|
IV TABLE,I. - Tangents and Externals to a' 1° Curve.
<br />Chord= 100 ft.
<br />Int.Int.
<br />Angle
<br />Tangent
<br />External
<br />Angle
<br />Tangent
<br />Externa l
<br />Int.
<br />Angle
<br />Tangent
<br />External
<br />43°, '
<br />2257.0:
<br />423.5,
<br />50°
<br />2671.8
<br />592.3.,
<br />570
<br />3110.9
<br />790.1
<br />10'
<br />2266.6
<br />432:0
<br />10'
<br />2681.9
<br />596.6
<br />IO'
<br />3121.7
<br />795.2
<br />20
<br />2276.2
<br />435.6,
<br />20
<br />-2692.1
<br />600.9,
<br />20.,
<br />3I32.5
<br />800.4
<br />30
<br />2285.9
<br />.439.2
<br />30
<br />2702.3
<br />605.3
<br />30
<br />3143.4'
<br />805.6
<br />.40
<br />2295.6
<br />442.8
<br />40
<br />2712.5
<br />609.6'
<br />40
<br />3154:2
<br />810.9
<br />.50.,
<br />2305.2
<br />,446.4,
<br />50;
<br />2722.7
<br />,614.0
<br />50
<br />3165.1
<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 />10
<br />3186.9
<br />826.7
<br />20
<br />233.1,3
<br />457.3
<br />20
<br />2753.4
<br />627.2
<br />20
<br />.3197:8
<br />832.0
<br />89
<br />2344.1
<br />461.0
<br />30
<br />2763.7
<br />631.7
<br />30
<br />3203,8
<br />837.3
<br />40
<br />2353,8
<br />464.6
<br />40
<br />2773:9
<br />636.2
<br />40
<br />"3219.7
<br />842.7
<br />50
<br />2363.5
<br />468.4
<br />50
<br />2784.2
<br />.640.7
<br />50
<br />3230:'7
<br />848.1
<br />4b
<br />2373.3-
<br />472.1
<br />52 .
<br />2794.5
<br />645:2
<br />59' '"
<br />-3241'.7
<br />853.5
<br />10
<br />2383.1
<br />475.8
<br />10
<br />2804.9
<br />649.7
<br />10.
<br />3252.7
<br />858.9
<br />" 20
<br />2392.8
<br />479.6
<br />20
<br />2815.2
<br />.654.3
<br />20.
<br />3263.7
<br />864.3
<br />30
<br />2402.6
<br />483.4
<br />30
<br />2825.6
<br />658.8
<br />30
<br />3274.8
<br />869.8
<br />40
<br />2412.4
<br />487,2
<br />40
<br />2835.9
<br />663.4
<br />' 40
<br />3285.8
<br />875.3
<br />50
<br />2422,3
<br />491,0
<br />1 50
<br />2846.3
<br />668.0
<br />50
<br />3296.9
<br />880.8
<br />462432.1
<br />3792.4
<br />494.8
<br />53 •
<br />2850.7
<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 />10
<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 />33.52.6
<br />008.8
<br />50
<br />-2481.4
<br />.514.3
<br />•50
<br />2908.9
<br />606.1
<br />5O'
<br />3363.8
<br />014.5
<br />47 -
<br />2491:3
<br />518.2
<br />54 •
<br />2919.4
<br />700.9
<br />611
<br />;3375.0
<br />920.2
<br />10
<br />2501.2
<br />522.2
<br />10
<br />2929.9
<br />705.7
<br />10'
<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 />5397:5
<br />931.6
<br />-30
<br />2521.1,
<br />530,1
<br />30
<br />2951.0
<br />715.3
<br />30'
<br />3408.8
<br />937.3
<br />40
<br />2531.1:
<br />534.2
<br />40
<br />2961.5
<br />720.1
<br />40
<br />3420.3
<br />943.1
<br />50
<br />25-11.0,
<br />538.2
<br />50
<br />2972.,1
<br />725.0
<br />50
<br />3431.4
<br />948.9
<br />69
<br />2551.0
<br />542.2
<br />55. -
<br />2982.7
<br />720.9
<br />62
<br />3442.7
<br />954,8
<br />.48
<br />10
<br />2561.0
<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
<br />2581.0
<br />554.5
<br />30
<br />3014.5
<br />744.6
<br />30
<br />-3476.8
<br />-..972A
<br />40
<br />2591.0
<br />558.6'
<br />40
<br />3025.2
<br />749.6
<br />40
<br />3488.3
<br />978.3
<br />50
<br />.2601.1
<br />562.8
<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 />56
<br />3046,5
<br />750.6
<br />63
<br />3511.1
<br />990,2
<br />'.10
<br />2621.2
<br />571.1
<br />10
<br />3057.2
<br />764.6
<br />10
<br />3522.G
<br />006.2
<br />20
<br />2633.3
<br />575.3
<br />.20
<br />3067.0
<br />760.7
<br />20
<br />3534.1
<br />1002.3
<br />30
<br />2641.4
<br />.579.5
<br />30
<br />3078.7
<br />774,7
<br />30
<br />3545.0
<br />1008.3
<br />40
<br />2651.5
<br />553.8
<br />40
<br />3089.4
<br />779.8
<br />40
<br />3557.2
<br />1014,4
<br />50
<br />2661.6
<br />.588.0
<br />50
<br />3100.2
<br />784.0
<br />50
<br />3568.7
<br />1020.5
<br />Corrections to be Added`(T-=Tangent. E`=Exteenal.) -
<br />Bugle
<br />Currie 50
<br />10° 15°' 200 250 30°
<br />35°
<br />400 45° 50°
<br />55° 600' 65°
<br />70°
<br />Tangent
<br />External
<br />'64°.
<br />3580,3
<br />1026.6
<br />71°
<br />4086.9
<br />400
<br />T=-13
<br />E =:023
<br />'.26 .40 .53 .57 .80
<br />.046 .070 .093 .117 .141
<br />-.93
<br />.172
<br />.10E 1.20 1.34
<br />.203 .234..265
<br />1.49 16400 1.395
<br />.277
<br />1.341
<br />10'
<br />4099.5
<br />1315.6
<br />1 .00
<br />.37 1 .52
<br />1.21H.345
<br />1 1 .87 2.411 .04
<br />21
<br />?
<br />-45'
<br />E =.030
<br />.060 .093 .819 .153 .189
<br />21G
<br />325
<br />3�1 378
<br />445
<br />1660.5
<br />T=.17
<br />.34 .51 .68 .85' 1.02
<br />1.19
<br />1.361.72
<br />1.91. 2.10 2,20
<br />2.48
<br />50°
<br />E =.037
<br />.075 .110 .151 .189 .227
<br />.256
<br />.30 .384
<br />.425 .467 .508
<br />.550
<br />4137.4
<br />T=.19
<br />.38 .57 .76 .95' 1.I4
<br />132
<br />1.52 1.72 1.92
<br />2.14 2.35 2.56
<br />2.77
<br />1057:7
<br />E=.040
<br />.093 x42 .188 .236 .263
<br />.332
<br />3.81 .420 .479
<br />.530 .582 .641
<br />.70C
<br />65
<br />*T=M
<br />.42 G3 84 1.05 1.27
<br />1.49
<br />1.71 1.04 2.17
<br />2.38 2.60 2.63
<br />3.07
<br />60'
<br />E =.056
<br />.112 .168 .225 .283 .340
<br />'.398
<br />.457 516 .575
<br />.636 .697 .774
<br />.851
<br />a
<br />T= 23 -
<br />93 1.16 1.40
<br />1.64
<br />1.86 2.13 '2.38
<br />2.63 2.68 3.13
<br />3.39
<br />20
<br />.46, .69
<br />E=.067 .135 .204 273 .343 ':412
<br />.483
<br />.554 .625 .697
<br />.711 .845 .922
<br />1.01
<br />I
<br />TABLE I. = Tangents and Externals to a 1! Curve, . v
<br />Chord =100 ft.
<br />I
<br />::Angle
<br />Tangent
<br />External
<br />'i ' Angle
<br />Tangent
<br />External
<br />Angle
<br />Tangent
<br />External
<br />'64°.
<br />3580,3
<br />1026.6
<br />71°
<br />4086.9
<br />1308.2
<br />78°
<br />4639:8
<br />1643.0
<br />•10'
<br />3591.9
<br />1032.8
<br />10'
<br />4099.5
<br />1315.6
<br />10'
<br />4653.6
<br />1651.7
<br />20
<br />3603.5
<br />1039.0
<br />20_
<br />4112.1
<br />1322.9
<br />20
<br />4667.4
<br />1660.5
<br />30
<br />3615.1
<br />1045.2
<br />30
<br />4124.8
<br />1330.3
<br />30
<br />4681.3
<br />1669.2
<br />40
<br />3626.8
<br />1051.4
<br />40'
<br />4137.4
<br />1337.7
<br />40
<br />4695.2
<br />1678.1
<br />50
<br />3638.5
<br />1057:7
<br />50
<br />4150.1
<br />13-15.1
<br />50
<br />4709.2
<br />1636.9
<br />65
<br />3650.2
<br />1663,9
<br />72
<br />4162.8
<br />1352.6
<br />.79
<br />4723.2
<br />1095.8
<br />10
<br />3661.9
<br />1070.2
<br />10
<br />4175.6
<br />1360.1
<br />10
<br />4737.2
<br />1704.7
<br />20
<br />3673.7
<br />1076.6
<br />20
<br />4188.5
<br />1367.6
<br />20
<br />4751.2
<br />1713.7
<br />30
<br />•3685.4
<br />1082.9
<br />30
<br />4201.2
<br />1375.2
<br />30
<br />4765.3
<br />1722.7
<br />40
<br />3697.2
<br />1089.3
<br />-40
<br />4214.0
<br />1382.8
<br />- 40
<br />4779.4
<br />1731,7
<br />.50
<br />3709.0
<br />1095.7
<br />50
<br />!4226.8
<br />1390.4
<br />50
<br />4793.6
<br />174 0. 8
<br />66
<br />3720:9
<br />1102,2
<br />73
<br />4239:7
<br />1395:0
<br />SO
<br />4807.7
<br />1749.9
<br />10
<br />3732.7
<br />1108.6
<br />10
<br />4252,6
<br />1405.7
<br />10
<br />4822.0
<br />1759.0
<br />20
<br />3744.6
<br />1115,1
<br />20
<br />4265.6
<br />1413.5
<br />` 20
<br />4836.2
<br />1768.2
<br />' 30
<br />8756.5
<br />1121.7
<br />30
<br />j427S.5
<br />1421.2
<br />30
<br />4850.5
<br />1777.4
<br />40
<br />.9768,5
<br />1128,2
<br />40
<br />14291.5
<br />1429.0
<br />40
<br />4864.8
<br />1785.7
<br />50
<br />3780.4
<br />I134,8
<br />-59
<br />4304.6
<br />1436.8
<br />50
<br />4879.2
<br />1795.0
<br />67
<br />3792.4
<br />1141.4
<br />74,
<br />4317.6
<br />1444,6
<br />81
<br />4893.6
<br />.1805.3
<br />10
<br />.3804.4
<br />1148.0
<br />10
<br />,4330.7
<br />1,152.5
<br />10
<br />4908.0
<br />1814.7
<br />20
<br />3816.4
<br />1154.7
<br />20
<br />4343.8
<br />1460.4
<br />20
<br />4922:5
<br />1824.1
<br />30
<br />3828.4
<br />1161.3
<br />30
<br />4350.91463.4
<br />30
<br />4937.0
<br />1833.6
<br />40
<br />3840,5
<br />1168.1
<br />40
<br />4370,1.
<br />1470-4
<br />.40
<br />4951.5
<br />1843.1
<br />60
<br />3852.6
<br />1174.8
<br />•50
<br />,4383,3
<br />1484.4
<br />50
<br />4966.1
<br />I852.6
<br />68
<br />3864.7
<br />1181.6
<br />75
<br />439G.5
<br />1492.4'
<br />82
<br />4980.7
<br />1862.2
<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 />20
<br />3589.0
<br />1195.2
<br />20
<br />4423.1
<br />1508.6
<br />20
<br />5010.0
<br />1881.5
<br />30
<br />3900.2
<br />1202.0
<br />30
<br />4436.4
<br />'1516.7
<br />30
<br />5024.8
<br />1891.2
<br />40,
<br />3913.4
<br />1208.9
<br />40
<br />4449.7
<br />1524.9
<br />40
<br />5039.5
<br />1900.D
<br />"50
<br />3925.6
<br />1215.8
<br />50
<br />4463.1
<br />1533.1
<br />50
<br />5054.3
<br />1910.7
<br />69
<br />3937.9
<br />1222.7
<br />76.
<br />4476,5
<br />1541.4;
<br />I. S3
<br />5069.2
<br />1920.5
<br />LO
<br />3950.2
<br />1220.7
<br />t 10
<br />4489.9
<br />'1549.7
<br />- 10
<br />5084.0
<br />1930.4
<br />20
<br />3962,5
<br />1.236.7
<br />20 '
<br />4503.4
<br />1558.0
<br />20,
<br />5099.0
<br />1940.3
<br />30'
<br />3974.8
<br />1.243.7
<br />30
<br />451G.9
<br />1566.8
<br />30
<br />5113.9
<br />1950.3
<br />40
<br />3937.2
<br />12.50.8
<br />40
<br />4530,4
<br />1574.7
<br />40
<br />5128.9
<br />1960.2
<br />50
<br />3999.5
<br />1357,9
<br />50
<br />4514'_0
<br />1583.1
<br />50
<br />5143.9
<br />1970.3
<br />70
<br />4011.9
<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 />4571.2
<br />1600.1
<br />10
<br />5174.1
<br />1990.5
<br />20
<br />4036.8
<br />1279.3
<br />20
<br />4584.8
<br />1608,6
<br />20
<br />5189.3
<br />2000.6
<br />30,
<br />4049.3
<br />1286.5
<br />30
<br />4508.5
<br />1617.1
<br />30
<br />5201.4
<br />2010.8
<br />40
<br />4061.8
<br />1293.6
<br />40
<br />4612.2
<br />1625.7
<br />40
<br />5219.7
<br />2021.1
<br />50
<br />4074.4
<br />1300.9
<br />50
<br />4620.0
<br />1634.4
<br />50
<br />5234.0
<br />2031.4
<br />Corrections to be Added (T=Tangent. E=External.)
<br />Angle Curve 50 100 150
<br />200
<br />25° 30°
<br />350
<br />400
<br />450
<br />50°
<br />550
<br />601
<br />65°
<br />70°
<br />600 T=:21 .42 .63
<br />.84
<br />1.05 1.27
<br />109
<br />t.71
<br />1.94
<br />2.17
<br />2.38
<br />2,60
<br />2.83
<br />3.07
<br />E =.056 .112 .168
<br />.225
<br />.283 .340..398
<br />.457
<br />.516
<br />.575
<br />.630
<br />.697
<br />,774
<br />,851
<br />650 T=.23 *.40 .69
<br />.03
<br />1.16 1.40
<br />1.64
<br />1.SS
<br />2.13
<br />2,3fi
<br />2.63
<br />2.88
<br />3.13
<br />3.39
<br />E =.067 ,135 .204
<br />373
<br />.343 .412
<br />.483
<br />.554
<br />.625
<br />.697
<br />.711
<br />.845
<br />.922
<br />1.01
<br />70° T=.25' .51 .70
<br />1.02
<br />1.28 1.54
<br />1.80
<br />2.06
<br />2.33
<br />2.60
<br />2.88'
<br />3.16
<br />3.44
<br />3.12
<br />E=.080 .159 .240
<br />321_
<br />.403 .485
<br />.568
<br />.652
<br />.135
<br />.819
<br />.905
<br />.994
<br />1.08
<br />1.17
<br />75- T=.27 . 56 .83
<br />1.12
<br />1.40 1.69
<br />1..98
<br />2.27
<br />2.57
<br />2.87
<br />3.16'
<br />3.47
<br />3.76
<br />4.09
<br />E=.0 5 .182 .286
<br />.383
<br />.460 x78
<br />.678
<br />.777
<br />.877
<br />.977
<br />1.07
<br />1.18
<br />1:29
<br />1.39
<br />$Oo T=.30 .61 .91
<br />1.22
<br />183 1.84
<br />2.15
<br />2,43
<br />2.78
<br />3.10
<br />3.44
<br />3.78
<br />4.12
<br />4.46
<br />E=.110 .220 :332
<br />.445
<br />.558 .671
<br />,787
<br />.903
<br />1.02
<br />1.13
<br />1.25
<br />1.38
<br />1.50
<br />1.62
<br />85' T =.33 .66 1.00
<br />1.33
<br />1.68 2.02
<br />2.36
<br />2.70
<br />3.05
<br />3.40
<br />3.77
<br />4.14
<br />4.55
<br />4.89
<br />E =.128 .259 .391
<br />.524
<br />.657 .790
<br />.926
<br />1.05
<br />1.20
<br />1.34
<br />1.47
<br />1.62
<br />1.76
<br />1.91
<br />
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