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VIII IX
<br />TABLE II. -- Radii, Ordinates and Deflections. Chord =100 ft. CURVE FORMULAS
<br />The middle ordinnte in inches for any cord of length (C) is equal-tv.0013 U -
<br />multiplied by the middle ordinate taken from the above table. Thus, if it
<br />desired to bend a 30 ft. rail to fita 10 degree curve, its middle ordinate :jbonld
<br />be .0012X900X2.183 or 2.36 inches.
<br />TABLE III. Deflections for Sub Chords for S'h'ort Radius Curves.
<br />Degree
<br />o f
<br />Curve
<br />Rad u"
<br />Mid:
<br />Ord,
<br />Tan.
<br />hist.
<br />Dcf..
<br />Dist.
<br />Oc('
<br />1 Ft.
<br />Dcg.
<br />Radius
<br />Mid.
<br />Ord.
<br />Pan.
<br />Dist.
<br />Def.
<br />Dist.
<br />Dei,
<br />lfFt.
<br />2° 17'
<br />ft,
<br />ft.ft.
<br />10I.15
<br />ft.
<br />!
<br />r° 59'
<br />it.
<br />it.
<br />it.
<br />it.
<br />34°
<br />0'I0'
<br />34377.
<br />.036
<br />.145
<br />291
<br />0.05
<br />7°
<br />519.0
<br />1.528
<br />6.105
<br />12.21
<br />2.10
<br />.20
<br />17189.'
<br />073.86
<br />291
<br />582
<br />0.10
<br />20'
<br />781.8
<br />1.000
<br />6.395
<br />12.79
<br />2.20
<br />30
<br />11459.
<br />,109
<br />',4
<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 />8594.4
<br />.145
<br />.582
<br />1,164
<br />0.20
<br />40
<br />747.9
<br />1:673
<br />6.655
<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 />0.976
<br />13.95
<br />2.40
<br />1
<br />5729.6
<br />.218
<br />.873
<br />1.745.
<br />0.30
<br />20.
<br />688.2
<br />1.619
<br />7.206
<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 />074.7
<br />1.855
<br />7.411
<br />I -L82
<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 />7.556
<br />1.5.11
<br />2.60
<br />30
<br />3819.8
<br />.327
<br />1.369
<br />2.018
<br />0.45
<br />9
<br />G37.3
<br />1.965
<br />7.846
<br />15. G9
<br />2.70
<br />40
<br />3437.0.
<br />.364
<br />1.454
<br />2.909
<br />0.50
<br />20
<br />G14.6
<br />2:037
<br />8.130
<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 />2
<br />2864•:9,
<br />.436
<br />1;745
<br />3-.490
<br />0.60
<br />40
<br />'593.4
<br />2:110
<br />8.420
<br />16.85
<br />2.90
<br />10
<br />' 2644.6
<br />.473
<br />1.591
<br />3:781
<br />0.63
<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 />2.03G
<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 />2.40.^.
<br />9.585
<br />19-1G
<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 />20.01
<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
<br />10.45
<br />20.01
<br />3.60
<br />8
<br />1910.1
<br />,.655
<br />2.61S
<br />5.235
<br />0.90
<br />30
<br />459.3
<br />2.730
<br />10.89
<br />21.77
<br />3.75
<br />16
<br />IS03.6
<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 />20
<br />1719.1
<br />.727
<br />2.903
<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 />.704
<br />3.054
<br />6.108
<br />1.03
<br />14
<br />410.3
<br />3.058
<br />12.18
<br />34.37
<br />4.20
<br />40
<br />1563.9
<br />.800
<br />3.199
<br />6.393
<br />1.10
<br />30
<br />396.2
<br />3.16$
<br />12.62
<br />25.24
<br />4.35
<br />50
<br />1495.0
<br />.836,
<br />3.345
<br />G.GS9
<br />1.15
<br />15
<br />383.1
<br />3.277
<br />13.05
<br />26. 1:1
<br />4.50
<br />1432.7
<br />.873
<br />3.490
<br />6.980
<br />1.20
<br />30
<br />376.8
<br />3.387
<br />13.49
<br />26.97
<br />4.65
<br />10
<br />1375:4
<br />.909'3.635
<br />7.271
<br />1.25
<br />16
<br />359.3
<br />3.496
<br />13.02!
<br />27.84
<br />4.80
<br />X20
<br />1322.5
<br />..945
<br />3.713
<br />7.501
<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 />20.56
<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 />3.03:1
<br />15.64
<br />31.29
<br />5.40
<br />50
<br />1135.$
<br />1.055
<br />4.217
<br />8.433
<br />1.45 '.
<br />19
<br />302.9
<br />4.135
<br />16.51
<br />33.01.5.70
<br />G
<br />1146.31.091
<br />4.362'
<br />8.724
<br />1.50
<br />20
<br />237.9
<br />4.374
<br />17.37
<br />34.73
<br />G.00
<br />10
<br />1109.3
<br />1.127
<br />41.507
<br />• 9.014
<br />1.55
<br />21
<br />274.4
<br />4.59418.22
<br />36.44
<br />G.30
<br />.20
<br />.1074.7'1.164
<br />4.653
<br />9.305
<br />1:60
<br />22
<br />2G2.0
<br />4.814
<br />PEW
<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 />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 />41.53
<br />7.20
<br />50
<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-.43.25
<br />7.30
<br />6
<br />955.4
<br />1.309
<br />5.234
<br />10.47
<br />1.80
<br />29
<br />222.3
<br />5.697
<br />'22.50
<br />44.99
<br />7.80
<br />10
<br />929.6
<br />1.340
<br />5.379
<br />10.76
<br />I'.S5 "
<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 />0.1,30
<br />24.19
<br />4.8.38
<br />8.40
<br />30
<br />SS1.9
<br />1.418
<br />5.059
<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 />1 859.9
<br />1.455
<br />5.814
<br />11.63
<br />2.00
<br />30
<br />193.2
<br />6.583
<br />25.88
<br />51.70
<br />9.00
<br />The middle ordinnte in inches for any cord of length (C) is equal-tv.0013 U -
<br />multiplied by the middle ordinate taken from the above table. Thus, if it
<br />desired to bend a 30 ft. rail to fita 10 degree curve, its middle ordinate :jbonld
<br />be .0012X900X2.183 or 2.36 inches.
<br />TABLE III. Deflections for Sub Chords for S'h'ort Radius Curves.
<br />Degree
<br />o f
<br />Curve
<br />' Radius
<br />50
<br />sub chord
<br />R = sin of a def. angle
<br />Length
<br />of arc
<br />for 100 ft.
<br />sin. A de€. ang.
<br />12.5 Bt.
<br />15 Ft.
<br />20 Ft.
<br />25 Ft:
<br />30''
<br />193.18
<br />1° 51'
<br />2° 17'
<br />2' 58'
<br />3' 43'
<br />10I.15
<br />32°
<br />181.39
<br />r° 59'
<br />2° 25'
<br />3° Io'
<br />3° 58'
<br />101.33
<br />34°
<br />171.01
<br />2° o6'
<br />2°'33'
<br />3° 21'
<br />4° 12'
<br />101.48
<br />36°
<br />161. So
<br />2°'13'
<br />s°'4i'".
<br />3°33'
<br />4°26'
<br />101.66
<br />38'
<br />153.'58
<br />2' 20'
<br />2° 491.-
<br />3° 44'..
<br />4° 401
<br />I01.85
<br />40°
<br />146. 19• .
<br />2° a7'
<br />2° 57'
<br />3' 55'
<br />4° 54
<br />1o2.06
<br />42'
<br />139 S2
<br />2°34'
<br />3'05'.
<br />4007,
<br />5° 08'102-29
<br />.7500
<br />44°
<br />133.47'
<br />2° 41
<br />3° 13
<br />4'° 18
<br />5° 22'
<br />102.53
<br />46.°
<br />127-97
<br />. 2° 48'
<br />'
<br />30 21'
<br />4° 29!
<br />5° 36'
<br />102.76
<br />48°
<br />122.92
<br />2° 551.
<br />3' 29, ..
<br />40 4o'
<br />50 50r
<br />103.00
<br />500 .
<br />. IIS -31
<br />3° 021
<br />3' 38,
<br />40 51,
<br />. 6° 04'
<br />'103.24
<br />52°
<br />I14.o6
<br />3° 09'
<br />3° 46'
<br />5° 02'
<br />6° 17'
<br />163.54
<br />54'
<br />110.11
<br />3° 16'
<br />•3'54'
<br />5° 131
<br />60 31'
<br />103.84 -
<br />_ 56°
<br />rob. So
<br />3' 22'
<br />4° 02'
<br />5° 23'
<br />6° 44'
<br />w4.14 .
<br />58' .
<br />103.14
<br />3' 29'
<br />4° lo'
<br />S° 34'
<br />6° :57'
<br />104.43,,'
<br />6o
<br />100.00
<br />3°35 ".
<br />4'i8'
<br />5'44'.
<br />7° 11'
<br />104.1-2
<br />--T = R tan I 1 1t .= T cot. 1 I Cliord def. = chord"
<br />T f 5o tan 1 I R
<br />Sin. D R - 50
<br />Sin. 1 D = go Sin. Z D No. chords = I"
<br />R E= R ex. sec ', I D
<br />- 5o tan a 1 Y
<br />Sin. D - I 11- = T tan 4 I - 'Tan. def. a chord def.
<br />The square of any distance, divided by twice the radios, 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 .01748 (def. for i* for, 1 ft.
<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 .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 ioo, Alt. Io.Io2 200 .5.. I000 - roo.5 hyp.
<br />Given Hyp. loo, Alt. 25.252-200 ' =-3-125. loo -3.125=96.875=1 ase.
<br />Efror in first example, .00a; 1n last, .045.
<br />To find Tons of Rail iii one mile of track: rlultiply weight per yard
<br />by I'I, and divide by 7.
<br />LuvrLING. The correction for curvature and refractio i, in feet
<br />and decimals of feetis equal to 0.574da,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;, d., d3, etc. are the discrepancies of various
<br />results from the mean, and if :fd2=the sum of the squares of these differ-
<br />ences anis n=the number of observations, then the probable -error of the
<br />mean= 0:6745 oda.
<br />1 n (n-1)
<br />SOLAR EPHEMERIS. Attention. is called to the Solar Ephemeris for
<br />the current year, published by Keuffel & Esser Co., and furnished free of
<br />charge upon request, which is 3. x5R in., with about 90 pages of data very
<br />useful to the Surveybr; 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 />T-, TAT - kl;rrttfpc in T)p im fa of n. lip vrop
<br />1'
<br />.0167
<br />11'
<br />1833.
<br />'21'
<br />.3500
<br />31'
<br />.5]67
<br />41'
<br />.G333
<br />51'
<br />.8500
<br />a.0333
<br />12
<br />.2000
<br />22
<br />.3667
<br />32
<br />.5333
<br />42
<br />.7000
<br />52
<br />.8667
<br />1
<br />.0300
<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 />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 />'1u
<br />.2667
<br />32
<br />.4333
<br />30
<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 />.6157
<br />41
<br />•7833
<br />57
<br />.9500
<br />8
<br />.1333
<br />13
<br />.3000
<br />28
<br />.4667
<br />38
<br />.6333
<br />48
<br />.woo
<br />58
<br />.9667
<br />9
<br />.1500
<br />1a
<br />3167
<br />20
<br />.4833
<br />30.
<br />.6500
<br />49
<br />.8167
<br />59
<br />.9833
<br />10
<br />.1667
<br />20
<br />1 ,3333
<br />1 30
<br />1 ,5000 11
<br />40
<br />1 .6667
<br />50
<br />.8333
<br />00
<br />1.0000
<br />I
<br />1'ABLr V. - inches 1n 1Jecunals of a root.
<br />31.3
<br />OU52
<br />U07B
<br />,3 04-
<br />.0156
<br />.068
<br />.02ff1.
<br />f17
<br />.021 .06Y425
<br />4729
<br />1
<br />2
<br />3
<br />4:
<br />5
<br />6
<br />7
<br />8
<br />9 - 10
<br />11
<br />Q833
<br />.1667
<br />.2500
<br />.3333
<br />..4167
<br />.5000
<br />.5533
<br />_.6667
<br />.7500...8333
<br />.9167,
<br />I
<br />
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