|
xo
<br />f� II
<br />TeHts I. -Tangents and Externals to a 1° -Curve. .Txn1.E I..=:Tangents.find-Externals-to`a 1°.Curve..' III':
<br />Chord=100 ft. Chord =100 ft)
<br />Int.
<br />Ante
<br />Tangent
<br />''
<br />External
<br />Iat :(
<br />:Angle:,
<br />;
<br />Tangent
<br />h.ternal
<br />;Angle
<br />Tangent
<br />External
<br />1'
<br />50.00
<br />.--:22 -
<br />`" B°zri�
<br />'406:66
<br />V13.99
<br />'-15° 7(:
<br />754.32
<br />49.44
<br />101
<br />58.34
<br />.30
<br />101
<br />409.03
<br />14.58
<br />10'
<br />762.80
<br />50.55
<br />20
<br />65.67
<br />-.39
<br />? 20-;
<br />;417.41-,,-
<br />15-.1811,<;'20
<br />E=.001
<br />771.29
<br />51.68
<br />30
<br />75.01
<br />- `:49-t
<br />,''u 30 4-425.M
<br />425.79
<br />t,' 15:80
<br />'30
<br />779.77
<br />52.82
<br />40-
<br />83.34
<br />.61
<br />40
<br />434.17
<br />. 16.43
<br />40
<br />788.26
<br />.
<br />53.97
<br />- 60•,
<br />- 91.68.
<br />_, x:73`,
<br />. �r h0.,
<br />..,442:55
<br />..,17.02.
<br />11 L,>50_r-796_:75,;
<br />.51 .5�5t7623
<br />' 55.13
<br />.9E=.006
<br />1165.7 ,
<br />117'38
<br />•011 'A17
<br />A22 .028
<br />.0.34 .038
<br />.045 .0
<br />.076
<br />.08325°
<br />A
<br />100:01
<br />- :87
<br />D_`t
<br />,450:93.17.72
<br />.67 .7,
<br />16t r
<br />805.25
<br />56.31
<br />10
<br />t:
<br />•108.35
<br />1'.02:
<br />10
<br />' '
<br />459:32
<br />18.38
<br />10'
<br />'813:75
<br />57.50
<br />20'
<br />116,68
<br />_1` 19'
<br />' 20
<br />"467:•71'
<br />`:19:06 `
<br />• 20•`
<br />'8221.25
<br />58.70
<br />_:30.`
<br />: 1251.02,
<br />ti 1•.36
<br />'30 t
<br />1.476.,10'
<br />1 19.75
<br />�,:30 2.
<br />830:76-
<br />59.91
<br /><<40 ;
<br />'•133.36
<br />`141'.70
<br />1:55,
<br />40 .
<br />x50492;88',
<br />,-484.49
<br />,,,,20.45 .
<br />' `21.16
<br />=.40
<br />''50
<br />,',.839.27
<br />61.14
<br />-50'
<br />1217:9
<br />1:75"
<br />31-'-
<br />1589:0
<br />216.3
<br />'
<br />847.78
<br />62.38
<br />10
<br />150.04
<br />1.90
<br />10
<br />'501:28'
<br />'21.89-
<br />17
<br />856.30
<br />63.63
<br />-••1 101
<br />`158.38
<br />2.19
<br />:---10
<br />509.68
<br />=-;22:62
<br />s
<br />? n 10
<br />>864:82
<br />64.90
<br />20-
<br />166.72
<br />2.43
<br />20
<br />518.08
<br />-'23:38,
<br />20 ,
<br />-:873.35
<br />66.18
<br />30
<br />175.06
<br />2.67
<br />30.
<br />. 52,6.48,_
<br />24.14
<br />30
<br />881.88
<br />67.47
<br />40
<br />183.40
<br />2.93
<br />401.:`534.89..�,i24.91
<br />1633.9
<br />228.4
<br />40
<br />890.41
<br />68.77
<br />50
<br />191.74
<br />3.21
<br />50
<br />543.29
<br />25.70
<br />50
<br />898.95.
<br />70.09
<br />' r •' 10
<br />1279.0
<br />141.01
<br />.44
<br />1652.0
<br />233.4 )
<br />_ :'10
<br />2038.4
<br />351.8
<br />4
<br />200:08
<br />'=. 3:49'
<br />"-110'' '
<br />-:55170
<br />-s!26.1'50
<br />1&=-`-
<br />907.49;
<br />'907.4 - 9.*
<br />71.42
<br />10
<br />208.43
<br />3.79
<br />10
<br />560.11
<br />27.31
<br />10 ,'916'.03.
<br />2057:2
<br />72.76
<br />20
<br />216.77
<br />4.10/
<br />20
<br />568.53
<br />28.14
<br />20
<br />924.58
<br />74.12
<br />30 ,
<br />225.12
<br />;:4:42'
<br />_`(1,30
<br />" 576:95:
<br />l 28:97,
<br />30!
<br />933.13
<br />75.49
<br />40
<br />233.47
<br />, 4.76 1
<br />=ryc 40.
<br />•.585:36
<br />.r 29:82.
<br />"
<br />;.^ 40
<br />941.69
<br />76.86
<br />50
<br />241.81
<br />, 5:10
<br />50•
<br />-593'.79'
<br />30:68- '
<br />'t 50
<br />950:25
<br />78.26
<br />20
<br />1340.4
<br />154.69
<br />•120
<br />1715.3
<br />251.3 !
<br />" 20
<br />2104.3
<br />374.2
<br />i
<br />250.16
<br />5.46
<br />12;" -
<br />-'602121-
<br />;.31.56
<br />18
<br />958.81
<br />79.67
<br />10
<br />258.51,
<br />5.83_
<br />10
<br />610.64
<br />32.45
<br />10
<br />967.38
<br />81.09
<br />20
<br />266.86,
<br />` J' 6.21.
<br />�; „20 -:,'619:07;
<br />1742:6
<br />.' ,33:351.
<br />- '; ;20:x..',.:975.96
<br />2132.7
<br />82.53
<br />30
<br />275.21
<br />.;.,6.61
<br />v,,-30.
<br />627:50
<br />34.26.
<br />; 30. ,
<br />; 984.53
<br />83.97
<br />40
<br />•283.57
<br />7.01'
<br />40"
<br />-635.93•
<br />'' '35.18 '
<br />' ' '40"
<br />' 993.12
<br />85.43
<br />50
<br />291.92
<br />J 7.43
<br />50
<br />,;644..37
<br />36.12-,12..,._50
<br />20
<br />1001.7
<br />86.90
<br />•=30
<br />1402.0
<br />169.04
<br />;30,
<br />1779.1
<br />269.9 r
<br />1-30
<br />2170.8
<br />397.4
<br />D300.28,,.
<br />1410:9 ';
<br />7.86
<br />13.y
<br />652.81,
<br />37.07
<br />20-,
<br />1010.3:.r
<br />88.39
<br />10
<br />308.64
<br />'t• 8.31
<br />10•
<br />661:25
<br />38.03°
<br />It): -10-)
<br />1018.9 "
<br />89.89
<br />20
<br />7 316. 99
<br />8.76
<br />20 ,
<br />-669:70.!
<br />39.01.
<br />20
<br />1027:5
<br />91.40
<br />30
<br />325.35
<br />9.23
<br />30'
<br />'678.15
<br />' 39.99
<br />30
<br />1036: 1 `
<br />92.92
<br />40 .
<br />333'.71-,-_
<br />9.71
<br />40,
<br />686:60
<br />40.99`
<br />° 40
<br />-104'4:7'1
<br />94.46
<br />50
<br />342.08
<br />'% 10.20
<br />_
<br />" -50
<br />-695.06.
<br />42.00-,
<br />50
<br />1053.3,-,_
<br />96.01
<br />7
<br />350.44
<br />_.10.71
<br />14
<br />703.51
<br />743.03'
<br />21
<br />1061:9'
<br />97.57
<br />10
<br />.358_.81
<br />11.22
<br />[ 10'•
<br />711.97
<br />9;44.07
<br />10
<br />1070.6
<br />.99.16
<br />20
<br />"367.17
<br />`,•11.75
<br />20'"
<br />'720:44
<br />; 45.12
<br />20
<br />1079.2
<br />.100.75
<br />30
<br />•-375.54
<br />..12.29
<br />30
<br />-728:90
<br />x:'46118`
<br />' .: 30,
<br />1087-.8'
<br />-102.35
<br />40
<br />383.91
<br />12.85
<br />- 40
<br />47.25,
<br />40
<br />1096.4
<br />103.97
<br />50
<br />392.28
<br />13.41
<br />-'" 50
<br />_737.37,
<br />745.85
<br />48.34•
<br />50
<br />1105.1
<br />105.60
<br />Corrections to be Added (T =Tangent. E = External.)
<br />Angle
<br />Curve 5°
<br />10° 15°
<br />20° 250
<br />z 30° 3S.,
<br />40° 45° 50° 55° 60°
<br />65°
<br />70°
<br />5.
<br />T-.02
<br />.03 .05
<br />.06 ,.08
<br />.10 ' .11
<br />:13. .15 .16 .18 .20
<br />.21
<br />.23.
<br />1861.7
<br />E=.000
<br />.000 .001
<br />.001 '.002
<br />- .002 ...002
<br />.003 -.003 .004 .004 .004
<br />.005
<br />.00�
<br />30°
<br />T=.03
<br />.OB .09
<br /><.13 .16
<br />.19 .22
<br />.25- :28- .31 .34 .38
<br />.42
<br />.46
<br />192.99 '
<br />E=.001
<br />.003 ..004
<br />.006 .007
<br />..008 .009
<br />.011 .012 '.014 .015 .017
<br />.018
<br />.020
<br />15o
<br />T=,04
<br />.10 .14
<br />19 .24
<br />.29 .84
<br />.39 .45 bl'.+.53 .58
<br />.63
<br />.68
<br />40
<br />E=.003 .
<br />-:007 .010
<br />.014 .018
<br />.023 .027
<br />.029 .032 .035':.039 .013
<br />.047
<br />.051
<br />20o
<br />T=.08'
<br />13 19
<br />.26 .32
<br />39 .45
<br />.51 .5�5t7623
<br />.84
<br />.9E=.006
<br />1165.7 ,
<br />117'38
<br />•011 'A17
<br />A22 .028
<br />.0.34 .038
<br />.045 .0
<br />.076
<br />.08325°
<br />x.10
<br />T08
<br />.16 .24 :
<br />.33 .40
<br />.49 .58
<br />.67 .7,
<br />1.06
<br />1.14
<br />'315.2
<br />E m,009
<br />.018 .027-
<br />.036 .048
<br />.056 .065
<br />.074 .0
<br />:127
<br />.135
<br />k Int.; ::
<br />Angle'
<br />Tangent
<br />iExternal'
<br />Int. _,,
<br />'Angle''
<br />Tangent
<br />External;
<br />Int.
<br />'Angle -
<br />Tangent
<br />External
<br />' 122...
<br />XIll 317
<br />107:24 7'
<br />29°;'
<br />1481.8
<br />188.51
<br />'36'.
<br />1861.7
<br />294.9
<br />101:
<br />'1122:4
<br />108.90
<br />10'
<br />1490.7
<br />190.74
<br />_10' 1870.9
<br />50°
<br />297.7
<br />'
<br />1 20
<br />X1131.0
<br />110.57 !
<br />x•4'20
<br />1499.6
<br />192.99 '
<br />�• 20
<br />1880.1
<br />`300.6
<br />30
<br />• '1139,.7.
<br />112.25
<br />1• 30
<br />1508.5
<br />195,25
<br />••30
<br />1889.4
<br />-303.5
<br />-•40
<br />1148.4
<br />113.95
<br />40
<br />1517..4
<br />197.53
<br />-" 40
<br />1898.6
<br />306.4
<br />S 1 50
<br />•1157:0
<br />115.66
<br />C =50
<br />1526.3
<br />199.82
<br /> 50
<br />1907-.9
<br />309.3
<br />,23
<br />1165.7 ,
<br />117'38
<br />$0`
<br />1535:3
<br />;202.12
<br />37.
<br />1917.1
<br />312.2
<br />x.10
<br />-
<br />119.12
<br />•'-10
<br />1544.2
<br />204.44
<br />10
<br />1926.4
<br />'315.2
<br />- 20
<br />,,1174.4
<br />A183:1 '
<br />120.87
<br />20
<br />1553.1
<br />206.77 •
<br />20
<br />1935.7
<br />-'318.1
<br />-, 30
<br />1191.8 ;
<br />122.63
<br />1'•-30
<br />1562.1
<br />209.12
<br />'30
<br />1945.0
<br />321.1
<br />40
<br />1200.5
<br />124.41 i
<br />`40
<br />1571.0
<br />211.48
<br />40
<br />1954.3
<br />324.1
<br />' 50
<br />1209.2 ;
<br />126.20 I
<br />-,50
<br />1580.0
<br />213.86
<br />50
<br />1963.6
<br />327.1
<br />124'"
<br />1217:9
<br />128.00
<br />31-'-
<br />1589:0
<br />216.3
<br />38
<br />d972:9
<br />330:2
<br />10
<br />1226.6.
<br />129.82:
<br />1.05
<br />1598.0
<br />218.7
<br />10
<br />1982.2
<br />333.2
<br />20-
<br />1235:3 .
<br />131.65.
<br />,'10
<br />• '201606.9
<br />.072
<br />221.1
<br />20
<br />1991.5
<br />336.3
<br />1,30
<br />4244. 0
<br />133.50
<br />•,30
<br />1615.9
<br />223.5
<br />�, 30
<br />2000.9
<br />339.3
<br />40
<br />1252.8
<br />135.35
<br />40
<br />1624.9
<br />226.0
<br />-• 40
<br />2010.2
<br />'342.4
<br />50
<br />3261.5
<br />137.23 j
<br />-•'-50'
<br />1633.9
<br />228.4
<br />"•-50
<br />2019.6
<br />345.5
<br />'.141
<br />1270.2
<br />139.11 :.32`
<br />'
<br />1643.0
<br />)
<br />230.'9
<br />39
<br />2029.0
<br />348:6
<br />' r •' 10
<br />1279.0
<br />141.01
<br />.44
<br />1652.0
<br />233.4 )
<br />_ :'10
<br />2038.4
<br />351.8
<br />-'20
<br />1287.7
<br />142.93
<br />,10
<br />20
<br />1661.0
<br />235.9
<br />20
<br />2047:8
<br />354.9
<br />30
<br />1296.5.
<br />144.85
<br />;-30
<br />1670.0
<br />238.4 i
<br />'30
<br />2057:2
<br />358.1
<br />40
<br />'1305,3 i
<br />146.79
<br />40
<br />167911
<br />241.0
<br />;• 40
<br />2066.6
<br />361.3
<br />=50
<br />1314.0 '
<br />148.75
<br />`•'50
<br />1688.1
<br />243.5
<br />'--=50
<br />2076.0
<br />364.5
<br />26 =i'
<br />1322.8
<br />150.71
<br />33
<br />169L -Y
<br />i
<br />246:1%
<br />40
<br />2085.4
<br />367.7
<br />YO
<br />1331:8:
<br />152.69
<br />--10
<br />1706.3;
<br />248.7
<br />10
<br />2094.9
<br />371.0
<br />20
<br />1340.4
<br />154.69
<br />•120
<br />1715.3
<br />251.3 !
<br />" 20
<br />2104.3
<br />374.2
<br />30
<br />1349.2 `
<br />156.70
<br />`•'30
<br />1724.4
<br />253.9
<br />F• 30
<br />2113.8
<br />.377.5
<br />40
<br />1358.0 ;
<br />158.72
<br />7•;40,
<br />1733.5
<br />256.5
<br />40
<br />2123.3
<br />380.8
<br />1-650
<br />1366.8
<br />160.76 ;
<br />• 50
<br />1742:6
<br />259:1'
<br />•-50
<br />2132.7
<br />'384.1
<br />27
<br />1375.6
<br />162.81
<br />34 ,=
<br />1751.7261.8'
<br />,
<br />ll
<br />2142.2
<br />387:4
<br />-10
<br />1384.4
<br />164.86 j
<br />:10,
<br />1760.8
<br />i 264'.5
<br />10
<br />2151.7
<br />390.7
<br />-20
<br />1393.2 ;
<br />166.95 ;
<br />: 20.
<br />1770.0.
<br />267.2
<br />20
<br />2161.2
<br />394.1
<br />•=30
<br />1402.0
<br />169.04
<br />;30,
<br />1779.1
<br />269.9 r
<br />1-30
<br />2170.8
<br />397.4
<br />40
<br />1410:9 ';
<br />171.15
<br />'• 40
<br />1788.2
<br />272.6
<br />40
<br />2180.3
<br />'400.8
<br />50
<br />1419.7•:
<br />173.27
<br />- 50
<br />1797.4
<br />275.3
<br />50
<br />2189.9
<br />404.2
<br />28=-
<br />1428.6 '
<br />175.41 !
<br />35
<br />1806:6•
<br />278:1%
<br />42
<br />2199.4
<br />407.8
<br />10,
<br />1437.4 '
<br />177.55 +
<br />- 10,
<br />1815.7
<br />280.8
<br />10
<br />2209.0
<br />'411.1
<br />-20�
<br />1446.3
<br />179.72 i
<br />a 120
<br />1824.9
<br />283.6
<br />20
<br />2218.6
<br />414.5
<br />30;
<br />1455.1 ;
<br />181.89
<br />- 30
<br />1834.1
<br />286.4
<br />{30
<br />2228.1
<br />418.0
<br />`40;'
<br />]464.0 ,
<br />}
<br />40
<br />1843.3
<br />289.2
<br />40
<br />2237.7
<br />421.4
<br />"50,
<br />1472.9 '
<br />1184.03
<br />186.29
<br />50
<br />1852.5•
<br />292.0
<br />-50
<br />2247.3
<br />'425.0
<br />Correctioifs-t6be.Added,-(T=Tangent. "E=External:)~
<br />Wit•'
<br />Angle
<br />CdrvW:
<br />10°,
<br />'15°'[.226
<br />25'
<br />30°•
<br />35°
<br />40°
<br />45°
<br />50°
<br />55°
<br />60°
<br />650
<br />70°,
<br />20°
<br />' T=.OB
<br />.13
<br />.19
<br />•:32
<br />.39
<br />.45
<br />.51
<br />.58
<br />.65
<br />.72
<br />.79
<br />:84
<br />.90
<br />E=.006
<br />.011
<br />'.017
<br />.028
<br />.:034
<br />':038
<br />.045
<br />.Gal
<br />.057
<br />:063
<br />.070
<br />.076
<br />.083
<br />25° ;'E=.009
<br />1.127
<br />1.14
<br />.018
<br />:027
<br />.046
<br />.056
<br />.065
<br />.074
<br />.083
<br />.093
<br />.106
<br />'.120
<br />.135
<br />300-:
<br />T=.10
<br />.19
<br />..29
<br />.49
<br />.59
<br />.69
<br />.79
<br />.89
<br />.99
<br />1.09
<br />1.20
<br />1.29
<br />1.39
<br />E=.013
<br />.025
<br />.038
<br />.065
<br />.078
<br />.090
<br />.103
<br />-.116
<br />.129
<br />.149
<br />.170
<br />..179
<br />.188
<br />., 35°
<br />*31-
<br />'.22
<br />.34.47
<br />58
<br />.69
<br />.80
<br />.93
<br />1.05
<br />1.17
<br />1.29
<br />1.42
<br />1.54
<br />1.66
<br />.
<br />E =.018
<br />.035
<br />.054
<br />.072
<br />'.086
<br />.109
<br />.131
<br />.153
<br />.175
<br />.197
<br />.213
<br />.230
<br />.247
<br />.264
<br />40°13
<br />.26
<br />.40
<br />.53
<br />.67
<br />.80
<br />.93
<br />1.06
<br />1.20
<br />1.34
<br />1.49
<br />1.64
<br />1.79
<br />1.94
<br />E =,T=•023
<br />.046
<br />.070
<br />.093
<br />.117
<br />'.141
<br />.172
<br />.203
<br />.234
<br />.265
<br />.277
<br />.290
<br />.315
<br />341
<br />450-}
<br />'T=,15 -
<br />.30
<br />.44
<br />.60
<br />.76
<br />.91
<br />1.06 11.21
<br />1.37.
<br />1.52
<br />1.70
<br />1.87
<br />2.04
<br />2.21
<br />E=.030 '
<br />.060
<br />.093
<br />:.119
<br />..153
<br />.184
<br />.216
<br />.254
<br />.289
<br />.325
<br />.351
<br />.378.411
<br />.445
<br />
|