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VIIT `
<br />TABLE II. - Radii, Ordinates -find Deflections. Chord =100 ft.
<br />Deg.
<br />-
<br />-Radius
<br />-
<br />hfid
<br />Ord.
<br />Yan:y
<br />Diet.
<br />•Def:
<br />Dist.
<br />-
<br />sfnr
<br />Deg.
<br />R�d��
<br />Mid.
<br />O:d.
<br />Tea
<br />1)ist,
<br />Dcf,
<br />hist.
<br />Dfcr
<br />1 Ft.
<br />2
<br />ft.
<br />It
<br />ft. I
<br />ft.
<br />181.39
<br />1°59'
<br />ft.ft.••
<br />3°10'
<br />It.
<br />it.
<br />34°
<br />0'10'
<br />34377.
<br />.036
<br />,145
<br />.291
<br />0.05
<br />71
<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 />30
<br />11459.
<br />.109
<br />.43G
<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 />.5S2
<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 />6375.5
<br />.182
<br />,.727
<br />•1.454.0
<br />2,,
<br />8
<br />716.8
<br />1.746
<br />6.97G
<br />13.95
<br />2,40
<br />1
<br />5729-0
<br />.218
<br />.873
<br />1.745
<br />0.30
<br />20
<br />688.2
<br />1.819
<br />7.2GG
<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 />674.7-1.855
<br />5° 23'
<br />7:411,14.82
<br />104.14
<br />2.55
<br />20
<br />4297.3
<br />.291
<br />1.164
<br />2.327
<br />0.40
<br />40
<br />061.7
<br />1.892
<br />7.5,56
<br />15,11
<br />2.60
<br />. X30
<br />3819,8
<br />,327
<br />11309
<br />2:618
<br />0.45
<br />9
<br />637,3
<br />1:965
<br />7:S46
<br />15.69
<br />2.70
<br />40
<br />-3437.9
<br />.U4
<br />1.454
<br />2:909
<br />0.50
<br />20
<br />614.G
<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 />E
<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 />2.18.3
<br />8.716
<br />17.43
<br />3.00
<br />20
<br />2455.7
<br />.509
<br />2,030
<br />4.072
<br />0.7030
<br />546.4
<br />2.29'2
<br />9.150
<br />15.30
<br />3.15
<br />30
<br />2292.0
<br />.545
<br />2.381
<br />4,363
<br />0.75
<br />ll
<br />521.7
<br />2.402
<br />9.liS5
<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 />171
<br />478.3
<br />2.020
<br />10,45 '20.01
<br />3.60
<br />$
<br />1910.1
<br />x: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 />X91
<br />2.763
<br />5:520
<br />0.95
<br />13
<br />441,7
<br />2,839
<br />11.32
<br />22.64
<br />3.90
<br />20
<br />1.719.1
<br />'`.727
<br />2:908
<br />51817
<br />1.00
<br />30
<br />425.4
<br />2.940
<br />11,75
<br />23.51
<br />4.05
<br />30
<br />1637.3
<br />.761
<br />3.054
<br />6,108
<br />2. 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 />356.2
<br />3.108
<br />12,62
<br />25.24
<br />4.35
<br />50
<br />1495.0
<br />.836
<br />3.345
<br />'.G.G89
<br />1.15
<br />'15
<br />383.1
<br />3.277
<br />13,05
<br />'1.50
<br />d
<br />1432.7
<br />.873
<br />3,490
<br />6.980
<br />1.20
<br />30
<br />370.8
<br />3.387
<br />.26.11
<br />13.49.,26.9'7
<br />4.65
<br />10
<br />1375.4
<br />.909
<br />3.035
<br />7.211
<br />1.25
<br />1G
<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 />71561
<br />1.30
<br />30
<br />348.5
<br />3.606.14:35
<br />,28,70
<br />4.95
<br />30
<br />127.3.6
<br />.982
<br />3.920
<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 />1.018
<br />4.071
<br />.8,143
<br />1.40
<br />'18
<br />319.6
<br />3:935
<br />15,64 ,81.29
<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 />6
<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 />G"30
<br />20
<br />1074.7,
<br />1.164.4.653
<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
<br />19.94
<br />39.87
<br />G.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 />4.1.58
<br />7.20
<br />60.
<br />932.6'1.273
<br />5.058
<br />19.18
<br />1.75
<br />25
<br />231.0
<br />5,476
<br />21.64
<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 />.43.28
<br />22.50
<br />44.99
<br />7.S0
<br />30'
<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 />5,10
<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 />1.4FS
<br />S.G69
<br />11,•34
<br />1.95
<br />29
<br />199.7
<br />0.360
<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 />Tho iniddlo 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 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 />59
<br />A sub chord
<br />R = sin of i def. angle
<br />Length
<br />of are
<br />for 100 ft.
<br />sin. I def. ago.
<br />12.5• Ft.
<br />15 Ft.
<br />20 Ft.
<br />25 Ft.
<br />30°
<br />193.18.L7'
<br />.5500
<br />2
<br />2°' 58'----
<br />,. _30.43'
<br />101.15
<br />32°
<br />181.39
<br />1°59'
<br />2025P
<br />3°10'
<br />3°58'
<br />101.33
<br />34°
<br />171.01
<br />2° 06'
<br />2°.33'
<br />3° 21'
<br />4' I2'.
<br />JOI , 48
<br />_36°
<br />161.810
<br />2° 13'
<br />2° 41'-
<br />3' 33'
<br />4° 26'
<br />1o1.66
<br />=380-
<br />153.58
<br />20 20'
<br />2° 49'
<br />: 3° 44
<br />4° 40
<br />101.85
<br />46°
<br />346-19
<br />2° 27'
<br />2° 57'
<br />3° 55
<br />4° 54'
<br />1o2. o6
<br />42'
<br />139.52
<br />2' 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° 18'
<br />S' 22'
<br />1o2.53
<br />46°
<br />127,97.
<br />2° 48
<br />3° 21'
<br />4° 29'
<br />5°'36'
<br />102,76.
<br />48°
<br />122, 92
<br />2°"55'
<br />3° 29'
<br />4° 40'
<br />5° 50'
<br />103.00
<br />50°
<br />118.31
<br />3° 02'.
<br />3° 38'4°
<br />51'
<br />6° 04'
<br />103.24
<br />520
<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° f6'
<br />3° 54'
<br />;° 13'
<br />6° 31'
<br />103.84
<br />56°
<br />1o6.5o
<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 />704.43
<br />60°.
<br />100.00
<br />3° 35'''
<br />4° 18'
<br />5° 44'
<br />7° 11,
<br />•104.72
<br />.IX ,
<br />CURVE FORMULAS
<br />T R tan I R= 'C cot. _r' I chord$
<br />T jD tan I Chord def.: = R -
<br />Sin, } ll50
<br />Sin. .
<br />Si .1 Sin.D
<br />D = = No. chords
<br />5a tan a I E =Rex. sec 1 D
<br />a Ta =T tan J 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 defection.
<br />Rule I. Multiply the given distance by .oi745 (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 />To find deflection for a given angle and distance. Multiply the angle
<br />by,.oi745, and the product by the distance.
<br />GENERAL DATA
<br />RFGHTtANQLE TRIANGLES. Square. the. altitude, divide by twice the
<br />base. Add quotient to base for hypotenuse.
<br />Given Base zoo, Alt. 10.102=200=.5. 100-}-.5=100.5 hyp.
<br />Given Hyp; zoo, Alt. 25:25-'-200=3.I2�. zoo-3.12$=96.875=Base.
<br />Error in.flrst example, .002; .in last, .045.
<br />To finch Tons of Rail in one mile of trach:: - multiply wei„ht per yard
<br />-by. ii, and divide by 7:
<br />LEVELING.- The correction for•'curvztvre and refraction, in feet
<br />and decimals of feetis.equal to 0.574d', where d is the distance in miles.
<br />The' correction for cul attire alone is closely; jd=,.. The combined cor-
<br />rection -is negative.
<br />d{
<br />PROBAeL>_ ERROR. If ; d ; d., etc. are the discrepancies of various
<br />results from the mean, and if Zd'=the sum of the squares of these differ-
<br />ences and n=the number of observations; then the probable error of the
<br />mean -+0.6745 fid$
<br />1 n (n-1)
<br />SOLAR EPEEMERIs. Attention'is called to the Solar Ephemeris for
<br />the current year, published by Kcuflel & Esser Co-, and furnished free of
<br />charge upon request, which is 34x5.1 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. - 111inutes in Decimnis of a Decree.
<br />1'
<br />•.0167
<br />.11'
<br />.1833
<br />21'
<br />.3500
<br />31'
<br />5167
<br />41'
<br />.6533
<br />51'
<br />.5500
<br />2
<br />.0333
<br />12
<br />.2000
<br />22
<br />.3667
<br />32
<br />15333
<br />42
<br />.7000
<br />62
<br />.8667
<br />b -
<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 />64
<br />.9000
<br />6
<br />.0533
<br />.15
<br />.2500
<br />25
<br />.4167
<br />35
<br />•5833
<br />45
<br />.7500
<br />06
<br />.9167
<br />G
<br />1000
<br />1G
<br />2067
<br />26
<br />.4333
<br />36
<br />6000
<br />46
<br />,7667
<br />56
<br />.9333
<br />?
<br />1167
<br />17
<br />Y2833
<br />21
<br />.4500
<br />37
<br />6167•
<br />47
<br />.7833
<br />57
<br />9500
<br />8
<br />.1333
<br />18 ','.3000
<br />28
<br />.4GG7
<br />3S
<br />•G333
<br />48
<br />.5000
<br />58
<br />.0667
<br />9500
<br />10
<br />•3167
<br />29
<br />.4833
<br />39
<br />•6500
<br />49
<br />,8167
<br />59
<br />.9533
<br />10
<br />.1667 11
<br />20
<br />,3333
<br />30 1
<br />.5000
<br />11 40
<br />1 .6667
<br />50
<br />.8333
<br />60
<br />11.0000
<br />•
<br />TADLB V. - Inches in Decimals of a Foot.
<br />1-16
<br />3-32
<br />);
<br />5-16
<br />/e
<br />o
<br />/a
<br />.0052
<br />.0078
<br />.0104
<br />,01.56
<br />0208
<br />.0260
<br />.]113
<br />.0117 .0521
<br />.0625
<br />.0729
<br />1
<br />2
<br />3
<br />4
<br />5
<br />6
<br />1
<br />S 9
<br />10
<br />11
<br />.0833
<br />.1667
<br />.2500
<br />.3333
<br />.4167
<br />.5000
<br />.5833
<br />.6667 .7500 1
<br />.8333
<br />1 .9167
<br />
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