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VIII
<br />r TABLE II. - Radii, Ordinates and Deflections. Oaord-10S t._
<br />Deg.
<br />Radius
<br />Mid,
<br />Ord.
<br />Tan.
<br />Diet,
<br />Def.
<br />Dist.
<br />for
<br />LBt.
<br />Deg.
<br />Radius
<br />Mimed''
<br />Old.
<br />1sa
<br />Dist,
<br />D f.
<br />Diet.
<br />~Dfef.
<br />or
<br />I Ft.
<br />2° 17
<br />t.
<br />t7
<br />I .
<br />M
<br />181.39
<br />1° 39'
<br />it.
<br />t.t.
<br />3° 58'
<br />t.
<br />34°
<br />0* to'
<br />34377,
<br />.036
<br />.145
<br />.291
<br />0.05
<br />7'
<br />619.0
<br />1.528
<br />6.105
<br />12.21
<br />2.10
<br />20
<br />17189.
<br />.073
<br />.291
<br />.532
<br />0.10
<br />20'
<br />781.8
<br />1.600
<br />6.395
<br />12-79
<br />2.20
<br />30
<br />114.59.
<br />.109
<br />.436
<br />.873
<br />0.15
<br />30
<br />764.5
<br />1.637
<br />6.540
<br />18.08
<br />2.2:7
<br />40
<br />8594.4
<br />.145
<br />'.582
<br />1.164
<br />0.20
<br />40
<br />747.9
<br />1.6173
<br />6.685
<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 />3729.6
<br />.213
<br />.873
<br />1.745
<br />0.30
<br />20
<br />688.2
<br />1.819
<br />7.266
<br />14.53
<br />2-:,
<br />10
<br />4911.2
<br />.2115
<br />1.018
<br />2.036
<br />0:35
<br />30
<br />674.7
<br />1.855
<br />7.411
<br />14.82
<br />2.;1+1
<br />20
<br />4297.3
<br />.291
<br />1.164
<br />2.327
<br />0.40
<br />40
<br />6611.7
<br />1.892
<br />7.555
<br />15.11
<br />2-60
<br />30
<br />3819.8
<br />.327
<br />1.300
<br />2.618
<br />0:45
<br />9
<br />637.3
<br />1.965
<br />7'.846
<br />15. G0
<br />2.70
<br />40
<br />3437.9
<br />.364
<br />1.454
<br />2.909
<br />0.50
<br />20
<br />614.6
<br />2.037
<br />8.130
<br />16.27
<br />2.50
<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 />2.83
<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 />16.85
<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 />2.183
<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.A
<br />2.202
<br />9.1.50
<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 />.552
<br />2.327:
<br />4.654
<br />0.80
<br />30
<br />499.1
<br />2.511
<br />10.02
<br />20.94
<br />3.45
<br />50
<br />2022.4
<br />.618
<br />2.472
<br />4.945
<br />0.83
<br />12
<br />47,4.3
<br />2.620
<br />10.45
<br />20.91
<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 />10.89
<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 />22,64
<br />3.90
<br />20
<br />1719.1
<br />.727
<br />2.908
<br />5.517
<br />1.00
<br />30
<br />425.4
<br />2.940
<br />11.75
<br />23.61
<br />4.05
<br />30
<br />1637.3
<br />.764
<br />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 />15 2.9
<br />.800
<br />3.199
<br />6.398
<br />1.10
<br />30
<br />396.2
<br />3.168
<br />12.65
<br />25.24
<br />4.35
<br />50
<br />.836
<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 />1432.7
<br />.873
<br />3.490
<br />6:080
<br />1.20
<br />30
<br />370.8
<br />3.387
<br />13.49
<br />26.97
<br />4.65
<br />10
<br />1375.4
<br />.909
<br />3.635
<br />7.271
<br />1.25
<br />10
<br />359-3
<br />3.196
<br />13.92
<br />27.84
<br />4.80
<br />20
<br />1322.5
<br />.945
<br />3.718
<br />7.0,61
<br />1.30
<br />30
<br />318-5
<br />3.608
<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 />336-3
<br />.716
<br />14.78
<br />29:.i6
<br />5.10
<br />40
<br />1228.1
<br />1.018
<br />4.071
<br />8.1-x3
<br />1.40
<br />18
<br />319-0
<br />3.935
<br />15.04
<br />31.295.40
<br />50
<br />1185.8
<br />1.055
<br />4.217
<br />8.433
<br />1.45
<br />19
<br />302-9
<br />4.15.5
<br />15.51
<br />33.01
<br />5.70
<br />S
<br />1146.3
<br />1.091
<br />4.362
<br />8.724
<br />1.50
<br />20
<br />.287.9
<br />4.37,4-17.37
<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 />5.035
<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 />41.58
<br />7.20
<br />50
<br />082.6
<br />1'.273
<br />5.088
<br />10.18
<br />1.75
<br />25
<br />231.0
<br />5.476
<br />21.64
<br />43.28
<br />7.50
<br />6
<br />055.4
<br />1.309
<br />5.234
<br />10.47
<br />1.80
<br />26
<br />222.3
<br />5.697
<br />22.50
<br />44.09
<br />7:50
<br />10
<br />929.6
<br />1.346
<br />5.379
<br />10.76
<br />1.85
<br />27
<br />214.2
<br />b.QlS
<br />23.35
<br />46.69
<br />S.10
<br />20
<br />905.1
<br />1.382
<br />5.524
<br />1.1.05
<br />1.90
<br />28
<br />206.7
<br />6.139
<br />24.19
<br />48.38
<br />S.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 />5.814
<br />11.63
<br />2.00
<br />30
<br />193.2
<br />6.583125.S9
<br />.51.7619-
<br />on
<br />The middle ordinate in inches for ai1N� cord of length (C) is equal to .0012 C'
<br />multiplied by the middle ordinate I Xon from the abovo table. Thus, if it
<br />desired to bend a80 ft. rail to fit a 10 degree curve, its rniddlo ordinate should
<br />be .0012X900X2.183 or 2.36 inches.
<br />TABLE IIL Deflections for Sub Chords for Short Radius Curves.
<br />Degree
<br />of
<br />Curve
<br />--30°
<br />Radius
<br />50
<br />I A sub chord. sin of i def. angle
<br />Length
<br />for 100 ft.
<br />sin. 2' dcf. ang.
<br />12.5 Ft.
<br />15 Ft.'
<br />20 Ft.
<br />25 Ft.
<br />.6833
<br />193. IS
<br />1° 51'
<br />2° 17
<br />2° 58'
<br />3° 43'
<br />101.15
<br />320
<br />181.39
<br />1° 39'
<br />20 25'
<br />3° 10'
<br />3° 58'
<br />101.33
<br />34°
<br />17[.01
<br />2° 06'
<br />2° 33'
<br />3° 21'
<br />4° 12'
<br />101.48
<br />360
<br />161.8o
<br />2° �3
<br />2° 41
<br />3° 33'
<br />4° 26'
<br />104-66
<br />38°
<br />153.58
<br />2° 2o'
<br />2° 49'
<br />3° 44'
<br />4° 40'
<br />201.8;
<br />40°
<br />146. Ig
<br />2° 27'
<br />2° 57'
<br />3° 55'
<br />4° 54'
<br />102.06
<br />42°
<br />139.5'-
<br />2°.34'
<br />3° 05'
<br />4° 07'
<br />.5° 08
<br />102.29
<br />44°
<br />13347
<br />2° 41'
<br />3° 13
<br />4° 18'
<br />5° 22'
<br />10e..5.3
<br />460-
<br />127.97
<br />2° 48
<br />3 21'
<br />4° 29
<br />J36'
<br />IO2.76
<br />48°
<br />122.92
<br />2° 55,
<br />3° 29'
<br />4° 40
<br />S° 50'
<br />103.00
<br />50°
<br />118.31
<br />3° 02'
<br />3° 38
<br />4° 51
<br />6° 04'
<br />103.24
<br />52°
<br />114.06
<br />3° 09,
<br />3° 46,
<br />5° 02'
<br />6° 17
<br />I03.54
<br />54°
<br />110.11
<br />3° 16'
<br />3° 54
<br />5° 13
<br />6° 3 t'
<br />143 - 84
<br />56°
<br />106.1150
<br />3° 22
<br />4° 02'
<br />5° 23`
<br />G° 44`
<br />104' 14 ,
<br />58°
<br />1Q3,r4
<br />3° 29
<br />4° 10'
<br />5° 34'
<br />6-57'
<br />i 104-,43^
<br />60°
<br />100.00
<br />3° 35' 1
<br />4° k 8
<br />50 44'-
<br />1 70 11'
<br />ro_f_.7z
<br />I
<br />CURVE FORMULAS
<br />F= R tan It=I R= T cot. I chord=
<br />I _ 5o tan I 1 Chord def. _
<br />Sin. '-z D 50 R
<br />R -a
<br />Sin. ; D = �o Sin' a D No, chords = 1
<br />It C = R ex. secz I 17
<br />Sin. -,' D =Sot 1 ` I F., = T tan [ - 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 for a given distance and deflection.
<br />Rule i. Multiply the given distance by .01745 (def. for. 1 ° for I ft.
<br />see Table II.), and divide given deflection by the product.
<br />Rule 2. Multiply given deflection by 57.3, and.divide the prndrlct 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 loo, Alt. 10.102-
<br />. 200-.5. 100+.5 = 100-5 hyp.
<br />Given Hyp. loo, Alt. 25.252-200=3.125. l0o-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: multiply weight per yard
<br />by 1 1, and divide by 7.
<br />L L•'VELING. 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 />The correction for curvature alone is closely, dY. The combined cur-
<br />rcction is negative.
<br />PROBABLE ERROR. If d,, dz, da, etc. are the discrepancies of various
<br />results from the mean, and if EdQ=the sum of the squares of,diese differ-
<br />ences and n=the number of observations, then the probable error of the
<br />mean=Xdz
<br />10.6745 n(n-1)
<br />SOLAR EPEE\1ERls. Attention is called to the Solar Ephemeris for
<br />the current year, published by Keuffel & Esser Co., and furnished upon
<br />request. This handy booklet, 38x6 in., has about 190 pages of data very
<br />useful to the Surveyor; such as the adjustments of transits, levels and solar
<br />attachments; directions and tables for determining the meridian and the.
<br />latitude from observations on the sum and Polaris; stadia measurements;
<br />magnetic declination; arithmetic constants, etc.
<br />TA13LE IV.-1%Iinutes in Decimals of a Degree.
<br />11
<br />.0167
<br />11'
<br />1833
<br />21/
<br />..3,500
<br />31'
<br />.5167
<br />41'
<br />.6833
<br />51'
<br />.8500
<br />2
<br />.0333
<br />12
<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 />.0833
<br />15
<br />2.500
<br />25
<br />.4167
<br />35
<br />.3533
<br />45
<br />7:700
<br />65
<br />.+.1[67
<br />6
<br />.1000
<br />16
<br />.2667
<br />26
<br />.4333
<br />36
<br />.6000
<br />46
<br />.7067
<br />56
<br />.4333
<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 />18
<br />.3000
<br />26
<br />.4667
<br />36
<br />.6333
<br />48
<br />.8000
<br />58
<br />966-
<br />9
<br />.1500
<br />193167
<br />29
<br />.4833
<br />39
<br />.6500
<br />49
<br />.8I57
<br />59
<br />95:33
<br />10
<br />.1667
<br />20
<br />.3333
<br />30
<br />.5000
<br />40
<br />.6667
<br />50
<br />.8333
<br />60
<br />1.0000
<br />T.�m,[-. V. --Inches
<br />in Decimals of a Fool.
<br />1-16 3-32
<br />yi
<br />3-I6
<br />�4
<br />1
<br />5-16
<br />71
<br />s
<br />12
<br />.,50.52 .0078
<br />.0104
<br />.0156
<br />.0208
<br />.0260
<br />.0313
<br />I` .0417
<br />.0:121
<br />.0625
<br />.0729
<br />'
<br />1 2
<br />3
<br />�1
<br />.1
<br />I 6
<br />I 7
<br />j S
<br />9
<br />19
<br />L7
<br />.0533 .1667
<br />.'2500
<br />3333
<br />.-4167
<br />.5000
<br />55:33
<br />I 11667
<br />.7500
<br />.8353
<br />.9167
<br />
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