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7YYI -
<br />TABrm IL -"Radii; Ordinates and Deflections Chord 100 ft.
<br />Deg.
<br />Radius
<br />Mid.
<br />Ord.
<br />Tan..
<br />Dist.
<br />Def. I
<br />Dist.
<br />Def •
<br />for
<br />1 Ft.
<br />'Deg'
<br />Radius
<br />Mid.
<br />Ord:
<br />Tan..
<br />:Dist,
<br />Def. ,
<br />Dist:
<br />Def.
<br />for
<br />1 Ft.
<br />51' ..
<br />t.
<br />177
<br />ft.
<br />It.
<br />/ ,
<br />101.15
<br />ft.-
<br />it.
<br />ft.
<br />IL
<br />>
<br />0"10'
<br />34377.
<br />.036
<br />.145
<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 />1.600
<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 />i8•
<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 />,
<br />- 20'
<br />688.2
<br />1.819
<br />7.266
<br />14.53
<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 />18. b6
<br />2.85
<br />8
<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 />17.43'3.00
<br />5044,
<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.
<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 />S. '.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
<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 />251.24
<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•: ';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'.1322.5
<br />.945
<br />3.718
<br />,7.56111.30.
<br />' :30;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 />1.35'17
<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
<br />33.01
<br />5.70
<br />a
<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 />19.9 4
<br />3987
<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 />5.478
<br />21..64
<br />43.28
<br />7.50
<br />0
<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 />1:348
<br />5:379
<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 />1 '859.9
<br />1.455
<br />5.814
<br />11.63
<br />2.00
<br />1 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 = sin of } def. angle
<br />R'
<br />Length
<br />of arc
<br />for 100 ft.
<br />sin. I def. ang.
<br />12.5+ Ft.
<br />15 Ft.
<br />20 Ft. 1
<br />25 Ft.
<br />30°.
<br />193.18
<br />1°
<br />51' ..
<br />- 2' i7' _
<br />__2°
<br />58'- _
<br />_ 3°
<br />43'-
<br />101.15
<br />-32°
<br />181.39
<br />1°
<br />59'
<br />2°
<br />25'
<br />3°
<br />Io'
<br />3°
<br />58'
<br />101.33
<br />34°
<br />171.01
<br />20
<br />06'
<br />2°
<br />331
<br />3°
<br />21'
<br />4°
<br />12'
<br />I01.48
<br />360
<br />161:8o_
<br />2°
<br />13! -
<br />'2°
<br />41,.."
<br />'3°
<br />33, ;
<br />_ 4°-26!:
<br />.9000
<br />.'io1.66
<br />38! _
<br />_ 153.58
<br />z'
<br />20'
<br />20
<br />49f
<br />3'=44!=
<br />46,
<br />4°
<br />40'
<br />101.85
<br />_
<br />40°
<br />146.19
<br />_2°
<br />27';
<br />2°,57!
<br />.
<br />30
<br />55'
<br />4°
<br />54' _
<br />102.o6
<br />42°,
<br />139.52
<br />- 2°
<br />34''-
<br />3°
<br />05'
<br />4°.07'
<br />'37
<br />5°
<br />o8'
<br />i02.29
<br />44°.
<br />133.47
<br />'z°
<br />41'
<br />3°
<br />i3'
<br />'.4°
<br />18.'
<br />..'5°-22'
<br />-.6333
<br />102.53
<br />-460
<br />- 127.97 - .
<br />'
<br />2°
<br />48�
<br />3°
<br />21-'
<br />4'-�9,.
<br />29..
<br />5°
<br />36'
<br />102.76
<br />48'
<br />122.92
<br />2°
<br />55'
<br />"oz�
<br />310
<br />29':
<br />4°
<br />40,
<br />5°
<br />50'
<br />103.00
<br />50,
<br />118.31
<br />3°
<br />"60
<br />--3°
<br />381'
<br />40
<br />51'
<br />60041
<br />103.24
<br />520'
<br />114.o6
<br />3°
<br />09'
<br />3°
<br />46'.
<br />5°02'
<br />6°
<br />17'
<br />--103-54
<br />540
<br />IIo.. II .
<br />30
<br />16'
<br />30
<br />541
<br />50
<br />13'
<br />.60
<br />3r'
<br />Io3.84
<br />.56'
<br />1o6.56
<br />3'
<br />22'
<br />4°•02'
<br />5023,
<br />60
<br />44'
<br />104.14
<br />58°;
<br />103.14
<br />3°
<br />i9'
<br />40
<br />I0'
<br />50341
<br />6°
<br />57'
<br />104.43
<br />600
<br />100.00
<br />3°
<br />35'
<br />4°
<br />18'
<br />5044,
<br />-70
<br />II'
<br />104.72
<br />CURVE " FORMUf AS Ix
<br />T- = R tan j i R= T ct. I. chord2
<br />,I, _:5o"tan j I - oz I Chord def. = R
<br />Sin. J; D : R = 50
<br />Sin. D- = 5o i . ;Sin.' } D No. chords = I
<br />R . E ='R ex. sec'; .I'
<br />aI
<br />Sin. -j D "='SotanT "T:ta i J I Tan. def.= J chord def.
<br />Th'e.square of any. distance, -divided by twice the radius, will equal
<br />the distance"frorn tangent to curve, very nearly'.'
<br />To find angle for -a given distancd and deflection."
<br />Rule I: - Multiply' the -given_ distance by .01745 (def. for I° 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 prodlict by
<br />the given distance.
<br />I 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 />'RIGHT ANGLE TRIANGLES: Square the altitude, divide. by twice 'the
<br />base.' Add quotient to base'for hypotenuse."
<br />Given " Base loo, Alt. 10.1021:-200 =.5., 100 -.5 =100.5 hyp. •
<br />Given. Hyp. loo, Alt. 25.252=200=3:125. 106-3.125=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 7•
<br />'LEVELING.' The correction for. curvature .and 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, ids. The combined cor-
<br />rection' is negative:
<br />PROBABLE ERROR.. If cis, da; da, etc. are the discrepancies of various
<br />results from the mean; and If 2211 --the sum of the squares of these dif'ler-
<br />ences and.n=the•number of observations,then the probable error of the.
<br />mean-. ± 0.674 Ida
<br />n (n-1)
<br />.'SOLAR EPHEMERIS. Attention is,called. to the -Solar Ephemeris.f&.'
<br />the currentyear, published by.Keuffel.&Esser Co:, and furnished'free of
<br />charge upon request, which is 3,x5 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 />j conversions; trigonometric formulas; Natural andLogarithmic Functions;
<br />and' Logarithms of Nutubers.
<br />I
<br />i�
<br />TABLE IV. - Minutes
<br />TABLE V: - Inches iwDecimals of a Foot.
<br />in "Decimals of a Degree.
<br />1!
<br />.0167-
<br />11'
<br />.1833
<br />21'
<br />.3500
<br />31'
<br />.5167
<br />41'
<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 />8
<br />-.0500
<br />,
<br />13
<br />•.2167
<br />23.
<br />•.3833
<br />33
<br />.5500
<br />43'
<br />-7167
<br />53
<br />.8833%
<br />,d:
<br />•.0667
<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 />46,
<br />_.7500
<br />55
<br />.9167
<br />0:
<br />.1000
<br />16
<br />::2667
<br />26
<br />.4333
<br />30
<br />6000
<br />46
<br />.7667
<br />56
<br />.9333
<br />,7•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 ".•.4667
<br />38
<br />-.6333
<br />48 •
<br />8000
<br />58
<br />.9667
<br />9
<br />:1500
<br />19.
<br />:3167
<br />29..
<br />'.4833
<br />39
<br />'.6500
<br />.8167
<br />69
<br />.:9833
<br />10
<br />.1667
<br />20
<br />.3333
<br />30-
<br />-.5000
<br />40
<br />•6667
<br />.'49
<br />-50
<br />.8333
<br />"60
<br />1.0000
<br />IQ
<br />TABLE V: - Inches iwDecimals of a Foot.
<br />'
<br />3-32
<br />p
<br />.0056 2 '
<br />� 0078 ., 104
<br />.O1 6 .0208
<br />0260 ' . 313
<br />.0417 5 1
<br />.0 25
<br />.0739
<br />1
<br />2 3
<br />4 b
<br />6 78
<br />9_
<br />10
<br />11
<br />.0833.
<br />.1667_ .2500
<br />.3333 .4167
<br />.5000 .5833
<br />.6667 :7500
<br />.8333
<br />.9167
<br />IQ
<br />
|