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TABLm IL - Radii, Ordinates and Deflections. Chord =100 ft. .
<br />%'Deg.::.
<br />Radius
<br />Mid.:
<br />Ord..
<br />Tan.
<br />Dist,;
<br />Def.
<br />Dist.
<br />Def.
<br />Def.
<br />Deg.
<br />RadiusOid.
<br />Mid.
<br />Tan
<br />. Dist.
<br />Def.-*
<br />Dist.
<br />Def.
<br />for
<br />1 Ft.
<br />_
<br />-ft-
<br />=L
<br />t. ;
<br />t
<br />/
<br />32°
<br />ft
<br />ft..
<br />ft._
<br />ft.
<br />t
<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 />2.30
<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 />80'
<br />11459:'
<br />:109
<br />.436
<br />;•:873
<br />0.45
<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 />60
<br />8875.5
<br />.182
<br />.727
<br />1:454
<br />0.25.
<br />`8
<br />716.8
<br />1:746.
<br />'6:978.13.95
<br />.6167
<br />2.40
<br />1 _
<br />5729.6
<br />:218
<br />,873
<br />'1:745
<br />0.30
<br />20
<br />688.2
<br />1'919
<br />7.26614.53
<br />'102.53
<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 />'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 />W
<br />3125.4
<br />.400'1.600
<br />6°
<br />'3:200
<br />0.55
<br />30 30
<br />603.8
<br />2.074
<br />8.281
<br />16.56'2.85
<br />02'
<br />a ,:
<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,
<br />2644.6
<br />•'.473
<br />1.891
<br />.3.781
<br />0.65
<br />'10 i
<br />573.7
<br />2:183
<br />X8:716
<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 />0.801;
<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 />10145
<br />20.91
<br />3.60
<br />fi.
<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--.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 />23.51'4.05
<br />r'. 80,
<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 />3495.0
<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 />:-
<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 />26.97.4:65
<br />;'•10.
<br />1375.4
<br />.909
<br />3.635
<br />17:271
<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
<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 />31.29:5.40
<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 />4
<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,:1!127
<br />4:507•
<br />,9.014
<br />1.55
<br />211,
<br />274.4
<br />4:594
<br />18.22..36.44
<br />6,30
<br />20:-
<br />1074..7,1:164
<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 />12200
<br />4.798
<br />9.596
<br />1.65,.23:
<br />..
<br />250.8
<br />5.035
<br />19.94.-39.87
<br />6.90
<br />;'.'40'
<br />1011.51:237
<br />4.943:9.886
<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 .43.28
<br />7.50
<br />4•-:,';955.4
<br />1.309
<br />5.234
<br />10.47
<br />1.80
<br />26-
<br />222.3
<br />5.697-22.50
<br />.44.99
<br />7.80
<br />'30-
<br />;929:6
<br />1:346
<br />5.379
<br />10.76
<br />1.85
<br />'27
<br />214.2
<br />5.918
<br />_
<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 />1881.9
<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 />:859.911.,455
<br />5.814
<br />11.63
<br />2.00
<br />30
<br />193.2
<br />6.583
<br />25.88
<br />51.78
<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 .0012X909X2;183 or 2.36 inches.
<br />TABLE III. Deflections for Sub Chords for Short Radius Curves.
<br />Degree
<br />Curve
<br />. 50us
<br />sub R chord =.sin of I def. angle `
<br />Length
<br />of arc
<br />for 100 ft.
<br />sin. $ def. ang.
<br />12.5 Ft.
<br />15 Ft. 20 Ft.
<br />25 Ft.
<br />300
<br />r 193-_18.
<br />,,1°'51'
<br />2°-17'
<br />_
<br />z°.58'
<br />.8500
<br />3°
<br />43'::
<br />- 101..15,.:
<br />32°
<br />181.39
<br />1°
<br />59'
<br />2°
<br />25'
<br />3°
<br />Io'
<br />3°
<br />58'
<br />101.33
<br />34°
<br />171.01
<br />20
<br />o6'
<br />20
<br />33',
<br />3°
<br />21'
<br />4°
<br />12'
<br />6
<br />360
<br />161:.80-.:
<br />-- s°
<br />13'
<br />`2°
<br />41'
<br />30
<br />33
<br />4°'26'
<br />54
<br />_101.48
<br />ioI.66
<br />380• ,.
<br />153.58,
<br />_2°
<br />20'...
<br />2°
<br />49'
<br />3°
<br />441 .
<br />-4°
<br />40'
<br />•,.101.85.:
<br />40°; .
<br />'146:19.
<br />2°
<br />27':
<br />29
<br />57!":
<br />3°
<br />55'
<br />: 4'.54'
<br />46
<br />162,o6 '..
<br />4?°
<br />139 52,
<br />- 2'
<br />34''..
<br />3°-05'
<br />.:2833
<br />40
<br />.07' _
<br />5008'.
<br />.6167
<br />.102.29'.',
<br />44'.
<br />.133.47-.
<br />20
<br />41'...
<br />3°
<br />13' .
<br />40
<br />18'
<br />5022'
<br />.:
<br />'102.53
<br />.46°•..
<br />:"127.97..
<br />20
<br />48'...
<br />3°
<br />21' '
<br />4°.29'
<br />.
<br />< 50
<br />36' -
<br />102:76
<br />'48': .:
<br />122.92
<br />`118.,31.
<br />2°
<br />55'
<br />3°
<br />291
<br />40.40,.
<br />°20
<br />5o
<br />So,
<br />103:00
<br />50';
<br />'.6667
<br />30
<br />o2'
<br />30
<br />38'
<br />4°
<br />51' •.
<br />:.'60-04'
<br />.03:24 .
<br />152° :
<br />'; ' 114-06,
<br />30
<br />09'
<br />3046,1-
<br />5°
<br />02
<br />60
<br />17' ".
<br />- ,103:54 ..
<br />540: "
<br />.110. I1 ,
<br />.3°
<br />16'3°
<br />54'
<br />50
<br />13';
<br />6°
<br />31
<br />103.84
<br />56°
<br />1o6.5o'
<br />3°'22'
<br />4°
<br />02'
<br />50
<br />23'-
<br />6°
<br />44' -
<br />104.14 .
<br />58°.
<br />.
<br />103. 14
<br />36
<br />?9_"
<br />4°
<br />10''
<br />5°
<br />34' :
<br />6°
<br />57'
<br />•104.43 ..
<br />600
<br />100.00
<br />3 °
<br />35'.
<br />4°
<br />18''
<br />°
<br />5
<br />44'
<br />°
<br />7
<br />11'
<br />104.72 .
<br />,: CURVE FORMULAS
<br />'K
<br />T= R tan 2 I R= T cot. 2 I Chord def. = chords
<br />5o.tan .2i I . R
<br />T�- - 'bo
<br />- - Sin.2,D_ - R-
<br />Sin. 2 D= R Sin. 2 D No. chords =
<br />�E R ex, sec 2 I .
<br />.5o tan I
<br />'Sin. };D 'E =T tan I I Tan. def.=;chord def.
<br />T ..
<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'giveri.distance and deflection.
<br />Rule 1: "Multiply the -given. distance by -'01745 (def. for 1°for 1 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 />thegiven 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: Add quotient to'base•foc hypotenuse. .
<br />Given Base'ioo;'Alt. I0.Io?=200=.5..ioo+.5=1oo,.5 hyp.
<br />-Given Hyp._ loo, Alt. 25.25x.=0=
<br />203.I25. 100-3.125=96.875=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'f, and -divide by 7.
<br />`LEVELING. The correction. for curvature' and refraction, in feet
<br />and decilnals:of feet is equal to 0.574 da, where d is the.distance in miles.
<br />The correction for•curvature alone is closely, Ida. The combined cor-
<br />rection is negative:
<br />PROBABLE ERROR., If 211, da', d'g, etc. are .the discrepancies of various
<br />results from -the mean;. and if'Y-da=the sum of the squares'of these Mar-
<br />e6ces and n -=the number of observations, then the probable error 0f the,
<br />mean;., ode
<br />f 0.6746 n (n-1)
<br />SOLAR EPHEMERIS. Attention is, called to the Solar .Ephemeras for'
<br />the current year, published.by Keuffel'&,Esser Co., and furnished free of
<br />charge upon request; which is: 32x5] 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 formulas; Natural andLogarithmic Functions;
<br />and -Logarithms ,of: Numbers.
<br />TABLE IV. -:-� Minutes
<br />TABLm Y. -- Inches in Decimals of a Foot.
<br />in Decimals of a Degree.
<br />3-18 Y
<br />.0167
<br />IV
<br />1833
<br />21'
<br />3500
<br />31'
<br />5167'
<br />41'
<br />6833
<br />51'
<br />.8500
<br />.2'
<br />.0333
<br />12 .:.2000
<br />22"
<br />.3667
<br />32 '
<br />.5333
<br />42
<br />-.7000
<br />52.8667
<br />g -
<br />x•.0500
<br />-13'
<br />-.2167
<br />23 .
<br />.3833
<br />33 .
<br />..5500
<br />43
<br />.7167
<br />53
<br />.8833
<br />6
<br />.0667
<br />14
<br />..2333
<br />24
<br />.4000
<br />34
<br />.5667
<br />44
<br />.7333
<br />54
<br />.9000
<br />6
<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,-;.:.1167
<br />:17 .
<br />.:2833
<br />27.
<br />.4500
<br />37
<br />.6167
<br />'47
<br />.7833
<br />57
<br />:9500
<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 />£i
<br />.1667
<br />°20
<br />:-.3333
<br />30
<br />.5000
<br />1 40 .
<br />'.6667
<br />50
<br />.8333
<br />60
<br />11.0000
<br />TABLm Y. -- Inches in Decimals of a Foot.
<br />1-16 3-323s
<br />3-18 Y
<br />5-16
<br />% Y ?�
<br />.:0052- .0078
<br />.0104. :0156 .0208
<br />.0260
<br />.0313 .0417 .0521 0625,1.0729
<br />1 2
<br />3 45
<br />6
<br />7 8 9 10 11
<br />.0833 ,.1667
<br />.2500, .3333_ .4167:
<br />.5000..
<br />,5833 ,.6667 ...7500 1 .8333 .9167
<br />
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