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TABLE IL - Radii, Ordinates.and Deflections. Chord= 100 ft.
<br />Deg'
<br />`Radius
<br />Mid,
<br />Ord.
<br />Tan.
<br />Dist.
<br />Def.
<br />Dist.
<br />Def.
<br />1f or
<br />Deg.
<br />Radius
<br />Mid.
<br />Ord.
<br />Tan
<br />Dint.
<br />Def,
<br />Dist.
<br />Det.
<br />for
<br />1 Ft.
<br />51'
<br />,
<br />t.
<br />t.
<br />t.
<br />/
<br />- 101.15
<br />ft,
<br />ft..
<br />ft.
<br />ft. '
<br />i
<br />6.10'
<br />34377.
<br />036
<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
<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
<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 />5: 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
<br />2.40
<br />1 -
<br />5729.6
<br />.218
<br />.873
<br />'1.745
<br />0,30
<br />j26
<br />688,2
<br />r:819
<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 />.2Q
<br />4297:3
<br />.291
<br />1r184'
<br />-2.327
<br />0.40
<br />40
<br />6611.7
<br />1:892
<br />7.556
<br />15.11
<br />2.60
<br />;•30
<br />3819.8
<br />.327
<br />1.309
<br />,2.618
<br />0.45;
<br />9637.3
<br />17.
<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
<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 />8.426
<br />16.85
<br />2.90
<br />10
<br />,2644:6,_.473
<br />70
<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 />2148.8,
<br />'.'582
<br />2:327
<br />4,654
<br />0.80
<br />30
<br />499.1
<br />2.511
<br />10.02
<br />20.04
<br />3.45
<br />50••2022.4
<br />".618
<br />2,472
<br />4.945
<br />0.85
<br />12 .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 />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
<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 />3.277.13.05
<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 />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 />3.718
<br />7.561
<br />1,30
<br />30
<br />348.5
<br />3.606
<br />14.35
<br />28.70
<br />4.95
<br />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 />29.56
<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 />'191
<br />302.9
<br />4':155
<br />16.51'
<br />33.01
<br />5.70
<br />6
<br />1146.3
<br />1.091
<br />4.362
<br />8.724
<br />1.50
<br />W
<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 />1:6523,
<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 />1.273
<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
<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 />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 />1881.9
<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 />'1'ne miQ(ue orulilate in inches Ior any cora oI length ((i) is equal to .U012 (1'
<br />multiplied by the middle .*ordinate! taken from the above table. Thus, if it
<br />desired to bend it 30 ft. rail to fit a 10 degree curve, its middle ordinate, should
<br />be .0012X900X2.183 or 2.36 inches. k
<br />TABLE IIL ` Deflections for Sub Chords for Short Radius Curves.
<br />Degree
<br />of
<br />Curve
<br />Radius
<br />j5 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. '
<br />25 Ft.
<br />30
<br />193.18
<br />1°
<br />51'
<br />2°°17=
<br />- 2°
<br />58'
<br />- -3°
<br />43' -
<br />- 101.15
<br />320
<br />181.39
<br />1°
<br />59'
<br />2°
<br />25'
<br />3°
<br />10'
<br />30
<br />58'
<br />101.33
<br />340
<br />171.01
<br />2°
<br />o6'
<br />2'
<br />33'
<br />3°
<br />21'
<br />4°
<br />12'
<br />101.48
<br />36°
<br />'161.8o
<br />-20
<br />13'
<br />20
<br />41''3°
<br />44
<br />33
<br />40
<br />26'
<br />ioI.66
<br />380"-
<br />40°
<br />153.58.
<br />146.19
<br />.2°_20'-.
<br />. -2°
<br />27'.
<br />-2°
<br />20-57'
<br />49'
<br />3°
<br />30
<br />44'
<br />55''
<br />4'
<br />4`
<br />40'
<br />54'
<br />101-85
<br />102.o6 .
<br />42'
<br />139.52.
<br />z'
<br />34='
<br />-3°
<br />05'
<br />4°
<br />07'
<br />- 5°
<br />08'
<br />IO2.29 .
<br />44°
<br />133•47
<br />2°
<br />41'
<br />30-13'
<br />-27
<br />4°
<br />18'
<br />50
<br />22'
<br />102.53
<br />46°
<br />127.97
<br />20
<br />48'
<br />30
<br />21'
<br />4°
<br />39'-5'
<br />38
<br />36:
<br />102:76
<br />48°
<br />122.92
<br />2'
<br />55'
<br />30
<br />29'
<br />4°
<br />40'
<br />50
<br />50'
<br />103.00
<br />50°
<br />118, 31
<br />3°
<br />02'
<br />3°
<br />38`'
<br />4°
<br />51'
<br />6°
<br />04'
<br />103.24
<br />52°
<br />114. o6_
<br />30.09'
<br />80
<br />3°46'
<br />5°02'
<br />6'
<br />17.
<br />103.54
<br />54°
<br />110. 11
<br />30
<br />16' '
<br />3°
<br />54'
<br />5°
<br />13'
<br />6°
<br />31'
<br />103,84.
<br />'56°
<br />1o6.50
<br />3°
<br />2z'
<br />4°
<br />oz'
<br />5°
<br />23'
<br />6°
<br />44'
<br />104.14
<br />58°
<br />103.14
<br />3°
<br />�9'
<br />4'
<br />10' '
<br />50
<br />34'
<br />6°'57'•
<br />104.43
<br />600
<br />100.00
<br />30
<br />35'
<br />40
<br />18'
<br />S°
<br />44'
<br />70
<br />I1'
<br />104.72
<br />ZK
<br />CURVE FORMULAS u
<br />T 5o tan I R = T cot. ; I . _ . Chord def. _ c10�2
<br />T
<br />_ b0 R
<br />- Sin. D R =
<br />D = 50 ;Sin. D No. chords :
<br />R E = R ez. sec ; I" c
<br />Sin, }. ,D 50 1.T I. E =T tan I I Tan. def. _ >t, 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 1. - Multiply the given distance by -01745 (def, for 1 ° for I ft:
<br />see Table II.): and divide given deflection by the product.
<br />Rule12. Multiply given deflection by 57.,3, and divide the pxoduct by
<br />the given distance.
<br />, TO.find deflection for a given angle and distance. Multiply the angle
<br />by :o1745, and the.. -product by the distance.
<br />GENERAL DATA o
<br />RIGHT ANGLE TRIANGLES. Square the altitude, divide by twice the
<br />base. Add.quotient to base'for hypotenuse. '
<br />Given" Base loo, Alt. Io.1o$=200=.5..100-}--5=100.5 hype.
<br />Given Hyp. ioo, Alt. 25.252 '200=3-I25- 100-3.125=96�.&75=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 Ii; and divide'by 7-
<br />LEvELiNG. The', correction for curvature and refraction, in feet
<br />and decimals of feet is equal to 0.674 ds, where d.is the distance in miles.
<br />The correction for curvature alone is closely, •ifde. The combined cor-
<br />rection is negative.
<br />:-,PROBABLE ERROR. If d;, da, da, etc. are the discrepancies ,of various
<br />results from the mean, and if 7-da=the sum of the squares of these differ-
<br />ences and n=the number of observations, then the probable error 0f the,
<br />mean= 0.6746
<br />.SOLAR EPHEMERIS. Attention is called to the Solar Ephemeiisfor'
<br />the current year, published,by. Keuffel.&-Esser Co., and furnished free of
<br />charge upon request, -whic_is 3'Jx5 f in., with about 90 pages cf 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 f ormulas; Natural andLogarithmic Functions;
<br />and Loearithms of Numbers.'
<br />TABLE IV. - Minutes
<br />.TABLE V. - Indies in Vecnnals 01 a 1''00t: -
<br />in Decimals of a Degree -
<br />e ee.1'
<br />1'
<br />.0167
<br />11'
<br />.1833
<br />21'
<br />3500
<br />31'
<br />.5167
<br />41'
<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 />8
<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 />.!667
<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 />,7867
<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 />.818'7
<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 />80
<br />1,0000
<br />- " '.
<br />.TABLE V. - Indies in Vecnnals 01 a 1''00t: -
<br />-
<br />1-16 3-32
<br />j¢
<br />3-16
<br />5-16
<br />v
<br />52 0078
<br />:0104
<br />.0156
<br />.0208
<br />1-0260L.0313
<br />L.0417_1'.021
<br />..0825 O7
<br />1'- 2
<br />3
<br />4
<br />5
<br />6
<br />7
<br />8 9
<br />10 11
<br />:0833 .1667
<br />.2500
<br />..333$
<br />..4187
<br />.5000•
<br />.5833
<br />.6667 .7500
<br />.10 .9167
<br />
|