|
II TABLE I. -- Tangents and Externals to a 1' Curve.
<br />Chord =100-f t:'
<br />Int.
<br />pn¢le
<br />Tangent
<br />External
<br />Int'
<br />Angle •
<br />Tangent
<br />Bxtennal
<br />Int
<br />Angle
<br />Tangent
<br />External
<br />1°
<br />50.00
<br />22
<br />8°-
<br />400:66
<br />- 13.99
<br />15°
<br />754.321
<br />43.44'
<br />10'
<br />58.34
<br />:3U
<br />10''
<br />409:03
<br />14.58
<br />l0'
<br />702,80
<br />50:55
<br />°0
<br />60.67
<br />.39
<br />20
<br />417:41
<br />15.18
<br />20
<br />771:29
<br />- 51.68
<br />30
<br />75.01
<br />.40
<br />30
<br />+ 425.79
<br />13.80
<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 />53.97
<br />50
<br />91.68
<br />- .73
<br />50 '
<br />442-.55
<br />.17.07
<br />50
<br />•790.75
<br />55.13
<br />2
<br />100.01.87
<br />.017 .022 .028
<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 />116.08
<br />1.19
<br />20
<br />4G7.71
<br />-19.06
<br />20•
<br />-822.25
<br />58.70
<br />W
<br />125.02
<br />1.36.
<br />30
<br />476:10'
<br />19.75
<br />30
<br />830.76
<br />59.91
<br />•..40
<br />133.8G
<br />1.55
<br />40
<br />484.49
<br />20,45'-40
<br />40
<br />'839.27
<br />61:14
<br />50
<br />141.70
<br />1.75
<br />A..,
<br />492.88
<br />21.16
<br />'` 50-
<br />647.78,
<br />62,38
<br />31.
<br />150.04
<br />1.96
<br />16 -
<br />501.28
<br />21,89
<br />17
<br />958.30
<br />63.63
<br />1.0
<br />158:38
<br />2.19
<br />10
<br />'-5119:68
<br />22.62
<br />10
<br />864.82
<br />64.90
<br />20
<br />1GG.72
<br />2.43
<br />20
<br />5LS:OS
<br />23.38
<br />20
<br />873.35
<br />66.18
<br />30
<br />175.06
<br />2,67
<br />30
<br />526.48
<br />24.14
<br />30
<br />881.88
<br />67.47
<br />40
<br />183.40
<br />_ 2.93
<br />40
<br />;534.89
<br />24.01
<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 />200.08
<br />3.40
<br />11�
<br />551.70
<br />26.50
<br />18
<br />907.49
<br />71.42
<br />M
<br />208.43
<br />3.79
<br />'10
<br />560.11
<br />27.31
<br />10
<br />916.03
<br />72.70
<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 />30
<br />576.95
<br />28.97
<br />30
<br />933,131
<br />75.49
<br />40
<br />233.47
<br />4.76
<br />40
<br />-585.36
<br />29.82
<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 />8 -
<br />250.16
<br />5.46
<br />12
<br />602.21
<br />31.50
<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 />2G6.SG
<br />6.21
<br />20.,
<br />619.07
<br />33:35
<br />20
<br />975.96
<br />82.53
<br />30
<br />275.21
<br />6.61•
<br />30 ,
<br />627.50
<br />33.26
<br />30
<br />984.53
<br />83.97
<br />40
<br />263:1)7
<br />7.01
<br />40
<br />635.93
<br />35.18
<br />4.0
<br />993.12
<br />85.43
<br />.50 ,'291.92
<br />1360.8
<br />7.43
<br />50
<br />644.37
<br />36.12
<br />50
<br />1001.7
<br />86.90
<br />630Q.98.
<br />1375:6
<br />7.86
<br />13
<br />652.81
<br />37.07
<br />20
<br />1610.3
<br />88.39
<br />10 "
<br />;308:64'
<br />.8:31
<br />_
<br />10
<br />G61..25
<br />38.03
<br />10
<br />1018.9
<br />89.89.
<br />-20
<br />316,:99
<br />8.76
<br />" ',:20-
<br />^ 069`.70
<br />39.01
<br />20
<br />1027.5
<br />91.40
<br />30325:35
<br />1402.0
<br />9.23
<br />30
<br />678.15
<br />39.99
<br />'30
<br />1036,1
<br />93.92
<br />40
<br />.333.71
<br />9.71
<br />40
<br />086.60
<br />40.99
<br />40
<br />1044.7
<br />94.46
<br />50
<br />--342.08
<br />t 10.20
<br />50
<br />095.OG
<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
<br />10G1.9
<br />97.57
<br />10
<br />358.81
<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 />720.4.4
<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 />46.18
<br />130'
<br />1087.8
<br />.102.35
<br />40
<br />333.91
<br />12.85
<br />40
<br />737.37
<br />47.25
<br />40
<br />1096.4
<br />-103.97
<br />50
<br />392.28
<br />13.41
<br />50
<br />'745.85
<br />48.34
<br />50
<br />1105,1
<br />105.60
<br />• I
<br />Corrections to be Added (T Tangent. E=External.)
<br />Int. Gurva 50 10°
<br />Aagla -
<br />150 20° 250
<br />30°
<br />1 350 1 40° 45°
<br />500
<br />55" 60°
<br />650
<br />70°
<br />50 T=.02 .03
<br />.05 .06 .08
<br />.10'
<br />.11 .1$ .l 5
<br />.16
<br />.18 .20
<br />.21
<br />.23
<br />E=.000-000
<br />.001 .001 .002
<br />-.002
<br />.002 .003 .003
<br />.001�0�15�0187
<br />0
<br />.005
<br />.005
<br />l0e =.03 OB
<br />09 13 .18:
<br />.19.
<br />.22 25 28
<br />.31
<br />3
<br />42
<br />4$
<br />E=,001 .003
<br />.004 .408 .007
<br />.008
<br />,009 All 412
<br />.014
<br />A-130: 7
<br />.018
<br />.020
<br />zru T-04 .10
<br />.14 .19 .24
<br />.29
<br />.34 .39 .45
<br />.51
<br />.53 -.58
<br />:83
<br />.68
<br />E=.003 , .007
<br />.010 .014 .018
<br />.023
<br />.027 .029 .032'
<br />.035
<br />.039 .043
<br />.047
<br />.051
<br />200 T=.06 .13
<br />.19 .26 .32
<br />.39
<br />.45 .51 .58
<br />.65
<br />.72 .79
<br />.84
<br />.90�
<br />E =.006 .011
<br />.017 .022 .028
<br />.034
<br />.038_.,0!5 .051
<br />.057
<br />.063 .070
<br />.076
<br />.083
<br />25o Tm,08 I .l6
<br />.29 33 40
<br />.49
<br />.58 .67 .75
<br />.83
<br />.90 .99
<br />1.06
<br />1.14
<br />E =,900 .018,
<br />.027 .036 018
<br />.056
<br />.065 074 .083
<br />.093
<br />.108 .120
<br />.127
<br />.135
<br />. r
<br />TAjiLE 1 --'Tangents and Externals to a 1° Carve. III
<br />Chord =100 ft.
<br />Angle .
<br />!Tangent
<br />IIII
<br />1 xlenrdL
<br />Ai�zle
<br />Tangent
<br />F-xcernal
<br />Angle.
<br />Tangent
<br />External
<br />2'^°
<br />1.113;7
<br />107.24
<br />2.9°
<br />1381:8
<br />188.51
<br />30°
<br />1861,7
<br />294.9
<br />lU+:
<br />4
<br />103.90
<br />10+
<br />1490.7
<br />190.74=
<br />- 10'
<br />1870.9
<br />297.7
<br />. 2U :
<br />-I'l31' U
<br />110,77
<br />20
<br />1499.6
<br />192.99
<br />20
<br />1880. 1
<br />300.6
<br />�3U a
<br />A-130: 7
<br />112.25 .
<br />.49
<br />1508:4
<br />195.25:
<br />30
<br />1889.4
<br />303.5
<br />4U
<br />1148.4
<br />113.95
<br />.30
<br />40 ,r
<br />1517.4 -
<br />197.53
<br />40
<br />I S. G
<br />306.4
<br />50
<br />1157:0
<br />115.06
<br />50
<br />1526.3-
<br />199.82
<br />50
<br />1907.9
<br />309.3
<br />-2i
<br />110S :7T
<br />.117.33
<br />30"--
<br />1535.3
<br />202.12
<br />37
<br />1917.1
<br />312.2
<br />10 ,.1174.4
<br />.)00 .103
<br />119.12
<br />10
<br />1544.2
<br />204.44
<br />10
<br />•1926.4
<br />315.2
<br />20
<br />1183.1
<br />120.87
<br />20
<br />1553.1
<br />20G.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 />1954.3
<br />324.1
<br />50
<br />1209.2'
<br />126.20
<br />50
<br />1580.0
<br />.213.80
<br />50
<br />1963.6
<br />327.1
<br />24
<br />1217.9
<br />128.00
<br />31
<br />1 589. 0
<br />216.3
<br />38
<br />-197.2,9
<br />: 330.2
<br />10
<br />1226.G
<br />129.82
<br />-10
<br />1508.0
<br />218.71
<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 />:',0
<br />1244.0
<br />133.5030
<br />16I5:9
<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 />1261.5
<br />137.23
<br />50
<br />.1633.9
<br />228.4
<br />50
<br />2010.6.
<br />345.5
<br />25
<br />1270.2
<br />139.11
<br />32
<br />1043.0
<br />230.9
<br />33 .
<br />2029.0
<br />348.6-
<br />48.610
<br />10
<br />1279.0
<br />141.01
<br />10
<br />105210
<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 />30
<br />1670.0
<br />238.4
<br />30
<br />2057.2
<br />358.1
<br />40
<br />1305.3
<br />146.79
<br />40
<br />1679.1
<br />241.0,
<br />40
<br />2066.6
<br />.361.3
<br />5U
<br />1314.0
<br />148.75
<br />50
<br />1688.1
<br />243.5
<br />50
<br />2076.0,.
<br />364.5
<br />2G
<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 />1706.3
<br />248.7
<br />10
<br />2094.9
<br />,. 371.0
<br />20
<br />1340.4
<br />154.69
<br />20
<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 />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 />380.8
<br />50
<br />1360.8
<br />160.76
<br />50
<br />1742.G '
<br />259.1
<br />50
<br />2132.7
<br />•384.1
<br />27
<br />1375:6
<br />162.81
<br />34•-_
<br />1751.7
<br />261.8
<br />4r.
<br />21'42.2
<br />387.4
<br />10
<br />1384.4
<br />164.80
<br />- 70
<br />1760.8•
<br />. •1264.'5,
<br />10 =';
<br />2151.7
<br />- 390.7
<br />20
<br />1303.2
<br />106.95
<br />20
<br />'1770.0
<br />-
<br />1267.2
<br />20
<br />=2161.2
<br />394.1
<br />30
<br />1402.0
<br />1(39.04
<br />30
<br />1779.1
<br />269.9
<br />30-
<br />2170.8
<br />397.4
<br />40
<br />1.110.9
<br />171.15
<br />40
<br />1788.2
<br />272.6
<br />40
<br />218013:
<br />400.8
<br />50
<br />1418.7
<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 />85
<br />ISOG.6
<br />.278.1
<br />42
<br />2199.4
<br />407.6
<br />10
<br />1437.4
<br />177.55
<br />LO
<br />1815.7
<br />280.8
<br />10
<br />2209.0
<br />411.1
<br />20
<br />1446.3
<br />179.72
<br />20
<br />1824.9
<br />283.6
<br />20-
<br />2218.6
<br />414.5
<br />"30
<br />1455.1
<br />151.89
<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 />Ink.
<br />Curve S°
<br />10°
<br />150
<br />25°
<br />30°.
<br />350 40°
<br />450 50° 550
<br />690 650
<br />700
<br />T=.06
<br />.13
<br />.19
<br />.32
<br />.39
<br />.45 .51
<br />.53 .65 .72
<br />.79 .84
<br />.90
<br />E =.006
<br />.011
<br />.017
<br />P20*-
<br />.028
<br />.034
<br />.038 .015
<br />.OSI .057 .053
<br /><G70 .076
<br />.083
<br />250
<br />T=.08
<br />.16
<br />.24
<br />.40
<br />.49
<br />.58 .07
<br />.75 .83 .00
<br />.99 1.06
<br />1.14
<br />E =.009
<br />.018
<br />.027
<br />.016
<br />.056
<br />.005 .074
<br />.033 .093 .106
<br />.120 .127
<br />.135
<br />30°T=.10.19
<br />.29
<br />.49
<br />.59
<br />.69.- .79
<br />.89 .09 1.09.
<br />1.:0 1.29
<br />1.30
<br />E=.013
<br />.025
<br />.038
<br />.065
<br />.078
<br />.)00 .103
<br />.116 .129 .149
<br />.1.0 .179
<br />.188
<br />35°
<br />T =.11
<br />.22
<br />1 .34
<br />.47
<br />.58
<br />.69
<br />.80 .93
<br />1.05 1.17 1.29
<br />1.42 1.54
<br />1.66
<br />E=.018
<br />.035
<br />.054
<br />.072
<br />.p80
<br />.109
<br />.131 .153
<br />.175 .197 .213
<br />.230 247
<br />.264
<br />400
<br />T =,13
<br />.20
<br />.40
<br />.53
<br />' .67
<br />.80
<br />.93 1.06
<br />1.20 1.34 1.49
<br />1.64 1.79
<br />1.94
<br />E =.023
<br />.01@
<br />.070
<br />.093
<br />117
<br />.141
<br />.172 .203
<br />.234 265 277
<br />,290 .316
<br />.341
<br />.30
<br />.44
<br />60,
<br />76
<br />.91
<br />1.06 1.21
<br />,1.37 1.52 1.70
<br />1:87 2.04
<br />2,21
<br />B=-030
<br />.060',.093
<br />.119
<br />.153
<br />.184
<br />.216 .254
<br />.289 .325 351
<br />.378 .411
<br />.445
<br />
|