|
I TAnLE I. Tangents and Externalsto a 1' Curve.
<br />Ch6rd.=100 ft.
<br />Inte
<br />Angle'Angle
<br />Tangent
<br />External'
<br />Int.
<br />Tangent External
<br />g
<br />Int. .
<br />Angle'
<br />Tangent
<br />External
<br />43° '
<br />2257.0
<br />428.5
<br />50: •
<br />2671.8
<br />592.3
<br />b7°
<br />3110:9
<br />790.1
<br />+.` 10'
<br />2266.6
<br />.432.0
<br />.101
<br />2681.9
<br />`596.6+
<br />10"
<br />3121.7
<br />795.2
<br />20
<br />.2276.2'
<br />(435A
<br />t. 20:
<br />2692.1
<br />600.9+
<br />'.20
<br />3132.6
<br />800.4
<br />30
<br />2285.9-
<br />A39.2
<br />,.30-
<br />2702.3
<br />605.3
<br />30
<br />31.43:4
<br />805.6
<br />40
<br />.2295.6
<br />:442.8
<br />:' 40'
<br />2712.5
<br />009.6
<br />+ 40
<br />3154.2
<br />810.9
<br />50
<br />2305:2
<br />446.41
<br />50
<br />2722.7;
<br />614.0(
<br />. +50
<br />31G5.1
<br />'816.1
<br />;44'
<br />2314.9
<br />450.0
<br />51 '
<br />2732.9,
<br />618:4;
<br />58-:'
<br />'3176.0
<br />821.4
<br />10
<br />2324.6
<br />'453.6
<br />10
<br />2743.1;
<br />622.8
<br />.110
<br />3186.9
<br />'.826.7
<br />120
<br />2334.3
<br />457.3' '.
<br />, 20 :
<br />2753.41
<br />627.2 :
<br />.+, 20
<br />3197: 8
<br />, 832.0
<br />`.30
<br />.2344.1
<br />461.0 ;
<br />30""'
<br />2763.7.
<br />631.7
<br />'.;,.30
<br />t3208.8
<br />837.3
<br />_,:40
<br />;2353.8
<br />:464.6
<br />40'1
<br />2773.9
<br />636.2'
<br />40
<br />3219.7
<br />:842.7
<br />1.; b0
<br />2363.5
<br />468,4 ;
<br />50 ;
<br />2784.2
<br />640.7
<br />'.150 .
<br />3230.7
<br />. 848.1
<br />45''
<br />2373.3;
<br />472.1.
<br />b2_:.;
<br />2794.5:
<br />645.2
<br />59,' :' 1
<br />.3241:7
<br />853.5
<br />10
<br />.2383.1
<br />475.8
<br />10
<br />2804:91
<br />649.7
<br />10
<br />:3252.7
<br />8M.0
<br />.;;•20
<br />2392.8'
<br />479.6 ;
<br />-20
<br />2815.2'
<br />654.3'
<br />20'
<br />3263:7.
<br />804.3
<br />:30
<br />2402.6
<br />1433.4',
<br />':30
<br />2325.6
<br />658.8
<br />.;30
<br />+3274.8
<br />869.8
<br />"AO
<br />2412.4
<br />'487.2.
<br />-,X.40
<br />2335.9
<br />663.4
<br />40:
<br />,3285.8
<br />:875.3
<br />Z.+ 50
<br />2422.3
<br />491.0
<br />..=.50
<br />2846:3
<br />668.0
<br />;'_'. 50.
<br />3296.9
<br />.880.8
<br />AG'
<br />2432.1
<br />494:8 '
<br />53
<br />2856:7
<br />672.7
<br />60. '
<br />3308.0
<br />886.4
<br />10
<br />2441.9'
<br />498.7
<br />10
<br />2867.1
<br />677.3 ,
<br />: 30
<br />3319.1
<br />892.0
<br />'-20
<br />-2451":8
<br />502.5
<br />20
<br />2877.5
<br />682.0 '
<br />.20
<br />3330.3
<br />897.5
<br />.'30
<br />2461:7
<br />506.4
<br />'30
<br />2888.0
<br />686,7
<br />30
<br />3341.4
<br />.903.2
<br />;40
<br />2471:5
<br />510.3
<br />40
<br />2898.4
<br />691.4
<br />40
<br />3352.6
<br />908.8
<br />,. '.50
<br />2481:4
<br />514.3
<br />.50
<br />208.9
<br />696.1 !
<br />v:. 50.
<br />3363.8
<br />914.5
<br />47 "'
<br />2491"3
<br />518'.2
<br />54•
<br />2919.4
<br />700:9
<br />1
<br />61.`
<br />3375'.0
<br />920.2
<br />10 !
<br />2501<2
<br />522.2 ;
<br />_10
<br />2929.9.
<br />705,7
<br />10 1
<br />3386.3
<br />925.9
<br />, '20
<br />2511.2
<br />526.1
<br />:20
<br />2940:4
<br />710.5
<br />.20
<br />3397.5
<br />,931.6
<br />:`30
<br />252M
<br />530.1
<br />130
<br />2951:0
<br />715,3
<br />30
<br />3408.8
<br />.937.3
<br />is. -•40 :
<br />2531:1
<br />534.2 '
<br />'40
<br />29G1:5
<br />720.1
<br />40+'
<br />3420:1
<br />943.1
<br />±..'50 j
<br />2541.0
<br />538.2 !
<br />50
<br />2972.1
<br />725.0
<br />50
<br />3431:4
<br />'948.9
<br />48 ' ."
<br />2551:0
<br />542:2
<br />55 ' .''
<br />2982.7
<br />72:9
<br />62. +
<br />3442.7
<br />954.8
<br />102561.0
<br />10 '.
<br />546.3.
<br />_.<10
<br />2993.3
<br />734.8
<br />; „ 10
<br />3454.1
<br />960.6
<br />20
<br />2571.0
<br />550.4 ;
<br />'_. 20
<br />3003:9
<br />739.7 '
<br />20,
<br />3465'4'
<br />966.5
<br />30 i
<br />2581.0
<br />554.5 1
<br />L'.;30
<br />3014,5
<br />744.6 .
<br />30.
<br />3476:8
<br />972.4
<br />:.-40
<br />2591:0
<br />558.6--
<br />i.. 40
<br />3025.2
<br />749.6 =
<br />40
<br />3488.3t
<br />978.3
<br />2031.4
<br />2601:1
<br />562.8 s
<br />.:.'50
<br />3035:8
<br />754.6
<br />50.:
<br />3499.7'
<br />•984.3
<br />-49,;'
<br />2611:2
<br />566:9
<br />" S8. •
<br />3046.5
<br />759:6 '.
<br />63.':,,
<br />3511.1
<br />990.2
<br />10
<br />221:2
<br />571.1
<br />.10
<br />.3057.2
<br />764.6 .
<br />',.10.
<br />3522.6
<br />996.2
<br />20.'
<br />2631.3
<br />575.3 '
<br />`, 20
<br />3067:9
<br />769.7
<br />20'
<br />3534:1
<br />1002.3
<br />'30 !
<br />2641.4
<br />579.5
<br />r .30
<br />. 3078:7.
<br />774.7
<br />30',
<br />3545:6
<br />1008.3
<br />_'40
<br />2051'.5
<br />553.8
<br />:40
<br />3089.4
<br />779.8
<br />,40::
<br />3557.2
<br />1014.4
<br />°50
<br />266116
<br />588.0 S
<br />6; 50
<br />3100.2:
<br />784.9 ;
<br />.-'.50.'
<br />3568:7
<br />1020<5
<br />C,ori'ectioris to:'be'Added (T=Tangent. "•`'E=`Ekieirial:).
<br />Angle_
<br />: Curde S°:
<br />10°
<br />15°
<br />20°
<br />'25°'
<br />30°
<br />35°
<br />40°
<br />45°,
<br />50°
<br />SS?
<br />'60°
<br />65°
<br />70°
<br />40° ;
<br />-T=.13 .'
<br />.26'.
<br />.40
<br />.53 .
<br />7:67,
<br />.80`
<br />:93
<br />108
<br />1.20.
<br />1.34
<br />1.49}
<br />1.64
<br />1.79
<br />1.94
<br />i
<br />30
<br />--B=.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 />50
<br />3638.5
<br />1057.7
<br />"70°
<br />T=.25.
<br />••:1.21
<br />63
<br />1.02
<br />1.06
<br />1.254
<br />65•
<br />1 .52
<br />1.351
<br />1 .87
<br />2.411
<br />2.445
<br />79-.... '
<br />10
<br />:E=.030
<br />.060
<br />.093
<br />_ 119
<br />1D70.2
<br />1076.6
<br />`.184
<br />216
<br />1360.1
<br />1367.6
<br />289
<br />325
<br />1713.7
<br />378
<br />3685.4
<br />1082.9
<br />SO°
<br />T=.17
<br />.34
<br />.51
<br />.68
<br />.85
<br />1.02
<br />1:19
<br />1.36
<br />1.54
<br />'1.72
<br />1.91
<br />2.10
<br />2.29
<br />2.48
<br />50 .;3709:0
<br />E=.037.
<br />.075_
<br />_.116
<br />.151
<br />:189
<br />_.227
<br />.266
<br />.305
<br />.345
<br />.384
<br />.425
<br />.467
<br />.508
<br />.5 0
<br />55°
<br />T=.19
<br />.38
<br />.57
<br />76
<br />:95
<br />1:14
<br />1.32
<br />1.52
<br />1.72
<br />1.92'
<br />2.14
<br />2.35
<br />2.56
<br />2.77
<br />30,
<br />:4275:5
<br />.093
<br />:142
<br />.188
<br />.236
<br />.283
<br />.532
<br />3.81
<br />.420
<br />-.479
<br />.530
<br />".582
<br />.641
<br />.700
<br />,6T21
<br />3792.4
<br />42
<br />63.
<br />.84
<br />1.05
<br />1.27
<br />1.49
<br />1.71
<br />1 94
<br />2.17
<br />2.38
<br />2.60
<br />2.83
<br />3.Oi
<br />4JE=.046
<br />E=.056
<br />.112
<br />'.168
<br />.225
<br />:283
<br />.340
<br />:398
<br />.457
<br />.516
<br />.575
<br />.636
<br />.697
<br />.774
<br />.851
<br />40
<br />T.23
<br />.46
<br />'.69
<br />.93
<br />1.16
<br />1.40
<br />1.64
<br />1.88
<br />2.13
<br />2.38
<br />2.63
<br />2.88
<br />3.13
<br />3.39
<br />68':;;
<br />E=.067
<br />..135
<br />1.204
<br />.273
<br />:343
<br />.412
<br />.483
<br />1551
<br />:625
<br />:697
<br />.711
<br />.845
<br />..922
<br />1.01
<br />TABLE I.-- Tangents•and Externals to,a l°.Curve. V
<br />Chord =100 ft.
<br />Int:
<br />-Angle •
<br />Tangent
<br />External
<br />' ingle
<br />Tangent -External
<br />30°
<br />Int.
<br />-Angle . '
<br />Tangent
<br />External
<br />64' 1
<br />3580.3
<br />1026.6
<br />.719,
<br />4086.9
<br />1308.2
<br />78°
<br />10'
<br />4639.8
<br />4653.6
<br />1643.0
<br />1631:7
<br />10'
<br />3591.9
<br />3603.5
<br />1032.8
<br />1039.0
<br />10'
<br />20.,
<br />4099.5
<br />4112.1
<br />131:1:6
<br />1322.9
<br />20
<br />4667..4
<br />1660.5
<br />20
<br />30
<br />3615.1
<br />1045.2
<br />i
<br />30
<br />4124.8
<br />1330.3
<br />30
<br />'46
<br />"4681.3
<br />4695.2
<br />1669.2
<br />1678.1
<br />40
<br />3626.8
<br />1051.4
<br />40
<br />50_
<br />4137..4
<br />4150.1
<br />1337.7
<br />1345.1
<br />/50
<br />4709.2
<br />1686.9
<br />50
<br />3638.5
<br />1057.7
<br />"70°
<br />T=.25.
<br />51 •,
<br />1.02
<br />P.28
<br />1.54
<br />65•
<br />3650.2
<br />1063:0,
<br />72
<br />4162.8
<br />1352:6
<br />79-.... '
<br />10
<br />4723.2
<br />-4737.:2
<br />1695.8
<br />1704:7
<br />10 •-3661:9
<br />3673.7
<br />1D70.2
<br />1076.6
<br />10'
<br />20
<br />4175.6
<br />4183:5
<br />1360.1
<br />1367.6
<br />20'
<br />4751.2
<br />1713.7
<br />20
<br />30
<br />3685.4
<br />1082.9
<br />30
<br />42011
<br />1375.2
<br />30. ''4765.3
<br />E =.095
<br />1722.7
<br />1731.7
<br />40
<br />3697.2
<br />1089.3
<br />1095.7
<br />40
<br />50
<br />4214.0
<br />422¢.8
<br />1382.8
<br />1390.4
<br />.40
<br />,.,50
<br />;,4779.4
<br />•4793.6
<br />1740.8
<br />50 .;3709:0
<br />1.22
<br />1.53
<br />1.84
<br />2:15'
<br />2.46
<br />2.78. 3.10. 3.44
<br />4.46
<br />80° j
<br />_
<br />66
<br />3720..9
<br />1102:2
<br />73 ; _
<br />4239:7
<br />1398.0 ',
<br />:80.. +
<br />10
<br />•4807.7
<br />%`4822.0
<br />1749.9
<br />1759.0
<br />10
<br />20
<br />3732.7
<br />3744:6
<br />1108.6
<br />1115.1
<br />10
<br />- 20,
<br />4252.G
<br />42G5:6
<br />1405.7
<br />1413.5 t
<br />c 20
<br />.4836.2
<br />1768.2
<br />30
<br />'3756:5
<br />1121.7
<br />30,
<br />:4275:5
<br />1421.2 ,
<br />142,0 !
<br />30
<br />`.406
<br />4850.'5
<br />;4864,8
<br />1777.4
<br />1786.7
<br />40 .-3768.5
<br />50
<br />.3780..4
<br />1128.2
<br />1134.8
<br />40
<br />50:
<br />.4291.5
<br />4304.6
<br />1436:8
<br />50
<br />'4879.2
<br />1796.0
<br />67
<br />3792.4
<br />1141:4
<br />74
<br />4317.6
<br />1444.6 i
<br />81
<br />10
<br />•4893.6
<br />;4908.0
<br />1805.3
<br />1814':7
<br />:•'10
<br />'3804:4
<br />3316.4
<br />1148.01
<br />1154.7
<br />- •10
<br />20
<br />4330.7
<br />4343.8
<br />1452.5
<br />1460.4 .
<br />20
<br />4922:5
<br />1824.1
<br />20
<br />30
<br />3828.4
<br />;
<br />1161.3 1
<br />;.
<br />30
<br />4356.9
<br />1468.4 r
<br />30
<br />.4937.0
<br />1833.6
<br />40
<br />3840.5
<br />1168.1;
<br />40
<br />4370.1
<br />1476.4 i
<br />.40
<br />4951:5
<br />3843.1
<br />:50
<br />'3852.6
<br />1174.8;
<br />'50:
<br />4383.3
<br />1484.4 ;
<br />i
<br />„50 i
<br />4966.1
<br />1852.6
<br />68':;;
<br />3864:7
<br />1181.6
<br />7b
<br />4396.5
<br />1492:4'
<br />-82 •
<br />-4980:7
<br />1862.2
<br />}
<br />10
<br />3876.8
<br />1188.4 '
<br />10
<br />4409.8
<br />1500.5
<br />10
<br />,4995..4'
<br />1871.8
<br />.
<br />20;3889.0
<br />1195.2
<br />20
<br />4423.1
<br />1508.6
<br />20
<br />'_:5024.8:
<br />5010.0
<br />1881.5
<br />30 _
<br />3901.2'
<br />1202.0.
<br />30 :.4436.4
<br />1516.7 i
<br />v 30
<br />-5039.5,
<br />1891.2
<br />1900.9
<br />40
<br />.3913.4
<br />1208.9
<br />1215.8'
<br />40
<br />50
<br />4449.7
<br />4463:1
<br />1524.9
<br />1533.1 ;
<br />40
<br />; 50
<br />5054.3
<br />1910.7
<br />."50
<br />3925.6
<br />.
<br />69
<br />3937,9
<br />1222.7
<br />76••
<br />4476:5
<br />1541:4 ;
<br />1549:7
<br />-83
<br />10
<br />5069.2'
<br />5054.0'
<br />1920.5
<br />1930:4
<br />10
<br />20
<br />,:3950:2
<br />3962.5,
<br />1229.7;
<br />1236.7
<br />1Q
<br />,+,• 20
<br />4489:9
<br />x;4503:4
<br />1558.0
<br />20
<br />5099.0
<br />1940.3
<br />30
<br />3974.8
<br />1243.7;
<br />30
<br />4516.9
<br />1566.31
<br />"
<br />30
<br />5113.91
<br />5128.9
<br />1950.3
<br />:1960.2
<br />40 ;
<br />3987.2
<br />3250.8
<br />1257.9
<br />146
<br />50.
<br />';.4530,:4
<br />4544.0
<br />1574.7
<br />1583.1',
<br />40
<br />'
<br />',5143.9.
<br />1970.3
<br />b0
<br />3999.5;
<br />{
<br />.,_50
<br />+'.70 ,x4011.91
<br />1265:0
<br />-77 --
<br />4557:6
<br />1591.6'
<br />.84•
<br />5159.0'
<br />1980.4
<br />10 '.
<br />4024:4
<br />•1272.1,
<br />10,
<br />-4"071:.2
<br />1600.1•
<br />;• 10
<br />,5174.1
<br />'.5159'.3
<br />1990.5
<br />20
<br />:4036:8'
<br />1279.3!
<br />; 20
<br />-4584.8
<br />1608.6
<br />' t ;,( 20 ,
<br />5204:4
<br />2000.6
<br />:2010.8
<br />^30
<br />, 4049.3
<br />'4061<8
<br />1286.5
<br />1293.6'
<br />i • -30
<br />: •'40
<br />•,4598:5
<br />,4012:2
<br />1617.1
<br />1025.7•
<br />30
<br />40
<br />5219:7
<br />2021.1
<br />40
<br />50
<br />4074.4
<br />1300.9
<br />•_,•,50
<br />;,4G2f:0
<br />1634.4
<br />50
<br />5234':9
<br />2031.4
<br />Corrections to be Added (T =Tangent. E=External.)
<br />Int.
<br />Carve 56
<br />10°15°
<br />20°
<br />25°
<br />30°
<br />35°
<br />'40°
<br />45° 50° 55° '606'
<br />65° 70°
<br />.Angle
<br />- -
<br />- .-
<br />T=.21 •
<br />=.42 :.63
<br />84
<br />1.05
<br />1 .27
<br />1.49
<br />1.71 .
<br />1.94 2.17, 2.38 2:60
<br />2.83 3.07
<br />60°
<br />E=.056
<br />J12 .168
<br />.225
<br />93
<br />.273
<br />'.283
<br />.340
<br />.398
<br />.457
<br />.516 .575 .636 '.697
<br />,774 .,851
<br />:165° T=.23
<br />*.X=.067', ,
<br />:46 :69
<br />' .135 :204
<br />1.16
<br />.343
<br />1.40:
<br />.412
<br />1.64.
<br />..483
<br />1.88
<br />.554
<br />2.13 '2.38 163 2.88
<br />.625..697 .711 ' :845
<br />3.13 3.39
<br />.922 1:01
<br />"70°
<br />T=.25.
<br />51 •,
<br />1.02
<br />P.28
<br />1.54
<br />1.80 .2.06
<br />233 2.60 2.88 3:16
<br />3.44 3.72
<br />E=.080
<br />.76.
<br />159
<br />:485
<br />'.568
<br />.652
<br />.735 .819 ..906 ,:994
<br />1.08 1:17
<br />'
<br />T=.27
<br />.240
<br />.321
<br />1.12
<br />.403
<br />1.40
<br />1.69
<br />1:98
<br />2.27
<br />2.57 2.87 3.16 3.47
<br />3.78 4.09
<br />76'
<br />E =.095
<br />.56 . .83
<br />•:182 .286
<br />.383
<br />:480
<br />.578
<br />.678
<br />.777
<br />.877 .977 1.07 1<18'
<br />1.29 1:39
<br />T=.30,
<br />91
<br />1.22
<br />1.53
<br />1.84
<br />2:15'
<br />2.46
<br />2.78. 3.10. 3.44
<br />4.46
<br />80° j
<br />_
<br />- E=.110
<br />.61
<br />.220 .332
<br />:445
<br />1558
<br />.671'.787
<br />:903
<br />1.02 1.13. 1.25.
<br />1.62
<br />';
<br />T =.33
<br />66 1:00
<br />1.33
<br />1.68
<br />2.02
<br />2:36
<br />2.70
<br />-.05 3.40 3.77 4.1414.89
<br />' E=.128 +
<br />- .259 .391
<br />.524
<br />.657
<br />.790
<br />.1926
<br />1'.06.
<br />1.20 1.34 1.47.191
<br />
|