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VIII' Ix
<br />TABLE II. - Radii,,' Ordinates and Dcflecti6ns..Choi'd=100 ft. CURVE FORMULAS.
<br />Deg'
<br />Radius
<br />I,fil
<br />Ord.
<br />Tan.
<br />Dist.
<br />Def.
<br />Diet
<br />Def'
<br />for
<br />1 Ft.
<br />"Deg.
<br />liadius
<br />Mill
<br />Ord.
<br />Tan
<br />Dist.
<br />Def.'
<br />Dist.
<br />Def.
<br />for
<br />1 Ft.
<br />^° 17,
<br />ft.
<br />it.
<br />t.-
<br />ft.
<br />!
<br />I° J9'
<br />ft,
<br />ft.
<br />ft.
<br />ft.
<br />34°
<br />0°10'34377.
<br />2° 06'
<br />.036
<br />.145
<br />.291
<br />0.05
<br />V •
<br />819.0
<br />1.528
<br />6.105
<br />12.21
<br />2.10
<br />20
<br />17159.
<br />.073
<br />.291
<br />.552
<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.OS
<br />2.25
<br />40
<br />8594':4
<br />.145
<br />.552
<br />1.164
<br />0.20
<br />-40
<br />747.9
<br />1.673
<br />6.635
<br />13.37
<br />2.30
<br />50-
<br />6875.5
<br />'.152
<br />.727
<br />1.454
<br />0.25
<br />8
<br />716.8
<br />1.746
<br />G.97G
<br />13.95
<br />2.40
<br />1
<br />5729.6
<br />.21S
<br />'.873
<br />1.745
<br />0.30
<br />' 20
<br />GSS.2
<br />1.519
<br />'7.260
<br />14.53
<br />2.50
<br />70
<br />4911.2
<br />.255
<br />1.018
<br />2.036
<br />0.35
<br />30
<br />674.7
<br />1.555
<br />7.411
<br />14.822.55
<br />58°
<br />20
<br />4297.3
<br />.291
<br />1.164
<br />2.327
<br />0.40
<br />40
<br />G61.7
<br />1.S92
<br />7.556
<br />15.11
<br />2.f0
<br />30
<br />3519.8
<br />.327
<br />1.309
<br />2.GIS
<br />0.4.5
<br />9
<br />G37.3
<br />1.965
<br />7.546
<br />15.69
<br />2.70
<br />40
<br />3437.9
<br />.3G4
<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 />8.251
<br />16.56
<br />2. Sr,
<br />2
<br />2504.9
<br />.430
<br />1.745
<br />3.490
<br />0.60
<br />40
<br />593.4
<br />2.110
<br />8.426
<br />16.55
<br />2.90
<br />10
<br />2644.6
<br />.473
<br />1.S91
<br />3.751
<br />0.65
<br />10
<br />573.7
<br />2.183
<br />5.716
<br />17.43
<br />3.Oi1
<br />20
<br />2455.7
<br />.509
<br />2.036
<br />4.072
<br />0.70
<br />1 30
<br />546.4
<br />2.292
<br />9.150
<br />18:20
<br />30
<br />2292.0
<br />.545
<br />2.181
<br />4.363
<br />0.75
<br />11
<br />521.7
<br />2._02,
<br />9.555
<br />19.16
<br />.3
<br />3.30
<br />-- 40-
<br />214S.S
<br />.5S2
<br />2.327
<br />4.654
<br />0.80
<br />30
<br />199.1
<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 />0.55
<br />12
<br />473.3
<br />2.G20
<br />10:45
<br />20 01
<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 />10.59
<br />21.77
<br />3.76
<br />10
<br />1809.G
<br />.G91
<br />2.763
<br />5.526
<br />0.95
<br />13
<br />441.7
<br />2.839
<br />11.32
<br />22.6=
<br />3.90
<br />20
<br />1719.1
<br />.727
<br />2.903
<br />5.517
<br />1.00
<br />30
<br />425.4
<br />2.949
<br />11.75
<br />23.51
<br />4.0:i
<br />30
<br />1637.3
<br />.754
<br />3.054
<br />6.108
<br />1.05
<br />14
<br />410.3
<br />3.058
<br />12.15
<br />2.1.37
<br />,1.20
<br />40
<br />1562.9
<br />.SOD
<br />3.199
<br />GMS
<br />1.10
<br />30
<br />366.2
<br />3.165
<br />12.62
<br />25.24
<br />4.35
<br />50
<br />1495.0
<br />.S30
<br />3.3.15
<br />6.689
<br />1.15
<br />15
<br />353.1
<br />3.277
<br />13.05
<br />23.11
<br />4.50
<br />4
<br />1432.7
<br />.S73
<br />3.490
<br />(3.980
<br />1.20
<br />30
<br />370.5
<br />3.357
<br />13.40
<br />23.97
<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 />1.50
<br />20
<br />1322.5
<br />.9.15
<br />3.713
<br />7.561
<br />1.30
<br />30
<br />343.5
<br />'1.GOG
<br />1.1.35
<br />28.70
<br />4.95
<br />30
<br />1273.6
<br />.DS2
<br />3.9213
<br />7.552
<br />1.35
<br />17
<br />338.3
<br />3.71G
<br />14.78
<br />29.5E
<br />5. P')
<br />40
<br />122S.1
<br />1.01S
<br />4.071
<br />8.143
<br />1.40
<br />18
<br />319.E
<br />3.935
<br />15.64
<br />31.29
<br />5.•10
<br />50
<br />1185.8
<br />1.055
<br />4.217
<br />S.433,
<br />1.45
<br />19
<br />302.9
<br />4.155
<br />16.51
<br />33.01
<br />5.70
<br />b
<br />11•!6.3
<br />1.091
<br />4.362
<br />5.724
<br />1.50
<br />20
<br />257.9
<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 />13.22'
<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 />4.514
<br />19.03
<br />3S. 1G
<br />6.60
<br />30
<br />1042.1
<br />1.200
<br />4.795
<br />9.596
<br />1.65
<br />23
<br />230.8
<br />5.035
<br />19.94
<br />39.S7
<br />6.90
<br />40
<br />1011.5
<br />1.237
<br />4.943
<br />9.SSG
<br />1.70
<br />24
<br />240.5
<br />5.255
<br />20.79
<br />41.53
<br />7.20
<br />50
<br />•952.6
<br />1.273
<br />5.OSS
<br />10.15
<br />1.75.
<br />25
<br />231.0
<br />5.•:7G
<br />21.64
<br />43.23
<br />'.60
<br />6055.4
<br />1:309
<br />5.234
<br />10.47
<br />1.SO
<br />26
<br />G 2.3
<br />5.697
<br />2%.50
<br />44.99
<br />7.SO
<br />10
<br />-929.6
<br />1.346
<br />5.379
<br />10.76
<br />1.85
<br />27
<br />214.2
<br />5.915
<br />_^3.35
<br />46.60
<br />G.!0
<br />20
<br />905.1
<br />1.353
<br />5.524
<br />11.05
<br />1.90
<br />23
<br />2UG.7
<br />G. 139
<br />24.19
<br />45.33
<br />SAO
<br />30
<br />581.9
<br />1.415
<br />5.669
<br />11.34
<br />1.95
<br />29
<br />199.7
<br />6.300
<br />25.04
<br />50.07
<br />S.70
<br />40
<br />1 S59.9
<br />1.455
<br />5.81-±
<br />11.63
<br />2.00
<br />30
<br />193.2
<br />6.553
<br />25.58
<br />51.76
<br />9. 06
<br />The middle ordinate in inches for any cord of icngth (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 ehonld
<br />be .0012X900X2.163 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 />A suh chord = sin of.' def. angle
<br />rt
<br />Length
<br />of arc
<br />for 1110 ft.
<br />sin..'_, def. ang.
<br />12,5 -Ft.
<br />15 Ft.
<br />20 Ft.
<br />25 Ft.
<br />30°
<br />193.18 .
<br />I° 51,
<br />^° 17,
<br />2° 58'
<br />3° 43'
<br />101.13
<br />320
<br />151.39
<br />I° J9'
<br />2° 25
<br />3° lo'
<br />;° 58'
<br />I0I.33
<br />34°
<br />.171.01
<br />2° 06'
<br />:2 33'
<br />3° 21'
<br />4° I2'
<br />I01.48
<br />36°
<br />161.8o-
<br />2° 13.'.
<br />2° 41'
<br />�° J3'
<br />° 26'
<br />ioi .66
<br />380
<br />153.58
<br />2° 20'
<br />z° 49'
<br />3° 44'
<br />4° 40'
<br />ioi.85
<br />40°
<br />r46. f9
<br />2° 27'
<br />°--° 57'
<br />3' 55'
<br />4' 54'
<br />IO2.06
<br />42'
<br />139.52
<br />'° 347
<br />3° 05'
<br />4° 07'
<br />5° 03
<br />102.29
<br />.102.53
<br />440
<br />133 •.47
<br />2° 41'
<br />3° 13'•
<br />4°' 18'
<br />5° 22'
<br />26
<br />q6°•
<br />127.97
<br />2°48'
<br />3°.2I'
<br />4°29'
<br />S°.36'
<br />102.76
<br />480
<br />122.92
<br />2° 55'
<br />3° 29'-
<br />4° 40'
<br />-. So'
<br />Io3.o0
<br />50°
<br />118.31
<br />3°'02'
<br />3°38'4°
<br />51'
<br />6°04
<br />103.24
<br />52°
<br />114.o6
<br />3° 09'
<br />3° 46'
<br />5° 02'
<br />6° 17'
<br />103.54
<br />54°
<br />110.11
<br />3° 16'
<br />3° J4'
<br />5° 13'
<br />6° 31'
<br />103.84
<br />SG°
<br />Io6. 5o
<br />3° 22'
<br />4° 02
<br />;5° 23'
<br />6° 44'
<br />104.14
<br />58°
<br />103.14
<br />3°29'
<br />4°10'
<br />5°34'
<br />6°57'
<br />104.43
<br />6o°
<br />100.00
<br />3° 35'
<br />4° 18'
<br />5044 ,
<br />°44'
<br />7° 11'
<br />104.72
<br />.T = R tan } I R= T cot. 3 I chord'
<br />So tan I Chord def. = R
<br />Sin. } D R = 50
<br />Sin. } D ='-' Sin. 2 D No. chords = D
<br />R I3 = R:ex. sec ' I .
<br />Sin:, j D. _ 50 tarn I. E ""= T tan JI-- Tan. def. = I 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 fora given distance and deflection.
<br />Rule I. 11'lultiply 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 J1.3, 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 AIGLF TRIANGLES. Square the altitude, divide by twice the
<br />base. Add quotient to base for hypotenuse.
<br />Given. Bare loo, Alt. 10.102=200=.5..100"7-.5=,I0o.5 hyP-
<br />Given'IIyp. loo, Alt. 25.25= .200=3.72.5. loo-3.125=96.875=Base.
<br />Error in first example, .002: in last, .045.
<br />To find Tons of Rail in one mile of trach: :multipiy weight per yard
<br />by rr, and divide by 7.
<br />LEVELING. The correction for curvature and refraction, in feet
<br />and decimals of feet is equal to 0.574 d', where d is the distance in miles.
<br />The correction for curvature alone is closely, I-. The combined cor-
<br />rection is negative.
<br />PPODABLE ERROR. If d, , &, d, etc. are the discrepancies of various
<br />result3 from the mean, and if fd2-the sum of the squares of these differ-
<br />ences and n=the number of obscr,ations, then the probable error of the
<br />Ineza= y 0.67451 YC1'
<br />-\ a (n-1)
<br />SOLAR EPHniirRIS. Attention is called to 'he Solar E -hemeris for
<br />the current year, published by Keuffel & Esser Co., and furnished free of
<br />charge upon request, which is 341-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 Ri ctric
<br />conversions; trigonometric formulas; Natural andLogarithmic Functions;
<br />and logarithms of -Numbers.
<br />TABLE IV. - ?'Iinutes in Decimals of a Degree.
<br />1'
<br />.0167
<br />TABLE V. -
<br />1533
<br />21'
<br />.35001
<br />31'
<br />.5167
<br />41'
<br />.6833
<br />51'
<br />.5500
<br />2
<br />.0333
<br />11P.
<br />12
<br />.2000
<br />22
<br />.3667
<br />32
<br />.0338
<br />42
<br />.7000
<br />52
<br />.5667
<br />•3'
<br />.0500
<br />13
<br />.21 G7
<br />23
<br />.3533
<br />33
<br />.5500
<br />43
<br />.7167
<br />53
<br />SS33
<br />4
<br />.0667
<br />-.
<br />.2333
<br />24
<br />.4003
<br />34
<br />.5667
<br />44
<br />.7333
<br />54
<br />.9000
<br />bOS33
<br />15
<br />.2500
<br />25
<br />1167
<br />35
<br />.5833'
<br />45
<br />.7500
<br />55
<br />.9167
<br />G•
<br />.1000
<br />1G
<br />.2667-
<br />26
<br />.4353
<br />36
<br />.6000
<br />16
<br />.7CG7
<br />56
<br />.9333
<br />7
<br />.1167
<br />1 17
<br />.2533
<br />27
<br />.4500
<br />37
<br />.6167
<br />'7
<br />.7S33
<br />57
<br />.9500
<br />8
<br />.1333
<br />18
<br />.3000
<br />28
<br />.4667
<br />38'
<br />.0333
<br />48
<br />.1.000
<br />58
<br />.9667
<br />9
<br />1.1500
<br />19
<br />1
<br />.3167
<br />29
<br />.4&3.3
<br />39
<br />.6509
<br />49
<br />.SI G7
<br />59 •
<br />9533
<br />10
<br />.1667
<br />20
<br />1 .3333 1130
<br />1 .5000
<br />11 40
<br />1 .(N
<br />50
<br />1 .5333
<br />60-
<br />I 1.0000
<br />TABLE V. -
<br />Inches in Decimals of a foot. '
<br />1-1G
<br />3-32
<br />X
<br />3-16
<br />Y
<br />516
<br />1 s
<br />X
<br />0052
<br />.OUTS
<br />.0104
<br />.0156
<br />.0203
<br />.0260
<br />.0313
<br />.0 17 .0 21
<br />.0620
<br />.0 9
<br />1
<br />2
<br />3
<br />4
<br />5
<br />G
<br />7
<br />S 9
<br />lU
<br />11
<br />.0933
<br />.1667
<br />.2500
<br />.33"1.3.
<br />.4167
<br />.5000
<br />.5S33
<br />.6667 .7500
<br />.5333
<br />.9167
<br />
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