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VIII
<br />TABLM IL -- Radii, Ordinates and, Deflections. Chord =100 ft.
<br />Deg,
<br />Radius
<br />Mid.
<br />Old.
<br />Tan.
<br />Diet.
<br />Def.
<br />Dist.
<br />1f Ft.
<br />�g
<br />i�
<br />Mid.
<br />Ord.
<br />Tall.Def.
<br />bist,.
<br />Diet.
<br />Def.
<br />1f Ft.
<br />193.18
<br />t.
<br />2° 17'
<br />2° 58'
<br />3° 43'
<br />T01. r5
<br />320
<br />t,
<br />t,
<br />I L.
<br />f L.
<br />3° 58'
<br />0'10'
<br />34377.
<br />.035
<br />.145
<br />.291
<br />0.05
<br />71
<br />819.0
<br />1.528
<br />6.105
<br />I2.21
<br />2.10
<br />20
<br />17189..
<br />.073
<br />.291
<br />.582
<br />0.10
<br />20'
<br />781.8
<br />1.600
<br />6-395,12.79
<br />40°
<br />2,20
<br />30
<br />11459.
<br />.109
<br />.436
<br />.873
<br />0.15
<br />30
<br />754.5
<br />1,637
<br />6.540
<br />13, U8
<br />2.25
<br />,40
<br />8594.4
<br />..145
<br />.582
<br />1.154
<br />0.20
<br />40
<br />747.9
<br />1:673
<br />6.685
<br />13,37
<br />2-30
<br />50
<br />6575,5
<br />.185
<br />.727
<br />1.454
<br />0,25
<br />8
<br />716.8
<br />1,746
<br />6.976
<br />13.95
<br />2-40
<br />3° 38'
<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 />14.53
<br />2.,0
<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 />14,83
<br />2,55
<br />20
<br />4297.3
<br />.291.
<br />1.104
<br />2.327
<br />0.40
<br />40
<br />661.7
<br />1,892
<br />7,556
<br />15,11
<br />2.60
<br />30
<br />3519.8
<br />.327
<br />1.300
<br />2.618
<br />0,45
<br />9
<br />637.3
<br />1,965
<br />7.846
<br />15.09
<br />2.70
<br />40
<br />3437.9
<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 />603.8
<br />2,074
<br />8.281
<br />16.50
<br />2.85
<br />Z
<br />2864.9
<br />.436
<br />1.745
<br />3.490
<br />0.60
<br />40
<br />593.4'2.110
<br />8.426
<br />16.652.90
<br />10
<br />2644.6
<br />.473
<br />1.891
<br />3.781
<br />0.65.
<br />10
<br />573.7
<br />2.183
<br />8.716
<br />17.433-00
<br />20
<br />2155.7
<br />.509
<br />2.036
<br />4.072
<br />0.70
<br />30
<br />516.4
<br />2,292
<br />9.150
<br />18.30
<br />3 J
<br />30
<br />2292.0
<br />.545
<br />2.181
<br />4.363
<br />0.75
<br />11
<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 />8.60
<br />a
<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 />3,73
<br />10
<br />IS09.6
<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 />30
<br />425.4
<br />2.949
<br />11.75
<br />23.51
<br />4.05
<br />30'
<br />1637.3
<br />.764
<br />9.054
<br />6.108
<br />1.05
<br />14
<br />410.3
<br />3.058
<br />12.18
<br />24.37
<br />4.20
<br />40
<br />1562,0
<br />.800
<br />3.199
<br />6.398
<br />1.10:
<br />30
<br />396:2
<br />3.168
<br />12.62
<br />2.5.24
<br />4.35
<br />50
<br />1495.0
<br />.836
<br />3.345
<br />6.659
<br />1.15
<br />15
<br />383,1
<br />3.277
<br />13-05
<br />26.11
<br />4.50
<br />0
<br />1132,7
<br />.873
<br />3.490
<br />6.980
<br />1.20'30
<br />370.8
<br />3.387
<br />13.49
<br />26.97
<br />4,65
<br />10
<br />1375.4
<br />.909
<br />3,635
<br />7.271
<br />1.25
<br />16
<br />359.3
<br />3.496
<br />13.92
<br />27.84
<br />4.80
<br />20
<br />1322.5
<br />.945
<br />3.712
<br />7.561
<br />1.30
<br />30
<br />348.5
<br />3.606
<br />14.35
<br />28,70
<br />4.95
<br />30
<br />1273.6
<br />.982
<br />3.928
<br />7.852
<br />1.35
<br />17
<br />338.3
<br />3.716
<br />14,78
<br />29,56
<br />5.10
<br />40
<br />1228.1
<br />1.018
<br />4.071
<br />8.143
<br />1.40
<br />18
<br />3I9.5
<br />3.935
<br />15.64
<br />31.29
<br />5.40
<br />50
<br />1185.8
<br />1.055
<br />4.217"-8.433
<br />1.45
<br />10
<br />302.9
<br />4,.155
<br />16.51
<br />33.01
<br />5.70
<br />5
<br />1146.3
<br />1.091
<br />4:362
<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 />27.4.4
<br />4.594
<br />18.22
<br />36.44
<br />6.30
<br />20
<br />1074.7
<br />I.t64
<br />4.153
<br />9.305
<br />1.60
<br />22
<br />252.0
<br />4.814
<br />19.08
<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 />5.03.5
<br />19.94
<br />39.87
<br />6.90
<br />40
<br />1011,5
<br />1.237
<br />4,943
<br />9.886
<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 />6.476
<br />21.64-
<br />43.28
<br />7.50
<br />6
<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 />7,50
<br />10
<br />929.6
<br />1,346
<br />5.379
<br />10.76
<br />1.85
<br />27'
<br />214.2
<br />6.51S
<br />23.35
<br />46.69
<br />8.10
<br />20
<br />905.t
<br />1,382
<br />5.524
<br />11.05
<br />1.90
<br />28
<br />206.7
<br />6.130
<br />24.19
<br />48.38
<br />S.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 />1.4-5515.814,11.63
<br />2.00 1
<br />30
<br />193.2
<br />6,583
<br />25.88
<br />51.76
<br />9.00
<br />The eliddIe ordinato •n inches for any cord of length (C) is e�nal to .0012 C`
<br />multiplied by the middle ordinate taken frenn the above table, Thue, if it
<br />desired to bend a 301t. rail to fit a 10 degree curve, its middle ordinate should
<br />be .0012X90OX2.183 or 2,36 inches.
<br />TASLt'1II. Deflections for Sub Chords for Short Radius Curves.
<br />Degree
<br />of
<br />Radius
<br />50
<br />M sU h chord = sin of i def. angle
<br />R
<br />Length
<br />of are
<br />Curve
<br />ein. f def.ang•
<br />12.5 Ft.
<br />15 Ft.
<br />29 Ft.
<br />25 Ft.
<br />for 100 ft.
<br />30°
<br />193.18
<br />t° 5r'
<br />2° 17'
<br />2° 58'
<br />3° 43'
<br />T01. r5
<br />320
<br />181.39
<br />10 59'
<br />2° 25'
<br />3° 10'
<br />3° 58'
<br />I0+.33
<br />34°
<br />171 .01
<br />2° o6'
<br />2° 33
<br />3° 21'
<br />4° 12'
<br />I0I.48
<br />360 -
<br />161, 8o
<br />2° 13'
<br />2° 41'
<br />3° 33'
<br />4° 26'
<br />101.66
<br />38°
<br />153.58
<br />2° 20'
<br />2° 49'
<br />3° 44'
<br />4° 40'
<br />101.83
<br />40°
<br />146.19
<br />2° 27'
<br />2° 57'
<br />3° 55'
<br />4° 54'
<br />1o2.06
<br />420
<br />139.52
<br />2° 34'
<br />3° 05'
<br />,5°
<br />4° 07
<br />08
<br />102.29
<br />44°
<br />133.47
<br />2° 41'
<br />3° 13'
<br />40 IS'
<br />5° 22'
<br />102.53
<br />46°
<br />1:27.97
<br />z° 48
<br />:3° 21
<br />4° 29'
<br />50 36'
<br />102.76
<br />480•
<br />122.92
<br />2° 55'
<br />3° 29'
<br />4° 40
<br />5° 50'
<br />103.00
<br />50°
<br />118.31
<br />3° 02'
<br />3° 38'
<br />4° 51'
<br />b° 04'
<br />103.24
<br />52°
<br />114.o6
<br />3° 09''
<br />3° 46'
<br />5° 02'
<br />6° 17'
<br />103.54
<br />54°
<br />110.,11
<br />3° 16'
<br />3° 54'
<br />S° 131
<br />. 6-31,
<br />103.84
<br />56°
<br />Io6.50
<br />3° 22'
<br />4° 02'
<br />,5° 23'
<br />6° 44'
<br />104.14
<br />580
<br />;03. 14 -
<br />3° 29'
<br />4° Io'
<br />50 34'
<br />6° 57'
<br />104-43
<br />600
<br />100.00
<br />,3° 35'
<br />4° 18'
<br />5° 44'
<br />7° 11'
<br />f 104.72
<br />!
<br />CURVE FORMULAS
<br />T= R tan 12 I R= T cot. 1 chord'
<br />1 5o tan y I - Chord .def. _
<br />Sill. z 1.) R = 150 R .
<br />Sin. i D. _' So Sin. 12 D No. chords = f
<br />R E= R ex. sec 7 T D
<br />Sin. -'s D' S0 t 7 Z 1 E = T tan } I Tan, def: 12 chord def.
<br />The square of any distance, divided by. Lwice the radius, lvill ,equal
<br />the distance from tangent to curve, very nearly.
<br />To find angle for a given distance and deflection.
<br />Rule I. Multiply the given distance by .01745 (def. for I° for I ft.
<br />see Table I1.),.and divide given deflection by the product.
<br />Rule 2. Multiply given deflection by 57.3, 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 />RIc11T ANGLE TRIANGLES. Square the altitude, divide by twice the
<br />base. Add quotient to base for hypotenuse.
<br />Given Base too, Alt. 10.10'-200=,5. 100-}-.5=100.5 hyp.
<br />Given Hyp. Ion, Alt. 25.251=200=3.125, 100-3.127=96.875=Base.
<br />Error in first example, .002; in last., .045:
<br />To find Tons of Rail in one mile of track: multiply weight per yard
<br />by 1 i, and divide by 7.
<br />LEVELING. The correction for curvature a.nd refraction, in 'feet
<br />and decimals of feet is equal to 0.574d2, where d is the distance in miles.
<br />The correction for curvature alone is closely, 9d'. The combined cor-
<br />rection i8 negative. `
<br />PROBA13LE ERROR, If dl, d2, d3, etc, are the discrepancies of various
<br />results from the mean, and if Zd2=the sum of the squares bf these differ-
<br />ences and n=the number of observations, then the probable error of the
<br />mean= d 2
<br />-0.6745 n(n_1)
<br />SOLAR Ertirnm-R1s. Attention is called tothe Solar Ephemeris for
<br />the current year, published by Keuffel & Esser Co., and furnished upon
<br />request. This handy booklet, 3$x6 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 />11
<br />.0167
<br />]V.1833
<br />211
<br />.3500
<br />311
<br />.5167
<br />41"
<br />.6833
<br />511
<br />.8500
<br />2
<br />.0333
<br />12
<br />.2000
<br />22
<br />.3567
<br />32
<br />.5333
<br />42
<br />.7000
<br />52
<br />.8667.
<br />3
<br />.0500
<br />13
<br />.2157
<br />23
<br />.3833
<br />33
<br />.5500
<br />43
<br />.71.57
<br />53
<br />.8833-
<br />4
<br />.0607
<br />14
<br />.2333
<br />24
<br />.4000
<br />34
<br />.5667
<br />44
<br />.7333
<br />54
<br />.9000'
<br />5
<br />.0833
<br />15
<br />.2500
<br />25 -
<br />.4167
<br />35
<br />.5833
<br />45
<br />,7500
<br />55
<br />.0167
<br />6
<br />.1000
<br />16
<br />.2567
<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 />.6167
<br />47
<br />.7833
<br />57
<br />.9:100
<br />8
<br />.1333
<br />18
<br />.3000
<br />28
<br />.4667
<br />38
<br />.6333
<br />48
<br />.5000
<br />58
<br />.9667
<br />9
<br />.1500
<br />19
<br />.3167
<br />29
<br />.4833
<br />39
<br />.6500
<br />49
<br />.5167
<br />59
<br />.9933
<br />10
<br />.1667
<br />20
<br />.3333
<br />30
<br />.5000
<br />40
<br />.6667
<br />50
<br />.8333
<br />60
<br />1.0000
<br />T-kmF. V --laches in Decimals of a loot.
<br />I-16 3-32 ;•s 3-15 1.71 5-15 ja ,'� s3 Y ,a
<br />.0052 .0078 .0104 .01,96 .0208 .0260 .0313 .0417 .0521 , .0635 .0729
<br />1 2 3 4 6 7 8 9 I 10 1 1
<br />.0833 ,1667 .2500 .37133 I .4167 I ..5000 .5833 � .6667 .7.500 f .8333 .9167
<br />
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