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7M E
<br />TABLE IL Radii; Ordinates and Deflections. Chord 100 ft.. CURVE .FOR114ULAS
<br />�.'
<br />Radius :
<br />Mid.
<br />Ord.
<br />Tan...
<br />Dist.
<br />Def..
<br />Dist.
<br />Def. '
<br />.1for
<br />Ft..-
<br />Deg.
<br />Itaditis
<br />Mid
<br />Ord.
<br />,Tan
<br />- Dist.
<br />.Def. +
<br />Dist.
<br />:Def.
<br />'or
<br />1 Ft.
<br />51'
<br />ft.
<br />ft.
<br />ft.ft.
<br />.
<br />?
<br />101- 15 ...
<br />ft.
<br />ft.
<br />ft.
<br />ft.
<br />i
<br />0°16'
<br />34377.
<br />.036
<br />.145
<br />.291
<br />6.05
<br />."7°- .
<br />819.0'1:528
<br />-
<br />6.105
<br />12.21,2.10
<br />43
<br />20
<br />17189:
<br />073
<br />.291
<br />.582
<br />0.10-
<br />20'
<br />781.8
<br />1600
<br />6:395.12.79
<br />41"3°
<br />2.20
<br />---30
<br />11459.
<br />.109.436
<br />1oI.66
<br />.873
<br />0.15
<br />30`
<br />764.5
<br />1.637
<br />'6.540
<br />13.08.2.25
<br />44.'
<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 />716.8
<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 />1L919
<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
<br />2.60
<br />30
<br />3819.8
<br />.327
<br />1.309
<br />2.618
<br />0:45
<br />9
<br />637.3
<br />1:965
<br />7.846
<br />15.69
<br />2.70
<br />46
<br />3437.9
<br />.364
<br />1.454
<br />2.909
<br />0.50:
<br />20
<br />614.6
<br />2037.
<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 />16.56.2.85
<br />4°;o2.'`
<br />:-.
<br />2864;9
<br />, .436
<br />1.745
<br />.3.490
<br />0.60
<br />40.593.4
<br />4°
<br />0
<br />:13.14
<br />2..110
<br />8.426
<br />16.85.2.90
<br />10'
<br />10
<br />2644 ..6
<br />,.473
<br />1.89P
<br />:3.781
<br />0.65..10
<br />loo.00
<br />573:7
<br />2.483
<br />.5.716
<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 />SO
<br />2022.4
<br />':618
<br />2.472
<br />A.94'5
<br />0.85 `
<br />12 ..478.3
<br />21620
<br />10.45 `
<br />20.91
<br />3.60
<br />1910.1-
<br />:655
<br />2.618
<br />-5.235
<br />0.90'
<br />'•- 30.459.3
<br />2.730
<br />10.89
<br />21.77.3.75
<br />10-
<br />1809.6
<br />'.691
<br />2.763
<br />'5:526
<br />0.95••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 />23.51-4.05
<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 />149$.0
<br />:836
<br />3.345
<br />.6.689
<br />1.15...15
<br />383.,1
<br />3.277
<br />13.05
<br />26.11
<br />4.50
<br />4 i-
<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 />3.49.6
<br />13.92 .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
<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 ':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 />31.29:5.40
<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 />6
<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 />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 />122.
<br />23
<br />250.8
<br />5.035
<br />19.94
<br />39.87.6.90
<br />.'.-40:
<br />1011:5
<br />1-:237.
<br />4.943
<br />9.886
<br />1.70
<br />24
<br />240.5
<br />5:255.20.79
<br />41.58.7.20
<br />50
<br />982.61273
<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,,5.234
<br />10.47
<br />1.80,
<br />26
<br />222.3
<br />5.G97:
<br />22:50
<br />44.99:7.80
<br />10
<br />929.6
<br />1346
<br />5.379
<br />10.76
<br />1.85
<br />27;
<br />214.2
<br />5.918
<br />23.35
<br />46.6918
<br />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.'45515.811
<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 in inches for any cord of length (C) 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 2.35 inches.,
<br />TABLE III. ` Deflections for Sub Chords for Short Radius Curves.
<br />Deet ee
<br />Curve
<br />50 Radius
<br />subR chord = sin of i def. angle
<br />Leefnagrteh
<br />for 100 ft.
<br />sin.1 def. ang.
<br />12.5 Ft.
<br />•15 Ft.
<br />20 Ft.
<br />25 Ft.
<br />300
<br />193.18.
<br />1°
<br />51'
<br />z' 17
<br />z°
<br />58'.
<br />3'
<br />43
<br />101- 15 ...
<br />32°
<br />181:39
<br />1059'
<br />.5333
<br />2°25'
<br />.7000
<br />3°
<br />10'
<br />3°
<br />58'
<br />101.33
<br />34°
<br />171.01
<br />20
<br />o6'
<br />2°.33'
<br />43
<br />3°
<br />21'
<br />4°
<br />12'
<br />101.48
<br />360
<br />161.80
<br />2'
<br />13'•
<br />2°
<br />41"3°
<br />44-
<br />33"
<br />4°
<br />26'
<br />1oI.66
<br />3$°.. ,..
<br />153-0 -.
<br />._ 2°
<br />20'
<br />2'.49
<br />35
<br />30 3°
<br />44.'
<br />-4°
<br />40'
<br />IOI.85 .
<br />40° -
<br />146.19
<br />2°
<br />2T
<br />2°
<br />57'
<br />3°•
<br />55'
<br />4°
<br />54'
<br />102.06 .
<br />42'..
<br />139-s52.
<br />_ 2°
<br />34' - •
<br />3°-05'
<br />:30
<br />27•
<br />4°
<br />07'
<br />5'.08'
<br />.
<br />IO2.29 ..
<br />102.53
<br />44°' ..
<br />133.47:
<br />20.41'.
<br />.1333
<br />18
<br />�3�-.
<br />4'
<br />18'
<br />.50,22'
<br />.6333
<br />48
<br />--46° :.
<br />-•127.97--
<br />2'48'-
<br />9
<br />-3°.21':
<br />19
<br />4°.29'
<br />;
<br />- 5°;36'
<br />39
<br />102.76
<br />480
<br />122:92
<br />20
<br />55' .
<br />3°
<br />29' ..
<br />, 40.40•
<br />.
<br />50
<br />50' ....103.00
<br />11 40 :1
<br />5o°..
<br />...
<br />.i18 31
<br />30
<br />02',
<br />30'381
<br />.
<br />.. 40.51'
<br />60
<br />04'.
<br />103.24
<br />52
<br />114.06".
<br />3°
<br />09'
<br />3'
<br />46' ..
<br />5°.02'
<br />.
<br />6'.17'
<br />103.54
<br />540
<br />L10. I I
<br />30.16
<br />' ;'
<br />3°
<br />54'.
<br />5'
<br />13, .
<br />6°
<br />31'
<br />103.84
<br />56° .
<br />._ Io6..50
<br />3'
<br />22'
<br />4°;o2.'`
<br />.
<br />5°
<br />2. 3' ;
<br />60.44'
<br />164.14 .
<br />58°
<br />4°
<br />0
<br />:13.14
<br />3°
<br />29'.
<br />10'
<br />`.50
<br />34'
<br />6'
<br />57'
<br />]•04.43
<br />60° '
<br />loo.00
<br />3035•.,
<br />:.40
<br />W :.
<br />.5044'
<br />70
<br />!1'
<br />104.72
<br />T R tan o tan I I R= T cot. 9' I Chord def. = chord2
<br />.1 = b0 R
<br />R=
<br />a
<br />Sm 1 D = 5° Sin. ' D No. chords = :
<br />R E =Rex. sec ; I
<br />Sin_ j' D = 5o tarn ; I' - E = T •tan. J I Tan. def. = ; 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'firid angle for a given -distance and deflection.
<br />Rule i. Multiply the given distance by,.01745 1. (def. for 1° for 1 ft.
<br />see Table II.), and divide given deflection by the product.
<br />-Rule 2: Multiply given deflection by g7.3, and. divide the product by
<br />the given distance.
<br />To find deflection for a given angle and distance.' Multiply the angle
<br />by.o1745, and the product by the distance.
<br />GENERAL ATA
<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.loz=too=.5.,100,-�.S:=Ioo.S:h3P.
<br />Given Hyp:_ ioo, Alt.25.252=206=3-12.5. loo -3.125=96.875=Base.
<br />Error in first example, .062; in last, .045•
<br />To find Tons .of. Rail in one mile of track: _ multiply -weight per yard
<br />by. I l; and divide by 7..
<br />LtykLING. The correction' for curvature and refraction, in feet
<br />and decimals'of•feetis equal to 0.574 de, where d is the distance in miles.
<br />The-correetiori'for curvature alone is closely, f de. _ The combined- cor-
<br />rection is negative.:.
<br />PROBABLE ERROR. If d;, de, da, etc.* are the discrepancies of various
<br />results from the mean, and if Y-da=the sum of the squares of these diffor-
<br />ences and n the number of observations,:then the probable error of the.
<br />mean- . Y -de
<br />±
<br />0.6745
<br />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 free of
<br />charge upon request, which is 3jx5j in., with about 90 pages of data very
<br />useful to the: Surveyor; such as the adjustments of transits, --levels and
<br />solar. attachments; directions and tables for determining the meridian
<br />and the latitude from observations on the:sun and Polaris; stadia meas.
<br />urements; magnetic declination; arithmetic constants; English and Metric
<br />conversions; trigonometric f ormulas; Natural andLogarithlnic Functions;
<br />and Logarithms :of Numbers:
<br />TABLE 1V. = Minutes
<br />TABLE V. - Inches in Decimals of a Foot.
<br />in Decimals of a Degree.
<br />1'.0167
<br />1-16 3-32
<br />I1'
<br />.1833
<br />21'
<br />.3500
<br />31';
<br />.5167
<br />41'
<br />.6833
<br />-51'
<br />.8506
<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 />g _-.0500
<br />89
<br />13
<br />.2167.
<br />23
<br />.3833
<br />33
<br />.5500
<br />43
<br />.7167
<br />53
<br />,.8333
<br />L.
<br />-.0667
<br />14
<br />.2333
<br />24.-
<br />.4000
<br />34
<br />.5667
<br />44-
<br />.7333
<br />54'
<br />..8833-
<br />.9000
<br />b
<br />.0833
<br />15
<br />.2500
<br />25
<br />.4167.
<br />35
<br />.5833
<br />45
<br />.750055��
<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 />.1167
<br />-17.:
<br />.2833.
<br />27•
<br />.4500
<br />37
<br />.6167
<br />47
<br />.7833
<br />57
<br />.9500
<br />6 -
<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 />29
<br />.4833
<br />39
<br />.6500
<br />49
<br />.8167
<br />59
<br />.9833
<br />10.
<br />.1667
<br />20 -
<br />".3167
<br />.3333 1130
<br />1 .5000
<br />11 40 :1
<br />:6667 11
<br />50
<br />1 .833311
<br />60
<br />11.0000
<br />- -
<br />TABLE V. - Inches in Decimals of a Foot.
<br />f
<br />1-16 3-32
<br />3-18
<br />Y4
<br />5-16
<br />1
<br />0052 ,.0078
<br />.0104
<br />.0156
<br />.0208
<br />.0260
<br />.0313
<br />•.0417 X521
<br />.0625.
<br />.0729
<br />1 2
<br />3
<br />4
<br />5
<br />6
<br />7
<br />89
<br />10
<br />11
<br />0833 -.1867
<br />.2500
<br />-.333$
<br />:4187
<br />.5000
<br />.5833
<br />.6667_ .7500
<br />,.8333
<br />.9167.
<br />
|