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VIIIq. I I . , • . -:,,
<br />TABiE' IL Radii, Ordinates and Deflections. Chord =100 f t.
<br />Deg..
<br />-amu
<br />Mid.
<br />Ord' :Dist.
<br />Tan.
<br />Def..
<br />Dist:
<br />Def for :
<br />1 Ft.
<br />. ;. Deg.
<br />Radius
<br />Mid.
<br />Ord:
<br />T.
<br />Dist.'
<br />. Def.
<br />-Dist.
<br />Def.
<br />7 Ft.
<br />0"10'
<br />34377:
<br />.036
<br />:145
<br />291
<br />0.05
<br />''7°
<br />t.;
<br />819.0
<br />t,
<br />1.528
<br />t,
<br />•6.10512.21
<br />t.
<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 />3033
<br />12.79
<br />2.20
<br />30
<br />11459.
<br />.109
<br />.436
<br />,873
<br />0.15
<br />30'764.5
<br />4o.a ,
<br />1.637
<br />.6.395
<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 />11.454
<br />0,25-
<br />8
<br />716.8
<br />1:746
<br />6.976.13.95
<br />102..76
<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 />7.556
<br />15.11
<br />2.60
<br />30.
<br />. 3819.8
<br />-.327
<br />':.364
<br />1:300
<br />'2:618
<br />0.45
<br />;9
<br />637.3
<br />1.965
<br />7.846.15.69
<br />7 11
<br />2.70
<br />40.
<br />3437.9
<br />1.454
<br />.2.909
<br />0.50.
<br />20
<br />614.6
<br />22037
<br />8.136:16.27
<br />2.80
<br />50-
<br />3125.4
<br />,400
<br />1.600
<br />3.2000.55'
<br />30
<br />603.8
<br />2.074
<br />8.281
<br />16,.56
<br />2.85
<br />2
<br />2864.9,.436'1.745
<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;.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 />' 2355.7
<br />'.509'2.036
<br />'4:072
<br />0:70--
<br />' ' 30
<br />546A
<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 />i . 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 />20.01
<br />3.60
<br />3
<br />1910.1
<br />'.655
<br />2.618
<br />5.235
<br />0.90
<br />30-459.3
<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 />$.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_.;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 />A '
<br />1432.7
<br />::873
<br />3.490
<br />6:980
<br />1.2030
<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 />.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 />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_'29.565.10
<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 "33.01.5.70
<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 />4.507
<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 />1011:5
<br />1,237
<br />4.943
<br />9.886
<br />1.70
<br />24
<br />240.5
<br />5:255'20.79
<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 />43.28.7.50
<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 />1.346
<br />5.379
<br />10.76
<br />1.85
<br />27
<br />214.2
<br />.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 />.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 />193.2
<br />6.583
<br />25.88
<br />51.76
<br />9.00
<br />T middle ordinate -n inches for any cord of length (0) is equal to .0012 C'
<br />multiplied by the midd e'ordinato taken from the above table.. Thus; if it
<br />desired to bend it 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 />sin.'a def. ang.
<br />Y2 sub chord _sin of 2' def. angle
<br />R
<br />Length
<br />of arc
<br />for 100 ft.
<br />12.5 Ft.
<br />15 Ft:
<br />20 Ft. -
<br />25 Ft.
<br />0
<br />-30
<br />193.18
<br />1 0
<br />'Sir
<br />o- ,
<br />2 17
<br />o r
<br />z 58
<br />3o 43,
<br />101.15
<br />-320,
<br />-' 181'.-39 ....10,.59—
<br />.3667
<br />�2o,251
<br />,..3o,•Io"...
<br />30.58,._.
<br />, 101.33
<br />340
<br />171,01
<br />2° 06
<br />2° 33'
<br />3° 21'
<br />4° 12'
<br />I01.48
<br />36°
<br />161-: 8o
<br />20 13.
<br />2° 41'
<br />3033
<br />4° 26':
<br />.. IoI.66
<br />38'
<br />153.58
<br />2° 20'
<br />2° 49'
<br />3° 44'
<br />4' 4o'
<br />io1.8.5
<br />4o.a ,
<br />146,19'
<br />20 2,7, -
<br />20.571
<br />30 55'
<br />-4a 54,..
<br />-102:06 .
<br />42 . ..
<br />139 � 52
<br />2' 34
<br />3' 05'
<br />4' 07,
<br />5' 68'
<br />'_-7I62.29
<br />44' •
<br />133.47
<br />2° 41.
<br />3°.13'
<br />49 18'
<br />5' 22'
<br />102.53
<br />46°:
<br />127.97
<br />2° 48'
<br />3° 21'
<br />4°'29'
<br />5° 36'
<br />102..76
<br />48°
<br />122.92
<br />20'55'
<br />3°'29'
<br />4° 40'
<br />5' 50'
<br />103.00 .
<br />50°
<br />118 31
<br />.j
<br />..3° 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 />S' 02'
<br />6° 17
<br />'I03.54
<br />54`'
<br />Ii0- 11
<br />3° 16'
<br />3� 54'
<br />5' 13'
<br />6° 31'
<br />103. 84
<br />56°
<br />106.56
<br />30 22''
<br />4° 02'
<br />5' 23'
<br />6° 44'
<br />104.14
<br />580
<br />103.14
<br />3o 29� :
<br />4o 10'
<br />50 341
<br />6o 57'
<br />104.43 .
<br />6o
<br />100.00
<br />3 35
<br />.
<br />4.- 18
<br />5 44
<br />7 11
<br />-104.72
<br />_ IX
<br />_ CURVE. FORMT LAS
<br />T- R tan l I R= T cot. 2 I chord'
<br />_ 5o tan .z I -Chord def.
<br />_ T Sin. z D 50 : .R
<br />Sin. z D = 50 R Sin. �_D No. chords = D
<br />R E R ex."sec z h
<br />t 5o tan z I - - • . Tan. def. = 'chord M.
<br />1 I
<br />Sin. 2 D = h E = T tan } I:' .
<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 .6i745 (def. for. I° for 1 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 Arid distance.' Multiply the angle
<br />by ,01745, and the product by the distance.
<br />GENERAL DATA-
<br />RIGHT
<br />ATA-
<br />RIGHT-ANGLE:TRIANGLES. `Square the altitude, divide bytwice the
<br />base. Add quotient to base for hypotenuse.
<br />Given Base Ioo, Alt. 10.102=200=.5. 100{-.5=100.5 hyp.
<br />Given Hyp: -i oo,- Alt. 25.252-200 = 3.125. Ioo -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 0.5714 d 2, '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. Udt, d2, d3; 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= Id2
<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,B3' cA 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 table"s'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 iii' Decimals of a Deeree.
<br />.1/
<br />.0167
<br />111-
<br />'.1833'
<br />211
<br />.3500
<br />311'
<br />.5167
<br />41'
<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 />13
<br />.2167
<br />-23 '
<br />.3833
<br />33
<br />.5500
<br />43
<br />.7167
<br />53
<br />.8833.
<br />•'4.
<br />..0500,,
<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 />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 />.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 />.19
<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 11
<br />30
<br />.5000 11
<br />40
<br />1 .6667 11
<br />50
<br />1 .8333 11
<br />60
<br />11.0000
<br />TABLE V. -Inches in Decimals of a Foot.
<br />1-16 3-33 Y 3-16 % 5-16 % Y2 % 3 ?�
<br />.0052 .0078 .0104 .0156 .0208 .0260 .0313 .0417 .0521 .0625 .0729
<br />.0833 I .1667 I .2300 I .3333 .4167 Ir.5000 I .5833 I .6667 .7500 .8333 I .9167
<br />
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