br />Rulc'l. 'Multiply" the given distance by .01745 (def. for r° 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. 1ltfvltiply 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 loo, Alt. 10-102-200=.S. T00+.5=10e.5 hyp,
<br />Given Hyp. roo,.Alt.?g:zsa..200=3.12$. 100-3.125=96.875=13ase.
<br />Error 1n first example, .002 ; in last, .045.
<br />To find Tons of Rail, in ono mile of track: multiply weight per yard
<br />_by 11, and divide by q.
<br />LEVELING. The correction for'curvature and refraction, in feet
<br />and decimals of feet is equal _to 0.574'd3 where d is the distance in miles.
<br />The correction for curvature alone is closely, jd The combined cor-
<br />rection is negative.
<br />PROBABLE ERROR. If d„ d,, d,, etc. are the discrepancies. of various
<br />results from the mean, and if �,dz=the sum of the squares of these differ-
<br />ences and n=the number of observations,'then the probable error of the
<br />a
<br />mesh= � O.G745�n n-1) ,
<br />.SOLAR EPIiEllt;itrs, Attention is called to the Solar Ephemeris for`
<br />the current year, published by Keuffel,& Esser Co., and furnished free of
<br />charge upon request, which is 81x58 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 andLOgaiithmic Functions;
<br />,and Logarithms of Numbers.
<br />TAi3LE IV. - Minutes in Decimals of a Degree.
<br />1'
<br />,0167
<br />11`
<br />.1833
<br />21'
<br />.3500
<br />31'
<br />:5IG7
<br />41'
<br />.6833
<br />51'
<br />.8500
<br />%
<br />.0313
<br />.0333
<br />12
<br />.2000
<br />22
<br />.3667
<br />aa'
<br />.5333
<br />49.
<br />.7000
<br />62
<br />.8667
<br />.2
<br />3
<br />11
<br />.9167
<br />23
<br />.3833
<br />33
<br />.5500
<br />43
<br />.7167
<br />53
<br />.8833
<br />4
<br />.0500
<br />-.0667'
<br />.13
<br />.2167
<br />24
<br />.4000
<br />34
<br />.5667
<br />-44
<br />,7333
<br />54
<br />.9000
<br />5
<br />.14
<br />15
<br />,2333
<br />2500
<br />25
<br />.4167
<br />33
<br />.5333
<br />45
<br />,7500
<br />55
<br />•9167
<br />6
<br />.0833
<br />.1000
<br />10
<br />,21367
<br />26
<br />.4333
<br />36
<br />:6000
<br />46
<br />.7667
<br />56
<br />57
<br />.9333
<br />7
<br />.1167
<br />17
<br />.2833
<br />27
<br />.4500
<br />37
<br />.0107
<br />47
<br />48
<br />,7833
<br />58
<br />-9500
<br />.9667
<br />B
<br />1333
<br />18
<br />.3000
<br />28
<br />.4667
<br />38
<br />.6333
<br />49
<br />,°11110
<br />69
<br />.9833
<br />9
<br />.1500
<br />19
<br />,3167
<br />.29
<br />.4833
<br />39
<br />.0500
<br />fi6fi7
<br />50
<br />.8167
<br />GO
<br />1,01100
<br />10
<br />.1667
<br />20
<br />1 .8333
<br />1 30
<br />i .50[30 11
<br />40
<br />,$333
<br />`I
<br />TABLE V. -
<br />Inches in Decimals of a Foot.
<br />1-113
<br />.0052
<br />3-32
<br />.0078
<br />Y
<br />.0104
<br />3-16
<br />.0156
<br />'4
<br />.0208
<br />0 113
<br />.02G0
<br />%
<br />.0313
<br />�s
<br />.01 .0521
<br />.Ofi25
<br />.0729
<br />r
<br />,0333
<br />2
<br />:1607
<br />3
<br />.2500
<br />4
<br />.3333
<br />5
<br />.4167
<br />0
<br />.5000
<br />7
<br />.5833
<br />8 0
<br />.6667 .7500
<br />10
<br />.5333
<br />11
<br />.9167
<br />`I
<br />
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