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TABLE II:- Radii, 6rdinates and Deflections. Chord=100 ft. CURVE FOR11AULAS
<br />Deg...
<br />Radiue'
<br />Mid
<br />Ord.,:
<br />Tan.
<br />Dint.
<br />Def.
<br />Dist:
<br />Def.
<br />IfFt.
<br />Deg.
<br />Radius
<br />Mid.
<br />Ord:
<br />Tan.
<br />Dist:'
<br />Def.
<br />Dist.
<br />Def.
<br />1 r
<br />z° 17`
<br />t.
<br />ft.
<br />- fr.-
<br />ft.
<br />I
<br />,
<br />15g
<br />ft,
<br />ft.
<br />; ft,
<br />ft. -
<br />i
<br />0' 10'-
<br />34377.:'
<br />'036
<br />'1145
<br />.:291
<br />0.05
<br />V
<br />819,0
<br />1.528
<br />6.105
<br />12.21
<br />2.40
<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 />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 />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 />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 />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 />34.53
<br />2,50
<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 />2.55
<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 />15.69
<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 />16.56
<br />2.85
<br />-
<br />2864.9
<br />.436
<br />1.745
<br />3.490
<br />'3.781
<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 />0.65
<br />10 •
<br />573.7
<br />2.1838.736
<br />17.43
<br />3.00
<br />20
<br />2455.7
<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
<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 />0.80
<br />- , 30
<br />499.1
<br />2:511
<br />10,02 .20.04
<br />3.45
<br />50
<br />2022.4,!,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 />:.655.2.618
<br />5.235
<br />0.90
<br />30
<br />459.3
<br />2:730
<br />10.89 .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
<br />11.75
<br />23.51'4.05
<br />^ 30
<br />1637.3
<br />.764
<br />3.054
<br />16.108
<br />1.05'
<br />':14 •
<br />410.3
<br />3,058
<br />12:18
<br />24.37.4.20
<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 />25.24
<br />4.35
<br />50 _
<br />1495.0
<br />:836
<br />3.345'
<br />,6.689,
<br />1.15
<br />15
<br />383.1
<br />3.277
<br />13.05
<br />26.11
<br />4.50
<br />A `'�
<br />. 1432,7
<br />.873
<br />3:490
<br />'6.980
<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 />Y.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
<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 />319.6
<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 />1.45
<br />'19
<br />302.9
<br />4.155
<br />16.51''33.01
<br />5.70
<br />6
<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 />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
<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 />'9.596
<br />1.65,
<br />23.
<br />250.8
<br />5.035
<br />19.94
<br />39.87
<br />6.90
<br />40'
<br />10115
<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 />7.80
<br />10'
<br />929.6
<br />1.3465.379
<br />10.76
<br />1.85
<br />•27:
<br />214.2
<br />5.918
<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 />4859.9
<br />1.455
<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 equal to .0012 C'
<br />multiplied by the middle ordinate: taken from the above table. Thus; if it
<br />desired to bend a 30 ft. rail to fit a 10 degree curve, its middle "ordinate should
<br />be .0012X900X2:183 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 />sub chord
<br />R = sin of } def. angle
<br />Length
<br />h
<br />e arc
<br />for 100 ft.
<br />sin. I def. ang.
<br />12.5' Ft.
<br />:15 Ft.
<br />20 Ft. '
<br />25 Ft.
<br />30°
<br />-
<br />193.1$
<br />1° 51'
<br />--°J
<br />z° 17`
<br />-�° 5$`.'_
<br />3° 43`
<br />101..15 .
<br />°
<br />32
<br />181.39
<br />,
<br />15g
<br />O� ,
<br />2 25
<br />° ,
<br />3 to
<br />O ,
<br />3 58
<br />101.33
<br />34°
<br />1'71.01
<br />2° o6'
<br />2° 33'
<br />3° 21'
<br />4° 12'
<br />101.48
<br />360
<br />161.80.-
<br />2° 13'.
<br />20 41!_',
<br />3° 33,'
<br />. 4' 26'
<br />ioi.66
<br />380
<br />_ 153-58-
<br />20 20' ,
<br />'2°2
<br />_.2° 49'
<br />-2°
<br />.3° 44'
<br />40.40'_ _
<br />_ 101.85
<br />'Io2.o6
<br />4 O°,r
<br />I 6.I
<br />4 9
<br />,
<br />7•
<br />-57 ,
<br />30-55"
<br />3 •55
<br />° '
<br />•4.54
<br />.9000
<br />42°'
<br />139 52
<br />.2°.34.
<br />.2333
<br />2500
<br />40:07'
<br />,
<br />. 5° 08' _
<br />102.29. .
<br />0
<br />44
<br />133.47
<br />0
<br />?, 41., '...•
<br />;:3°•05'
<br />3o .13, ...
<br />4o 18,.
<br />o� ,
<br />5-r 22
<br />102.53
<br />460'
<br />127.97 -
<br />2° 48'
<br />3° 21'
<br />4° 29
<br />50 36:.
<br />102.76
<br />48°
<br />'
<br />122.92
<br />'2° 55'
<br />3° ?9, ..
<br />4°.40,.
<br />,..5° 50'
<br />103:00
<br />500
<br />. ;118.31
<br />30 O2,
<br />3° 38,
<br />4° 51,
<br />6° 64'.
<br />103; 24
<br />52°
<br />114-o6
<br />• 3° o9'.
<br />3046, .
<br />_.5° 02'
<br />.-*6.* 17'
<br />.103.54....
<br />54°
<br />110.I1.
<br />3° 16',.
<br />30 54'
<br />5° 13'
<br />6° 1'.
<br />10 8.
<br />3. 4
<br />56°
<br />io6.5o
<br />3° 22'
<br />4° 02'
<br />5° 23'
<br />6,,"344'
<br />1194.14
<br />58°..
<br />10g. 14
<br />. 3° 29
<br />4` 4°. io' '
<br />5.34'-
<br />6° 57'
<br />104.43
<br />60°
<br />100.00
<br />3' 35'
<br />40 18'
<br />S° 44'
<br />70_11'
<br />104.72 .
<br />T= R tan i I R= T cot. ' I chord'
<br />,I, 5o tan j I Chord def. = R
<br />Sin. D. R = 50
<br />Sin. i D ='50 Sin. j D. No, chords = I
<br />R E =Rex. sec ; I D
<br />5o tan ; I
<br />Sin;' D" - ,I, E = T tan I 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 1°. for I ft:
<br />see Table'II.); 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
<br />istance.To' find deflection for a given angle and distance. Multiply the angle
<br />by.:0i74M, 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'Ioo,Alt. 10.10Q=200=.5. I0o+.S=Ioo.S hyp•
<br />Given Hyp. loo, Alt. 25.25'--200=3.125.100-3.125=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 i i, and divide by
<br />LEVELING.- The correction. for curvature and refraction, in feet
<br />and decimals of feet is equal, to 0.574 ds,where.d is the distance in miles.
<br />The correction for curvature alone is closely, fda. The "combined cor-
<br />rection is negative.
<br />-: PROBABLE ERROR. If d,., da, ds, etc. are the discrepancies of various
<br />results from the -mean, and if Fda=the sum of the squares of these dlflor-
<br />ene6s and n=the number of observations, then the probable error of the
<br />mean= +0.6746 n(n 1)
<br />SOLAR EPHEMBRIs. Attention is called to the Solar Ephemeris for:
<br />the current year, published by.Keuffel &-Esser. Co., and furnished free of
<br />charge upon request, which'is 31x5} in., with about 90 pages of data very
<br />useful to' the. Surveyor; such as..the adjustments of transits, levels and
<br />solar attachments; directions and tables 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 Metric
<br />conversions; trigonometric formulas; Natural andLogarithmic Functions;
<br />and Logarithms of Numbers.
<br />TABLE IV. -.Minutes
<br />TABLE V. - Inches in Decimals of a Foot.
<br />in Decimals of s Degree. -
<br />1'
<br />0167,
<br />11'
<br />1833
<br />21'
<br />.3500
<br />W.
<br />..5167
<br />41'
<br />.6833
<br />51'
<br />.8500
<br />a'-
<br />.0333
<br />'12
<br />.2000
<br />22
<br />.3667
<br />32 '
<br />.5333
<br />42
<br />.7000
<br />52
<br />.8667
<br />-8
<br />.0500
<br />-13
<br />.2167
<br />23.
<br />.3833
<br />33'
<br />.5500
<br />43
<br />.7167
<br />63
<br />.8833'
<br />4'
<br />.0667.
<br />14
<br />24
<br />.4000
<br />34
<br />.5667
<br />44
<br />.7333
<br />54
<br />.9000
<br />b
<br />.0833
<br />15
<br />.2333
<br />2500
<br />25
<br />.4167
<br />35
<br />.5833
<br />45
<br />.7500
<br />56
<br />.9167
<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 />.6167
<br />47
<br />.7633
<br />57
<br />.9500
<br />8 -,
<br />.1333
<br />18
<br />-28
<br />.4667
<br />38 '
<br />.6333
<br />48
<br />.8000
<br />58
<br />.9667
<br />" 9;. ::-.1500
<br />.3000
<br />29
<br />.4833
<br />39
<br />.6500
<br />49
<br />.8167
<br />59
<br />.9833
<br />1667
<br />.19
<br />20
<br />.3167
<br />-.3333
<br />30
<br />.5000
<br />40
<br />.6667
<br />50
<br />.8333
<br />60
<br />11,0000
<br />-
<br />TABLE V. - Inches in Decimals of a Foot.
<br />+
<br />1-16 3-32
<br />j� 3-16
<br />5-16
<br />'/s
<br />311
<br />°
<br />0052 .0078
<br />.0104- :0158 :0208
<br />.0260
<br />•.0313
<br />.0417 .C521-
<br />.0625 07"29
<br />1 2
<br />3 4 b
<br />8
<br />7
<br />8 9
<br />10 11 --
<br />.0833 ,.1667
<br />..2500. .3333- ..4167
<br />.5000
<br />.5833
<br />.6667 .7500
<br />.8333 .9167
<br />
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