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VIII IX
<br />TABLE IL - Radii, Ordinates and Deflections. Chord =100 ft. CURVE FORMULAS
<br />Mid Tan. Def." .
<br />Deg.
<br />Radius*
<br />Ord
<br />Dist.
<br />Dist.
<br />Dd.
<br />for
<br />1 Ft._
<br />_
<br />mus
<br />Arid.
<br />�
<br />Tan
<br />Dist.
<br />Def.
<br />Dist.
<br />Def.
<br />]f r
<br />2° 17'
<br />2° 5s''-
<br />t.
<br />IO I.i5
<br />320
<br />181-39
<br />10 59'
<br />t,
<br />t.
<br />t:
<br />t.
<br />34°
<br />0"10'
<br />34377.
<br />.036
<br />:145
<br />.291
<br />0.05
<br />.' V
<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 />16.395
<br />12.79
<br />2.20
<br />30'11459.
<br />4° 54',
<br />.109
<br />.436
<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 />.582
<br />..14164
<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
<br />0.25
<br />8
<br />716.8
<br />1.746
<br />6.976
<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 />11819
<br />7.266
<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
<br />1.855
<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 />15.11'2.60
<br />7"11'
<br />30
<br />3819.8
<br />.327
<br />1.300
<br />2;618
<br />0.45
<br />637.3.1:965,
<br />7.846
<br />15.69
<br />2.70
<br />40
<br />3437.9
<br />.364
<br />1.454
<br />2:909
<br />0.50
<br />.9
<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
<br />16.56
<br />2.85
<br />2
<br />2364.9
<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 />2155.7
<br />.5092,036
<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 />499.1'2.511
<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 />20.91
<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 />Q.eS
<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 />425.4
<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 />12.18
<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 />.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 />6.980
<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 />16
<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 />7:561
<br />1.36-
<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 />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
<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 />: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 />5.035
<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 />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 />43.28.7.50
<br />8,
<br />955.4
<br />1.309
<br />5.234
<br />10.47
<br />1.80
<br />222.3
<br />5.697-22.50
<br />44.99
<br />7.80
<br />10
<br />929.6
<br />1.346
<br />5.379
<br />10.76
<br />1.85
<br />,26
<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 />14.63
<br />2.00
<br />30
<br />193.2
<br />6.583
<br />25.88
<br />51.76
<br />9.00
<br />The middle ordinate }'n inches for any cora of length (Q) is equal to .0012 0'
<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 />50
<br />� sub chord _sin of } def. angle
<br />R
<br />Length
<br />of arc
<br />for 100 ft.
<br />sin. s def, ang.
<br />12.5 Ft.
<br />15 Ft.
<br />20 Ft. i
<br />25 Ft.
<br />30°193.18
<br />..
<br />51'
<br />1° 51'
<br />2° 17'
<br />2° 5s''-
<br />30 .43'
<br />.3°
<br />IO I.i5
<br />320
<br />181-39
<br />10 59'
<br />z° 25'
<br />3° 10,
<br />58,
<br />101.33
<br />34°
<br />171.01
<br />2° 06'
<br />2° 33'
<br />3° 21'
<br />4° 12'
<br />101.48
<br />36°
<br />161. 86
<br />2° 13'
<br />20 41'
<br />3° 33' .
<br />' 4' z6'
<br />fof .66
<br />380
<br />153.•58
<br />2°20'
<br />2° 49'
<br />3°44'
<br />4° 40'
<br />for. 8j
<br />40°
<br />146. f9
<br />2° 27'
<br />2° 57'
<br />3° 55'•
<br />4° 54',
<br />IO2.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 />20 41
<br />3° 13'
<br />4° 18'5°
<br />22'
<br />102.53
<br />.4500
<br />127,97
<br />2° 48'
<br />3° 21'
<br />4° 29'S°
<br />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 />IIS -31
<br />3° 02'
<br />3° 38' • .'
<br />4° SI'
<br />6°.04'
<br />103.24
<br />:52?
<br />114-06
<br />3° 09'
<br />3° 46'-.
<br />5° O2,•
<br />6° 17,
<br />103.54.
<br />54°.
<br />Ila 11
<br />3° t6'
<br />3°. 54'
<br />5° 13'
<br />6° 31'
<br />103, SC
<br />'560
<br />1 1o6.50
<br />3°,22'
<br />4° 02'
<br />5° 23'
<br />60:414'
<br />104.. 14
<br />'580
<br />i 103-1 ' 4
<br />30 29'
<br />4° lo'
<br />5° 34
<br />6°• 57' ,
<br />-104.43
<br />6o° -
<br />100.0
<br />3° 35'
<br />40 18'
<br />5° 44'
<br />7"11'
<br />104.72
<br />T= R tan -2' I R. _ .T cot. z I chord'
<br />T so. tart z I Chord"def. R
<br />Sit].Ill __ 50
<br />1 50 R' Sin. z D No. chords = I
<br />Sin. a .D = 2Z,
<br />E = Rex. sec z I D
<br />Sin: z. D, = 50 tan s I E,= T tan I I Tan. def. = s 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 I° for I ft.
<br />see Table IL); 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 fora -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. 10,102=200=.5. Ioo-1-.5=Ioo.S hyp.
<br />Given Hyp. Ioo, Alt. 25.25'=200=3.125. 100-3.125=86.875=Base.
<br />Error in first example, .002; in last, .045.
<br />To find Tons of Rail in one mile of track: multiply weight per yard
<br />by I I, and divide by 7.
<br />..LEVELING., 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, 8d?. The combined cor-
<br />rection is negative.
<br />..PROBABLE ERROR. If d,, d2, d,, etc. are the discrepancies of various
<br />results from the mean, and if Ede=the sum of the squares of these differ-
<br />ences and'n=the number of observations, then the.. probable error of the
<br />mean id'
<br />0.6745 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 upon
<br />request. This handy booklet, 38x6 in., has about 1130 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.
<br />- 'P -.v TV -Minutes in Decimals of a Degree.
<br />1
<br />.0167 •
<br />11' ✓-.1833
<br />in Decimals of a Foot.
<br />21'
<br />.3500 -
<br />31' ,
<br />.5167
<br />41 f
<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 />53
<br />.8667
<br />-3
<br />.0500
<br />13 •
<br />.2167
<br />23
<br />24
<br />.3833
<br />33
<br />34
<br />.5500
<br />43
<br />44
<br />.7167
<br />.7333
<br />54
<br />.8833
<br />.9000
<br />4
<br />5.
<br />.0667
<br />14
<br />15
<br />.2333
<br />25
<br />•.4000
<br />.4167
<br />35
<br />.5667
<br />.5833
<br />45
<br />.7500
<br />55
<br />.9167
<br />6,
<br />.0833
<br />.1000
<br />16
<br />.2500
<br />.2667
<br />26
<br />.4333
<br />36
<br />.6000
<br />46
<br />.7667
<br />56
<br />57
<br />.9333
<br />7
<br />.1167
<br />17
<br />.2833
<br />27
<br />.4500
<br />37
<br />.6167
<br />47.
<br />.7833
<br />58
<br />.9500
<br />8
<br />_:1333
<br />18
<br />.3000
<br />28
<br />.4667
<br />38
<br />39
<br />.6333
<br />48
<br />49
<br />.8000
<br />8167
<br />59
<br />.9667
<br />.9833
<br />9
<br />10.
<br />.1500
<br />.1667
<br />19
<br />20
<br />.3167
<br />.3333
<br />29
<br />30
<br />.4833
<br />.5000
<br />40
<br />.6500
<br />' .6667
<br />50 '
<br />.8333
<br />60
<br />1.0000.
<br />TABLE V. --Inches
<br />in Decimals of a Foot.
<br />1-16
<br />„0052
<br />.0078
<br />.0104
<br />3-16
<br />.0156
<br />'/s
<br />.0208
<br />5-16
<br />.0260
<br />.0313
<br />.0417
<br />I .0521
<br />0625 I
<br />.0729
<br />�3-32
<br />1
<br />.0833
<br />2
<br />.1667 12500
<br />3
<br />4
<br />.3333
<br />5
<br />I ..4167
<br />0
<br />I ..5000
<br />7
<br />.5833 ,
<br />8
<br />.6667
<br />9
<br />.7500
<br />10
<br />.8333
<br />11
<br />.9167 '
<br />
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