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Table VI. Deflections for gut Chorrls•far Sha,•f'R.u.r1i„p 11nr•aac
<br />• Degree .�,
<br />Of
<br />Curve
<br />Radius '�
<br />•50
<br />iif def: ang,
<br />. -� =sin of def. angle -
<br />R,� n
<br />g
<br />of arc
<br />for 100 ft.
<br />y2.5•Ft.
<br />1 L•5iFt. " 20 -Ft • :1.
<br />_
<br />25 Ft.
<br />300
<br />193.18
<br />i° 51'-21,17,
<br />orifi
<br />2' j8' -
<br />3°'43'
<br />-- Ior-15
<br />32. _
<br />x81.39
<br />I°.59.
<br />2°'�5,
<br />;_. 3° La'
<br />3° 58'
<br />:101.33
<br />340
<br />171.61
<br />"Zo 06 ..
<br />233, .
<br />,. 3' 21'
<br />" 4' 12'
<br />IOL -48
<br />36'
<br />'...
<br />161.80'
<br />¢° 13',2°'49'
<br />.
<br />, -3° 33 '
<br />:. ° 26'
<br />4
<br />101.66
<br />38°
<br />-
<br />-[53.58,
<br />"-.-�9
<br />2°-20, .
<br />2° 49
<br />3' 44
<br />4° 40' '
<br />10[.85
<br />40
<br />..
<br />.2° z7,.
<br />2'i57' �_
<br />3°55' •'�
<br />454'.
<br />i92.b6
<br />4 2°'
<br />t
<br />3952 _ •'
<br />2"34"
<br />3°05'4°
<br />07' -'
<br />'66 08'
<br />-
<br />IO2.29
<br />.44°
<br />r33.47• 7
<br />z°41'
<br />3'.13,
<br />6841
<br />6862
<br />•[02.53
<br />46°r•_;
<br />-:_- T-97
<br />49' 2°48',..
<br />3°;21,,'
<br />4° 29 1
<br />5° 36'-
<br />102.76
<br />6°
<br />4 ,'-
<br />122.92
<br />2,° 55`
<br />:3°.29,
<br />4° 40!'
<br />:. 5° 50'
<br />163.00
<br />Soa
<br />178,31 ;.
<br />3° 6.2
<br />3°'38'
<br />4° 51
<br />6 04'.,
<br />'. 103:24
<br />5z°
<br />1.14.06.; ..
<br />31 09'
<br />.3°.'46'
<br />5° o2"
<br />6° 17'1
<br />10 54.
<br />3
<br />54°'.'.
<br />1IV, IL•
<br />3 - 16'.
<br />3 °54'
<br />5° 13
<br />6° 3['
<br />x03.84
<br />56° ....j7o6:50
<br />Ir'13 1132
<br />3° sz'
<br />4°.a2'.
<br />5a"23' "
<br />, 6° 44
<br />t 109:14.
<br />58°
<br />TP 3,114
<br />3' 29-
<br />'4-10'
<br />'.5' 34`•-,
<br />•6° 57'
<br />-;104.43
<br />60°
<br />Ioo:oo
<br />3°"R S'
<br />a 18
<br />c° e.r
<br />-71. rr'.
<br />7f1Q•72
<br />` CURVE: FORMULAS,
<br />T - R tan :I R- T cot. } I Chord 'def: __chorda '
<br />T - 50!taii'. fl
<br />Sin. D 50 1.70. "chords =". I
<br />R'
<br />E -Rea. eec. I D .
<br />Sin, D 50aan. } I
<br />T _ E =,T tau a Tan: def, .= I chord deft
<br />'The square of any distance; divided by twice the radius,' will equal the -
<br />distance from'tanneat to curve, very.'nearly. . -
<br />Table IV.. 60nt0ns Tangents and Exteruals'to a 10 curve. 'Pan. apd Ext.
<br />to any- other_eadins may, be found: neRrly'enough; by dividing. the, Tau. -or
<br />-Ext. opposite the,given,Ccutral Angle -by the given degree of curve.
<br />To tind'Deg.`gf Curve, having the Ce'tral Angle and angent: Divide
<br />Tan. opposite the given Central Angle by the given Tangent.
<br />To ,fin&-D`ig. of Curve; having the (ventral Anzle and Tangent.' Divide
<br />Ext. opposite the, ggiven Central Angle by the given Extemai.
<br />To Sail. Nat: Tan. and Nat. Ex. Sec. for any angle by Table . IV.: Tan. i.
<br />or Ext. of twice the-given'angle divided by the radius of a 111•curve will be I
<br />the Nat.-Tan°;or.Nat. Ex.'Sec.
<br />,jo find' angle for a•given distance,and deflection:
<br />Rule 1. Multiply the given distance liy .01746 (def. for 11 for 1 -ft.), and
<br />divide iven deflection by the product. ' •
<br />Rine 2. Multiply given deflection b7 57.3, and divide the product b9
<br />thegiven distance.
<br />To find deflection for a given angle and distance: Multiply the angle
<br />by .0 1745, and the product by the distance.
<br />Rwirr ANGLE TalAxcll.ss. Square the altitude, divide by twice the base ]
<br />Add quotient to base for hypotenuse:
<br />Given Rase 100, Alt 10. 108 200 = .5. 100 + .5 = 100.5 hyp.
<br />Given Hyp. 100, Alt. 25. 25- 200=3.125. 100-3.125=96,875 =Base.
<br />Error in first example, .002 ; in last, .045.
<br />To find lions of Rail in one mile of track: multiply weight per yard
<br />by 11, and'divide by 7.
<br />$aturll Sines
<br />pea.1 0' 1 LO'- 1 20' 1 30'
<br />f 40' 1 50' 1e,o.4otq.
<br />01
<br />1 10'
<br />120' 1
<br />30' 1 40' 1 SO' -fora.
<br />0
<br />0000
<br />0029
<br />0058 0oB7
<br />orifi
<br />0145
<br />89
<br />40
<br />6428
<br />645o
<br />6472
<br />6494
<br />6517
<br />6539
<br />49
<br />i
<br />or75
<br />0204
<br />0239 6262
<br />o2gi
<br />o32o
<br />BS
<br />41
<br />6561
<br />6583
<br />6604
<br />6626
<br />6648
<br />6670
<br />48
<br />2
<br />0349
<br />0378
<br />0407 0436
<br />046=
<br />6494
<br />87
<br />42
<br />6691
<br />6713
<br />6734
<br />6756
<br />67714799
<br />147
<br />3
<br />0523
<br />0552
<br />0581 06 to
<br />0.640
<br />0669
<br />86
<br />43
<br />6820
<br />6841
<br />6862
<br />6884
<br />6905
<br />6926
<br />46
<br />4
<br />o698
<br />0727
<br />0756 0785
<br />0814
<br />0643
<br />85
<br />44
<br />6947
<br />6967
<br />6986
<br />7009
<br />7030
<br />7050
<br />45
<br />5
<br />0872
<br />090,
<br />0929 0958
<br />0987
<br />ro16
<br />8¢
<br />45
<br />707[
<br />7092
<br />71r2
<br />7133
<br />7F53
<br />7173
<br />44
<br />6
<br />1045
<br />1674
<br />Ir'13 1132
<br />L16t
<br />1190
<br />83
<br />•46
<br />7193
<br />7214
<br />7234
<br />7254
<br />7274
<br />7294'43
<br />71219
<br />1248
<br />1279 1305
<br />"1334
<br />1363
<br />82
<br />'47
<br />7314
<br />7333
<br />7353
<br />73737
<br />392
<br />7412'92
<br />81392
<br />r421
<br />[449 1478
<br />r5o7
<br />r536
<br />81
<br />48
<br />7431
<br />7151
<br />7476
<br />7:4.90
<br />7509
<br />7528
<br />41
<br />9
<br />4564
<br />1593
<br />1622 1650
<br />r679
<br />1708
<br />8,
<br />49
<br />7547
<br />7566
<br />7585
<br />7694
<br />7623
<br />7642
<br />40
<br />101736
<br />1765
<br />x794
<br />1822
<br />1851
<br />r880
<br />79
<br />0
<br />7660
<br />7679
<br />7698 7.716
<br />7735
<br />7753i34
<br />11
<br />1908
<br />1937
<br />1965
<br />1994
<br />2022
<br />2051
<br />"78
<br />Sr
<br />777117790
<br />7808 7826
<br />7844
<br />7862
<br />38
<br />12
<br />2079
<br />2108
<br />2136
<br />2164
<br />2193
<br />2221
<br />77
<br />'52
<br />7880
<br />7898
<br />7916 7934
<br />7951
<br />7969
<br />37
<br />13
<br />2250
<br />2278
<br />2306
<br />2334
<br />2363
<br />2391
<br />76
<br />53
<br />7.98618004
<br />8021 8039
<br />8056
<br />8073
<br />36
<br />14
<br />2419
<br />2447
<br />2476
<br />2504
<br />2532
<br />2560
<br />75
<br />54
<br />8090
<br />8107
<br />8124 8'41
<br />8158
<br />8175
<br />35
<br />15
<br />2588
<br />26[6
<br />2644
<br />2672
<br />2700
<br />2728
<br />7
<br />55
<br />8192
<br />8208
<br />822518241
<br />8258
<br />8274
<br />34
<br />16
<br />2156
<br />27S4
<br />28r
<br />2840
<br />2568
<br />2896
<br />73
<br />56
<br />8290
<br />8307
<br />8323 8339
<br />8355
<br />8371
<br />33
<br />17
<br />2924
<br />2952
<br />2939
<br />3007
<br />3035
<br />3062
<br />72
<br />578387
<br />8403
<br />841.8'8934
<br />8450
<br />8465
<br />32
<br />T8
<br />3090
<br />3118
<br />3745
<br />3173
<br />3201
<br />3228
<br />71
<br />58
<br />8480
<br />8496
<br />851 ri8526
<br />8542
<br />8557
<br />31
<br />19
<br />3256
<br />3283
<br />3311
<br />3338
<br />336510
<br />-70
<br />59
<br />8572
<br />8587
<br />86o1 8616
<br />8631
<br />8646
<br />30
<br />20
<br />3420
<br />3446
<br />3475
<br />3502
<br />3529
<br />3557
<br />69
<br />60
<br />866o
<br />8675
<br />8689
<br />8704
<br />8718
<br />8732
<br />29
<br />21
<br />3584
<br />3611
<br />3638
<br />3665
<br />3692
<br />3719
<br />68
<br />6t
<br />8746
<br />8760
<br />8774
<br />8788
<br />E8o2
<br />8816
<br />28
<br />22
<br />3746
<br />3773
<br />3800
<br />3827
<br />3854
<br />3881
<br />67
<br />62
<br />8829
<br />8843
<br />8857
<br />8870.8884
<br />8897
<br />"27
<br />23
<br />3907
<br />3934
<br />3961
<br />3987
<br />4or4
<br />4041
<br />66
<br />63
<br />8910
<br />8923
<br />8936
<br />8949
<br />8962
<br />8975
<br />26
<br />?4
<br />4067
<br />4094
<br />4120
<br />4147
<br />4173
<br />42oo
<br />65
<br />64
<br />8988
<br />9oor
<br />9or3
<br />9026
<br />g638
<br />9051
<br />25
<br />25
<br />4226
<br />4253
<br />4279
<br />4305
<br />433r
<br />4358
<br />64
<br />65
<br />9063
<br />9075
<br />9088
<br />9100
<br />9112
<br />9124
<br />24
<br />'26
<br />4384
<br />4410
<br />4436
<br />4462
<br />4488
<br />4514
<br />63
<br />66
<br />9135
<br />9r47
<br />9159
<br />9771
<br />9182
<br />9194
<br />23
<br />27
<br />4540
<br />4566
<br />4592
<br />4617
<br />4643
<br />466'
<br />62
<br />67
<br />9205
<br />9216
<br />9228
<br />9239
<br />9250
<br />026r
<br />22
<br />28
<br />4695
<br />4720
<br />4 746
<br />4772
<br />4797
<br />4823
<br />61
<br />68
<br />9272
<br />9263
<br />92939304
<br />9315
<br />9325
<br />21
<br />29
<br />4848
<br />4-74--
<br />4924
<br />4950
<br />4975
<br />6
<br />69
<br />9336
<br />9346
<br />9356
<br />9367
<br />9377
<br />9387
<br />20-
<br />30'5000
<br />5025
<br />5050
<br />5075 5100
<br />5125
<br />59`70
<br />9397
<br />9407
<br />9417
<br />9426
<br />943619446
<br />19
<br />3 r
<br />5150 5175
<br />5200
<br />5225 5250
<br />5275
<br />58
<br />.71
<br />9455
<br />9465
<br />9474
<br />9483
<br />9492
<br />9502
<br />18;
<br />32
<br />5209. 5324
<br />5348
<br />5373 5396
<br />5422
<br />57
<br />72
<br />9511
<br />95.20
<br />9528
<br />9537
<br />95445
<br />9555
<br />77-
<br />7-33
<br />33
<br />54 t -X471
<br />5495
<br />5519 5544
<br />5568
<br />56
<br />73
<br />9563
<br />957:2
<br />9580
<br />9588.9596
<br />9605
<br />16
<br />44
<br />5592 5616
<br />5640
<br />5664 5688
<br />5712
<br />55
<br />74
<br />9618
<br />962 r
<br />()628
<br />9636
<br />9644
<br />9652
<br />15:
<br />35
<br />5736 5760
<br />5783
<br />5807 5831
<br />5854
<br />5
<br />75
<br />9654
<br />9667
<br />9674
<br />968r
<br />g68<)9696'
<br />74
<br />365878
<br />590T
<br />5925
<br />594615972
<br />5995
<br />53
<br />76
<br />9703
<br />9710
<br />9717
<br />9724
<br />9730
<br />9737
<br />-13 •
<br />37
<br />6018 6o4t
<br />6065
<br />6o88 6tr1
<br />6134
<br />52
<br />77
<br />9744
<br />97501975
<br />7
<br />9763.9769
<br />9775
<br />12
<br />38
<br />6157 618o
<br />6202
<br />6225 62¢8
<br />6271
<br />51
<br />:78
<br />9781
<br />9787
<br />9793
<br />9799
<br />9805
<br />9811
<br />11
<br />3916293
<br />63 t6
<br />6338
<br />6361 6383
<br />6906
<br />5
<br />79
<br />9816
<br />9822
<br />9827
<br />9833
<br />9838
<br />9843
<br />10 .
<br />aEal
<br />60' 1 50'
<br />{ 40' 130' 120' 1 10' lorolloeo.l
<br />6Q'
<br />130'
<br />1 40' p'30'j .20'
<br />1.10'
<br />faro.
<br />oto.l 0' I tO' f 20' 1 30' 40' I 501 faro.
<br />80 98 48 9853 985B 9863 9868 98729
<br />81 9877 681 9886 9890 9894, 98998
<br />32 9903 9907 9911 9914 9918 99227
<br />83 9925 9929 9932 9936 .9939 9942 6
<br />84 9945 9948 9951 9954 9957 99595
<br />65 9962 9964 99679969 9971 99744
<br />86 9976 9978 9980 99819983 9985 3
<br />67 9986 9988 99899990 9992 9993 2
<br />88 9994 9995 999619997 9997 9998 1
<br />89 9998 9999 99999999 1.0000 1.a000.o
<br />wal 60' 1 50' I 40' i 30' 1 20' I 10' 1010, r
<br />Natural Cosines
<br />W
<br />
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