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VIII
<br />TAnLn IL - Radii, Ordinates and Deflections. Chord -100 ft.
<br />Deg.
<br />Radius
<br />Mid.
<br />old.
<br />Tan,
<br />Dist,
<br />Def,
<br />Dist.
<br />De'
<br />IIPt
<br />Deg.
<br />Radius
<br />Mid
<br />Ord.
<br />Tan
<br />Dist.
<br />Def.
<br />Dist.
<br />Def,
<br />for
<br />193.18 '
<br />10 51'
<br />2°° 17'
<br />2° 58'
<br />3° 43'
<br />IOL. 15
<br />3z°
<br />151.39
<br />I° 59'
<br />2 25'
<br />3° 10'
<br />3° 58'
<br />0'10'
<br />34377.
<br />.036
<br />.145
<br />.291
<br />0.05
<br />7°
<br />819.0
<br />1.528
<br />,6.105
<br />121.21
<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 />.436
<br />.873
<br />0.15
<br />30
<br />764.5
<br />1.537
<br />6.540
<br />13.08
<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 />6.685
<br />13.37
<br />2.30
<br />50
<br />6875.5
<br />.182
<br />.727
<br />1.454
<br />0.25
<br />8
<br />716.5
<br />1.746
<br />6.976
<br />13.95
<br />2.40
<br />1
<br />5720.6
<br />.218
<br />.873
<br />1.745
<br />0.30
<br />20
<br />638.2
<br />1.819
<br />7.266
<br />14.53
<br />2.b0
<br />10
<br />4911.2
<br />.255
<br />1.018
<br />2.036
<br />0.35
<br />30
<br />674.7
<br />1.855
<br />7.411
<br />14.82
<br />2.15
<br />20
<br />4297.3
<br />.291
<br />1.164
<br />2.327
<br />0.40
<br />40
<br />661..7
<br />1.992
<br />7.556
<br />15.11
<br />2. Go
<br />30
<br />3819.8
<br />.327
<br />1.309
<br />2.615
<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 />31.25.4
<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 />.435
<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 />.4731.891
<br />3.781
<br />0,G5
<br />10
<br />573.7
<br />2.183
<br />8.716
<br />L7.43
<br />3.00
<br />20
<br />2355.7
<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. la
<br />a0
<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 />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 />8
<br />1910.1
<br />.65.5
<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 />5.817
<br />1.00
<br />30
<br />430.4
<br />2.949
<br />11.75
<br />23.51
<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 />12.15
<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 />.836
<br />3.345
<br />6.689
<br />1.15
<br />15
<br />333.1
<br />3.277
<br />13.05
<br />26.11
<br />4.50
<br />4
<br />1132.7
<br />.873
<br />3.490
<br />6.950
<br />1.20
<br />30
<br />370.8
<br />3.387
<br />13.49
<br />26.97
<br />4.63
<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 />27.54
<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 />4.93
<br />30
<br />1273.6
<br />.982
<br />3.926
<br />7,852
<br />1.35
<br />17
<br />338.3,3.716
<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 />19
<br />319.6
<br />3.035
<br />15.64
<br />31.29
<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 />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 />13,305
<br />1.60
<br />22
<br />262.0
<br />4.814
<br />10.0S-
<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 />9.686
<br />1.70
<br />24
<br />240,5
<br />5.255
<br />20.79 '41.58
<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
<br />43.28
<br />7.50
<br />6
<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 />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 />6.139
<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 />6.360
<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 />1 30
<br />193.2
<br />6.583
<br />25.88
<br />51.76,9-00
<br />The middle ordinate'}n inches for any cord of length (C) is equal to .0012 C'
<br />multiplied by the muddle ordinata 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 .0012X909X2.183 or 2.36 inches.
<br />TABLE III. Deflections for Sub Chords for Short Radius Curves.
<br />Degree
<br />of
<br />Radius
<br />50
<br />lis sub chord = sin of def, angle
<br />R '
<br />Length
<br />-of arc
<br />Curve
<br />sin. I def. ang.
<br />L2,5 Ft.
<br />15 Ft.
<br />20 Ft.
<br />25 Ft.
<br />for 100 ft.
<br />300
<br />193.18 '
<br />10 51'
<br />2°° 17'
<br />2° 58'
<br />3° 43'
<br />IOL. 15
<br />3z°
<br />151.39
<br />I° 59'
<br />2 25'
<br />3° 10'
<br />3° 58'
<br />161.33
<br />340
<br />171.01
<br />2° o6'
<br />2° 33'
<br />3° 21'
<br />4° I2'
<br />101 .48
<br />360
<br />161.So
<br />2° 13`
<br />2° 41'
<br />30 33'.
<br />4° 26'
<br />1,)1.66
<br />38°
<br />153.58
<br />2° 20'
<br />2° 49'
<br />3° 44'
<br />4° 40'
<br />lot. S,;
<br />40°
<br />146.ig
<br />2° 27'
<br />20 57'
<br />3° 55`
<br />4 54'
<br />1o2.06
<br />42°
<br />134.52
<br />2° 34'•
<br />3° 05
<br />4° 07
<br />3° 08
<br />102.29
<br />440
<br />133.47
<br />2° 41
<br />3° 13
<br />4° IS'
<br />5° 22'
<br />102.53
<br />46°
<br />127.97
<br />2° 48
<br />3° 21'
<br />4.° 29'
<br />5° 3('
<br />102.76
<br />480
<br />122.92
<br />2° 55
<br />3° 29'
<br />4° 40
<br />S° 50'
<br />103.°0
<br />50°
<br />118.31
<br />30 02
<br />30 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 />103.54
<br />540
<br />110.11
<br />3° 16'
<br />3° 54'
<br />5° 13'
<br />6-31
<br />103.84
<br />56°
<br />1-06,50
<br />3° 22'
<br />4 02'
<br />5° 23'
<br />6° 44
<br />104.14.
<br />58°
<br />103.,t4
<br />3° 29'
<br />4° 10'
<br />S° 34'
<br />6° 57'
<br />104.43
<br />6o°
<br />11'
<br />1oo.,00
<br />3° 35°.
<br />4 IS
<br />5° 44'
<br />7°
<br />104 72
<br />IR
<br />CURVE FORMULAS
<br />_R tan t
<br />50 tan lII R = T cot. ' I chord'
<br />Chord def. = R .
<br />Sin. -11) 50
<br />R T
<br />Sin, z D = 5° Sin. . D No, chords =
<br />R E = R ex. sec I
<br />Sin. l L) = 90 t`111 1 G T tan I Tan. def. = s chord def.
<br />T
<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 (clef. for I' for 1. ft.
<br />see Table I1.), and divide given deflection by the product.
<br />Rule 2. Multiply given deflection by 57.3, and divide the pi oduct 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_200=.5. 100+,5=100.,5 hyp.
<br />Given Hyp. loo, Alt. 25.2,92=200=3.125. 100-3.125=96.875=13ase.
<br />Error in first example, .002; in last, .o45.
<br />To find Tons of Rail in one mile of trach: multiply, weight per yard
<br />by 11, and divide by 7.
<br />LEVELING. The correction for curvafure and refractip, in feet
<br />and decimals of feet is equal to 0.574d2, where d is the distance in miies.
<br />The correction for curvature alone is closely, ,d2. The combined cor-
<br />rection is negative.
<br />PROBABLE ERROR. If d1, d2, d$, etc. are the discrepancies of various
<br />results from the mean, and if Ids =the sum of the squares of these differ-
<br />ences and n=the number of observations, then the probable error of the
<br />Wean = gd2
<br />-0.6745 n(n-1)
<br />SOLAR EPHENIERis. Attention is called to the Solar Ephemeris for
<br />the current year, published by Keuffel & Esser Co., and furnished upon
<br />request. This handy booklet, 3$x6 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 sun and Polaris; stadia measurements;
<br />magnetic declination; arithmetic constants, etc. h
<br />TABLE IV. -Minutes in Decimals of a Degree.
<br />If .0167 11 .1833 210
<br />Trott'. 1'. --Inches in Decimals of a hoot.
<br />1-16
<br />.3500
<br />3t
<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 />2600
<br />26
<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 />n333
<br />7
<br />.1167
<br />17
<br />.2833
<br />29
<br />.4500
<br />37
<br />.6167
<br />47
<br />.7833
<br />57
<br />.9500
<br />8
<br />.1333
<br />18
<br />.3000
<br />28
<br />4667
<br />38
<br />.6333
<br />48
<br />.8000
<br />59
<br />.9667
<br />9
<br />.1500
<br />19
<br />.3167
<br />29
<br />.4833
<br />39
<br />6500
<br />49
<br />.8167
<br />59
<br />.9$33
<br />10 1
<br />1667 11
<br />20
<br />1 3333 11
<br />30
<br />1 .5000 11
<br />40
<br />1 .6667 11
<br />50
<br />.8333 11
<br />Be
<br />11,0000
<br />Trott'. 1'. --Inches in Decimals of a hoot.
<br />1-16
<br />3-32
<br />ye
<br />3-16
<br />SS
<br />5-16
<br />5''
<br />I V4
<br />A
<br />0052
<br />.0078
<br />.0104
<br />.0156
<br />.0208
<br />.0260
<br />.0313
<br />0521
<br />1 .0625
<br />.0720
<br />1
<br />3
<br />4
<br />,
<br />I
<br />6
<br />I
<br />,
<br />917,,,
<br />.0833
<br />.0833
<br />I
<br />•1667
<br />.1667
<br />.2.500
<br />.2.500
<br />I! .3333
<br />.3333
<br />.4167
<br />.4167
<br />;,000
<br />,,00a
<br />5833
<br />.5333
<br />.7500,3333
<br />.9167.9167
<br />
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