|
VIII
<br />TABLE IL -Radii, Ordinates and -Deflections. Chord= 100 ft,
<br />Deg.'
<br />'Rad us.
<br />Ifid.
<br />Ord.
<br />Tan.
<br />Diet,
<br />Dd.
<br />Dista
<br />Def'
<br />for
<br />I Ft
<br />Deg.
<br />Radius
<br />Mid.
<br />Ord.'
<br />Tan.
<br />Dist;`
<br />DcE,
<br />Dist.
<br />Dei.
<br />far
<br />I Ft.
<br />2° 17'
<br />it.
<br />ft.
<br />ft.
<br />ft.
<br />r
<br />I° 59'
<br />it,•
<br />ft.
<br />it,
<br />ft.
<br />34
<br />0'10'
<br />34377.
<br />.036
<br />.145
<br />.201
<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 />1 .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 />.100
<br />.436
<br />.873
<br />0.15'
<br />30
<br />764.5
<br />1.637
<br />'6.540"13.03
<br />44°
<br />2.25
<br />40
<br />8594.4
<br />,145
<br />.552
<br />1,164
<br />0.20
<br />40
<br />747.9
<br />1,875
<br />6,635
<br />13.37
<br />2.30
<br />50
<br />.6875.5
<br />.182
<br />.727
<br />1.454
<br />0.25
<br />8
<br />715,8
<br />1 740
<br />6.0,76
<br />1a.9
<br />2.40
<br />1
<br />5729.6
<br />.218
<br />.873
<br />1,745
<br />0.30
<br />20
<br />658.2
<br />1.519
<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 />674.7.1.855
<br />5 23
<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 />0.95
<br />9-. .'
<br />637.3
<br />1.905
<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 />G14.0
<br />2;037
<br />8.136
<br />10.27
<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 />10.56
<br />2.85
<br />2
<br />2864.9
<br />,430.1.745
<br />3.490
<br />0.60
<br />40
<br />593.4
<br />2.113
<br />8.426
<br />16.85
<br />2.90
<br />10
<br />2644.6
<br />.473
<br />1.591
<br />3.731
<br />0,65
<br />10
<br />573.7
<br />2:183
<br />S.71n
<br />1.7.43
<br />3.00
<br />20
<br />2455.7
<br />.509
<br />2.03G
<br />4.072
<br />0_70
<br />' 30
<br />540.4
<br />2.292,
<br />9. 1.50
<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 />2.40.^.
<br />0_5&5
<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 />20.0,1
<br />3.45
<br />50
<br />: 2022:4
<br />.:618
<br />2.472
<br />4.945
<br />0.8;5
<br />12
<br />478.3
<br />2.G20
<br />10.45
<br />20.91
<br />3.60
<br />S
<br />1910.1
<br />,655
<br />2.618
<br />5.235
<br />0.90-,
<br />30
<br />459.3
<br />2.730
<br />10.59
<br />21.77
<br />3.75
<br />10,
<br />ISOM
<br />.6912.763
<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 />6.10S
<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 />G,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 />3S3.1
<br />3.277
<br />13.05
<br />26.11
<br />4.50
<br />1432.7
<br />.873
<br />3.490
<br />G.980
<br />1,20
<br />30
<br />370.8
<br />3.357
<br />13:49
<br />26107
<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 />13192
<br />27.S4
<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 />25.70
<br />4.95
<br />30
<br />1273.6
<br />.9S2
<br />3.92G
<br />7.852'1,35
<br />17
<br />335.3
<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 />15AA
<br />31.29
<br />5.40
<br />50
<br />1185.8
<br />1.055'4.217
<br />8.4331.45
<br />19
<br />302.9
<br />4.155
<br />16.51
<br />33.01
<br />5.70
<br />6
<br />1140,3
<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 />0.00
<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 />30.4-1
<br />6.30
<br />20
<br />1074.7
<br />1.164
<br />4.653
<br />0.305
<br />1,60'
<br />22
<br />262.0
<br />4:814
<br />19.08
<br />38.16
<br />0.60
<br />30
<br />'40
<br />1042.1
<br />1.200
<br />4.798
<br />9.596
<br />1,05
<br />23 -
<br />250.8
<br />5.035
<br />19.94'
<br />39.87-6.90
<br />1011.5
<br />1.237
<br />4.943
<br />9.586
<br />1.70
<br />24
<br />240.5
<br />5.255
<br />20.79
<br />41.55
<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 />21.6t
<br />43.21
<br />7.50
<br />6.
<br />955.4
<br />1.300
<br />5.234
<br />10.47.
<br />1.80
<br />26
<br />222.3
<br />5.697
<br />22,50
<br />44,000
<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 />5.915
<br />23.35
<br />96.69
<br />5.10
<br />20
<br />905.1
<br />1.382
<br />5.524
<br />11.05
<br />3.90
<br />28
<br />206,7
<br />6,139
<br />24.19
<br />48.35
<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 />6.3GO
<br />25.04
<br />50.07
<br />8.70
<br />40
<br />859.9
<br />1.455
<br />5.814
<br />11,63
<br />2.00
<br />30
<br />_193.216.683126.88
<br />51.76
<br />9.00
<br />111�te 1n iuenes Lor any coru of length tui is equal to .0012 U -
<br />multiplied by the middle ordinate taken ,from the above table. Thus, if it
<br />desired to bend as 30 ft. rail to fit 10 degree curve, its middle ordinate':lieuld
<br />be .0012X90OX2.183 or 2.36 inches,
<br />TABLE III. Deflections for Sub Chords for Short Rndhis C"urxm,
<br />Degree
<br />Cnrre
<br />1ZaUs
<br />50
<br />'sub chord = gin of I def. angle
<br />Leagtn
<br />of are
<br />Tor 100 it.
<br />sin. I def: ane.
<br />12.5 Ft.
<br />I5 Ft.
<br />20 Ft.
<br />25 Ft.
<br />30°
<br />193..18
<br />0 51.'
<br />2° 17'
<br />2'.58'
<br />-
<br />43'I01.15
<br />.2000
<br />320
<br />181,39
<br />I° 59'
<br />° 25,
<br />3° Io'
<br />.3°
<br />30 58'
<br />EOE .33
<br />34
<br />171-01 -
<br />2'OG
<br />2°33 '
<br />3°2I'
<br />4' 12'
<br />ICIT .48
<br />36°
<br />161.8o
<br />2° 13'
<br />2° 41
<br />3° 33'
<br />4° 26'
<br />foi.66
<br />38°
<br />153.53
<br />2° 20'
<br />2° 49'
<br />3° 44'.
<br />4° 40'
<br />I0I.85
<br />4.00.
<br />14.6. ][g
<br />2° 27
<br />2° 57
<br />3° JJ'
<br />4° 54'
<br />r02.06
<br />42
<br />139.52
<br />2 34'
<br />3° 05'
<br />4° 07'
<br />S°os
<br />102.29
<br />44°
<br />133.47
<br />2° 41'
<br />3° 13'
<br />4° 18'
<br />5° 22'
<br />102.53
<br />4F°
<br />17-97
<br />2° 48'
<br />3° 21'
<br />4°z9'
<br />5° 36'
<br />162.76
<br />43°
<br />122.92
<br />2° 55'
<br />3° 2g'
<br />4° 40'
<br />5° 50'
<br />103.00
<br />50°
<br />IIS,31
<br />3° 02'
<br />3° ,ig'
<br />4° 51'
<br />6° 04'
<br />103,-'4
<br />52°
<br />114.06
<br />3° 09'
<br />3° 46'
<br />3° 02'
<br />60 '7'
<br />-!
<br />10 54
<br />3.84
<br />540
<br />I1o.11
<br />3o IG'
<br />30 54`
<br />50 13'
<br />6° 31'
<br />P03 84
<br />56
<br />1o6.5o
<br />3 22
<br />4 42
<br />5 23
<br />6° 44'
<br />104.14
<br />58°
<br />103, 14
<br />3° 29
<br />4° 40'
<br />y° 3.1
<br />6° 57'
<br />104-43
<br />60°
<br />I00.00
<br />3° 35
<br />4.° 18'
<br />5044 '
<br />7° 1 I'
<br />104-72
<br />..
<br />CLiRVE FOR1l4i,LkS IX
<br />1= It tan t 1 R= T cat. z I chord2
<br />T _ Jo tan 2 I Chord def. =- R
<br />^ Sin. D R = 50
<br />I,-
<br />Sin.,D =' Sin. a D No. chords= I
<br />"'' " E= R ,ex. sec a I D
<br />Sin; 'D = S° tT ' I E = T tan 11 : Tan.1f.= 3 chard 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 -0174.5 (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 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 />GENERAL DATA
<br />RIGHT ANGLE TRIANGLES. Square the altitude, divide by twice the
<br />base. Add quotient to base for hypotenuse..
<br />Given Base 100, Alt. 10.][02=200=-5.•Ioo+.5=loo•5 hyp•
<br />Given'Hyp. Ioo,AIt.25-25E-200=3-125. roo-3.1$
<br />25=96.875=ase.
<br />Error in first example, .002; an last, .045.
<br />To find Tons. of Rail in one mile -of track: multiply weight per yard
<br />by II;.and divide by 7.-
<br />. LEVELING. The correction forcurvature and refraction, in feet
<br />and decimals of feet is equal to 0.574d2,wheve d is the distance in miles.
<br />The correction, for curvature alone is closely', id2.. The combined .cor-
<br />rection is negative.
<br />PROBABLE ERROR. If dtd2, d$, etc. are the discrepancies of various
<br />results from the mean, and if 7-d2=the sum of the squares of these differ-
<br />ences and n=the number of obsen>ations, then the probable error of the
<br />mead 0A45 �d2 '
<br />n (n-1)
<br />SOLAR EFHE',iER1s. Attention is called to the Solar Ephemeris, for
<br />the current year, published by Keufiel c0,. Ewer Co., and furnished free of
<br />charge upon request, which is 31,x51 in., with about 90 pages of data very
<br />usefuI,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 tTumbers.
<br />TA.RLP, TV. - 1Viinutps in Doairnnb; of a. DP.arne..
<br />V
<br />0167
<br />11'
<br />.1833
<br />21'
<br />.3500
<br />31'
<br />ZI67
<br />41'
<br />.US33
<br />51'
<br />.8500
<br />2
<br />.0333
<br />12
<br />.2000
<br />22
<br />.3667
<br />.0104
<br />.5333
<br />42
<br />.7000
<br />52
<br />.S667
<br />3.0500
<br />.0625-_.0720
<br />13
<br />.2167
<br />23
<br />.3833
<br />132
<br />33-
<br />.:500
<br />43
<br />.7167
<br />53
<br />.5833
<br />4
<br />,0667
<br />14
<br />.2333
<br />24
<br />.4000
<br />3-.
<br />.1667
<br />44
<br />.7333
<br />54
<br />.9000
<br />5
<br />.;0533
<br />15
<br />.2500
<br />25
<br />.4167
<br />35
<br />.SS33
<br />45
<br />.7500
<br />55
<br />.9167
<br />6.1000
<br />1G
<br />.2667
<br />26
<br />.4333
<br />3e.
<br />.43000
<br />46
<br />.7667
<br />543
<br />.9333
<br />'7
<br />.11G7
<br />17
<br />.2533
<br />27
<br />.4560
<br />37
<br />.6167
<br />47
<br />.7933
<br />57
<br />.9500
<br />6
<br />.133;
<br />18
<br />.3000
<br />28
<br />.4667
<br />38
<br />.6333
<br />48
<br />3000
<br />58
<br />.9(367
<br />9
<br />1500
<br />19
<br />.3167
<br />29
<br />.4833
<br />39
<br />.6500
<br />49
<br />.�,167
<br />59
<br />.0833
<br />10
<br />.1667 11
<br />20
<br />.3333 11
<br />30
<br />1 :5000
<br />40
<br />. 6-367 11
<br />50
<br />£313
<br />I'C(I
<br />1.0000
<br />=
<br />II_ABLE V. - Inches in Dccira,02 of _a• Foot.
<br />1-16
<br />3-32
<br />l
<br />3-16
<br />/4
<br />5-1G
<br />It
<br />?/2
<br />V$
<br />3r
<br />o
<br />0052
<br />.0078
<br />.0104
<br />.0155
<br />.020S
<br />.0260
<br />.0313
<br />.0-117
<br />.0521
<br />.0625-_.0720
<br />1
<br />2
<br />3'
<br />5
<br />6
<br />7
<br />8
<br />9
<br />10
<br />11
<br />.0833
<br />.1667
<br />.2500
<br />.3333
<br />,4167
<br />.5000
<br />.5x33
<br />6667
<br />,7500
<br />..5833
<br />,9167
<br />
|