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TADLU IL - Radii, Ordinates and Deflections. Chord -100 ft.
<br />Deg.
<br />Radium
<br />Mid.
<br />Ord.
<br />Tan.
<br />Dist.
<br />Def•
<br />Dist.
<br />lfor
<br />1 Ft
<br />Aeg.
<br />Radius
<br />Mid.
<br />Ord.
<br />Tan
<br />Dist.
<br />•D€.•
<br />-Dist.
<br />Da'
<br />I Ft.
<br />2°.17'
<br />20 58'
<br />3° 43'
<br />for - 15
<br />320
<br />181.39
<br />t0 59'
<br />2° 25`
<br />3° 10'
<br />3° 58'
<br />101-33
<br />34°
<br />0°l0
<br />34377.
<br />.036
<br />.145.231
<br />4° 12'
<br />0.05
<br />7°
<br />819.0
<br />1.528
<br />6 105
<br />12.21
<br />2.1,0
<br />20
<br />17189.
<br />073
<br />.291
<br />.582
<br />0.10
<br />20'
<br />781.8
<br />1.600
<br />6.3955
<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
<br />6875.5
<br />.182
<br />.727
<br />1.454
<br />0.25
<br />S'
<br />716.8
<br />1.746
<br />6.976
<br />13.95
<br />2.40
<br />1
<br />5729.6
<br />.218
<br />.573
<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 />14.83
<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 />2.69
<br />30
<br />3919.8
<br />.327
<br />1.300
<br />2.618
<br />0.45
<br />9
<br />637.3
<br />1.965
<br />7.546
<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 />S.116
<br />16.27
<br />2.80
<br />50
<br />3123.4
<br />.400
<br />1.600
<br />3.200
<br />0.55
<br />30
<br />603.8
<br />2.074
<br />8.281
<br />1G. 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 />1.801
<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 />499.1
<br />2.511
<br />10.02
<br />20.04
<br />3.45
<br />50
<br />2022.4
<br />.61S
<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 />8
<br />1910.1
<br />.655
<br />2.618
<br />5.235
<br />0.90
<br />30
<br />459.3
<br />2.730
<br />10.S9
<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 />22.64.3.90
<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 />T.10
<br />30
<br />396.2
<br />3.168
<br />12. G2
<br />25.24
<br />4.35
<br />50
<br />1495.0
<br />.830
<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 />6.930
<br />1.20
<br />: 30
<br />370.8
<br />3.387
<br />13.49
<br />2G.97
<br />4.65
<br />10
<br />1375.4
<br />.909
<br />3.635
<br />7.2e71
<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
<br />348.5'3.606
<br />14.35
<br />23.70
<br />4.95
<br />30
<br />1273.6
<br />:982
<br />3:920
<br />7.852
<br />1.35
<br />17
<br />338.3
<br />3.716
<br />14.78
<br />29.56
<br />6.10
<br />40
<br />1228.1
<br />1.018
<br />4.071
<br />8.143
<br />1.40
<br />48
<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 />5.724
<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 />ill
<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 />9.596.1.65
<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 />6.476
<br />21.64
<br />43.28
<br />7.50
<br />e
<br />955.4
<br />1.309
<br />5.234
<br />10.47
<br />].SO
<br />26
<br />222.3
<br />5.697
<br />22.50
<br />4.1.99
<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 />5.918,23.35
<br />46.69
<br />8.10
<br />20
<br />905.1
<br />1.382
<br />5.b24
<br />11.05 '1.90
<br />28.
<br />206.7
<br />6.139
<br />24.19
<br />48.38
<br />8.40
<br />30
<br />S81'.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 />559.9
<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 cor(I of length (0) is equal to .0012 C'
<br />multiplied by the ((fiddle ordinate taken from the aboVoL table. Thns, if it
<br />desired to bend it 30 ft, rail to fit a 10 degree curve, its middle ordinate should
<br />be .0012X90OX2.183 or 2.36 inches.
<br />7TA71LE III. Deflections for Sub Chords for Short Radius Curves.
<br />Degree
<br />of
<br />Curve
<br />�.1
<br />Radius
<br />s0
<br />r5 sub chord _ sin of }def, angle
<br />H
<br />Length
<br />of arc
<br />for 100 ft.'
<br />sin, s def. ang.
<br />12,5 Ft.
<br />15 Ft.
<br />20 Ft.
<br />25 -Ft.
<br />.6833
<br />Ig3.18.
<br />I° 51'
<br />2°.17'
<br />20 58'
<br />3° 43'
<br />for - 15
<br />320
<br />181.39
<br />t0 59'
<br />2° 25`
<br />3° 10'
<br />3° 58'
<br />101-33
<br />34°
<br />171.01
<br />2° 06'
<br />2° 33'
<br />3° 2I'
<br />4° 12'
<br />101.48
<br />36°
<br />161-8o
<br />2° 13'
<br />2°41'
<br />3° 33'.
<br />4° 26'
<br />ioi.66
<br />380
<br />153.58
<br />z° 20'
<br />2° 49
<br />3,41"
<br />4° 40'
<br />l0t_8,i
<br />40° .
<br />146.19
<br />2° 27'
<br />2° 57'
<br />3° 55'
<br />4° 54
<br />Ioz.ob
<br />42'
<br />139.52
<br />2' 34'
<br />3° o5' .
<br />4° 07'
<br />5° 08
<br />102."29
<br />44°
<br />13347
<br />2° 413°
<br />13'
<br />4' 18'
<br />'5°-22'
<br />102.53
<br />460
<br />127.97
<br />2° 48.
<br />3°21'
<br />4° 29'.
<br />50 36'
<br />102.76
<br />48
<br />122.)2
<br />2° 55`
<br />3°29'
<br />4° 40'-
<br />5050'
<br />103.00.
<br />So°
<br />118.3'
<br />3' 02'
<br />3° 38'
<br />40 51'
<br />6° 04'
<br />103.24
<br />52'
<br />114,06
<br />3° 09'
<br />3° 46'
<br />5° 02'
<br />60 17'
<br />103..54
<br />54°
<br />110.11
<br />3° 16'
<br />3'-54'
<br />5° 13'
<br />6° 31'
<br />103.84
<br />g6°
<br />1o6.5o
<br />3°-22'
<br />4° 02'
<br />5° 23'
<br />6° 44
<br />104.14
<br />58°
<br />103.14
<br />3° 29�
<br />4° 10'
<br />S° 34
<br />6° 57
<br />104 43
<br />60°
<br />100.00
<br />3° 35'
<br />4° 18`
<br />5° 44'
<br />7° 11'
<br />10:1:72
<br />ix
<br />CURVE FORMULAS
<br />T= R tan ; E R T cot. I chords
<br />T r 5o fan a I Chord lief. _
<br />Sin. .'r D _5011
<br />Si., Z D No. chords = f
<br />lZ E= R ex. see e I D
<br />Sin. 2 D-
<br />go, l E = T tan 3 I Tan. def.,- 1 chord def.
<br />The square of any distance, divided bytwice 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 .o1745 (def. for I° for1 ft.
<br />see Table IL), and divide given deflection by the product.
<br />Rule 2. Multiply given defection by 57 .3, and divide the product by
<br />the given distance.
<br />To find deflection for a given angle and distance. Nlultiply the ankle
<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. Io.1oE 2oo=.5: loo+.5=too.,5 hyp.
<br />Given Hy -p. too, Alt. 25.25E-200=3.125.'ioo-3:125=o6.87a=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 />LEVELINri.' The correction for curvature and . refraction, in feet
<br />and decimals of feet is equal to 0.574dE; where d is the distance in miles.
<br />The correction for curvature alone is closely, 102. The -combined cor-
<br />rection is- negative.
<br />PRO13ABLF ERROR. If di, d2, da, etc. are the discrepancies of -various
<br />results from the mean, and if ZdE=the srim of the squares of these differ-
<br />ences and n -the number of observations, then the probable error of ,the
<br />mean= Ids
<br />O.t3745 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 uion
<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 tahles for determining the meridian and Clic
<br />latitude from observations on the sun and Polaris; stadia measurements;
<br />magnetic declination; arithmetic constants, etc.
<br />TABLE IV. -Minutes in Decimals ofa Degree.
<br />1
<br />.0167
<br />HP
<br />.1833
<br />21+
<br />.3500
<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 />50933
<br />15
<br />.2500
<br />25
<br />.4167
<br />35
<br />.5833
<br />45
<br />.7800
<br />55
<br />.!1167
<br />6
<br />.1600
<br />16
<br />.26(17
<br />26.4333
<br />36
<br />.6000
<br />46
<br />.7067
<br />56
<br />.0333
<br />7
<br />1167
<br />17
<br />2833
<br />2 7
<br />A50
<br />37.7533
<br />57
<br />8
<br />.1333
<br />IS
<br />5000
<br />28
<br />4667
<br />38
<br />.6333
<br />48
<br />.8000
<br />58
<br />.9657
<br />9:1667-'..
<br />1500.
<br />19
<br />.3167
<br />29
<br />.4833'
<br />39
<br />.6500
<br />49
<br />.816-159
<br />.9833
<br />10
<br />.1667
<br />20
<br />.3333
<br />30
<br />.5000
<br />40
<br />.6667 1
<br />50
<br />.8333
<br />60
<br />1.0000
<br />1 ani,[t %'.--Inches in Decimals of a Foot.
<br />1-16
<br />3-32
<br />y9
<br />3-16
<br />i,�
<br />;-16
<br />.6052
<br />.0078 1
<br />.0101
<br />.0208
<br />.o2s0
<br />.0313
<br />I .O3E7
<br />I.05z1
<br />.os2.;
<br />.oY'z0
<br />-1
<br />'? I
<br />�_.oiss
<br />3
<br />4
<br />:i
<br />G
<br />7
<br />111 S
<br />L 9
<br />I
<br />10
<br />11
<br />0833
<br />.166T
<br />.2500
<br />.3333
<br />.4167
<br />,U00
<br />.5833
<br />.6667
<br />.7500
<br />.8513
<br />91t;7
<br />
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