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0 J
<br />VIII r
<br />TADLE H. -- Radii, Ordinates and Deflections. Chard 100 ft.
<br />Deg.
<br />Radius
<br />Mid.
<br />Ord,
<br />Tan,
<br />Diet.
<br />Def.
<br />Dist.
<br />D,f,
<br />for
<br />11't.
<br />Deg.
<br />Radius
<br />Mid.
<br />01d,
<br />Tan
<br />Dist..
<br />Def.
<br />Diaz.
<br />Def'
<br />for
<br />1 Ft,
<br />z' S8'
<br />3°43'
<br />t•
<br />32°
<br />181,39
<br />1° S9'
<br />2° 25`
<br />t.
<br />t.
<br />t
<br />u
<br />171.01
<br />9'10'
<br />34377.
<br />.036
<br />.145
<br />.231
<br />0.05
<br />7'
<br />819.0
<br />1.528
<br />6.105
<br />12.21
<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
<br />J2.79
<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 />1.164
<br />0.20
<br />40
<br />747.9
<br />1.673
<br />6.685
<br />13.37
<br />2.30
<br />50
<br />6375.5
<br />.182
<br />.727
<br />1.454
<br />0.25
<br />8
<br />716.8
<br />1.746
<br />6.97G
<br />13.95
<br />2,40
<br />11
<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 />a20,
<br />4911.2
<br />.235
<br />1.018
<br />2.036
<br />0.35
<br />30
<br />674.7
<br />1.855.7.411
<br />104 14,
<br />14.83
<br />2.1,5
<br />/
<br />4297.3
<br />.291
<br />1.164
<br />2.327.0.40
<br />bo°
<br />40
<br />661.7
<br />1.892
<br />7.556
<br />15.11
<br />2.60
<br />130
<br />3319:8
<br />.327
<br />1.300
<br />2.018
<br />0.45
<br />9
<br />637.3
<br />1.061.5
<br />7.846.15.69
<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 />10.27
<br />2.80
<br />IY50
<br />3125.4
<br />.400.1.600
<br />3.200
<br />0.55
<br />30
<br />603.8
<br />2.074
<br />8.281
<br />10-56
<br />2.55
<br />j2 `4
<br />10
<br />2864.9
<br />2644.6
<br />.436
<br />.473
<br />1_745
<br />1.891
<br />3-490
<br />3.781
<br />0.60
<br />0.65
<br />40
<br />10
<br />503.4
<br />573.7
<br />2.110
<br />2.183
<br />8.426
<br />8.716
<br />16,85
<br />17.43
<br />2.90
<br />3.00
<br />20
<br />2155.7
<br />.509
<br />2.036
<br />4:072
<br />0.70
<br />30
<br />546.4
<br />2.292
<br />9.150
<br />18.30'3.1,5
<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 />9.58.5
<br />10.16
<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 />3
<br />1910.1
<br />.055
<br />2.618
<br />5.235
<br />0.90
<br />30
<br />459:3
<br />2.730
<br />10.89
<br />2t.77
<br />3+75
<br />10
<br />1809.6
<br />.Gill
<br />2.703
<br />5.526
<br />0.95
<br />13
<br />441.7'2.839
<br />11.32
<br />22.64
<br />3..90
<br />201719.1
<br />,727
<br />2.908
<br />5.817
<br />1.00
<br />30
<br />435.4
<br />2.949
<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 />24.37
<br />4.20
<br />40
<br />1562.9
<br />.800
<br />3.199
<br />6.398
<br />1.10
<br />30
<br />396.2
<br />3.168
<br />12.62
<br />25.2.1
<br />4.35
<br />50
<br />1495.0
<br />.836
<br />3.345
<br />6.689
<br />'1.15
<br />I5
<br />383.1
<br />3.277
<br />13.05
<br />26.11
<br />4.50
<br />4
<br />1132.7.873
<br />3.490
<br />6.930
<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 />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 />348.5
<br />3.606
<br />14.35
<br />28.70
<br />4.95
<br />30
<br />1273.6
<br />.982
<br />3.926
<br />7,852'1.35
<br />17
<br />338.3
<br />3.716
<br />14.78
<br />24.56
<br />5,10
<br />/ 40
<br />1228:1
<br />1.018
<br />4.071
<br />8,143
<br />1-40
<br />18
<br />310,.6
<br />3.935
<br />15.64
<br />31:29
<br />5.40
<br />50
<br />1185.8
<br />1.055
<br />4.217
<br />8.433
<br />J.45
<br />19
<br />302.9
<br />4.155
<br />16.51
<br />33.01
<br />5.70
<br />b
<br />1.146.3
<br />1.091
<br />4.362
<br />8.724
<br />1.50
<br />20
<br />2&7,:0
<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 />4.04
<br />18.22
<br />36.44
<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 />4.814
<br />19.08
<br />38.16
<br />6.60
<br />30
<br />1042.1
<br />1.200
<br />4.798
<br />9.590
<br />1.. G5
<br />23
<br />250.8
<br />.5.035
<br />19,94
<br />39.87
<br />6.00
<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 />5.476
<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 />44.99
<br />7.S0
<br />10
<br />929.6
<br />1.346
<br />5.379
<br />10.76
<br />1.85
<br />21
<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 />.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 />1.795
<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 />5.814
<br />11._93
<br />2.00
<br />30
<br />193.2
<br />6.583
<br />25.88
<br />51-7619.00
<br />xuu lwuuie orutuaw in mcaes Tor any ,;oT(t oT length tVJ 1s equai to 0012 t'`
<br />multiplied by the middle ordinate taken from the above table. Thus, if it
<br />leaired to bends :i0 ft. rail to fit a 10 degree curve, its middle ordinate should
<br />be .0012Xo00X2.183 or 2.36 inches.
<br />TABLE III. Deflections for Sub Chords for Short Radius Curves.
<br />Degree.
<br />of
<br />Curve
<br />Radius
<br />50
<br />ain, $ def.ang,
<br />Mauh chord _ sin of ¢def. angle
<br />_.R
<br />' Length -
<br />of arc
<br />for L00 ft.
<br />12.5 Ft,
<br />15 Ft.
<br />20 Ft.
<br />1 25 Ft.
<br />300
<br />193.18
<br />1° 51'
<br />2° ri`
<br />z' S8'
<br />3°43'
<br />m1.15
<br />32°
<br />181,39
<br />1° S9'
<br />2° 25`
<br />3° 1o'
<br />3' 58,
<br />101.3:3
<br />34''
<br />171.01
<br />2° o6'
<br />2° 33
<br />3' 21'
<br />4° 12'
<br />I01.48
<br />36°
<br />161.8o
<br />2° 13'
<br />2° 41'
<br />3' 33'
<br />4° 26'
<br />Int -66
<br />38°
<br />153.58
<br />2° 20'
<br />2° 49'
<br />3° 44'
<br />4°.40'
<br />101.8;
<br />40°.
<br />146.19
<br />2°27'
<br />2° 57
<br />3'55'
<br />4° 54'
<br />102.06
<br />42'
<br />139.52
<br />2' 34'
<br />3° 05
<br />4° 07'
<br />9° 08
<br />102:29
<br />44°
<br />133 47
<br />2' 41
<br />3° 13'
<br />4° 18'
<br />S° 22'
<br />102.53
<br />46°
<br />127.97
<br />2° 48'
<br />3° 2I'
<br />4° 29'
<br />5° 36'
<br />102.76
<br />48°
<br />122.92
<br />2055'
<br />3° 29'
<br />4° 40'
<br />5°•5o'
<br />103.00
<br />50°
<br />118.31-
<br />3° 02'
<br />3° 38'
<br />4° 51'
<br />6° 04' -
<br />lo3.21
<br />52°
<br />114.06
<br />3° o9'
<br />3° 4.6'
<br />5° o2'
<br />60 17'
<br />103. 54
<br />54°
<br />110.I1 1
<br />3° 16'
<br />3' 54'
<br />S' 13'
<br />6° 31'
<br />143.84
<br />56°
<br />ro6.5o
<br />3° 22'
<br />4° 02'
<br />S' 23'
<br />6° 44
<br />104 14,
<br />58°
<br />103. r4
<br />3' 29'
<br />4° 10'
<br />5° 34'.
<br />6° 57'
<br />10443
<br />bo°
<br />100.00'
<br />3° 35`
<br />4° 18`
<br />5° 4'
<br />7° .11'
<br />104,72
<br />CURVE FORMULAS �� fIx
<br />T= R tan ; I R- T cot. I I chord=
<br />T _ 5o tan I Chord,def. = R
<br />Sin. t D __ 50
<br />Sin. D= 50 E Sin. i D ISI
<br />N _
<br />R E = R ex. sec -I O. chords = Q
<br />Sin D _ go tez I E = T tan s I Tan. def. = z 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 t. Multiply the given distance by .01745 (def. for i' for l ft.
<br />see Table IL), and divide given deflection by the product.
<br />Rulc 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 />K7' GENERAL DATA
<br />RIGHT ANGLE TRIANGLES. Square the altitude, divide by twice the
<br />base. Add quotient to base for hypotenuse.
<br />Given Base ioo, Alt. 10.10'=200=.5. lOO+.S=100.5 hyp.
<br />Given Hyp. 1 oo, Alt. 25.2,52=200=3-12,5. 100 -3,12, = 96,875 = Basc.
<br />Error in first example, .002; in last, .045.
<br />To find "Pons of Rail in one mile of track: multiply weight per yard
<br />by 1 I, and divide by 7. /
<br />LEVFLINc. The correction, for curvature and refraction, in fce.t
<br />and decirnals of feet is equal to 0.574d2, where d is the distance in miles.
<br />The correction for curvature alone is closely, ;d'. The combined cor-
<br />rection iA negative. -'
<br />�PAOIIADLE ERROR. If ell, d2, da, etc. are the discrepancies of various
<br />results from the mean, and if Ed'=the sum of the squares of these differ-
<br />ences and n=the number of observations, then the probable error of the
<br />Mean
<br />-0.6745 NJn(n-1)
<br />SOLAR EPHEAIERIS. Attention is called to the Solar Ephemeris for
<br />the current year, published by Keuffel & Esser Co., and. furnished upon
<br />request. This handy booklet, 38x6 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 frorn observations on the sun and Polaris; stadia measurements;
<br />magnetic declination; arithmetic constants, etc.
<br />TA13LE IV.-MinnteS.in Decimals of a Deeree.
<br />it
<br />A167
<br />Ile
<br />.1833
<br />211
<br />.;1500
<br />311
<br />:5167
<br />411
<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 />9000
<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 />01.67
<br />14
<br />.2333
<br />24
<br />.4000
<br />34
<br />.5667
<br />-44
<br />.7333
<br />54
<br />.9000
<br />0833
<br />15
<br />12500
<br />25
<br />.4167
<br />35
<br />..5833
<br />45
<br />.7400
<br />55
<br />.9167
<br />6
<br />.1000
<br />16
<br />2007
<br />26
<br />A333
<br />36
<br />.6000
<br />46
<br />.7667
<br />36
<br />.9331
<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 />.9667
<br />9
<br />.1500
<br />19
<br />.3167
<br />29
<br />.4533
<br />,
<br />39
<br />.6500
<br />49
<br />.8107
<br />S9
<br />.9833
<br />10
<br />.1667
<br />20
<br />.3333
<br />30
<br />.:1000
<br />40
<br />.8667
<br />50
<br />.8333
<br />60
<br />1.0000
<br />I.vtr.1•: \'.---IItches
<br />in Uecrnhals of a I•ool.
<br />1-16
<br />3-32
<br />1.•q
<br />3-16
<br />�.( n-16
<br />?a
<br />0052
<br />.0078
<br />.0104
<br />..0156
<br />.0208 I .0360
<br />.0313
<br />.0117
<br />A:521 -06 25
<br />.0729
<br />I
<br />-�
<br />;
<br />.0833
<br />.1647
<br />2500
<br />.3333
<br />.4167 000
<br />.:5337
<br />.a667
<br />.7fi00 1 8333
<br />.1!167
<br />
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