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VIII
<br />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 />De .
<br />if or
<br />Deg,.
<br />Radius
<br />Mid.
<br />_ Ord.
<br />Tan.
<br />Dist,
<br />Def.
<br />Dist.
<br />Def.
<br />1f Ft.
<br />2° 58' '
<br />3° 43'
<br />It.
<br />ft.
<br />ft.
<br />I
<br />2° 25'
<br />ft.
<br />t.t.
<br />I01.33
<br />t.
<br />171.01
<br />0"10'
<br />34377.
<br />.036
<br />.145
<br />,291
<br />0.05
<br />7.
<br />819.0
<br />1.528
<br />6:10512.21
<br />40 z6' ,
<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 />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 />20
<br />688.2
<br />1.819
<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 />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 />30
<br />3819.8
<br />.327
<br />1.309
<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
<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
<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 />2155.7
<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
<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
<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 />1195.0
<br />.836
<br />3.345
<br />6.G89
<br />1.15
<br />15
<br />383.1
<br />3.277
<br />13.05
<br />26.11
<br />4.50
<br />4
<br />1132.7
<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 />1322.5.945
<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 />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 />29.56
<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 />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 />4.814.19.08
<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 />1.273
<br />5.088
<br />10.18
<br />1.75
<br />25
<br />231.0
<br />5.476.21.64
<br />43.28
<br />7.50
<br />6..
<br />955.4
<br />1.309
<br />5.234
<br />10.47
<br />1.50
<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 />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 middle ordinate in inches for any Cord of length (C) is equal to .0012 C'
<br />multiplied by the middle ordinate taken from the above table. Thus, if it
<br />desired to bend tt 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 />50
<br />sin.'z def, ang•
<br />/a sub chord _sin of z def. angle
<br />R
<br />Length
<br />of arc
<br />for 100 ft.
<br />12.5 Ft.
<br />15 Ft.
<br />20 Ft.
<br />25 Ft.
<br />30°
<br />193.18
<br />1° 51'
<br />2° 171
<br />2° 58' '
<br />3° 43'
<br />101.15
<br />32°
<br />181.39.
<br />1° 59'
<br />2° 25'
<br />3° 10
<br />3° 58'
<br />I01.33
<br />34°
<br />171.01
<br />2° 06'
<br />20 33
<br />3°-21'
<br />4° 12'
<br />101.48
<br />36°
<br />161.8o
<br />2° �3
<br />2° 41,
<br />3° 33
<br />40 z6' ,
<br />IOI.66
<br />38°
<br />153.58
<br />2° 20'
<br />2° 49'
<br />30 44'
<br />4° 40'
<br />101.85
<br />40° -
<br />146. i9
<br />20 27'
<br />20 5730
<br />55'
<br />4° 54'
<br />IO2. o6
<br />15
<br />139.52
<br />2°34'
<br />3°05
<br />4°07,
<br />5°08
<br />102.29
<br />_42°
<br />: 44°,
<br />133.47
<br />20,41
<br />3° 13'-
<br />4° 18'
<br />5° 22'_'
<br />102.53
<br />460
<br />127.97
<br />2° 48'
<br />3°21'
<br />4°29'
<br />5° 36'
<br />102.76.
<br />480
<br />122.92
<br />2° 55'•
<br />30 29'
<br />4° 40'
<br />5° 5f
<br />103.00
<br />_
<br />50°.
<br />11&31
<br />3° 02'
<br />3° 38'
<br />4° 51'
<br />6° 04:
<br />103.24
<br />520
<br />114. o6
<br />3° 09
<br />3° 46'
<br />5° 02'
<br />60 17'
<br />103.54
<br />54°
<br />110 it
<br />3° 16
<br />3° 541
<br />5° 131
<br />6°31'
<br />103.84
<br />56°
<br />106.50
<br />3° 22
<br />4° 02'
<br />5° 23'
<br />6044/. _
<br />104.14
<br />58?,
<br />.. 103: 14
<br />30 29
<br />40 10,
<br />50 34
<br />60 57
<br />104:43
<br />60
<br />100.00
<br />3 35
<br />4 18
<br />.5 .44
<br />17 11
<br />I04.72
<br />IX
<br />CURVE FORMULAS
<br />T= R tan 1. I R= T cot. z I chord'
<br />_ 5o tan z I Chord def. _
<br />T Sin. 2 D R 50 R
<br />Sin. a D = 50 Sin. I D No. chords = I
<br />R E= R ex. sec ; I D
<br />Sin. z .D = 50 tan
<br />I E = T tan } I Tan. def. = z 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 ioo, Alt. 10.102=200=.5. 100-.5=100.5 hyp.
<br />Given Hyp. ioo,-Alt. 25.252=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 0.574d2, where d.is the distance in miles.
<br />The correction for curvature alone.is closely, W. The.combined cor-
<br />rection is negative.
<br />PROBABLE ERROR. If dl, d2, d3, etc. are the discrepancies of various
<br />results from the mean, and if Ede=the sum of the squares -of these differ-
<br />ences and n=the number of observations, then the probable--eiror of the
<br />mean= 2;d2
<br />-0.6745 n(n-1)
<br />SOLAR EPHEMERIS. Attention is called to the Solar Ephemeris for
<br />the currentyear, 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 />11
<br />.0167
<br />11/
<br />.1833
<br />21t
<br />.3500
<br />W
<br />.5167
<br />41f
<br />.6833
<br />511
<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 />.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
<br />20
<br />1 .3333 11
<br />30
<br />1 .5000 11
<br />40
<br />1 .6667 11
<br />50 1
<br />.8333 If
<br />60.
<br />11.0000
<br />TABLE V. -Inches in Decimals of a Foot.
<br />1-16 3-32 % 3-16 X 5-16 Y
<br />.0052 .0075 .0104 .0156 .0208 .0260 .0313 .0417 0521 0625 0729
<br />.0833 .1667 .2500 .3333 .4167 .5000 .5833 .6667 I .7900 I .8333 I .9167
<br />
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