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TABLE II. •- Radii, Ordinates and Deflections. Chord =100 ft.
<br />Deg.
<br />Radius
<br />Hid.
<br />Ord.
<br />Tan.
<br />Die:.
<br />Def.
<br />,Dist.
<br />Def'
<br />for
<br />1 F6
<br />Deg.
<br />Radius
<br />bl d.
<br />Ord.
<br />Ten
<br />Dist,
<br />Def.
<br />Dist.
<br />Def.
<br />fcr
<br />1 I't.
<br />2° 171
<br />t,
<br />ft.
<br />ft.
<br />ft.
<br />181.39
<br />1° 59"
<br />tt,
<br />it.
<br />- 1t.
<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 />6.10512.21
<br />3°'33'
<br />2.10
<br />20
<br />17189.
<br />.073
<br />.291
<br />,582
<br />0,10
<br />2D''
<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 />0.540
<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 />0.685
<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 />6729.6
<br />.218
<br />.873
<br />1.745
<br />0.30
<br />`20
<br />(388.2
<br />1.819
<br />7.266
<br />14.53
<br />2.50
<br />10
<br />4911.2
<br />.255'1.018
<br />103.84
<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 />15.11'2.60
<br />7° 1 V
<br />"30
<br />3819.8
<br />.327
<br />1.309
<br />2.618
<br />0.45
<br />9
<br />G37.3
<br />1.965
<br />7.846
<br />15.69
<br />2.70
<br />.40'•.'3437.9
<br />.364
<br />1.454
<br />2.909
<br />0.50
<br />20
<br />G14.6
<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 />3
<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 />3.791
<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 />19.10
<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 />.619
<br />2.472'.4.945
<br />0.85
<br />12
<br />478.3
<br />2.620
<br />10.45
<br />20.91
<br />3.60
<br />1910.1
<br />.G55
<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 />22.04
<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 />6.103
<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 />:830
<br />3.34.5
<br />6.689
<br />1.15
<br />383.1
<br />3,277
<br />13.055
<br />20.11
<br />4.50
<br />?-
<br />1432.7
<br />.873
<br />3.490.
<br />6,980
<br />1.20
<br />,15
<br />30
<br />370.8
<br />3.387
<br />13.49
<br />26:97
<br />4.G5
<br />10.'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 />30
<br />1273.6
<br />.982
<br />3.925
<br />7.852'1.35
<br />17
<br />338.3
<br />3.716
<br />14.78
<br />29,56
<br />5.10
<br />40
<br />1228.1
<br />1.0184.071
<br />S. 143
<br />1.40
<br />18
<br />319.6
<br />3.935
<br />15.64
<br />31.29
<br />5.40
<br />50
<br />1185.81.055
<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 />8 `
<br />1146.3
<br />1.091
<br />4.362
<br />8.724
<br />.1.50
<br />20
<br />237.9
<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 />4.594'18.22
<br />36.44
<br />GM
<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 />38.1G
<br />6.60
<br />30
<br />1042.1
<br />'1.011.5
<br />1.200
<br />4.793
<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 />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 />231.6
<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 />5.097
<br />22.50
<br />44.9'3
<br />7.S0
<br />10
<br />929.6
<br />1:846
<br />5.379
<br />10:76
<br />1.85
<br />27
<br />214.2
<br />5.918:23.8.5
<br />46.69
<br />S.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 />5.514
<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'he middle ordinate in inches for any cord of length (C) is equal to .0012 C=
<br />mnitinlito by the middle ordinate from the above table. Thue,if it
<br />deeired to bend a 30 ft, rail to fit a 10 degree curve, ite middlo 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 />�J sub chard.
<br />R' = sin of , def. angle
<br />of arc
<br />for 100 ft.
<br />sins def. ang.
<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 />IoI. 15
<br />32°
<br />181.39
<br />1° 59"
<br />2°25'
<br />3° 10'
<br />3°58'
<br />lot -33
<br />340
<br />171.01
<br />2°06'
<br />2° 33'
<br />3°21'
<br />4° 12'
<br />101.48
<br />36°
<br />161.80.
<br />2° 13'
<br />2° 41'
<br />3°'33'
<br />4° 26'
<br />Io1.66
<br />3$°
<br />r53 .58
<br />2° :iY
<br />2°-49'.3-,44,
<br />.4000
<br />4° 40'
<br />i,oI.85
<br />40_
<br />146:19
<br />2° 27'
<br />2° 57`.
<br />-3"551
<br />4° 54'.
<br />Io2:o6
<br />4?
<br />139 52
<br />?° 34'"
<br />3° 05'
<br />4° 07`
<br />5° 08'
<br />102.29
<br />44
<br />133:47.'
<br />2° 41'
<br />3° 13'
<br />4° i8'
<br />5° 22'
<br />102.53
<br />46°
<br />127.97
<br />2° 481
<br />30 210
<br />4° �9'
<br />50.36'
<br />io2.._76
<br />48°
<br />:122:922'
<br />55'
<br />3' 29'.-
<br />4° 40.
<br />5° 5O'
<br />103.00
<br />50°
<br />•-118.31-
<br />3° 02'
<br />3° 38'
<br />4° 51'
<br />6° 04'
<br />103._24
<br />520.
<br />114.'06
<br />30 09"
<br />3° 46'
<br />5° oz'
<br />6° 17' '
<br />103 :54
<br />54°
<br />.. 110.11
<br />3° 36`
<br />3° 54'
<br />-1500
<br />6° 31'
<br />103.84
<br />56°
<br />106.50
<br />3° 22'
<br />4° 02
<br />50 23'
<br />6° 44'
<br />10:1.14
<br />58°
<br />103- 14
<br />3° 2g'
<br />' 4° 10'
<br />5° 34`
<br />60 57'
<br />1043
<br />6o°
<br />100.00
<br />3° 35'
<br />4° 18'
<br />5° 44'
<br />7° 1 V
<br />104.72
<br />CURVE FORMULAS - - IX
<br />1 li tan t 1 IL = T cot. i I chordQ
<br />I . = 5o tan s I 2 Chord def. = 50' R
<br />50 Sin. JD 1Io. chords = I
<br />RI E= R ex. sec i I D
<br />Sin. 1 1) - tan T i • = T tan 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 f. Multiply the given distance by ,01745 (def. for r° for I ft.
<br />see"fable II.), and divide given deflection by the product.
<br />Rule z. 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 .oi 745, and the product by the distance.
<br />GENERAL DATA.
<br />R1GaT ANGLE TRIANGLES. Square the altitude, divide by twice the
<br />base. Add quotient to base for hypotenuse.
<br />Givcu Base foo, Aft. Yo.IO2=2oo=.5. Ioo-1-.5=Io0.5 hyp.
<br />Given.l-lyp. Ioo,Alt. 25.25$=zoo-3.125. t00-3.125=96.875=13ase.
<br />Error in first example, .oc,2; in last, .o45•
<br />To find'Tons of Raid in one mile.of trach: 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 0.574d3, 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 d„ a, da etc. are the discrepancies of various
<br />results from the mean, and if Id'=the sum of the squares of these differ-
<br />ences and n=the number'of observations, then the probable error of the
<br />E
<br />mean + 0.6745 id
<br />n
<br />SOLAR
<br />EPHEMERIS. Attention is Called to the Solar Ephemeris for'
<br />the current year, published by lseuffel & Esser Co., and furnished free of
<br />charge upon request, which is 3}x5J 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 f orinulas; Natural and Logarithmic Functions;
<br />and Logarithms of Numbers.
<br />TABLE IV. -Minutes in Decimals of a Deuree,
<br />1'.0167
<br />11'
<br />.1833
<br />21'
<br />.3500
<br />31'
<br />.5167
<br />41'
<br />6833
<br />51'
<br />.5500
<br />2..
<br />.0333
<br />i2.2000
<br />22
<br />.3667
<br />32
<br />.5333
<br />42
<br />.7000
<br />52
<br />SG67
<br />3
<br />:0500
<br />13
<br />.2167
<br />23
<br />.3933
<br />33
<br />.5500
<br />'43
<br />.7167
<br />53
<br />.5333
<br />4;
<br />.0667
<br />14
<br />.2333
<br />24
<br />.4000
<br />34
<br />.5067
<br />44
<br />.7333
<br />54
<br />.9000
<br />5
<br />.0833
<br />15
<br />.2500
<br />25
<br />.4167
<br />35
<br />.5333.
<br />45
<br />.7500
<br />55
<br />.9167
<br />6
<br />.1000
<br />16
<br />.2G67
<br />26
<br />.4333
<br />36
<br />.6000
<br />46
<br />.7667
<br />66
<br />.9333
<br />7
<br />:.1167
<br />17
<br />.2833
<br />27
<br />.4500
<br />37
<br />•.6167
<br />47
<br />.7533
<br />'57
<br />'.9500
<br />8
<br />.1333
<br />IS
<br />.3000
<br />28
<br />.4G67
<br />36
<br />-.0333.
<br />48
<br />-.°000
<br />5S
<br />-.9667
<br />9,
<br />-1500
<br />10
<br />.3167
<br />29
<br />.4833
<br />39
<br />59
<br />.9S33.
<br />10
<br />1607
<br />20•.2333
<br />30
<br />.5000
<br />40'
<br />.6500
<br />.6667
<br />_49
<br />50
<br />.8167
<br />.8333
<br />60
<br />11.0000
<br />-
<br />TABLE V. -
<br />Inches in Decimals of -a Foot.
<br />1-16
<br />332
<br />Y8
<br />3-10
<br />%
<br />5-16
<br />j
<br />y He
<br />Y
<br />0052
<br />.0079
<br />.0104
<br />.0156
<br />.0208
<br />.0260
<br />.0313
<br />.0417 .0521
<br />.0625
<br />.0729
<br />1
<br />2
<br />3
<br />4
<br />b
<br />6
<br />7
<br />8 9
<br />10
<br />11
<br />.0833
<br />.1667
<br />,2500
<br />.3333
<br />.4167
<br />.5000
<br />.5833
<br />1 .6667 .7500
<br />.8333
<br />.9167
<br />
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