|
II
<br />TABLE I. - Tangents and Externals to a 1° Curve. ( TAi1LEJ: -.;Tangents: and Externals to a-1°:Crlrve..." III
<br />Chord= 100 ft.
<br />_ Chord:=•100,ft' ^
<br />Int.-
<br />Angle
<br />Tangent
<br />External
<br />_ Int: "- i,t
<br />Angle :
<br />-. .-
<br />Tangent
<br />External
<br />- -Int.
<br />- Angla
<br />Tangent
<br />External
<br />loo T=,03 OB .09-,::13 .16 .19 .22 .25 " .28'
<br />.31 .34 38
<br />46
<br />E=,001 .003 .004 .006 .007 ,.008 :.009 .011.012
<br />.42
<br />`.014 .015 .017 .018
<br />.020
<br />15° T=,04 .10'.,.14 .19 24 .29 .34 .39 .45
<br />.51 ..53 .58
<br />294:9 '
<br />1°
<br />50.00
<br />^-:22='
<br />-~8°'--
<br />400.66-
<br />13.99
<br />'`'15°
<br />754.32
<br />. 49.44
<br />10'
<br />58.34
<br />.30
<br />10'
<br />409.03
<br />14.58
<br />10'
<br />762.80
<br />50.55
<br />20
<br />66.67
<br />= -.39,:
<br />t, 20:
<br />:-417.41'
<br />_
<br />15.18
<br />'- .. 20
<br />771.29
<br />51.68
<br />30
<br />75.01
<br />47 .49 '`.'
<br />30"
<br />.425.79
<br />.- 15.80
<br />30
<br />1898.6
<br />52.82
<br />40
<br />83.34
<br />.61
<br />40
<br />'434.17
<br />16.43
<br />40
<br />_779.77
<br />788.26
<br />53.97
<br />60
<br />:1 91.68_
<br />-• .73„
<br />50.
<br />442.55-
<br />17.07
<br />50j
<br />-796.,75,
<br />-..55.13
<br />,-2s
<br />100 O1
<br />87
<br />9',
<br />.450.93
<br />17.72
<br />.16
<br />805.25
<br />-56.31
<br />10
<br />, 108.35
<br />1.02
<br />10
<br />459.32
<br />18.38
<br />10'
<br />813..75
<br />` 57.50
<br />'20
<br />318:6&
<br />1=:39
<br />= • - 20`
<br />. •467..71'
<br />-'19:06-`
<br />20
<br />822:25
<br />4 58.70
<br />30
<br />e125.02
<br />1:36'
<br />;`30:
<br />•'476.10
<br />-19.75
<br />'- 30.
<br />'830.76
<br />:59.91
<br />40.'•.:133.36
<br />1209.2
<br />-;,1:55 '
<br />.*-40 :
<br />x484.49:.:20.45-
<br />213.86
<br />-40
<br />.839.27
<br />61.14
<br />50.
<br />141.70
<br />1'.75 '
<br />- '= 50
<br />.492:88
<br />-21.16
<br />50
<br />847.78
<br />62.38
<br />3
<br />150:0.4'
<br />'1.96.
<br />1'0 '-:
<br />501:28
<br />21.89
<br />17 '
<br />856:30
<br />63.63
<br />` 10'=
<br />158.38
<br />• 2:19-.
<br />= 10 -
<br />-- 509.68
<br />'' ;22.62
<br />_
<br />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 />2000.9
<br />'339.3
<br />30
<br />175.06
<br />2.67
<br />30
<br />526.48...:24.14
<br />226.0
<br />30
<br />.873.35.:-,66.18
<br />881.88
<br />67.47
<br />40
<br />183.40
<br />2.93
<br />40'..:4534.89
<br />1633.9
<br />., 24.91
<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 />4
<br />; •200108
<br />- % 3:49'
<br />'1T "
<br />551.70
<br />26.50
<br />18
<br />907.49:
<br />71.42
<br />10
<br />208.43
<br />3.79
<br />10
<br />560.11
<br />27.31
<br />.10 .'916.03.
<br />2047.8
<br />72.76
<br />20
<br />216.77
<br />4:10
<br />20
<br />568.53
<br />28.14
<br />20.
<br />024.58
<br />74.12
<br />30
<br />225.12
<br />:4.42;
<br />_ 'U-30_
<br />_' 576.95;
<br />28.97
<br />40
<br />933.13
<br />75.49
<br />40
<br />233.47
<br />,_4.76
<br />40.
<br />.585.36.
<br />29.82
<br />.30.
<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 />50
<br />950.25
<br />78.26
<br />10
<br />1331.6 •
<br />152.69
<br />.. 10
<br />170G.3
<br />2487
<br />.:10
<br />2094:9
<br />'371.0
<br />5
<br />250.16
<br />5.46
<br />12_
<br />--602.21
<br />--.$1.56
<br />19
<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 />6.21-",
<br />`ZJ120 •
<br />; 619'.07,
<br />' 33.35
<br />20
<br />975.96
<br />82.53
<br />30
<br />275.21
<br />6:61
<br />" `7:01'"
<br />30..
<br />627:50
<br />:! 34.26-
<br />30.
<br />'
<br />•984.53
<br />83.97
<br />40
<br />50
<br />283.57
<br />291.02
<br />. , ,7,.43.
<br />40"
<br />.,„ 50 r
<br />635.93'
<br />:.644.37
<br />35.18"
<br />.: 36:12.
<br />40
<br />.. , :50
<br />993.12
<br />4001.7
<br />85.43
<br />86.90
<br />;27 . '
<br />13756:
<br />162.81
<br />31--,-
<br />1751.7.
<br />261.8 '.
<br />41
<br />2142.2
<br />387.4.
<br />6
<br />300.28.
<br />, ?.86
<br />13
<br />652.81
<br />37.07
<br />20 - -
<br />1010.3 -
<br />- 88.39
<br />10
<br />308:64-=
<br />8.31
<br />10-
<br />G61.25
<br />,
<br />38.03
<br />-• 10 '
<br />1018.9
<br />89.89
<br />20
<br />-316.99;
<br />8.76
<br />20
<br />669.70
<br />;- 39.01•
<br />20
<br />2170.8
<br />91.40
<br />30
<br />:325.35`
<br />9.23
<br />30"
<br />-678.15
<br />39.99',
<br />30
<br />.1027.5:
<br />1036.1.
<br />02.92
<br />40.::333:71,,'
<br />1419:7 ;
<br />9.71
<br />40
<br />686.60.
<br />40.99'
<br />40
<br />1044.7
<br />94.46
<br />50
<br />342.08=='`10.20
<br />c
<br />175.41'
<br />50-
<br />695.06
<br />- -
<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 />` 43.03
<br />21 1
<br />1061.9
<br />97:57
<br />10 .:358'.81.
<br />1446.3
<br />• 11.22
<br />-10
<br />711.97
<br />.-.,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 />'418.0
<br />30
<br />=°375454
<br />.' 12.29
<br />;'._ 30
<br />:728.90
<br />. 46.18'
<br />.] :''30::
<br />1087.8
<br />.100.75
<br />102.35
<br />40
<br />333.01
<br />12.85'
<br />... 40
<br />737.37,
<br />292.0 -
<br />40
<br />1096.4
<br />103.97
<br />50
<br />392.28
<br />13.41
<br />= - 50
<br />745.85
<br />..47.25
<br />48.34
<br />50
<br />1105.1
<br />105.60
<br />Corrections to be Added (T =Tangent. E = External.). -
<br />Int.
<br />Angle Cl -e 5° 10° 15° 20°, 25° 3U° 35° 40° 45°
<br />50° 55° 60° 65°
<br />70°
<br />50 T=:02 .03 .05 .06- .08 .10 .11 .13, '.15
<br />.16 .18.20
<br />.23
<br />E=,000 .000 .001 .001 .002 -.•002 ..002 .003 .003
<br />.21
<br />.004 .004 .004 .005
<br />.005
<br />loo T=,03 OB .09-,::13 .16 .19 .22 .25 " .28'
<br />.31 .34 38
<br />46
<br />E=,001 .003 .004 .006 .007 ,.008 :.009 .011.012
<br />.42
<br />`.014 .015 .017 .018
<br />.020
<br />15° T=,04 .10'.,.14 .19 24 .29 .34 .39 .45
<br />.51 ..53 .58
<br />294:9 '
<br />E=.003 ,..007 .010 .014 .018 .023 .027 .029 .032
<br />.63
<br />.035 .039 .043 .047
<br />.68
<br />.051
<br />200 ? T=.06 .13 r19 .26 .32 .39 .45 .51 .58
<br />.65: .72 .79
<br />190.74
<br />E =.006 .011 :017 .022 .028 .034 .038 .045 .051
<br />.84
<br />,:057 .063 .070 -.076
<br />.90
<br />.C83
<br />250; T=.08 .16 .24` :.33 .40 .49 .58 .67 .75
<br />E=.009
<br />.83 .90 .99 1.06
<br />1.14
<br />.018 .027 .038 .046 •056 .065 .074 .083
<br />.093 .106 .120 .127
<br />.135
<br />Int.Int.
<br />:',Assgle •
<br />Tangent'
<br />Ezteznal'
<br />Angle
<br />Tangent
<br />External
<br />Int.
<br />Angle
<br />Tangent
<br />External,
<br />.':32
<br />:1113.,7
<br />107.24
<br />•290.
<br />1481.8
<br />188.51
<br />:36°-
<br />1861.7
<br />294:9 '
<br />10'
<br />'1122.4
<br />108.90
<br />10'
<br />1490.7
<br />190.74
<br />.10'
<br />1870:9
<br />297.7
<br />20
<br />.1131.0
<br />110.57
<br />20 i
<br />1499.6
<br />192.99
<br />20
<br />1880.1
<br />300.6
<br />30
<br />1139:7.
<br />112.25 '
<br />'. 30
<br />1508.5
<br />195.25
<br />30
<br />1889.4
<br />303.5
<br />40
<br />11148A
<br />113.95
<br />6.-40
<br />1517.4
<br />197.53
<br />40
<br />1898.6
<br />306.4
<br />50
<br />1157.0
<br />115.66
<br />i, 50
<br />1526.3
<br />199.82
<br />50
<br />1907.9
<br />.309.3
<br />23-
<br />11G5.7.
<br />117.38
<br />30 '
<br />1535:3
<br />202.12
<br />37 -
<br />1917.1
<br />312.2
<br />:10
<br />1174:4
<br />119.12
<br />"'10
<br />1544:2.
<br />204.44 i
<br />10
<br />'1926.4
<br />315.2
<br />20
<br />:1183.1
<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 />-.•30
<br />1562:1
<br />209.12
<br />�--30
<br />1945.0
<br />321.1
<br />40
<br />'1200:5
<br />124.41
<br />.40
<br />1571.0.
<br />211.48
<br />-40
<br />7954.3.
<br />'324.1
<br />50
<br />1209.2
<br />126.20
<br />...50
<br />1580.0
<br />213.86
<br />- 50
<br />1963:6
<br />1327.1
<br />24:
<br />1217:9
<br />128.00
<br />31,:- -
<br />1589.0
<br />216:3
<br />38
<br />1972.9'
<br />330.2
<br />-10
<br />1226.6:
<br />129.82
<br />-10
<br />1598.0
<br />218.7
<br />10
<br />1982.2
<br />333.2
<br />20
<br />'1235.3
<br />131.65
<br />20
<br />1606.9
<br />221.1
<br />20
<br />1991.5
<br />:336.3
<br />30
<br />1244:0
<br />133.50
<br />30
<br />1615.9
<br />223.5
<br />30
<br />2000.9
<br />'339.3
<br />40 ::1252.8
<br />135.35 !
<br />`40
<br />1624.9
<br />226.0
<br />-40
<br />2010:2
<br />342.4
<br />50
<br />1261":5
<br />137.23
<br />>50
<br />1633.9
<br />228.4
<br />50
<br />2019.6
<br /><345.5
<br />25 -
<br />1270.2;
<br />139.11
<br />32`-•
<br />1643:0
<br />230.9
<br />39 "
<br />2029.0
<br />348.6
<br />10
<br />1279.0
<br />141.01
<br />'.`10
<br />1652.0
<br />233.4
<br />10
<br />2038.4
<br />351,8
<br />20
<br />1287.7
<br />142.93
<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 />:.c30
<br />1670:0
<br />238.4
<br />30
<br />2057:2
<br />358.1
<br />40
<br />1305:3 '
<br />146.79 '•
<br />X40
<br />1679.1
<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 -
<br />•1322.8
<br />150.71
<br />33 -
<br />1697.2
<br />246:1
<br />40 '
<br />2085.4 .
<br />367.7
<br />10
<br />1331.6 •
<br />152.69
<br />.. 10
<br />170G.3
<br />2487
<br />.:10
<br />2094:9
<br />'371.0
<br />20
<br />3340.4 '
<br />154.69 !
<br />.20'
<br />1715.3
<br />251.3
<br />20
<br />2104.3 .
<br />374.2
<br />30 j
<br />1349:2:
<br />156.70
<br />':.'30
<br />1724:4
<br />253.9
<br />'. 30
<br />2113.8
<br />377.5
<br />40
<br />1358:0
<br />158.72
<br />'. 40'
<br />1733.5'
<br />256:5
<br />40
<br />2123.3 ,
<br />X380.8
<br />50
<br />1366:8:
<br />1G0.76 •
<br />v.'50
<br />1742.6
<br />259.1 ;
<br />:••i50
<br />2132.7
<br />384.1
<br />r
<br />;27 . '
<br />13756:
<br />162.81
<br />31--,-
<br />1751.7.
<br />261.8 '.
<br />41
<br />2142.2
<br />387.4.
<br />1384.4
<br />104.86
<br />..'10
<br />1760.8
<br />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 />1G9.04
<br />30.
<br />1779.1•
<br />269.9
<br />30
<br />2170.8
<br />397.4
<br />40 i
<br />•1410.9 ;
<br />171.15
<br />40
<br />1788.2'
<br />272.6
<br />•.•=40
<br />2180.3
<br />400.8
<br />L 6 £
<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 />1423:6
<br />175.41'
<br />35:
<br />1806:6:
<br />278.1
<br />42"° '
<br />2199.4
<br />407.6
<br />10
<br />•1437.4
<br />177.55
<br />10'
<br />1815:7
<br />280.8
<br />c .' 10
<br />2209.0 .
<br />411.1
<br />20'
<br />1446.3
<br />179.72
<br />20 :1824:9'
<br />2836
<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 />1464.0
<br />184.08
<br />40
<br />1843,3
<br />289.2
<br />40
<br />2237.7
<br />421.4
<br />50.
<br />1472.9
<br />186.29
<br />'.. =50
<br />1852.5
<br />292.0 -
<br />.. 50
<br />2247:3
<br />425.0
<br />Corrections.to,be Added .(T_=Tangent.- •E=External.)_
<br />Angle '.CurveS`10°
<br />15°
<br />-200
<br />'25°
<br />30° 35° 40° 45° 50° 55° 609 -65° 70°-
<br />ypo
<br />T=.06.
<br />13 '.19
<br />26
<br />.':32
<br />.39 .45 .51 .58 .65 .72 .79 84 90
<br />E=.006
<br />.:011 .017
<br />.022
<br />.025
<br />.034 :038 .045 .051 .057 .063 .070 .076 .083
<br />- 25o' '
<br />-T=:08.
<br />.16 .24
<br />*.018
<br />.33
<br />.40
<br />:.49 .58 -.67 .75 :83 .90 .99 1.06 1.14
<br />'.033
<br />E=:009
<br />.027
<br />.036
<br />.046
<br />.056 .035 .074 .093 .106 .120 .127 .135
<br />30'_"
<br />'T=.10
<br />19 .29
<br />39
<br />':.40
<br />..59 .69 .79 .89 .99 1.09 1.20 1.29 1.39
<br />E=1.013
<br />:025 .038
<br />.051
<br />.065
<br />.078 .000 .103 .116 .129 .149 .170 .179 .183
<br />35°
<br />' T=.11
<br />.22 .34
<br />:47
<br />.58
<br />.69 .80 .93 1.05 1.17 1.29 1.42 1.54 1.66
<br />E =:018
<br />.035 ,.054
<br />.072
<br />.086
<br />.109 .131 .153 .175 .197 .213 .230 .247 .264
<br />40°
<br />T=.13
<br />.26 .40
<br />.53
<br />.67
<br />.80 '.93 1.06 1.20 1.34 1.49, 1.64. 1.79 1.94
<br />^E =.023
<br />.046 .070
<br />.093
<br />-.117
<br />.141 .172 .203 .234 .265 .277 .290 .315 .341
<br />459
<br />T=.15
<br />•.30 .44
<br />.60
<br />.76
<br />.91 1.06 1.21 1.37. 1.52 1.70 1.87 2.04 2.21
<br />E =.030
<br />.060 .093
<br />.119
<br />.153
<br />.184 .216 .254 .289 '.325 .351 .378 .411 .445
<br />
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