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VIII IX
<br />TABLE IL - Radii, Ordinates and Deflections. Chord =100 ft. CURVE FORMULAS
<br />Deg
<br />Radius
<br />Mid.
<br />Ord
<br />Tan.
<br />Dist.
<br />Def.
<br />Dist.
<br />De
<br />1 Ft's
<br />12.5. Ft.
<br />15 Ft.
<br />Mid •
<br />Ord.Dist
<br />Tan
<br />Def.
<br />Def
<br />for
<br />I Ft.
<br />1°
<br />51'
<br />2°
<br />17'
<br />2°
<br />58'
<br />30
<br />43'..
<br />t
<br />,32';
<br />t.
<br />,
<br />I
<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 />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 />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 />1.637
<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'r
<br />6875:5
<br />".188
<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 />1.819
<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 />x,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 />2.60
<br />3.0,.
<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 />15.69
<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 />8.136
<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 />1 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 />546.4
<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
<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 />20.91
<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.,.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 />425.4
<br />2.049
<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 />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
<br />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 />1.30.
<br />30.348.5
<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 />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 />5.035
<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
<br />7.50
<br />0
<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 />45.38
<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 />30
<br />193.2
<br />6.583
<br />25.88
<br />51.76
<br />9.00
<br />The middle ordinate }"n inches for any cord of length (0) is equal to .0012 C'
<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 />sin. z def. ang.
<br />111
<br />sub chord =sin
<br />R
<br />of $ def. angle
<br />Length
<br />of arc
<br />for 100 ft.
<br />12.5. Ft.
<br />15 Ft.
<br />20 Ft. '.
<br />25 Ft.
<br />30°
<br />193. 8
<br />1°
<br />51'
<br />2°
<br />17'
<br />2°
<br />58'
<br />30
<br />43'..
<br />101.15
<br />,32';
<br />. _39 ..
<br />x•181.'
<br />,
<br />I
<br />59,
<br />_ °
<br />2
<br />2 5, .
<br />3°.
<br />,. _ ...
<br />IO
<br />3°
<br />58' `
<br />-
<br />101.33
<br />34°
<br />171.0I
<br />2°
<br />o6'
<br />2°
<br />33'
<br />3°
<br />21'
<br />4°
<br />12'
<br />101.48
<br />360
<br />161.$0 _:•
<br />2°
<br />13'
<br />20
<br />41'
<br />3°
<br />33''
<br />4°
<br />26'
<br />ioi.66
<br />3$°
<br />153. 58
<br />2°
<br />20'
<br />2°
<br />49
<br />3°
<br />44'
<br />4°
<br />40
<br />101.85
<br />40° .`'146.19.
<br />_
<br />•-2°
<br />27'.
<br />2°
<br />57'
<br />.:3°
<br />55'
<br />4°
<br />54'
<br />102.o6
<br />42°: •
<br />. 139x52
<br />2°
<br />34'.
<br />3°.05'
<br />.7833
<br />4°
<br />07''
<br />5°
<br />08
<br />102.29
<br />.44'
<br />133.47
<br />2°
<br />41,
<br />3°
<br />13'
<br />4°
<br />18'
<br />5°
<br />22'
<br />102.53
<br />,46o
<br />' "127.97
<br />2°'48'
<br />.4833
<br />3°
<br />21'
<br />4°
<br />29'
<br />5°
<br />36'
<br />102.76 .
<br />48°
<br />122.9? '
<br />?°
<br />55'
<br />3°
<br />29'
<br />.4°
<br />40
<br />5°
<br />50'
<br />103.00
<br />50°:'
<br />._.:118.31 -
<br />30.02'
<br />3°
<br />38'
<br />4°
<br />51'
<br />6°
<br />04'
<br />103.24
<br />°
<br />5? :..:
<br />i i o6 `
<br />4•
<br />3'.69'
<br />3°.46
<br />5°
<br />oz'
<br />6°
<br />17'
<br />103.54
<br />X54°; :
<br />140.11
<br />3°
<br />16'
<br />3°
<br />54'
<br />5°
<br />13'
<br />6°
<br />31'
<br />103.84
<br />_x56° '.
<br />:io6.56
<br />30
<br />22'
<br />t
<br />O2,
<br />5°
<br />23,.
<br />6°
<br />44'
<br />104.14
<br />58'.
<br />10-3-.14.-
<br />30
<br />29'
<br />4°
<br />Io'
<br />150
<br />34'
<br />60
<br />57'
<br />,104.43
<br />60°
<br />100:00 - ..
<br />3°
<br />35'
<br />4°
<br />18'
<br />S°,44�
<br />7°
<br />ii'
<br />104.7z
<br />T= R tan 211 R= T cot. -' I chord'
<br />__ 5o tan 22 -I 2 Chord def. _
<br />T Sin. 2 D R= 50 R
<br />a
<br />Sin. s D = 50 Sin. , D No. chords = I
<br />R. E R ex. sec I D
<br />Sin. Z D- 50 tT 2 I E = T tan } I Tan. def. = -2 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 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. Acid quotient to base for hypotenuse. �'
<br />Given Base loo, Alt. 10.102_200=.5. 100+:5=100.5 hyp•
<br />Given Hyp. loo, Alt. 25.252=200=3.][25. IOO-3.125=86.875=13ase.
<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, ;d2. The combined cor-
<br />rection is negative.-
<br />PROBABLE
<br />egative.PROBABLE ERROR. If dl, d2, d3, 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 />meanids
<br />10.6745 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, 31x6 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.
<br />TABLE IV. -Minutes in Decimals of a Degree.
<br />1t
<br />.0167
<br />111
<br />.1833
<br />21'
<br />.3500
<br />31'
<br />.5167
<br />41'
<br />.6833
<br />511
<br />.8500
<br />2
<br />12
<br />.2000
<br />22
<br />.3667
<br />32
<br />.5333
<br />42
<br />.7000
<br />52
<br />.8667
<br />3
<br />.0333
<br />13
<br />.2167
<br />23
<br />.3833
<br />33
<br />.5500
<br />43
<br />.7167
<br />53
<br />.8833-
<br />4
<br />.0500
<br />14
<br />.2333
<br />24
<br />.4000
<br />34
<br />.5667
<br />44
<br />.7333
<br />54
<br />.9000
<br />5
<br />.0667
<br />.0833
<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 />.9333
<br />7
<br />17
<br />.2833
<br />27
<br />.4500
<br />37
<br />.6167
<br />47
<br />.7833
<br />57
<br />.9500
<br />8
<br />.1167'
<br />.1333
<br />18
<br />.3000
<br />28
<br />.4667
<br />38
<br />.6333
<br />48
<br />.8000
<br />58
<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 />.9833
<br />10
<br />1 .1667 11
<br />20
<br />1 .3333 11
<br />30
<br />1 5000 11
<br />40
<br />1 .6667
<br />50
<br />.8333
<br />60
<br />1.0000
<br />TABLE V. -Inches
<br />in Decimals of a Foot.
<br />•1-163-32
<br />Ye
<br />3-16
<br />%
<br />5 -16
<br />%
<br />'/•a
<br />.0052
<br />.0104
<br />.056
<br />.0208
<br />I .02660
<br />.0313,
<br />.04817.
<br />.0521
<br />.06225
<br />"0119
<br />,,.0078 I
<br />3
<br />4
<br />I
<br />I
<br />I
<br />10
<br />I
<br />.083 3 .1667
<br />.2500
<br />.3333
<br />.4167
<br />.5000
<br />.5833.
<br />.6667
<br />.7500
<br />.8333.
<br />.9167
<br />
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