|
VIII ..• _,... . . „",
<br />TABLE IL - Radii, Ordinates aIid. Deflections. Chord -100 ft.
<br />iDeg,..
<br />Radius
<br />Ord
<br />Det
<br />D st.`!
<br />Def.
<br />for^'^
<br />1 Ft.
<br />"Deg.
<br />Radius
<br />Mid.
<br />Ord.
<br />Tan. .
<br />'.Det.
<br />Def.
<br />Dist.
<br />Dor.
<br />YR.
<br />193:18
<br />191.-39-
<br />1° 51'
<br />=.036
<br />-:J45
<br />.291
<br />O.b5'
<br />- 7.
<br />819.0
<br />1.528
<br />16 105
<br />12.21
<br />2.10
<br />20
<br />17189...
<br />?.073
<br />.291
<br />'; :582
<br />0.10 '
<br />--* 201
<br />781.8
<br />1:600
<br />6:395
<br />12.792.20
<br />• 20-41';
<br />:-30;
<br />114'59.:
<br />:.109
<br />.436
<br />v .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 />,'
<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 />716.8
<br />1!746
<br />6.976
<br />13.95
<br />2.40
<br />..5° 36.�
<br />-5729:6
<br />•.218
<br />.873
<br />'1:745
<br />0.30
<br />20
<br />688.2
<br />1:819
<br />50..
<br />14:53
<br />2.50
<br />10
<br />4911.2
<br />.255
<br />1.0I8
<br />2.036
<br />0.35
<br />130
<br />674.7
<br />1.855
<br />,7:266
<br />X7.411
<br />14,82
<br />2.55
<br />20::4297.3
<br />:.3° 16'
<br />.201
<br />1:164
<br />-2;327
<br />0.40,,,,.;
<br />40
<br />661.7
<br />1.-892
<br />7.556.15.11
<br />. 5° 23
<br />2:60
<br />30;`3819.8
<br />'5
<br />..327
<br />1:309,
<br />:2:618
<br />0.45,:Y9(
<br />6°'57'
<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 />.26.*614.6
<br />2:037.
<br />-16.27
<br />2.80
<br />50.
<br />3125.4
<br />1.400
<br />1.600
<br />3.200
<br />0 551
<br />30,
<br />603.8
<br />2:074
<br />.8.136
<br />:8.281
<br />16.56
<br />2.85
<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'=2644:6
<br />3
<br />'.47'183
<br />1.891
<br />3.781
<br />0.65
<br />10
<br />573.7
<br />2.
<br />3:716
<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 />18.303.15
<br />30
<br />2292,0
<br />.545
<br />2.181
<br />4.363
<br />0.75
<br />IV
<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 />-.6182.472
<br />,4.945
<br />0.85 ':12_
<br />,
<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 />15.235
<br />0.90
<br />' i 30'
<br />459.3
<br />2.730
<br />10.89
<br />21:77
<br />3.75
<br />.10
<br />1809:'6"-.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 />2.949
<br />11.75
<br />23.51
<br />4.05
<br />.30':16373
<br />-.764
<br />3.054
<br />6.108
<br />1.05:
<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 />.14;
<br />30
<br />396.2
<br />3.168
<br />12.62
<br />25:24
<br />4.35
<br />50,.1498.0,
<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 />1432:7,
<br />-,873
<br />3`.490
<br />6.980'1.20-
<br />30.370.8
<br />3.38T
<br />13.49.'26.97
<br />4.65
<br />I0
<br />" 1375.4
<br />:.909'$.635
<br />7.271
<br />1.25
<br />-10
<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 />!30348.5
<br />3.606
<br />14.35
<br />28.70
<br />4.95
<br />30
<br />: 1273..G
<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 />1.018:4.071
<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 />4.455
<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 />10-1109.3
<br />1.427
<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 />,1074:7.1.164,4:653
<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.::1042;1
<br />1.20
<br />4.798
<br />9.596
<br />1.6•,•
<br />23
<br />250.8
<br />5.035
<br />19.94 .39.87
<br />6.90
<br />6•.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 .41.58
<br />7.20
<br />50•
<br />.982',6
<br />1:273'5.088
<br />10'.18.
<br />1.75"
<br />25
<br />231.0
<br />5.476
<br />21.64
<br />43.28
<br />7.50
<br />8"'
<br />956:4
<br />1:30
<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 />1.348
<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 />5524
<br />1105
<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 />1.41815:669111:34
<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 1
<br />30
<br />193.2
<br />6.583
<br />25.88
<br />51.76
<br />9.00
<br />The middle ordinate in inches for any , ord of length (0) is equal to 0012 0'
<br />multiplied by the middle ordinate take.. from the above table. Thus, if it
<br />desired to bend a 30 ft.
<br />rail to fit a 10 degree curve, its middle ordinate should
<br />be .0012X900X2.183 or 2.36 inches. ,
<br />TABLE TIL ! Deflections for Sub Chords for Short Radius Curves.
<br />Degree
<br />of
<br />` Radius
<br />50 !
<br />r/%i sub chord
<br />R = sin of Idef. angle
<br />Length
<br />of arc
<br />Curve
<br />sin, i def. ang•
<br />12.5. Ft.
<br />15 Ft.
<br />20 Ft. r
<br />25 Ft.
<br />for 100 ft.
<br />30°
<br />193:18
<br />191.-39-
<br />1° 51'
<br />_ 2° 17'
<br />2° 58';
<br />3° 43'
<br />101.15
<br />32°.-
<br />.5333
<br />42
<br />2, 25'`-
<br />.._3"1o'-_..._3°
<br />58,
<br />101:33
<br />340
<br />171,01
<br />2° o6'
<br />2° 33'
<br />30 21'
<br />40 12'
<br />101.49
<br />360
<br />i161 -AO ,'
<br />.29 13'::.
<br />• 20-41';
<br />' - 3° 33" -'
<br />.. 4° 26..
<br />_ '101.66
<br />380
<br />24
<br />20;....,_2o.
<br />49�
<br />30,44',....40.46'
<br />-
<br />101.85 .. ,
<br />,40
<br />.
<br />146 .i9
<br />..--20
<br />2 .27
<br />.,
<br />2 57- -
<br />3. 55- .
<br />-4 54
<br />-
<br />162:o6
<br />4?°
<br />s.139 52
<br />,° 341
<br />3° 05'
<br />4° 07''
<br />5° o8.
<br />102,29..
<br />_
<br />X44-°'
<br />'133.47
<br />a� 41,
<br />; 3° i3'
<br />..
<br />4° 18'''S°_2z'
<br />.4333
<br />36
<br />69
<br />= 127,97
<br />2- 48' '
<br />_e 21:;
<br />_4°•29
<br />..5° 36.�
<br />"_10276
<br />' 17 :..2833
<br />"
<br />?0 55�
<br />30 z9y:
<br />40 40''.;
<br />50'So� .
<br />'. 103:.00
<br />50..
<br />118 '31
<br />3002 '
<br />3 38
<br />4 51_
<br />6-4
<br />.103.24
<br />52°; i.
<br />.' it ..o6:
<br />3' 09'
<br />� 3° 46'
<br />5° oz':
<br />6° 17,
<br />103 54'
<br />54° :
<br />-110:11
<br />:.3° 16'
<br />3° 54�
<br />5i3'
<br />Vi,
<br />6°;31`
<br />103.84
<br />,--56-
<br />106-50
<br />30.12'
<br />4° 02,...
<br />. 5° 23
<br />6°'44!
<br />104.14-
<br />'5
<br />.:' 103.;14 '
<br />3° 29'
<br />4° 10' ..
<br />" 5° 34'..
<br />6°'57'
<br />'-.104•.43
<br />6e' ,,
<br />:16o;0o
<br />3°.35'
<br />4° i8'
<br />5°_441
<br />7°.111
<br />--104-72
<br />CURVE FORMULAS '. IX
<br />T R tan 2 I R= T cot. Z I chord= W
<br />T _.So tan 12A Chord def. ..R.. ^.
<br />Sin. I D R = 50
<br />Sin. -r2 D = 50 . Sin. all No. chords = I
<br />R- E = R ex. sec a I, D
<br />Siri. Z D = 5O t T ?.I E = T tan } I' Tan.'def. _, a ehord def.
<br />The square of any distance, divided by twice the radius, will equal
<br />4he-distance from tangent to'curve, very nearly.
<br />-To find angle fora given distance and deflection.
<br />Rule,i. Multiply the given distance by .61745 (def.=ford°-for i ft
<br />see Table II.), and divide given deflection by theproduct.
<br />Rule -2. Multiply givenL deflection by 57.3, and divide the productliy
<br />the given distance.
<br />To find deflection', fora given angle and distance. Multiply,the angle
<br />by .oi745, and the product by the distance.
<br />-GENERAL DATA_
<br />RIGHT ANGLE -TRIANGLES.' ,Square the. altitude, divide, by1wice the
<br />base. 'Add quotient to base for hypotenuse.
<br />Given Base loo, Alt.10"102_200=.5.-IOO+-5=IOo.5 hyp.
<br />`Given Hyp. loo, Alt: 25.252- 200=3.125. 100-3.125=96.875=Base.
<br />Error in first example, .002; in last, .045..
<br />To find Tons of Rail in tone„mile of track: multiply' weight -per yard
<br />by> 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' 6or-
<br />rectidni8 negative.:'- ' I . i _ .. - . _ : .
<br />BL -
<br />' PROBABLE ERROR. If d,, dz, d2, etc. are the discrepancies of various
<br />restilts'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 Ede :
<br />0.74
<br />65 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; 3'94 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 suri"•and. Polaris; stadia 'measurements;
<br />magnetic declination;.arithmetic constants, etc.,
<br />TAM.F TV: -Minutes in Decimals of9aL Deeree. `
<br />V
<br />.0167
<br />111"-:1833-
<br />211
<br />.3500
<br />311
<br />.5167
<br />411
<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'.0500'_
<br />12
<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 />'.2500
<br />25
<br />'.4167
<br />35
<br />.5833
<br />45
<br />.7500
<br />55
<br />.9167
<br />6 `
<br />.100
<br />16
<br />•.2667
<br />26
<br />.4333
<br />36
<br />.6000
<br />46
<br />.7667
<br />56
<br />.9333
<br />7 _:
<br />;.1167_
<br />' 17 :..2833
<br />"
<br />27-
<br />.4500
<br />37
<br />.6167
<br />47
<br />.7833
<br />57 ,
<br />.9500
<br />8 -
<br />.1333,
<br />18
<br />.3000
<br />_
<br />28
<br />.4667
<br />38
<br />.6333
<br />48
<br />.8000
<br />58
<br />.9667
<br />-9
<br />.150019
<br />.31 67,
<br />29
<br />.4833
<br />39
<br />.6500
<br />49
<br />.8167
<br />59
<br />.9833
<br />A0
<br />'.1667
<br />20
<br />3333
<br />30 -
<br />.5000
<br />40
<br />6667
<br />50
<br />.8333
<br />60
<br />1.0000
<br />- TABLE V.
<br />-Inches in Decimals of a Poot.
<br />1-16 3-32Y
<br />3-16
<br />%
<br />5-16
<br />.0052 .0078
<br />.0104
<br />.0156 1
<br />.0208
<br />.0260
<br />.0313
<br />.0417
<br />.0521
<br />.0625
<br />.0729
<br />12
<br />I
<br />I
<br />I
<br />0833 .1667
<br />00
<br />.3333 I
<br />.4167
<br />.5000
<br />.5833
<br />.6667
<br />.7500
<br />.8333.
<br />.9167
<br />
|