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VIII
<br />TABLE H. - Radii, Ordinates and Deflections. Chord =100 ft.
<br />Deg.
<br />Iladiue
<br />Mid.
<br />Ord.
<br />Tan.
<br />Dist.
<br />Df.
<br />Dist.
<br />De'
<br />1f Ft.
<br />Deg.',
<br />Radius
<br />Mid.
<br />Mid.
<br />Tan ..
<br />Dtat.
<br />Def.
<br />Dist.
<br />_Def,
<br />)f Ft.
<br />193.18
<br />1° 51
<br />2° 17
<br />2° 58'
<br />3° 43' .
<br />1oi. 15
<br />320
<br />181.39
<br />1° 59'
<br />2° 25'
<br />3° Io'
<br />3° 56'
<br />0'10'
<br />34377.
<br />.03G
<br />,145
<br />.29 1
<br />0.05
<br />7°
<br />$10.0
<br />1,528
<br />fi 105
<br />12t� 21
<br />2.10
<br />20
<br />17189.
<br />.073
<br />.291
<br />.582
<br />0.10
<br />20'
<br />781.$
<br />1.600
<br />6,395
<br />12.79
<br />2.20
<br />30
<br />11459.
<br />.109
<br />.436
<br />.873
<br />0.15
<br />30
<br />764.5
<br />1.637
<br />6.540
<br />13.08
<br />2.25
<br />40
<br />8594.4
<br />.145
<br />.582
<br />L 164
<br />0.20
<br />40
<br />747.9
<br />1.673
<br />6.685
<br />13.37
<br />2.30
<br />50
<br />6875.5
<br />.182
<br />.727
<br />1.454
<br />0.23
<br />8
<br />716.8
<br />1.746
<br />6.976
<br />13.95
<br />2:40
<br />1
<br />5729.6
<br />,218
<br />,873
<br />1.745
<br />0.30
<br />20
<br />688.2
<br />1-819
<br />7.266
<br />L-1.53
<br />2.W
<br />10
<br />4911.2
<br />.255
<br />1.018
<br />2.036
<br />0.35.
<br />30
<br />674.7
<br />1.855
<br />7.411
<br />14.82
<br />2.53
<br />20
<br />4297..3
<br />.291
<br />1.164
<br />2.327
<br />0.40
<br />40
<br />661.7
<br />1.892
<br />7.556
<br />15. tl
<br />2.60
<br />30
<br />3519.8
<br />.327
<br />1.300
<br />2.61$
<br />0.45
<br />9
<br />637.3
<br />1-965
<br />7.846
<br />15.69
<br />2.70
<br />40
<br />3937.9
<br />.364
<br />1.454
<br />2.909
<br />0.50
<br />20
<br />614.6
<br />2.037
<br />8,136
<br />16.27
<br />2.80
<br />50
<br />3125.4
<br />.400
<br />1.600
<br />3.200
<br />0:55'
<br />30
<br />G03.8
<br />2-074
<br />8.281
<br />16.56
<br />2.85
<br />3
<br />2864.9
<br />.436
<br />1.745
<br />3.490
<br />0.60
<br />40
<br />593.4
<br />2.110
<br />8.426
<br />16.85
<br />2.90
<br />1D
<br />2544.6
<br />.473
<br />1.891
<br />3-781
<br />0.65.
<br />10
<br />573.7
<br />2.183
<br />8.716
<br />17.43
<br />3.00
<br />20
<br />2355.7
<br />.509
<br />2.636
<br />4-072
<br />0.70
<br />30
<br />516.4
<br />2.292
<br />9.150
<br />18.30
<br />3.15
<br />30
<br />2292.0
<br />.545
<br />2.181
<br />4.363
<br />D.75
<br />1t
<br />521.7
<br />2.402
<br />9.585
<br />19.16
<br />3.30
<br />40
<br />2148.8
<br />.582
<br />2.327
<br />4.654
<br />0.80
<br />30
<br />499.1
<br />2-511
<br />10,02
<br />20.04
<br />3.45
<br />50
<br />2022.4
<br />.618
<br />2.472
<br />4.945
<br />0.85
<br />12 ,
<br />478.3
<br />2.620
<br />10.45
<br />20.91
<br />3.60
<br />S
<br />1910.1
<br />.655
<br />2.618
<br />5.235
<br />0.90
<br />30
<br />459.3
<br />2.730
<br />10.89
<br />21.77
<br />3.75
<br />10
<br />1809.6
<br />.691
<br />2.763
<br />5.526
<br />0.95
<br />13
<br />441-7
<br />2.839
<br />11.32
<br />22. 64
<br />3.90
<br />20
<br />1719.,1
<br />.727
<br />2.908
<br />5.817
<br />1.00
<br />1 30
<br />425-4
<br />2.948
<br />11.75
<br />23.51
<br />4.05
<br />30
<br />1637.3
<br />.764
<br />3.054
<br />6.108
<br />.1.05
<br />14
<br />410-3
<br />3.058
<br />12.18
<br />2.3.37
<br />4.20
<br />40
<br />1552.9
<br />.800
<br />3.199
<br />6.398
<br />1.10
<br />30
<br />396.2
<br />3.168
<br />12,62
<br />25.24
<br />4.35
<br />50
<br />1495.0
<br />.836
<br />3.345
<br />6.699
<br />1.15
<br />15
<br />383.1
<br />3.277
<br />13.05
<br />26. 11
<br />4:50
<br />4
<br />1132.7
<br />.873
<br />3.490
<br />'6.080
<br />1.20
<br />30
<br />370.8
<br />3.387
<br />13.49
<br />26:97
<br />4.65
<br />10
<br />1375.4
<br />.900
<br />3.635
<br />7.271
<br />1.25
<br />141
<br />359.3
<br />3.496
<br />13.92
<br />27.84
<br />4.80
<br />20
<br />1322.5
<br />.945
<br />3.718
<br />'7.561
<br />1.30
<br />30
<br />3.18.5
<br />3.G06
<br />14.35
<br />28.70
<br />4.95
<br />30
<br />1273.6'
<br />.982
<br />3.926
<br />7.852
<br />1.35
<br />1.7
<br />338.3
<br />3.716
<br />14.78
<br />20.56
<br />5.1.0
<br />40
<br />1228.1
<br />1.018
<br />4.071
<br />8,143
<br />1.40
<br />18
<br />319.6
<br />3.935
<br />15.64
<br />31.29
<br />5.40
<br />50
<br />1185.8
<br />1.055.4.217
<br />8.433
<br />1.45
<br />19,
<br />302.9
<br />4.155
<br />16.51
<br />33.01
<br />5.70
<br />5
<br />1146.3
<br />1.001
<br />4,3132
<br />8.724
<br />1.50
<br />20
<br />287.9
<br />4.374
<br />17.37
<br />34:73
<br />6.00
<br />10
<br />1109:3
<br />1.127
<br />4:507
<br />9..014
<br />1.55
<br />21
<br />274.4
<br />4.594
<br />18.22
<br />30.44
<br />6.30
<br />20
<br />1074.7
<br />1.164
<br />4.653
<br />9.305
<br />1.60
<br />22
<br />262.0
<br />4.81419.08
<br />38.16
<br />6.60
<br />30
<br />.,1042:1
<br />1.200
<br />4.798
<br />9.596
<br />1.65
<br />23
<br />250.8
<br />5.035
<br />19.94
<br />39.87
<br />6.90
<br />40
<br />10tt.5
<br />1.237
<br />4.943
<br />9.880
<br />1.70
<br />24
<br />240.5
<br />5.255
<br />20.79
<br />41.58
<br />7.20
<br />50
<br />982.6
<br />1:273
<br />5.088
<br />10.18
<br />1'.75
<br />25'
<br />231.0
<br />5.476
<br />21.64
<br />43.28
<br />7.50
<br />d
<br />955.4
<br />1.309
<br />5.234
<br />10.47
<br />1.80
<br />26
<br />222.3
<br />5.697
<br />22.50
<br />41.99
<br />7. SO
<br />10
<br />929.6
<br />1.346
<br />5.379
<br />10.76
<br />1.85
<br />27
<br />214.2
<br />5.918
<br />23.35
<br />40.69
<br />8.10
<br />20
<br />905.1
<br />1'.382
<br />5.524
<br />11.05
<br />1.90
<br />28
<br />206.7
<br />6.139
<br />24.19
<br />48.38
<br />8.40
<br />30
<br />.881.9
<br />1.418
<br />5.669
<br />11.34
<br />1-95
<br />29
<br />199.7
<br />6.360
<br />25.04
<br />50.07
<br />8.70
<br />40
<br />:859.9
<br />1.4.55
<br />5.814
<br />11.63
<br />2.00
<br />30
<br />193.2
<br />6.583
<br />25.88
<br />51.76
<br />9.00
<br />The middle ordinate in inches for any cord of length (C) is eqqual to .0012 C'
<br />multiplied by the middle ordinate takon front the above table. Thus, if it
<br />desired to bend a 30 ft, rail to fit a 1.0 degree curve, its middlo ordinate should
<br />be .0012X990X3.183 or 2.36 inches.
<br />TABLE III. Deflections for Sub Chords for Short Radius Curves.
<br />Degree
<br />of
<br />Radius
<br />- 50
<br />rra sub c€nerd = gun of I def. angle.
<br />I2
<br />f ength
<br />of are
<br />Carve
<br />sin:•§def, ang.
<br />12,5 Ft.
<br />15 Ft.
<br />24 Ft.
<br />25 Ft.
<br />for 100 ft.
<br />--30°
<br />193.18
<br />1° 51
<br />2° 17
<br />2° 58'
<br />3° 43' .
<br />1oi. 15
<br />320
<br />181.39
<br />1° 59'
<br />2° 25'
<br />3° Io'
<br />3° 56'
<br />181.33
<br />34°
<br />171.01
<br />2' 06'
<br />2° 33'
<br />3° 21'
<br />40 12'
<br />101.48
<br />36°
<br />161.80.
<br />2,°13'
<br />2°41'
<br />3°33'
<br />4°•26'
<br />tot 66
<br />38°'
<br />153.58
<br />2° 2o'
<br />z° 49
<br />3° 44'
<br />4° 40
<br />101 8,5
<br />40°
<br />146. ig
<br />2° 27'
<br />20 57
<br />3° 55'
<br />4° 54
<br />m. b6
<br />42°
<br />139.52
<br />2° 34'
<br />3° 05'
<br />4° 07'
<br />S° 08
<br />102.29
<br />44°
<br />133.47
<br />2° 41'
<br />3° 13''
<br />40 18'
<br />5° 22'
<br />102:53
<br />46°
<br />127.97
<br />2° 48'
<br />3° 21'
<br />}° 29'
<br />5° 36'
<br />102.76
<br />48°
<br />122-92
<br />2° S5'
<br />3' 29'
<br />4° 40'
<br />j° 50'
<br />103.00
<br />50°'
<br />I18.31
<br />3° 02'
<br />3° 38
<br />4° g1.'
<br />, 6° 04'
<br />103.,24 .
<br />52°.
<br />114.06
<br />3° 09'
<br />3° 46'
<br />5° 02'
<br />6° e.7,
<br />1.03.54.
<br />54°
<br />110. 11
<br />3° 16
<br />3° 54'
<br />,5° 13
<br />G° 31'
<br />( 103.84
<br />56°
<br />106..50
<br />3° 22'
<br />4° 02'
<br />5° 23'
<br />6° 44
<br />104. t4
<br />58°
<br />103-14
<br />3° 29'
<br />4° 10'
<br />5' 34'
<br />6° 57
<br />104 43
<br />6b°
<br />3do. 001
<br />3° 35'
<br />4' 1H'
<br />50 44' •C
<br />,7° 11'
<br />C 104.72
<br />ill
<br />CURVEFORMULAS
<br />T = R tan iI R - T cot. = I chord'
<br />T o 5o tan z 1 Chord clef.
<br />. in. _a I_l R - 50 fd
<br />Sin: i D 50 ;Sin. a D No. chords - f
<br />11 E = R ex. sec I D
<br />SO tan ' 1 -
<br />Sin: s U " I, F. =Tian } I Tan. clef. - Ichord def.
<br />The square of any distance, divided by twice the radius, will. equal
<br />the distance from tangent to curve; very nearly.
<br />To find angle for a given distance and deflection.
<br />Rule 1. Multiply the given distance by _01745 (def. for 1°'for i ft.
<br />6ce Table IL), and divide given deflection by the product.
<br />Rule 2. Multiply given deflection by57.3,.and divide the product by
<br />the given distance.
<br />To find deflection for a given angle and distance. Multiply the angle
<br />by .01745, and the product by the distance-'
<br />GENERAL DATA
<br />RI6n-I' ANGLE TRIANGLES. 'Square the altitude, -divide by twice the
<br />base. Add quotient to base for hypotenuse.
<br />Given Base loo, Alt. 1o.1o5=Zoo=.5. Ioo+.5=100.,5 hyp.
<br />Given Hyp. loo, Alt. 2,5.255 ' 2oo=3.i25. loo-3.125=96.875=Base.
<br />Error in first example, .002: in last, .0+5.
<br />To find Tons of Rail in one mile of track: multiply weight per yard
<br />by 11, and divide by 7.
<br />LEVELING. The correction for curvature and refraction, in- feet
<br />and decimals of feet is equal to 0.574d5, where d is .the distance in .cniIvs.
<br />The correction for curvature alone is closely, ds. The combined cor,
<br />e .l
<br />rection iegative. i
<br />PROBABLE ERROR. If ell, d2,�cls, etc. are the discrepancies of various
<br />results from the mean, and if Cdr=the sum of the squares of these differ-
<br />ences and n=the number of observa(ions, then the probable error of the
<br />mean= 2d5
<br />=k:0.6745 n(n-1')
<br />SOLAR EPHEME'Ri&. Attention is called to the Solar Ephemeris for
<br />the current year, published by Keuffe6 &Esser Co., and furnished upon
<br />request. This handy booklet, 3'8x6 in., has about 190 pages of data very
<br />useful to the Surveyor; such as -the adjustments of transits, levels and solar
<br />attachments; directions and tables- for determining the meridian and the
<br />latitude from observations on the sun and Polaris; stadia measurements;
<br />magnetic declination; arithmetic constants, etc.
<br />TABLE IV. -Minutes in Decimals of a Degree.
<br />1+
<br />0167
<br />]1'
<br />.1833
<br />21'
<br />.3500
<br />311
<br />.5167
<br />43'
<br />.6833
<br />51'
<br />.8600
<br />2
<br />.0333
<br />12
<br />.2000
<br />22
<br />,3667
<br />32
<br />.5333
<br />42
<br />.7000
<br />52
<br />.8667
<br />3
<br />;0500
<br />13
<br />.2167
<br />23
<br />.3833
<br />33
<br />:5500
<br />43
<br />.7167
<br />53
<br />.8833
<br />4
<br />.0667
<br />14
<br />.2333
<br />24
<br />.4000
<br />34
<br />.5667
<br />44
<br />.7333.
<br />54 .
<br />.)000
<br />5;
<br />.0833
<br />15
<br />.2500
<br />25
<br />.4167
<br />35
<br />.5833
<br />45
<br />.7500
<br />55
<br />.4167
<br />6
<br />:1000
<br />16
<br />.2667
<br />26
<br />.4333
<br />36
<br />.6000
<br />46
<br />.7667
<br />56
<br />.9333
<br />7
<br />1167
<br />17
<br />.2833
<br />27
<br />.4500
<br />.37
<br />.6t67
<br />47
<br />.7833
<br />57
<br />.9500
<br />8
<br />.1333
<br />18
<br />.3000
<br />28
<br />.4667
<br />38
<br />.6333
<br />48'
<br />.8000
<br />58
<br />.9667
<br />9
<br />1500
<br />3167
<br />29
<br />A933
<br />39
<br />.6500
<br />49
<br />.8167
<br />59
<br />.9833
<br />10
<br />1 .1667 11
<br />.19
<br />20
<br />1 .3333 11
<br />30
<br />1 ..000 11
<br />40
<br />6667 11
<br />50
<br />1 8333 ij
<br />60.
<br />I 1.0000`
<br />TA R1.1t 1.
<br />-Inches in Decimals of a FooI
<br />1-16
<br />3-32
<br />}iy
<br />3-16
<br />'-(
<br />5
<br />.0052
<br />.0078
<br />.0104
<br />.0156
<br />.0208
<br />.0260
<br />.0313
<br />.0117
<br />.0521 I
<br />.0623
<br />.0729
<br />-0833
<br />_ •�
<br />:1667
<br />3
<br />' .2500
<br />.I
<br />.3333
<br />:i
<br />_ 4167
<br />6
<br />I . ,000
<br />7
<br />.5833
<br />3.
<br />.0567
<br />9 10
<br />.7500 I 8333
<br />11
<br />.!1167..
<br />
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