|
VIII
<br />TABr m IL - Radii, Ordinates and.Deflectione. Chord -100 ft.
<br />D"g
<br />Hauius:
<br />Mid
<br />ped, •
<br />Tan.
<br />Diet.
<br />Def.
<br />Diaz
<br />D� ef
<br />I Ft.
<br />�
<br />'Pathos
<br />Mid.'
<br />Ord.
<br />Taz: Diet.
<br />-
<br />Def.
<br />Divi.
<br />Dior
<br />1 xi.
<br />193. IS
<br />10 51'
<br />2' 17'
<br />2° 58'
<br />3° 43'
<br />101:15
<br />32°
<br />t.
<br />1° 592.
<br />2' 25'
<br />L.
<br />3°.582
<br />D"10'.
<br />34377.
<br />036
<br />.145
<br />.41'6.05
<br />3° 21'
<br />7"
<br />819.0
<br />1.528
<br />6.105
<br />12.21
<br />2.10
<br />• 20
<br />17180.
<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 />0.45
<br />30-
<br />754.5
<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 />.,.162
<br />.727
<br />'1:454
<br />0, 2.5''
<br />8
<br />716,8
<br />1:746
<br />6.976
<br />13.952.40
<br />30 o2'
<br />1
<br />5729.6
<br />.218
<br />.87a
<br />1.745
<br />0.30 -
<br />20
<br />688.2
<br />1.819
<br />7:256
<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 />14282
<br />2.55
<br />2D
<br />•4297.3
<br />•.291
<br />1.164
<br />;2.327
<br />0.40
<br />40
<br />651.7
<br />1:892
<br />:7.556
<br />15:11
<br />2.60
<br />3D
<br />3819.8
<br />.327
<br />1,309
<br />2;618
<br />0.45
<br />9
<br />637.3
<br />1.965'7:846
<br />15,69
<br />2.70
<br />40
<br />3137.9
<br />.364
<br />1.454
<br />'2,909
<br />0.50'
<br />20
<br />614.6
<br />2.037
<br />'8.135
<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 />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 />19.585
<br />19.16
<br />3.30
<br />40
<br />.2148.8
<br />•..582
<br />2,327
<br />•4:654'0.80.,
<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 />3,,
<br />1910.1
<br />' .655
<br />2.618
<br />5.235'0.90.
<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 />2.949.11.75
<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 />3.058.12.18,•
<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 />18',
<br />383.1
<br />3.277
<br />13.05_
<br />26.,11
<br />4.50
<br />! - ..1132.7
<br />.873
<br />3'.490
<br />6.980
<br />1.20
<br />'30
<br />370:8'
<br />.387'13:49.
<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 />7'.561
<br />1.30
<br />1 30,348.5
<br />3.606
<br />14•.35
<br />28,70
<br />4.95
<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 />.30
<br />40
<br />1228.1
<br />1. 018
<br />4.071
<br />8:141.40
<br />3
<br />18
<br />319.6
<br />3:035
<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 />49•
<br />302.0
<br />4.155.16.51
<br />33.01
<br />5.70
<br />8
<br />1146.3
<br />1.091
<br />4.362
<br />8.724
<br />1.50
<br />20
<br />287.9
<br />'.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 />6.36
<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 />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 A7
<br />1.80
<br />20
<br />222.3
<br />5.697
<br />22.50
<br />44.99
<br />7.80
<br />10
<br />•929.6
<br />3.346
<br />5.379
<br />10.76
<br />1.85
<br />27•
<br />214.2
<br />.018
<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 />.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 />859.9
<br />1:455
<br />5.814
<br />11.63
<br />2.00
<br />30
<br />193.26.5$3
<br />25.88
<br />51.76
<br />9.00
<br />The middle ordinate 'n inches for any "rd of length (4) is equal to 0012 C'
<br />multiplied by the n-uNe ordinate taken from the above table. Thus, if it
<br />desired to band 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 />of
<br />Radius
<br />50
<br />A sub chord _ sin of I def. angle - -
<br />R
<br />Length
<br />of arc
<br />Curve
<br />sin. }def. ang.
<br />12.5 Ft.
<br />15 Ft.
<br />20 Ft,
<br />25 Ft.
<br />for 100 ft.
<br />300
<br />193. IS
<br />10 51'
<br />2' 17'
<br />2° 58'
<br />3° 43'
<br />101:15
<br />32°
<br />181:34
<br />1° 592.
<br />2' 25'
<br />3° 10'
<br />3°.582
<br />.101.33
<br />34°
<br />171.01
<br />2° 06'
<br />2' 33'
<br />3° 21'
<br />4', 12'
<br />I01.48
<br />361
<br />161.'. 8o- "
<br />2° 13'
<br />2' 47'
<br />3° 33'
<br />4° 26'-
<br />101.66
<br />380
<br />153: 5 $
<br />2 20
<br />0 '
<br />6 49'
<br />2
<br />30 44�
<br />O
<br />40 4 '
<br />1017 8i
<br />40
<br />146. 1.9
<br />2 272• -
<br />2° 57'
<br />-3 55
<br />4 54' .
<br />lo2.o6
<br />42°
<br />139; 52
<br />2° 34'
<br />30.051
<br />4°.072
<br />5' 08
<br />102.29
<br />44°
<br />133.47
<br />2° 41'
<br />3' 13'
<br />4° 18'
<br />5° 22'.
<br />205.53
<br />46°
<br />127•.97
<br />2° 48'
<br />3°21'
<br />4° 29
<br />5' 36'
<br />102.76
<br />49°
<br />122.92
<br />2° 55'
<br />30 2�'
<br />40 40'.
<br />50 50'.
<br />103.00
<br />50°
<br />128 -31
<br />30 o2'
<br />3a 381
<br />4°51'
<br />6° 04'
<br />•. 103-24
<br />52°
<br />114-o6
<br />3° 09'_
<br />3° 46'
<br />.5° D2'
<br />6° 17'
<br />I03"54 .
<br />54°
<br />110. 111 '
<br />3° 16'
<br />3054 1
<br />:5° 13'. '
<br />6' 31'.
<br />103.84
<br />56°
<br />1o6.50
<br />.3° 22'
<br />4° 02'5°
<br />23'
<br />6° 44'
<br />104:'14
<br />58°
<br />103. 14
<br />3° 29
<br />4° ro'.
<br />5° 34'
<br />6° 57'
<br />, 104:43
<br />600.
<br />I00.00
<br />3° 35'
<br />4° r8'
<br />. 5° 44'
<br />7' 11'
<br />I 104.72
<br />Ix
<br />CURVE FORMULAS
<br />T = fl tan, 2 I .R, = T cot. I chorda
<br />I 5o -tan 2 .I• . Chord def. _
<br />Sin..4 D R = 50 R
<br />Sin. 11 D _ 50Sin. D No. chords = D
<br />" R ' E = R ex. sec ; I
<br />Sin: a',D 5o tT z 1 • 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
<br />I. Multiply the given distance by .01745 (def. for 1 for 1 ft..
<br />see Table IL), and divide given deflection by the product.
<br />Rule 2. Multiply given deflection by 57.3, and divide the.pioduct by
<br />'the -
<br />given distance.
<br />To find deflection for a given angle and distance. 'Ivfultiply;the angle.
<br />by .01743, 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. IO.Io2=200=.5: Ioo+.5=IW5llyp.
<br />Given,I-Iyp. loo, Alt. 25.252-200=3.125. loo-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 II, 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, ;d2. The.combined cor-
<br />_recti'on is negative. .
<br />PROBABLE. ERROR. If dt, d2, da, etc. are the discrepancies of various
<br />results from the mean, and if 2:d2= the sum of the squares of these differ-
<br />ences and n -the number of observations, then the probable eiror of the
<br />mean=
<br />- 0.6745' n(n-1) .
<br />SOLAR EPHFmF9is.- Attention. is called to the Solar' Epliemeris for
<br />the current year, published by Keuffel'& Esser Co.;'and fu'rni'shed upon
<br />request. This handy booklet, 3'1x6 in., -has about 190 pages df '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 />:11
<br />.0167
<br />111
<br />'.1833
<br />211
<br />.3500
<br />311
<br />.5167
<br />411
<br />.6833
<br />51'
<br />,8500
<br />2
<br />.0333
<br />12.2000
<br />.200
<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 />24.4000
<br />4
<br />34
<br />.5667
<br />4d
<br />,7333
<br />54
<br />.9000
<br />5
<br />,0933
<br />15
<br />.2500
<br />25
<br />,4167
<br />35
<br />.5833
<br />45
<br />-.7500
<br />55
<br />.9167
<br />6
<br />.1000
<br />16
<br />.2667
<br />26
<br />.4333
<br />36
<br />.6000
<br />46
<br />.7657
<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 />1 20
<br />.3333 1.
<br />30
<br />.5000.
<br />40
<br />.6667 11
<br />50
<br />.8333
<br />50
<br />1.0000
<br />TAB1•F V.
<br />-Inches in Decimals of a Foot.
<br />1-16
<br />3-32
<br />)a
<br />3-16
<br />i4
<br />5-16
<br />%
<br />%A00.52
<br />.0078
<br />.0104
<br />.0156
<br />.0208
<br />.0260
<br />.0313
<br />.0417
<br />.0.06250721
<br />1
<br />H
<br />1
<br />3
<br />4
<br />5
<br />6
<br />7
<br />8
<br />10.
<br />11
<br />0833
<br />.1687
<br />.2500
<br />.3333
<br />.4167
<br />.5000
<br />.5833
<br />.6667
<br />.7.8353
<br />.9167
<br />,
<br />
|