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■
<br />VIII
<br />TABLE II. -- Radii, Ordinates and Deflections. Chord =100 ft.
<br />Deg.
<br />fisdius
<br />Mid
<br />Ord:'
<br />Tan.
<br />Dist.
<br />Def.
<br />Di3t'
<br />Def.
<br />far
<br />1 or
<br />Dco.
<br />Radius
<br />mid.
<br />Ord.
<br />Tan
<br />Dist.
<br />Aef.
<br />Dist,
<br />Def.
<br />fer
<br />l Bt.
<br />-
<br />t,
<br />ft.
<br />it.
<br />ft.
<br />L.8i 39
<br />-i° 59'
<br />ft:
<br />ft.
<br />it.
<br />-ft.
<br />34°
<br />0°16'
<br />34377.
<br />.036
<br />.14'0'
<br />.291
<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_000
<br />6.395
<br />12.79
<br />2.20
<br />30
<br />11459.
<br />.109
<br />.436
<br />S73
<br />0.15
<br />30
<br />764.5
<br />1.637
<br />6.540
<br />13.08
<br />2.25
<br />46
<br />8594.4
<br />.145
<br />.582
<br />1,161
<br />0.20
<br />40
<br />747.9
<br />1.673
<br />G,GS5
<br />13.37
<br />2.;30-
<br />50
<br />.6875.5
<br />.182
<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 />6°,04
<br />5729.6
<br />.218
<br />.873
<br />1.745
<br />0.30
<br />20
<br />688.2
<br />1.519
<br />7.266
<br />14.53
<br />2.50
<br />10
<br />4911.2
<br />,25.5
<br />1.013
<br />2.036
<br />0.35
<br />30
<br />674.7
<br />1.855
<br />7.411
<br />14.82
<br />2.55
<br />20
<br />4297.3
<br />.291
<br />1.164
<br />2,327
<br />0.40
<br />40
<br />081.7
<br />.1.892
<br />7.556
<br />15.11
<br />2.60
<br />30
<br />3319.8
<br />.327
<br />1:309
<br />2.618
<br />0.45
<br />9;
<br />637.3
<br />1.965
<br />7.S46
<br />15.69
<br />2.70
<br />40
<br />3437.9
<br />.361
<br />1.454
<br />2.'309
<br />0.50
<br />20
<br />014.6
<br />2.037
<br />8.136
<br />IG.27
<br />2.80
<br />50
<br />3125.4
<br />A00
<br />1.600
<br />3.200
<br />0.55
<br />30
<br />003.8
<br />3.674
<br />4.281
<br />16.56
<br />2.85
<br />2
<br />2564.9
<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 />2.99
<br />10
<br />2644.6
<br />".473
<br />1.991
<br />8.781
<br />0.65
<br />10
<br />573.7
<br />2.183
<br />4,710
<br />17.43
<br />3.00
<br />20
<br />2455.7
<br />:500
<br />2.03G
<br />4.072
<br />0,70
<br />30
<br />540.4
<br />2:292
<br />0.150
<br />13:30
<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 />2.403
<br />0.5.95
<br />19.16
<br />3.30
<br />40
<br />2148.8
<br />-532
<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 />.613
<br />2.472
<br />4.045
<br />0.85
<br />1^;
<br />478.3
<br />2.G20
<br />10.45
<br />20.91
<br />3.60
<br />3'
<br />1010.1
<br />.655
<br />2.613
<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 />-1$09:6
<br />-691.
<br />2.763
<br />5.526
<br />0.95,
<br />13
<br />441.7
<br />2.839
<br />11.32.
<br />22.64
<br />3.90
<br />.20
<br />1719.1
<br />.727
<br />2.A03
<br />5,817
<br />1.00
<br />''30425.4
<br />2.949
<br />11.75
<br />23.51
<br />4.05
<br />X30
<br />1637.3
<br />.764'3-054
<br />'6:103
<br />1,05.
<br />14 -
<br />410.3
<br />3.058
<br />12:18
<br />24,37
<br />4.20
<br />-40
<br />.1562.9
<br />',800
<br />3,109
<br />6.303
<br />1.10
<br />,30
<br />396.2
<br />3.168'12.62
<br />25.24
<br />4.35
<br />50
<br />1495.0
<br />.S36
<br />3,345
<br />6.659
<br />1.15
<br />15
<br />333.1
<br />8.277
<br />13.05
<br />26,11
<br />4.50
<br />d
<br />1432.7
<br />.873
<br />?.490
<br />6AS0
<br />1.20
<br />30
<br />370.8
<br />3.387
<br />13,49
<br />26:97
<br />4.65
<br />10
<br />1375.4
<br />.909
<br />3.635
<br />7.271
<br />1.20
<br />16
<br />359.3
<br />3.496
<br />13:92
<br />27,84
<br />4.80
<br />20
<br />1322.5
<br />.945
<br />3.718
<br />7.561
<br />1.30
<br />30
<br />348.5
<br />3.606
<br />14.35
<br />28.70
<br />4.95
<br />30
<br />1273.0
<br />.932
<br />3.926
<br />1.852
<br />1.35
<br />17'
<br />33S.3
<br />3.716
<br />14.73
<br />29.56
<br />5.10
<br />40
<br />,1228.1
<br />1.013
<br />4.071
<br />8.143
<br />1.40
<br />18
<br />319.6
<br />3.935
<br />15.64
<br />31.29
<br />5.40
<br />50
<br />1155.8
<br />1.055
<br />4.217
<br />3.433
<br />1.43
<br />19
<br />302.9
<br />4.15516.51
<br />23.01
<br />3.70
<br />5
<br />1146.3
<br />1.091
<br />4.362
<br />8.724
<br />1,50
<br />20
<br />237.9
<br />4.374
<br />17.37
<br />34.73
<br />G,00
<br />10_1109.3
<br />1.127
<br />4.507
<br />0.014
<br />1.55
<br />'.1
<br />274.4
<br />4.594
<br />18.22
<br />.^,6:44
<br />6,30
<br />20
<br />1074.7
<br />1.164
<br />4.653
<br />9.305
<br />1.60
<br />22
<br />262:0
<br />4.814.19.08
<br />88.16
<br />6:60
<br />30'
<br />1042.1
<br />1.200
<br />1.79$
<br />9.596
<br />1.65
<br />23
<br />250.3
<br />5.035
<br />19.94 '39.87
<br />G.90
<br />40
<br />1011.5
<br />1.237
<br />4.943
<br />9.836
<br />1.70
<br />24
<br />240.5
<br />5.255
<br />20.79
<br />41.53
<br />7.20
<br />50
<br />982.6
<br />1.273
<br />6.088
<br />10.18,
<br />1.75
<br />25
<br />231.0
<br />5,476
<br />21,64
<br />43-23
<br />7.50
<br />6
<br />955.4
<br />I.309
<br />5.234'10.47
<br />1.80
<br />26
<br />222.3
<br />5.607
<br />22,50
<br />44.99
<br />7.80
<br />10
<br />929.6
<br />1.346'5.379
<br />10.76
<br />1.85
<br />27
<br />214,2
<br />5.918
<br />23.35
<br />40.60
<br />3.10
<br />20
<br />905:1
<br />1.382
<br />5.524
<br />11.05
<br />1.90
<br />R8
<br />206.7
<br />6.139
<br />24,19
<br />48.38
<br />8.40
<br />30
<br />531,9-1.4I8
<br />5.669
<br />11.34
<br />1,'95
<br />29
<br />199,7
<br />6,360
<br />'25.04 .50.07
<br />8.70
<br />40
<br />1 559.9
<br />1,455
<br />5.314
<br />11.63
<br />2.00
<br />1 30
<br />193.2
<br />6.583
<br />25.85
<br />51.76
<br />0.00
<br />:Cha middle ordinate in inches for any cord of length -(C) is equal to 0012 C'
<br />multiplied by the middle 'ordivato taken from the above table. Thus, if it
<br />desired to bend;1;30ft. rail to fit a 10 degree curva, ita middle ordinato should
<br />be .0012X90012'.153 or 2416 inches.
<br />TABLE III. Deflections for Sub, Chords for ,Short radius Curves,
<br />Degree
<br />of
<br />Curve
<br />ltadiud
<br />59
<br />1� sub chord _ sfn of ' def. angle
<br />Y.'
<br />I Length
<br />of arc
<br />for 106 ft.
<br />sin: i def, ang,
<br />12.5 Ft.
<br />15 Ft.
<br />20 Ft,
<br />25 Ft-
<br />•300
<br />ICI3. 18
<br />I° 5i'
<br />2° 17'
<br />^° 58'
<br />3° 43
<br />101.I5
<br />22
<br />L.8i 39
<br />-i° 59'
<br />2,:25'
<br />J° 10'
<br />.. 30 58'
<br />=101:33
<br />34°
<br />171..0I
<br />2° 06'
<br />° 33`°
<br />21'
<br />4° 12'
<br />101-43
<br />36°
<br />IG1.So
<br />2° 13'
<br />2°41'
<br />30 33'
<br />4°26
<br />IoI.66
<br />3&°
<br />153. 58
<br />2"20'
<br />20 49' -
<br />3� `i4'
<br />4 40`
<br />101,85
<br />_.
<br />40°
<br />_ _
<br />1: 6 19
<br />2° 27'
<br />.Y° 57'..
<br />3°'J.7'
<br />_
<br />4° 54' .
<br />IO2.06
<br />42°
<br />139 S2
<br />'° 34'
<br />3° OS'
<br />4° 07'
<br />5° 08•
<br />102.29
<br />"4° .
<br />133. 47
<br />2° 4i' .'
<br />3° 13
<br />4 18'.
<br />5 :22r..-
<br />102.,53
<br />46°
<br />127.97
<br />2° 48'
<br />3°21'
<br />4 29'
<br />5°36,
<br />102.76
<br />480
<br />1-12. e,
<br />2° 55'
<br />3° 29,
<br />4° <10` •
<br />5° 50
<br />103.00
<br />so
<br />11$.31
<br />3° c2-'
<br />3° 38'
<br />}° -1r
<br />6°,04
<br />103.24
<br />5='°
<br />I14., oG .
<br />3° 09'
<br />3° q.G`
<br />5° oz'
<br />G° 17`
<br />103.54
<br />54°
<br />I Io. i i
<br />3° 16'
<br />3° 5+
<br />;° z3,
<br />6° 31'
<br />Io3:84
<br />5G°
<br />106. 50
<br />3° 22'
<br />4° 021
<br />°23
<br />6°
<br />104-14
<br />58°
<br />103.14
<br />3° 29
<br />4° 10'
<br />5° 34
<br />6° 57'
<br />14.43
<br />60°
<br />1-50.00
<br />3° 35'
<br />4° a8'
<br />5° 44'
<br />7° W
<br />104.72
<br />Ix
<br />CURVE FORMULAS
<br />1 5o tali I R = I cot..', I Chord def. = chord°
<br />R
<br />Sin: i D R 50
<br />Sin. D = R Sin. D No. chords = I
<br />E=ReY:Sec;�. D
<br />Sin.. D = 50 to a I L - T tan I Tan. clef, = a chord def.
<br />The square of, any distance, divided by twice Che radius, will equal
<br />the. distance from tangent to curve, very.3learly.
<br />To find an0e for a given distance and deflection..
<br />Ruled: Multiply the given distance by .01745 (def; for i° for i ft.
<br />wee. Table II:), and divide given defleetion by the product..
<br />Rule 2. Multiply given deflection by 57.3, and divide the product by
<br />the given distance.
<br />To find'defiection for a given angfc acid distance. Multiply the angle
<br />by-.o1745,.and the product by the distance.
<br />GENERAL'DATA
<br />RIGHT A1vGLE TRIANGLES. Square the altitude, divide by twice the
<br />base. Add quotient to base for hypotenuse,
<br />Given Base. Ioo, Alt, 10.102-260=.5. loo +.5=100.5, hyp,
<br />Given Hyp. ioo, Alt, 25.25 200=3.125, loo-3:x25-96.875=Base•
<br />Error in fir. --t example, .002; In last, .045•
<br />To •find Tons of Rail in one mile of track: multiply weight per yard
<br />by zi, and divide by 7.
<br />LEVELING. The correction 'for curvature -and refraction, in feet
<br />and decimals of feet is equal to 0.5740,w i here d is the distance in miles.
<br />The correction for curvature alone is cloel, jd=. The combined cor-
<br />rection is negative. - -
<br />ProurixLE Ei2ROR. If d;, d , dn, etc., are the discrepancies of various
<br />results from the mean; and if Yd"=the surd of the squares of these differ-
<br />ences. and n -the number of observations; then the probable error of the
<br />mean-' oda
<br />0.6745 11 (n-1)
<br />SOLAR EP11MIERIS. Attention is Called to the Solar -Ephemeris for
<br />the current year, published by Keufr`el & Esser Co., and furnished free of
<br />charge upon request, which is 3 jx58 in., with about 90 glages of data very
<br />useful to the Surveyor; such as the adjustments of transits, levels and
<br />solar attachments; directions and-tahles for determining the- meridian
<br />and the latitude from observations on the sun and Polaris; stadia meas-
<br />urements; magnetic declination; arithmetic constants; English and i',Setric
<br />conversions; trigonometric formulas; Natural andLoaarithmic Functions;
<br />and Logarithms of Numbers.
<br />TAi11.'bl IV. - Minutes in Decimals of a Dea'ree.
<br />V
<br />.0167
<br />1V
<br />.1833
<br />1211
<br />.3500
<br />31'
<br />.516: I`
<br />41'
<br />6333
<br />51'
<br />8500
<br />2
<br />.0333
<br />12_
<br />.2000
<br />22
<br />3667
<br />.3833
<br />32
<br />;333
<br />42
<br />.7000
<br />52
<br />,8067
<br />3
<br />.0500
<br />13
<br />.21G7
<br />23
<br />,
<br />33
<br />.5500
<br />43
<br />,7167
<br />53
<br />.5533
<br />4
<br />,0667
<br />14
<br />.2333
<br />24
<br />.4000
<br />34
<br />.5liiU
<br />44
<br />7333
<br />54
<br />.9000
<br />5
<br />.083.3
<br />15
<br />.2500
<br />25
<br />.4167
<br />35
<br />.5333
<br />45
<br />,7500
<br />55
<br />.9167
<br />6
<br />.1000
<br />16..
<br />,2667
<br />26
<br />.4333
<br />36 -
<br />.0000
<br />4G
<br />.7667
<br />66
<br />'
<br />.9333
<br />7
<br />.1167
<br />17
<br />.°833
<br />27
<br />A600
<br />37
<br />.0167
<br />47
<br />.7533
<br />57
<br />.9500
<br />8
<br />:.1333
<br />13
<br />,3000
<br />28
<br />:4567
<br />33
<br />.6333
<br />4.8
<br />1000
<br />53
<br />.9567
<br />9
<br />.1500
<br />19
<br />,3167
<br />''.9
<br />.4533
<br />39
<br />.6500
<br />411)
<br />G167
<br />59
<br />.9833
<br />10" .1
<br />.1667 11
<br />20
<br />.3331
<br />30 -
<br />.5000
<br />40
<br />.GIi67I
<br />.50
<br />.63331
<br />60
<br />11.0000
<br />TABLE V. - inches in I7eeiinal3 of a, Foot. '
<br />1-1.6 3-32 �.9 3-16 '3� 5-16 e!3 a f ° 74
<br />0052 .0678 .(71D,1 .0156 .0268 .0260 .0313 .0:417 .0:121 .0625 :0719
<br />] 2 3 4 5 6 7 8 9 10 11
<br />.0833 .1667 ,2x00 .3333 .4167 .5000 .5833 .6667 .7500 .6333 1.9107
<br />
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