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I� ' ' .. -
<br />TABLE IL itadii, Ordinates and Deflections. Chord=100 ft. -: CURVE FORMULAS
<br />"=D�'�
<br />Radius
<br />Mid.
<br />Ord>
<br />Tan.
<br />Dist,
<br />Def.
<br />Dist.
<br />Def.
<br />IfFt.Deg.
<br />15 Ft.
<br />adius
<br />Mid.
<br />Ord:
<br />Tan
<br />Dist.
<br />Dei.
<br />Dist.
<br />Def.
<br />for
<br />1 Ft.
<br />51'
<br />2°
<br />-ft.
<br />t.
<br />ft.
<br />3°
<br />43'
<br />ft:,
<br />ft.
<br />it. •
<br />ft.'
<br />i
<br />0"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 />f:.30
<br />11459.
<br />.109.
<br />.436
<br />,873.0.15
<br />38°
<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 />13.372.30
<br />55'
<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 />II
<br />5729.6
<br />.218.873
<br />133.47.
<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.b5
<br />20.
<br />4297.8
<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 />.327.1:309
<br />3°38'
<br />2:613
<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 />0.60
<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 />3.200'0.55
<br />6°31'
<br />; 30
<br />603.8
<br />2.074
<br />8.281
<br />16.56
<br />2.85
<br />9:` ,
<br />2864.9
<br />.436
<br />1,745
<br />3."490"0.60,
<br />44'
<br />;40"593.4
<br />58°
<br />2.110
<br />8.426
<br />16.85
<br />2.90
<br />-10:.2644.6
<br />50
<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 />2148.8
<br />.582
<br />2,327
<br />4.654
<br />0.80
<br />80
<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 />2.620.10.45
<br />20.91
<br />3.60
<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 />'20
<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 />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 />13.05
<br />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
<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"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 />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 />a
<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
<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"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 />59
<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.'to
<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 1
<br />30
<br />193.2
<br />6.583
<br />25.88 151;7619.00
<br />The middle ordinate in inches for any cord of length (C) is equal to .0012 0'
<br />multiplied by the middle ordinate taken from the above table. Thus, if it
<br />desired to bend a 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 />M sub chord _0 R sin of }def. angle
<br />��
<br />for 100 ft.
<br />sin. J def. ang,
<br />12.5 Ft. -
<br />15 Ft.
<br />20 Ft.
<br />25 Ft.
<br />30°193.18
<br />.5167
<br />1°
<br />51'
<br />2°
<br />17'
<br />2°
<br />58'
<br />3°
<br />43'
<br />IOI.15
<br />3i°_.
<br />181.39
<br />1°
<br />59'
<br />2°
<br />25'
<br />3°
<br />I0'
<br />3°
<br />58'
<br />101.33
<br />34°
<br />171.01
<br />2°
<br />o6'
<br />2°33'
<br />.7167
<br />3°
<br />21'
<br />4°
<br />12'•
<br />I01.48
<br />360
<br />16i.8o
<br />2°
<br />13'
<br />'2°41'
<br />44
<br />3°33'
<br />54
<br />4°26'
<br />50833
<br />1oI.66
<br />38°
<br />153.58
<br />2°20'
<br />.4167
<br />2°
<br />49'
<br />3°
<br />44'
<br />4°40'
<br />.9167
<br />101.85
<br />40°
<br />146.19
<br />i°
<br />27'
<br />2°
<br />57'
<br />30
<br />55'
<br />4°
<br />54'
<br />102. o6
<br />42'
<br />139.52
<br />?°
<br />34'
<br />30
<br />05'
<br />40
<br />07'
<br />5°
<br />o8'.
<br />102.29
<br />44°
<br />133.47.
<br />2°
<br />41'
<br />30
<br />13' •
<br />.4667
<br />18'
<br />50
<br />22
<br />102.53
<br />W.
<br />127.97
<br />2048'
<br />'.1500
<br />3°21'
<br />.3167
<br />.4°
<br />4°29'5°36
<br />.4833
<br />39
<br />.6500
<br />102.76
<br />48°
<br />122.92
<br />2055
<br />,
<br />3°29'
<br />'20"•
<br />4°
<br />40'
<br />5°50'
<br />40
<br />103.00
<br />50°
<br />118.31
<br />3°02'
<br />1.0000
<br />3°38'
<br />4°
<br />61'
<br />6°04'
<br />103.24
<br />52°
<br />114.06..
<br />30
<br />09'
<br />30
<br />46'
<br />50
<br />02' "
<br />6°
<br />17'
<br />.103: 54
<br />540
<br />II0.II
<br />3°16'
<br />3°54'
<br />S°13'
<br />6°31'
<br />103.84
<br />56°
<br />io6.5o
<br />30
<br />22'
<br />4°
<br />02'
<br />50
<br />23'
<br />60
<br />44'
<br />104.14
<br />58°
<br />103.14
<br />3°
<br />29'
<br />40
<br />10'
<br />50
<br />34'
<br />6°
<br />57'
<br />104.43
<br />600
<br />100.00
<br />3°35'.
<br />4°18'
<br />5°
<br />44'
<br />7°.11'
<br />10442
<br />T= R tan A I R= T cot. z
<br />5o tan -I Chord def. R
<br />T Sin. JD - R = 60
<br />Sin. J D =LO Sin' D No. chords = I
<br />RE R ex. sec L I D
<br />5o tan I ` -
<br />D = r E T tan I I Tan. de,. - �, 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 IIi)', 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 loo, Alt. 10.102_200=.5. 100+.5=100.5 hyp•
<br />Given Hyp..Ioo, Alt. 15:252-200=3.125. I00-3.225=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'I1, and divide by 7.
<br />LEVELING. The correction for, curvature and refraction, in' feet
<br />and decimals of feetis equal to 0.574d2,where d is the distance in miles.
<br />The correction for curvature alone is closely, Jda. The combined cor-
<br />rection is negative.
<br />PROBABLE ERROR. If dl, d„ d„ etc. are the discrepancies of various
<br />results from'the mean, and 1f i da=the sum of the squares of these dif or-
<br />ences and n=the number of observations; then.the probable error of the.
<br />mean= ds
<br />4- 0.6746 n n-1
<br />SOLAR EPHEMERIS. Attention is called to the Solar Ephemefis f6i'
<br />the current year, published by Keuffel & Esser Co., and furnished free of
<br />charge upon request; which is 31x58 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 andLogarithmic Functions;
<br />and Logarithms of Numbers.
<br />TABLE IV. - Minutes
<br />in
<br />Decimals of a Degree.
<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 />a
<br />.0333
<br />12
<br />.2000
<br />22'
<br />.3667
<br />32
<br />.5333
<br />42
<br />.7000
<br />52
<br />.8667
<br />g
<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 />50833
<br />15
<br />.2500
<br />25
<br />.4167
<br />-35
<br />.5833
<br />45
<br />' .7500
<br />55
<br />.9167
<br />8 -
<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 />49.8167
<br />59
<br />.9833,
<br />10 :
<br />.1867
<br />'20"•
<br />.3333
<br />30
<br />.5000
<br />40
<br />.6667
<br />60
<br />.8333
<br />60
<br />1.0000
<br />TABLE V. - Inches in Decimals of a Foot.
<br />1-16 382
<br />N
<br />3-16
<br />5-16
<br />&
<br />'rfa
<br />,0052 .0078
<br />.0104
<br />.0156
<br />.0208
<br />.0260
<br />.0313
<br />.0417 X521
<br />.0625 .0719
<br />1 2
<br />3
<br />4
<br />5
<br />6
<br />7
<br />8 9
<br />10 11
<br />.0883 .1667
<br />.2500
<br />.3333"
<br />.4167
<br />.b000
<br />.5833
<br />.6667 .7500
<br />.8333 .9167
<br />
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