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VIII
<br />TABLE IL - Radii, Ordinates and Deflections. Chord =100 ft.
<br />Deg..
<br />Radius
<br />Mid.
<br />Ord 'Dist.
<br />Tan.
<br />Def.
<br />Dist '
<br />for
<br />i Ft.
<br />Deg.
<br />Radius-Mid.,Tan..
<br />Oid.
<br />, Dist,
<br />Def.
<br />Dist.
<br />' Dor
<br />I Ft.
<br />2° 17'
<br />2° °
<br />58'
<br />3° 43'.
<br />101.15
<br />'32° -
<br />-- 181.39
<br />- -1° 59
<br />..202',5,-.-
<br />3°_ ,
<br />10
<br />30 58,..
<br />101--33
<br />340
<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 />16.685
<br />13.37
<br />2.30
<br />50,
<br />6875:5
<br />.182
<br />.727
<br />1.454
<br />0.25;;.5
<br />103.00
<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 />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 />17.556
<br />15.11
<br />2.60
<br />30.
<br />3819.8
<br />.327
<br />1.309'.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 />8.281'16.56
<br />2.85
<br />2''.-
<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
<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 />2:32T
<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 />3
<br />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 />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 />,22.64
<br />11-.75'
<br />23.51
<br />4.05
<br />30
<br />: 1637.3
<br />.764
<br />31054
<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 />25.24
<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 />4 ''
<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 />.909.3.635
<br />7.271
<br />1.25.'
<br />16 .i
<br />359.3
<br />:496
<br />13.92.
<br />27.84
<br />4.80
<br />20,
<br />1322:5
<br />` .945
<br />1.30
<br />3.718,
<br />7.561
<br />30
<br />348.5
<br />.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 />1S
<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 />5
<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 />4.5071
<br />0.014
<br />1.55
<br />21'
<br />274.4
<br />4.594
<br />18.22
<br />36.44
<br />6.30
<br />20,
<br />1074.7.1.164
<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 />1042:1'1.200
<br />4.798
<br />9.596
<br />1.65
<br />23
<br />250.8
<br />5.035
<br />19.94 :39.87
<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 />5:476
<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-;44:99
<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 />5.918
<br />23.35"'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 />5.669.11.34
<br />1.95
<br />29
<br />199.7
<br />6.360
<br />25.04
<br />50.07
<br />8.70
<br />40
<br />859.9
<br />1.4 55
<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 (0) is egnal to ,0012 C2�
<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 />34 sub chor t
<br />R = sin of i def. angle
<br />Length
<br />of arc
<br />for 100 ft.
<br />sin. I def. ang.
<br />12.5, Ft.
<br />15 Ft.
<br />20 Ft. a
<br />25 Ft.
<br />30°
<br />193.18
<br />1° 81'
<br />2° 17'
<br />2° °
<br />58'
<br />3° 43'.
<br />101.15
<br />'32° -
<br />-- 181.39
<br />- -1° 59
<br />..202',5,-.-
<br />3°_ ,
<br />10
<br />30 58,..
<br />101--33
<br />340
<br />171.0I
<br />2° 06'
<br />2° 33
<br />3° 21'
<br />4° 12'
<br />101.48
<br />36°
<br />a61.80 .
<br />:.2° 13'• -
<br />2° 41'
<br />3° 33' ;
<br />_4° 26'
<br />ioi .66
<br />38°
<br />15.3.58
<br />2° 20'
<br />2° 49'.
<br />3° 44'.
<br />4° 40'
<br />101.85
<br />40°
<br />•i46A§__,_^
<br />20 2.7'-
<br />-i° 57' -
<br />3°,55'
<br />4°'54" `
<br />102.o6
<br />42°
<br />139.52
<br />z° 34'
<br />3° 05
<br />4° 07'-
<br />g° 08
<br />IO2.29
<br />'440
<br />133-147.,
<br />20 41,
<br />.-3° 13'
<br />4° 18'
<br />5° 22'
<br />102.53
<br />46°.'
<br />127.972,.48'
<br />..
<br />3o 2I'
<br />4° 29' ''
<br />-5° 36'
<br />102.76
<br />48°
<br />(22.92
<br />2°55'
<br />3°29'
<br />4°40'.
<br />5°50'
<br />103.00
<br />.509
<br />118.31
<br />30 02'
<br />3° 38'_
<br />4° 51'
<br />6° 04'
<br />103.24
<br />52°
<br />114.06
<br />3° 09'
<br />3° 46''
<br />5' Oz,
<br />6° 17'
<br />103 54
<br />54°
<br />IIO.II
<br />3° 16'
<br />3° 54:
<br />50 13' .
<br />6° 31'
<br />103.84
<br />560
<br />106.50
<br />3° 22
<br />4° 02'•
<br />5° 23'
<br />6° 44%
<br />iO4. 14
<br />:58*1
<br />103.14
<br />30 29�
<br />4o Io'
<br />50 34f
<br />60 57'
<br />104.43
<br />60
<br />100.00
<br />3 .35
<br />4 18.
<br />5 .44
<br />7 11
<br />104.72
<br />CURVE FORMULAS IX
<br />T R tan 21 1 y R= T cot. l I Chord def. = chord'
<br />r o tan -f I _ 2 _
<br />DR = 50 R . .
<br />Sin. ll
<br />Sin. a D = 5o . 2 No. chords = I
<br />R. E = R ex. sec; I D
<br />Sin. ;'D _ 5o t T ; I E = T tan } I Tan. def. = a 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 .01945 (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 />fhe 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 loo, Alt. 10.102 -200=.5. IOO+-5=1oo.5`hyp•
<br />Given Hyp. loo, Alt. 25.252=200=3.125, loo -3.125=96.875 =Base.
<br />Error in first example, .002; in last, .o45• -
<br />-To find Tons of Rail in one -mile, of track: multiply weight per yard
<br />-by.I I,, and divide by 9..
<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, 'd2. The combined cor-
<br />rection is negative.
<br />PROBABLE ERROR. If d,, d2; ds, 'etc. are the discrepancies of various
<br />results from the mean, and if Ede=the sum of the squares of these differ-
<br />ences and n=the number of observations, then the probable error of the
<br />mean = 2;d2
<br />-0.6745 n(n_1)
<br />SOLAR EPHEMERIS. 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 from observations on the sun and Polaris; stadia measurements;
<br />magnetic declination; arithmetic. constants, etc.
<br />TABLE IV. -Minutes in Decimals of a Degree.
<br />1f
<br />.0167
<br />111
<br />.1833
<br />211
<br />.3500
<br />311
<br />.5167
<br />41f
<br />.6833
<br />511
<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 />.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 />.0667
<br />14
<br />.2333
<br />24
<br />.4000
<br />34
<br />.5667
<br />44
<br />.7333
<br />54
<br />.9000
<br />5 '
<br />15
<br />.2500
<br />25
<br />.4167
<br />35
<br />.5833
<br />45
<br />.7500
<br />55
<br />.9167
<br />6
<br />.0833
<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 />.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 />.4833
<br />39
<br />.6500
<br />49
<br />.8167
<br />59
<br />.9833
<br />10
<br />.1667
<br />20
<br />.3333
<br />30
<br />.5000
<br />40
<br />.6667
<br />50
<br />1 .8333 11
<br />60
<br />11.0000
<br />_
<br />TABLE V.
<br />-Inches in Decimals of a Foot.
<br />1-16 3-32Y
<br />3-16
<br />%
<br />5-16
<br />Y2'
<br />.0052 .0078
<br />.0078 Ij
<br />.0104
<br />.0156
<br />0208
<br />.02660
<br />.0313
<br />04817
<br />.0521
<br />.06225
<br />.0
<br />729
<br />I
<br />1
<br />10
<br />.0833 I .1667 I
<br />.2500
<br />.3333
<br />.4167
<br />.5000
<br />.5833
<br />.6667
<br />.7500
<br />.8333
<br />.9167
<br />
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