|
VIII
<br />TABLE II. - Radii, Ordinates- and'Deflections. Chord 100 ft,
<br />Deg:
<br />- _
<br />Radius
<br />50
<br />Mid.
<br />Ord"
<br />_
<br />Tan.
<br />Dist.
<br />- _
<br />`lAef.
<br />Dist.
<br />- _ _
<br />Def
<br />for
<br />1 Ft._
<br />Dcg.
<br />- - -
<br />Radius
<br />{ Mid.
<br />.Ord.
<br />Tan
<br />uu -
<br />- Dist..
<br />Dcf.
<br />_Dist.
<br />-
<br />Def.
<br />Cor
<br />1 Ff.
<br />-193.18
<br />ft.
<br />it.
<br />ft.
<br />ft. .r
<br />2°-58'
<br />.2000
<br />ft.
<br />' , ft.
<br />ft,
<br />ft.
<br />181.39
<br />G', 10'
<br />34377.
<br />.036
<br />..1'45
<br />1x.,291
<br />0.05;
<br />7°
<br />819.0
<br />1.523
<br />6.105
<br />12.21
<br />2.10
<br />c20,
<br />17189..
<br />.073,
<br />.291
<br />.5S2
<br />0.16
<br />20'
<br />781.8
<br />1.600
<br />6.39512.79
<br />2°
<br />2.20
<br />-30
<br />11459.
<br />.109
<br />.430
<br />.873
<br />0.15•
<br />30
<br />764.5
<br />1.637
<br />6.540
<br />13.03
<br />2.25
<br />40
<br />5594.4
<br />.145.582
<br />4°
<br />",1:164
<br />0.20
<br />40
<br />'747.9
<br />1.673
<br />6.G35
<br />13.37
<br />2.30
<br />,50
<br />G875.6
<br />=,182
<br />,727
<br />1.4540.25
<br />42'
<br />$
<br />716.
<br />1:746
<br />,6.976
<br />13.95
<br />2.40
<br />1
<br />5729.6
<br />.218
<br />.873
<br />il.745
<br />0.30 '
<br />20
<br />638,2
<br />1,8 810
<br />7.266
<br />14.53
<br />2,50
<br />10
<br />4911.2
<br />.255
<br />1.018
<br />12.036
<br />0.35
<br />30
<br />674.7.
<br />1.855
<br />7.411
<br />14:82
<br />2,55
<br />120
<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 />130:
<br />3819,8
<br />.327
<br />1.309
<br />.2.618
<br />0.45
<br />9
<br />637.3
<br />1.965
<br />7,816
<br />15.69
<br />2,70
<br />'40 ;
<br />3437.9
<br />.361
<br />1.454
<br />2.909
<br />0.-
<br />20
<br />614.0
<br />2.037
<br />18,136
<br />16.27
<br />2.80
<br />`50-'3125.4
<br />3°
<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 41.1
<br />-,2864.9
<br />".436
<br />1.745`.3.490
<br />5°,z3'
<br />0.60:
<br />40
<br />593.4
<br />2'110
<br />8,426.
<br />16.85
<br />2.90
<br />40
<br />2544.6
<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 />2455.7
<br />.509
<br />2.036
<br />4.072
<br />0.70
<br />30
<br />'546.4
<br />3.292
<br />9.150
<br />13.30
<br />3.15
<br />,30
<br />2292.0
<br />.545
<br />2.151
<br />`4.363
<br />0.75
<br />11
<br />521.7
<br />2.402
<br />9.585,19.1G
<br />.3.30
<br />40
<br />214.8,8
<br />;532
<br />2.327
<br />4:654
<br />(Y.So
<br />30
<br />X99:1
<br />2:511
<br />10,02„
<br />20.04
<br />3.45
<br />50
<br />2022,4
<br />' .CAS
<br />2.472
<br />-4.945
<br />0.85
<br />El
<br />478.3
<br />2:620
<br />10.45
<br />20.91
<br />3.60
<br />8 :
<br />1910.1
<br />.655
<br />2:613
<br />5:235
<br />0.90
<br />- 30
<br />459.3
<br />2`730
<br />10.89
<br />21.77
<br />3.75
<br />1.0:.
<br />1809'.G
<br />.601
<br />2.762
<br />,5:526'0.95
<br />13 '.
<br />441.7'2:830
<br />11.32 "
<br />22.01
<br />3.90
<br />'20'
<br />-1719'.1
<br />.727
<br />2.903
<br />.5:817
<br />7.00
<br />:30
<br />425.4
<br />2'049
<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 />1`2.18'
<br />24.37
<br />4.20
<br />40
<br />1562.9
<br />.800
<br />3.199
<br />6.393
<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 r,,
<br />- 1432.7
<br />,.873
<br />3;490
<br />..61.980
<br />1.20
<br />30
<br />370.8
<br />3.387
<br />13.49
<br />26.97
<br />4.65
<br />,10
<br />1375.4909
<br />3.635
<br />'7,271
<br />1.25,
<br />16
<br />359.3
<br />3.49 0
<br />13.92
<br />27.84
<br />4.80
<br />20
<br />1322.5
<br />:945
<br />3.713
<br />7.5fil
<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 />,082
<br />3.92G
<br />7.852
<br />1,35
<br />17
<br />338.3
<br />3.710
<br />14.78
<br />29.56
<br />5.10
<br />40
<br />,1228.1:1.018
<br />4.071'
<br />8.143
<br />1.40
<br />-18
<br />319.6
<br />3.935'15.64
<br />31.29
<br />5.40
<br />50,
<br />1185.8
<br />1.055
<br />4.217
<br />8.433
<br />1.45
<br />0
<br />302.9
<br />4.155
<br />16.51
<br />33.01
<br />5.70
<br />•4 1t
<br />1146.3
<br />1.091
<br />4.862
<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 />!9.074.1.55
<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 />I:60;
<br />-,22
<br />262.0
<br />4.814
<br />19.08
<br />38,15
<br />6.60
<br />30>•'-1042.1
<br />1.200
<br />4.798
<br />'9.506
<br />1.65,
<br />23'
<br />250.8
<br />5;035
<br />19.94
<br />.39.87
<br />6.00
<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 />41.53
<br />7.20
<br />50
<br />982,6
<br />1.273
<br />5.08$
<br />10.18
<br />"1.75
<br />25
<br />231.0
<br />5.476
<br />21:64
<br />43.28
<br />7.50
<br />Bim•
<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.S0
<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 />24.10
<br />4S.38
<br />3-40
<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 (0) is eryrynaIto 0013 C2
<br />multiplied by the middle o-rdinato taken from the above tahle, 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 />T"LE'III. Deflections for Sub Chords for Short Radius Curves.
<br />Decree
<br />of
<br />Curve lain.
<br />Radius
<br />50
<br />in Decimals of a Degree.
<br />A sub chord
<br />R chord.,
<br />, ang
<br />of , def. le
<br />Length
<br />of arc
<br />for 100 ft.
<br />Y def. ang.
<br />12.5 Ft.
<br />35 Ft.
<br />20 Ft,
<br />25 Ft.
<br />30°
<br />-193.18
<br />1°
<br />51'
<br />2°
<br />17'
<br />2°-58'
<br />.2000
<br />3°
<br />43' -
<br />101.15-
<br />32°
<br />181.39
<br />1°
<br />59'
<br />:
<br />25'
<br />3°
<br />lo'
<br />3°
<br />58'
<br />101.33
<br />34°
<br />171-01
<br />2°
<br />o6'
<br />2°.33'
<br />.8833
<br />30
<br />21'
<br />4°
<br />12'
<br />101-48
<br />-36°
<br />16i.8o
<br />2°
<br />13'"
<br />,°
<br />41'
<br />3°
<br />3,3'
<br />4°
<br />26'
<br />Io1.66
<br />38°
<br />X.53.58
<br />- 2°
<br />20'
<br />2°
<br />49'
<br />3°
<br />44'
<br />4°
<br />40'
<br />rot -85
<br />40°
<br />146. 19 .
<br />2°
<br />27'
<br />2°
<br />57':
<br />7 30
<br />55'
<br />4°
<br />54'
<br />102.06
<br />42'
<br />139.52.
<br />2°
<br />34'
<br />3°
<br />05'
<br />4'
<br />o7'
<br />S°
<br />08
<br />102.29
<br />44°
<br />133.47
<br />2°
<br />41
<br />3°
<br />131
<br />4°:IS'
<br />48
<br />S°
<br />22'
<br />102.53
<br />46°
<br />127.97
<br />2°48'
<br />.3167
<br />3°
<br />21.'.
<br />4°
<br />29' ..
<br />5°
<br />36''
<br />102.76
<br />48°
<br />122.92
<br />2°
<br />55'
<br />3°
<br />29'
<br />4°
<br />40'
<br />5°
<br />50'
<br />103.00
<br />500
<br />118,31
<br />30021
<br />3°
<br />38,
<br />4°
<br />51r
<br />60
<br />04'
<br />103.24
<br />10.3-24
<br />52°
<br />114,06
<br />3°
<br />09'
<br />3°
<br />46'
<br />50
<br />O2'
<br />6°
<br />11
<br />103-5.4
<br />54°
<br />110.11
<br />3°
<br />16'
<br />3°
<br />54'
<br />5°
<br />13'
<br />6°
<br />31'
<br />103-84
<br />56°
<br />Io6.5o
<br />3°
<br />22'
<br />4°
<br />02'
<br />5°,z3'
<br />6°
<br />44'
<br />304.14
<br />58°
<br />103,14
<br />3°
<br />29'
<br />4°
<br />10'
<br />50
<br />34'
<br />6057'
<br />104,43
<br />60°
<br />100.00
<br />3° 35'
<br />4°
<br />18'
<br />5°
<br />44'1
<br />7°
<br />i 1'
<br />104.72
<br />Ix
<br />CURVE rbi IAit''LA5 -
<br />T= R'tan I R= T cot. z I. chord2
<br />T _ 56 tan r L ' --. - Chord def.
<br />Sin 8 D R__ . 50
<br />1 D
<br />Sin. I D-= R .. Sin' 2
<br />. No. chords = I
<br />E = R es. see , I. D.
<br />50 tan�, I
<br />Sin. I D;= T 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. h1ultiply the.given distance by .01745 (def. for I° for I It.
<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 />Tofind deflection for a given ankle and distance.' Multiply the angle
<br />liy .017.45, and -the product by the distance. .
<br />~GENERAL DATA
<br />t r RIGHT ANGLE'TRIANGLES. Square the altitude,; divide, by twice the
<br />base.- Add quotient to base,for hypotenuse:
<br />Given Base 1o0; Alt:_16.iC)2 : 200-.5, 100+.5-100.8 hyp.
<br />Given Hyp. Ioo, Alt; -g5.252.=200=3.125. TOO -3"125=96.875=Base.
<br />Error in first example, .00.in last, .045.
<br />To find Tons of Rail in one mile of track: multiply .vyeight per pard
<br />by i r, and divide, by 7.
<br />Lr;vrLING. The correction for curvature and refraction,. in feet
<br />and decimals of feet is equal to 0.574 da, where d is the distance in miles.
<br />The correction for curvature alone is closely, jd2. The combined. cor-
<br />rection is negative.
<br />• PROBABLE ERROR. If dk, d3, da, etc. are the discrepancies of various
<br />results from the mean, and if Yd2--.the sum of the squares of these differ-
<br />ences and n=the number of observations, then the probable error of the
<br />me- n= + O.G745 �d
<br />a
<br />_. n (n-lj
<br />SOLAR F,PHEA1ERIs. Attention is'called.;to the Solar Ephemeris for
<br />the current y=ear, published by Keuffel & Esser Co., and furnished free of
<br />charge upon request, which is 3;x58 Jul, with -about 90 pages of data very
<br />useful to the Surveyor; such as the adju-stments of transits, levels and
<br />solar attachments; directions and tables for determining-. the meridian .
<br />and the latitude from observations on the sun and Polnris; -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. - 1'linutes
<br />in Decimals of a Degree.
<br />1'
<br />.0167
<br />11'
<br />.1833
<br />2Y,
<br />.3500
<br />31' 1
<br />.5167
<br />41'
<br />.G813
<br />51'
<br />.8500
<br />2'
<br />..0333
<br />12
<br />.2000
<br />22
<br />.3607.
<br />32
<br />.5333
<br />42
<br />.7000
<br />52
<br />.8607
<br />3
<br />.0500
<br />13
<br />.2167
<br />23
<br />,3833
<br />33
<br />.5500
<br />43
<br />.7107
<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 />1G
<br />.2667
<br />26
<br />.4333
<br />36
<br />.6000
<br />46
<br />.7067
<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 />I8
<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 />.4333
<br />39
<br />.G500
<br />49
<br />.8167
<br />59
<br />.9833
<br />10
<br />1 .1G67
<br />20
<br />1 "3333 1130
<br />1 .5000
<br />11 40
<br />1 .6667
<br />1 50
<br />1 8333 1,
<br />69
<br />1.0000
<br />` TAimE V. - Inches in Decimals of a Foot.
<br />1 -IG 3-32. A 3-16 � 5-1G Y �
<br />.0052 ,0078 •.010.1 .0156 .0208. .0260 .0313 -0417 .0521 .0625.0+"29
<br />1- 2- 3 4 5 G 7 8 9 10 11
<br />0833 .1667 ;2500 ,3333 .4167 .5000 .5833 1 .6667 1 .7500 .8333 .9167
<br />
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