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TABL'm IL - Radii, Ordinates and. Deflections. Chord -100 f
<br />>
<br />X19°
<br />Mid
<br />Ord.
<br />Tan.
<br />Dist.
<br />Def.
<br />Dist.
<br />for
<br />iFt.
<br />Deg..
<br />Radius
<br />Mid .
<br />.Ord.
<br />Tam' .
<br />Dist.
<br />Def.
<br />Dist.
<br />Def.
<br />for
<br />1 Ft*
<br />2
<br />1.511
<br />2' 17'
<br />2° 58'
<br />3° 43'
<br />101,15
<br />:,32°
<br />181.39
<br />I° 59,.
<br />2° 25'
<br />3° 10'::
<br />30 58'
<br />4`10'
<br />34377.
<br />.036
<br />.145
<br />" .291
<br />O.b5
<br />7'
<br />819.01.528
<br />43
<br />;6.105
<br />12.21
<br />2.10
<br />20
<br />17189.
<br />.073
<br />.291
<br />x-.582
<br />0.10
<br />20'
<br />781.8
<br />1.600
<br />6.395
<br />12.79
<br />2.20
<br />30
<br />{1459.
<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 />1.164
<br />0.20
<br />-40
<br />747.9
<br />1:673
<br />16.68513.37
<br />3° 21'
<br />2.30
<br />:'b0 2
<br />'6875.5
<br />.162.727
<br />122.92
<br />`1.454
<br />0.25
<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 />14.53
<br />2.1,0
<br />10
<br />4911.2
<br />.255
<br />1.018
<br />12.036
<br />0.35
<br />30
<br />674,7
<br />1.855
<br />7.41114.82
<br />50 23'
<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 />15.11
<br />2.60
<br />30
<br />3819.8
<br />.327
<br />1.309
<br />2.618
<br />0.45
<br />9 '"
<br />637,3
<br />1.965
<br />.7.846
<br />13.09
<br />2.70
<br />40
<br />3137.9
<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 />16.86
<br />2.85
<br />2,
<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 />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 />17.43
<br />3.00
<br />20'
<br />2455.7
<br />;509
<br />2,030
<br />4.072
<br />0.70
<br />30
<br />546.4
<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 />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 />O.SO-30
<br />499.1
<br />2.511
<br />10102
<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 />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 />3.75
<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 />.30
<br />425.4
<br />2.949.11;75
<br />23.51
<br />4.05
<br />`.30
<br />1837.3
<br />'.764
<br />3.054
<br />6.108
<br />1.05
<br />14 '410.3
<br />.058
<br />12.18
<br />24.37
<br />4.20
<br />40
<br />1562,9
<br />.800
<br />8.199
<br />6.398
<br />1.10
<br />30
<br />396.2
<br />3:168
<br />12.62 -25.24
<br />4.35
<br />50
<br />1495.0
<br />.836
<br />3.345
<br />; 6.689'1.15
<br />16383.1
<br />3.277
<br />13.0'26.11
<br />5
<br />4.50
<br />4
<br />1432.7
<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 />.909
<br />3,635
<br />7.271
<br />1.25
<br />16
<br />359.3
<br />.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 />30,348.5
<br />.606
<br />14.35
<br />28.70
<br />4.98
<br />30'
<br />1273.6
<br />,.982
<br />3.926
<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 />1225.1
<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 />60
<br />1185.8
<br />1.055
<br />4.217
<br />8.433
<br />1.45
<br />-19'
<br />302..9
<br />4.155.16:51
<br />33.01
<br />5.70
<br />1i
<br />1.091
<br />4.362
<br />8.724
<br />1.50
<br />20
<br />287.9
<br />.374
<br />17.37'
<br />34.73
<br />6.00
<br />10
<br />.1146.3
<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 />36.44
<br />6.30
<br />20
<br />" 1074.7
<br />1.164
<br />4.653
<br />9.305'1.60
<br />22 ,'
<br />262.0
<br />4.814
<br />19.09
<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 />+'3011.5
<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 />5.476
<br />21.64
<br />43:28
<br />7.50
<br />8
<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 />44.99
<br />7.80
<br />10
<br />929.6
<br />1.346
<br />5.379
<br />10.76
<br />1.85
<br />27:
<br />214.2
<br />-•918
<br />23.35-
<br />46.69
<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 />1.455
<br />b.814
<br />11.63
<br />2.00
<br />1 30
<br />193.2
<br />6.583
<br />25.88
<br />51.7619.00
<br />The Middle ordinate'n inches for my card of length (C1 is tan
<br />to 0012 W
<br />multiplied by the midd o ordinate taken from the above table. Thus, if it
<br />deslr6d to bend a 30 ft. rail to fit a 10 degree curve, its middle ordinate should
<br />be .0012X909X2.183 or 2.36 inches. -
<br />f TABLE III. Deflections for Sub Chords for Short Radius Curves.
<br />Degree
<br />o{
<br />Radius'mss
<br />50'
<br />sub chord sin of I def. angle
<br />g
<br />Length
<br />of are
<br />Curve
<br />sin. }def. ang.
<br />12.5 Ft.
<br />15 Ft.
<br />20 Ft.
<br />25 Ft.
<br />for 100 Et.
<br />30°193.18.
<br />2
<br />1.511
<br />2' 17'
<br />2° 58'
<br />3° 43'
<br />101,15
<br />:,32°
<br />181.39
<br />I° 59,.
<br />2° 25'
<br />3° 10'::
<br />30 58'
<br />101.33
<br />34°
<br />X36°
<br />171.01
<br />2° 06'
<br />2° 33`
<br />3° 21'
<br />40 12'
<br />101.48
<br />43
<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° 20'
<br />2° 49'
<br />3° 44
<br />4° 40
<br />10I.85
<br />40°146.19
<br />:0000
<br />2° 27'
<br />2' 57'
<br />3° 55'
<br />4° 54'
<br />102.06
<br />42°13952
<br />35
<br />2° 34
<br />3° 05'
<br />4° 07'
<br />5° 08
<br />102.29
<br />44°133,47
<br />.1000
<br />2° 41
<br />3°.13'
<br />4° 18'
<br />5° 22'
<br />102.53
<br />46°
<br />127-97
<br />2° 481
<br />3° 21'
<br />4 29'
<br />50 36'
<br />102.76
<br />48°
<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 />6-04 1
<br />103.24
<br />52°
<br />114.06
<br />3° 09'
<br />3° 46'.
<br />5° 02'
<br />6° 17'
<br />103.54
<br />54°
<br />110.11
<br />3° i6'
<br />3° 54'
<br />5° 13'
<br />60311
<br />103.84
<br />560
<br />E66. So
<br />3° 22'
<br />4°n 02'
<br />50 23'
<br />6° 44'
<br />104.14
<br />58°
<br />103-14
<br />3°�9P.
<br />41O,
<br />5°34'
<br />6° 57'
<br />104.43
<br />_600
<br />100.00
<br />3° 35'
<br />4° 18'
<br />5° 44'
<br />7° [1',
<br />104.72
<br />EK
<br />CURVE FORMULAS
<br />T= R tan ; IR T cot. 3 1 chord=
<br />T - 5o tart }•1 Chord def. =
<br />Sin. 7 D R = 50 R
<br />3
<br />Sin. ;.D = 5-Ro Sin. D No. chords = I
<br />E = R ex. sec z [ D
<br />Sin. ;.D' - 90 1taI 22 1 E = T tan } I Tan. def. _ '� chord 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 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 .oi745; and the product by the distance.
<br />GENERAL DATA
<br />RIGHT ANGLE TRIANGLES. Square the altitude, divide by twice the
<br />base, Add quotient to Base for hypotenuse.
<br />Given Base loo, Alt. ro.Iol=2oo=.5. 100-}-.5=100.5 hYp• .
<br />Given Hyp. too, Alt. 25.25' =200 =3:125. 100 -3.125 =96.1375 = 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 I I, and divide by 7•
<br />LEVELING. The correction for curvature .and refraction,. in 'feet
<br />and decimals of feet is equal to 0.574ds, where d -is the distance in miles.
<br />The correction for curvature alone is closely, ;d2. The combined cor-
<br />rection is negative. .
<br />- - PROBABLE ERROR. If di, d2, da, etc: are the discrepancies of various
<br />results from the mean, and if Edk=the sum of the squares of these differ-
<br />ences and n=thc number of observations, then the -probable error of the
<br />mean= Ids
<br />-0.6745 n(n-1)
<br />SOLAR ErurHERls. Attention is called t0 the 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 1.90 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 s6n and Polaris; stadia measurements;
<br />magnetic declination;; arithmetic constants, etc.
<br />TABLE (V. -Minutes in Decimals of a Degree.
<br />1P
<br />•0167
<br />11?
<br />.1833
<br />211
<br />.3500
<br />3V
<br />.5167
<br />-41t
<br />.6833
<br />51,
<br />.8500
<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 />:0000
<br />5
<br />.0833
<br />15
<br />.2500
<br />25
<br />.4167
<br />35
<br />.5833
<br />45
<br />.7500
<br />55
<br />M67
<br />6
<br />.1000
<br />16
<br />.2667
<br />26
<br />.4333
<br />36
<br />.6000
<br />46
<br />.7667
<br />56
<br />10333
<br />7
<br />.1167
<br />17
<br />.2833
<br />27
<br />.4500
<br />37
<br />.6167
<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 />9607
<br />9
<br />.1500
<br />19
<br />.3167
<br />29
<br />.4833
<br />39
<br />.6500
<br />49
<br />.8167
<br />59
<br />.9833
<br />10 1
<br />•1667 11
<br />20 1
<br />.3333 11
<br />30 1
<br />.5000 11
<br />40
<br />1 .6667 11
<br />50 f
<br />.8333 11
<br />60 11,0000
<br />T:1RI.E V. --Inches in Decimals of a Foot.
<br />5-163-32
<br />}re
<br />3-I6
<br />'•y
<br />5's
<br />.0052
<br />.0078
<br />.0104
<br />.0156
<br />.0205
<br />.0260
<br />.0312
<br />.0417
<br />.0521
<br />.0625
<br />.07 29
<br />r
<br />?
<br />3
<br />4
<br />6
<br />I
<br />7
<br />I
<br />9
<br />9
<br />10
<br />11
<br />0$33
<br />.1667'
<br />.2500
<br />.3x33
<br />.4167
<br />"Wo
<br />.5833
<br />.661
<br />.7500
<br />.8333.
<br />.91#37
<br />
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