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i7IIF
<br />TABLE IL - Radii, Ordinates and Deflactions. Chord =100 ft.
<br />Dag
<br />Radius
<br />Mid.
<br />Ord.
<br />Tan.
<br />Diet.
<br />Def.
<br />Dist.
<br />Dd.
<br />11Y6.
<br />Deg.
<br />Rediae
<br />Mid.
<br />Ord.
<br />Tan
<br />Dist.
<br />Def.
<br />'Diet.
<br />D'
<br />1f r
<br />193.18
<br />t.t.
<br />2° 17'
<br />2° 58'
<br />3°43'
<br />101.15
<br />320
<br />t.
<br />t.
<br />t,
<br />t, -
<br />'
<br />0'10'
<br />34377.
<br />.036
<br />.145
<br />.291
<br />0.u5
<br />7"
<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 />20'781.8
<br />3° 44'
<br />1.600
<br />6.39512.79
<br />4o°
<br />2.20
<br />30
<br />11459,
<br />.109
<br />.436
<br />.373
<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 />.582
<br />1.[64
<br />0.20
<br />40
<br />747.9
<br />1.673
<br />6.685
<br />.13.37
<br />2.30
<br />50
<br />6875.5
<br />.1821
<br />122.92
<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 />658.2
<br />1.819
<br />7.266.14.53
<br />103.54
<br />2.50
<br />10
<br />4911.2
<br />.255
<br />1.018
<br />2.036
<br />0.35
<br />30
<br />674.7
<br />1.8-55
<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
<br />2.90
<br />30
<br />3819.8
<br />.327
<br />1.309
<br />2.618
<br />0.45
<br />9
<br />637.3
<br />1.965
<br />7.846
<br />15.69
<br />2.70
<br />40
<br />3137,9
<br />.364
<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 />8.281'16.56
<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 />8.426
<br />16,55
<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 />2.183
<br />8.716
<br />17.43
<br />3.00
<br />20
<br />2155.7
<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 />19.16
<br />3.30
<br />40
<br />2148.8
<br />.582
<br />2.327
<br />4.654
<br />0.80
<br />30
<br />409.1
<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 />12
<br />478.3
<br />2.620
<br />10.45
<br />20.01
<br />3.60
<br />a
<br />1910.1
<br />.655
<br />2.618
<br />5.235
<br />0.90
<br />`30
<br />459.3
<br />2.730
<br />10.80
<br />21.77
<br />3-75
<br />10
<br />1 1809.6
<br />.691
<br />2.763
<br />5.526
<br />0.95
<br />13
<br />441.7
<br />2.839
<br />11.32 .22.64.3`.90
<br />20
<br />17L9.1
<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 />.764-3.054
<br />6:108
<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 />.S36
<br />3.345
<br />6.689
<br />1.15
<br />15
<br />383.1
<br />3.277
<br />13.05''-'26.11
<br />4.50
<br />4
<br />1132.7
<br />.873
<br />3,490
<br />6.930
<br />1.2030
<br />370.8
<br />3.387
<br />13.40
<br />26.97
<br />4.65
<br />10
<br />'1375.4
<br />.909
<br />3.635
<br />. 7.271
<br />1.25
<br />16
<br />359.3
<br />3.496.13:92
<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 />3.926
<br />7.852
<br />1.35
<br />11
<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 />15.04
<br />31.29
<br />5.40
<br />50
<br />1185.8
<br />1.055
<br />4.217
<br />8.433
<br />1.45
<br />10
<br />302.9
<br />4.155
<br />16.51.
<br />33.01
<br />5.70
<br />5
<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 />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 />4.814
<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 />5,033
<br />29.94
<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 J
<br />240.5
<br />5.25.5
<br />20.70
<br />41-58
<br />7.20
<br />50
<br />982.6
<br />1.273
<br />5.088
<br />WAS
<br />'1.75
<br />26 {
<br />231.0
<br />5.476
<br />21.64-
<br />43.28
<br />7.50
<br />e
<br />955.4
<br />1.309
<br />5.234
<br />10.47
<br />1.80
<br />26 /
<br />222.3
<br />5.697
<br />22.50
<br />44.99
<br />7.80
<br />10
<br />929.6
<br />1.346
<br />5.379
<br />10.76
<br />1.85
<br />27f
<br />214.2
<br />0.018
<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 />206.7'4',.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 />6.300
<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 ordinate1�n inches for any cord of length (ti) is equal to .001`2 U'
<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 .0012X90OX2.183 or 2.36 inches.
<br />TABLE III. Deflections for Sub Chords for Short Radius Curves.
<br />De ree
<br />f50
<br />Radius
<br />sub chord ,
<br />R =sin of a def. angle
<br />Length
<br />of arc
<br />Curve
<br />sin.I def, ang.
<br />12.5 Ft.
<br />15 Ft.
<br />20 Ft,
<br />25 Ft.
<br />for IOO ft.
<br />30°
<br />193.18
<br />1° 511
<br />2° 17'
<br />2° 58'
<br />3°43'
<br />101.15
<br />320
<br />181.39
<br />I° s�,
<br />2' �5.
<br />3° lo'...
<br />3° 58'
<br />101.33
<br />34°
<br />171.01
<br />2° OG'
<br />2° 331
<br />3° 21'
<br />4° 12'
<br />101.48
<br />36°
<br />161.80
<br />2' 13'
<br />2° 41
<br />3° 33'
<br />40 26'
<br />lot .66
<br />38°
<br />153.58
<br />2° 20'
<br />20 49'
<br />3° 44'
<br />-45.40'
<br />101.8;
<br />4o°
<br />-146.19
<br />2° 27'
<br />2° 57'.
<br />3° 5S'
<br />4° 5&'
<br />[o2.o6
<br />42°
<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° 18'
<br />5° 22'
<br />102.53
<br />46°
<br />127.97
<br />2° 48'
<br />3° 21'
<br />4° z9'
<br />5° 36'
<br />102.76
<br />48°
<br />122.92
<br />20 55.,
<br />3° 29`
<br />4° 40'
<br />5° 50'
<br />103.00
<br />500
<br />118.31
<br />3° 02'
<br />3° 38'
<br />4° 51'
<br />6° 04'
<br />103, �4
<br />5z°
<br />114.0G
<br />3°.og'
<br />3° 46'
<br />S° oz.'
<br />6° 17
<br />103.54
<br />54°
<br />110. t1.
<br />3° 16'
<br />3° 54'
<br />S° 13'
<br />6°31
<br />103.84
<br />56
<br />lo6.5o
<br />3° 22'-
<br />4° 02'
<br />5.23 1
<br />6° 44
<br />104.14
<br />58'
<br />103-143'
<br />29'
<br />4° lo'
<br />5° 34
<br />b° 576
<br />144.43
<br />6o°
<br />loo.06
<br />3° 35'
<br />4° 18'
<br />5° 44
<br />7° [ 1'
<br />10,1.72 ii
<br />Ix
<br />CURVE FORMULAS
<br />T= R tan 2 I R= T cot. 2' 1 chord'
<br />_ 5o tan I I Chord def. _
<br />p Sin. 2 D R= 50 R
<br />a
<br />-Sing 2. D = go Sm. D No. chords = I
<br />It E -=Rex. sec I D
<br />Sin, '2D =got 7 2 I E - q tan } ITan. 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 for a given distance and deflection.
<br />Rule I.Multiply the given distance by .01745 (def. for 0 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 />:= a - To find deflection for a given angle and distance. -Multiply the anglc.
<br />°U,y,.bi745, and the product by the distance.
<br />GENERAL DATA
<br />RIG1;T ANGLE 1 R1ANGLFS, Square the altitude, divide by twice -the
<br />base. Add quotient to base for hypotenuse.
<br />Given Base loo, Alt. 10-10' 200=.5. loo+.g=1oo.5 hyp,
<br />.Given Hyp. loo, Alt. 25.258_200=3.125.''.-]()0-3.125=96.87,5=Base.
<br />Er_or,in,first example,,,00a; to last, .045.
<br />To find `Tol s of Rail In'onZ�,iiile of track: multiply weight per yard
<br />by 11, and _divide by'7
<br />1.,EVELING. The correction for curvature and refraction, in feet
<br />and decimals of feet -is equal to 0.574d2, where d is the distance in miles.
<br />7'he correction for curvature alone is- closely, 'ad'. The combined cor-
<br />rection, is negative.
<br />1 PROBABLF ERROR.- If d,, d2, d,, etc. are the discrepancies of various
<br />restilts from the mean, and if Ede=the sum of the squares of these differ-
<br />ences and n=ihe number of observations, then the probable error of the
<br />mean f J;d 2
<br />SOLAR Ertmmukis. Attention is calledto the Solar Ephemeris for
<br />the current' year, published by Kcuffel & Esser Co., and furnished upon
<br />request., This handy booklet, 36x6 in., has about 190 pages of data very
<br />useful to the Surveyor; such as the adjustments of transsts, levels and solar
<br />attachments; directions and tables for determining the meridian and the
<br />latitude from observations on the sun and Polaris; stadia measurements;
<br />magnetic declination; arithmetic constants, etc.
<br />TAFIVE fV--Minutes in Decimals of a Degree.
<br />1/
<br />.0167
<br />W
<br />211
<br />.3500
<br />311
<br />.5167
<br />411
<br />,6833
<br />511
<br />.8500
<br />1.2
<br />.0333
<br />12
<br />_.1833
<br />2000
<br />22
<br />.3667
<br />32
<br />.5333
<br />42
<br />.7000
<br />52
<br />.8667
<br />3
<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 />54
<br />-9000
<br />5
<br />.083.3
<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 />16
<br />.2667
<br />26
<br />.4333
<br />36
<br />.6000
<br />46-
<br />.7667
<br />56
<br />'1333
<br />7
<br />..L167
<br />17
<br />.2833
<br />27
<br />.4500
<br />37
<br />'.61;57
<br />47
<br />-7833
<br />57
<br />.9500
<br />e1333
<br />18
<br />.3000
<br />28
<br />.4667
<br />38'
<br />.6333
<br />48
<br />.8000
<br />58
<br />.9667
<br />s
<br />.1500
<br />19
<br />.3167
<br />29
<br />.4833
<br />39
<br />.6500
<br />49
<br />.8167
<br />59
<br />.9833
<br />10
<br />.1667
<br />20
<br />,.3331
<br />30
<br />,.5000 11
<br />40
<br />.6667 11
<br />50.
<br />1 .8333
<br />60
<br />1.0000
<br />TAH1,1`1 V. --I uCh(-S in Decimals of a
<br />toot.
<br />1-16
<br />3-32 5'a
<br />3-16
<br />1•
<br />5-1 G-
<br />f
<br />:�
<br />4'a
<br />a
<br />.0052
<br />I .0078 .0104
<br />.01.56
<br />.0208
<br />.0260 I
<br />.0313
<br />.0417
<br />.0521
<br />.0625
<br />.0729
<br />-1
<br />I
<br />6 1
<br />7
<br />S
<br />9
<br />10
<br />11
<br />.33
<br />08
<br />Ij
<br />.1667 .25 00
<br />.3 :333
<br />.41:i67
<br />.2000
<br />.5833
<br />.6667
<br />-7.500
<br />.8333
<br />.9157
<br />
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