|
VIII• ,
<br />.-TABLE ILS- Radii, Ordinatee and.Deflection& Chord =100 ft.
<br />-Deg.
<br />Radius .Mid.
<br />'Ord.Diet..
<br />, Tan.
<br />Def.
<br />Dist.
<br />D
<br />1 FE.
<br />Dc8•
<br />Rediae
<br />Mid
<br />Ord.
<br />Tan
<br />Dist.
<br />Def.
<br />Dist.
<br />Dar
<br />7 Ft:
<br />2° 58'
<br />3° 43'-101.15
<br />12
<br />32°
<br />181.39
<br />1° 59'
<br />2° 25'
<br />3° 10'
<br />4° 58< .
<br />101.33
<br />34°
<br />171,01
<br />0"10'
<br />34377:
<br />036
<br />.145
<br />.291
<br />0.05
<br />7'
<br />819.0
<br />1.528
<br />6.106
<br />12.21
<br />2.90
<br />20
<br />17189:
<br />.073
<br />.201
<br />.582
<br />0,10
<br />.20'
<br />781.8
<br />I.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 />0.23
<br />'8
<br />716.8
<br />1.746
<br />6.976
<br />13.95
<br />2.40
<br />1
<br />5729.6
<br />.21a
<br />.873
<br />1.745
<br />0.30
<br />20.
<br />688.2
<br />1.819
<br />7.266
<br />1.1.53
<br />2.10
<br />10
<br />4911:2
<br />.255
<br />1.018
<br />2.036
<br />0.36
<br />30
<br />674.7
<br />1.855
<br />7,411
<br />14.83
<br />2.53
<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 />1.300
<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 />1G. 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 />16:65
<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 />2155.7
<br />.509
<br />2.036
<br />4.072
<br />0.70
<br />_30
<br />546.4
<br />2.292
<br />9.150
<br />18.303.15
<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 :9 1
<br />3 G
<br />8
<br />1910.1
<br />.655
<br />2.518
<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 />22.04
<br />3.9D
<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 />39G.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 />16 ''
<br />383.1
<br />3.277'13.05
<br />26.11
<br />4.50
<br />L
<br />1432.7
<br />.873
<br />3.490
<br />6.480
<br />1.20'
<br />30
<br />370.8,3.387
<br />13.49
<br />26.97
<br />4. 5
<br />10
<br />1375:,4
<br />.909.3.635
<br />7.271
<br />1.25
<br />10..
<br />359.3
<br />4.496
<br />13.92
<br />27,84
<br />4,818
<br />20
<br />1322..5
<br />'.945
<br />3.718
<br />7.561
<br />1.30
<br />30
<br />348.5
<br />.'606'
<br />14.35
<br />28.70
<br />4 '9u
<br />30
<br />1273:6
<br />.982
<br />3.026
<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 />1228.1'1.018
<br />4.071
<br />8.143.1.40
<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 />.19 •
<br />302.9
<br />4.155
<br />16.51
<br />33.01
<br />5.70.
<br />6
<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 />4:607
<br />9.014
<br />V55
<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.G0
<br />30
<br />1042:1,1.200.4.798
<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 />9.886-1.70,
<br />24 '
<br />340.5
<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 />26
<br />231.0
<br />5.476
<br />21.64 -43.28
<br />7.50
<br />6
<br />9551.4
<br />1.309
<br />5.234
<br />10:47
<br />180
<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 />6.018
<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 />GA39
<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 />S.70
<br />40
<br />859.9
<br />1.45$
<br />5.814
<br />11.63
<br />2.06
<br />1 30
<br />193.2
<br />6.583
<br />25.88 1.51.76
<br />9.00
<br />The middle ordinate in inches for any cerci of length {G) is eqqual to .0012 C'
<br />multiplied by the JlVddle ordinate taken from the above tabio. Thus, if it
<br />desired to bends 30 ft. rail to fit a 10 degree curve, ita middle ordinate should
<br />be .0012X900X2.18:3 or 2.36 inches.
<br />TABLE III.. Deflections for Sub Chords for Short Radius Curves.
<br />Degree •
<br />of
<br />Curve
<br />Radius
<br />sia.Idef.ang,
<br />1 sub chord = sin of I def. angle
<br />.1i
<br />Length
<br />of are
<br />for 100 ft.
<br />„ 12.5 Ft..
<br />15 Ft.
<br />20 Ft.
<br />25 Ft.
<br />30°
<br />193.18
<br />1.511
<br />2° 17'
<br />2° 58'
<br />3° 43'-101.15
<br />12
<br />32°
<br />181.39
<br />1° 59'
<br />2° 25'
<br />3° 10'
<br />4° 58< .
<br />101.33
<br />34°
<br />171,01
<br />2006
<br />2° 33'
<br />3° 2I'
<br />4° I2'
<br />i0I.48
<br />36°
<br />_16i. 8o
<br />2° 13'
<br />2° 41'3°
<br />33'
<br />4` 26'
<br />101.66
<br />,38°
<br />153.58
<br />2° 20'
<br />2° 49'
<br />3' 44'
<br />4° 40'.
<br />101.85 .
<br />40°
<br />346.tg
<br />20 27'
<br />2° 57'
<br />3° 55'
<br />4° 54'
<br />102:06
<br />42°
<br />139.52
<br />2°34'
<br />3°05'
<br />4°07'
<br />5°08
<br />102.29
<br />440
<br />133 47
<br />z° 41'
<br />3°13'
<br />4° 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 />162.76
<br />48"
<br />122:92
<br />2° 55'. ..
<br />3° 291.
<br />4° 40'
<br />5° 50'
<br />1o3.00
<br />50°
<br />l 18.31 .
<br />3° 02'-
<br />3° 38'
<br />4° 51'
<br />6° 04'
<br />103.24
<br />.52°
<br />114. o6
<br />3° 04'
<br />3° 46'
<br />5° 02'
<br />60 17'
<br />103:54"
<br />54°
<br />10. 11
<br />3°,16'
<br />3° 54'
<br />5° 13
<br />60 31'
<br />103.84
<br />56°
<br />io6. 5o .
<br />3° 22
<br />4° 02',
<br />5° 23
<br />6° 43
<br />104-14
<br />58°
<br />103.�41
<br />3° 29''
<br />4° io'S°
<br />34'
<br />6°°570
<br />104.43
<br />60°
<br />100.00
<br />13 35'
<br />4'° 18'
<br />5° 44'-'
<br />7° 11'
<br />104-72
<br />38�. ! 2 Z 7
<br />-273.4 .2a is z31o� Sp' IX '
<br />3 gyp' j' CURVE FORMULAS j 6, 3' -Li 3-
<br />T ,5 tan' 1. R ''= T cot. L Chord def. - chords .
<br />So tan n i
<br />Sin. x ID 2. C ti<
<br />Sin. z D= 50 �5 e R Sin. I D No. chords = I
<br />.K E = R ex. sec ID p
<br />Sin, -1 D - So tang 1 E - 'T 1-3
<br />tan ] Tan. def. chord def.
<br />1
<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$ (def. for t° for I ft. lS7:
<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 Igiven distance.11
<br />31 ' To find deflection for a given angle arid.distance. Multiply the angle
<br />by_01745, and the product by the distance. 3 1 S!
<br />GENERAL DATA
<br />I
<br />RIGHT ANGLE THIAN(A.E9'Square the altitude, divide by twice the
<br />base, Add quotient to base for hypotenuse. S p
<br />Given Base loo, Alt. ro.io2=2oo=:S. ro0+.5=roo.5 hyp.'
<br />? Given -Hyp. too, Alt. 25.252=200=;.125. 100-3.125=96.375=Base.. Co.
<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 r 1, and divide by 7.
<br />LEVELINi,. 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, 02. The combined cor-
<br />rection is negative.
<br />PROBABLE ERROR. If d1, d,, d2, etc. are the discrepancies of various
<br />results from the mean, and if -d'=the suns of the squares of these differ
<br />ences and n=the number of observations,, then the probable error' of the X-0
<br />mean=dx _° Af�4� t'?
<br />° -0.6745
<br />SOLAR EPHEMERIS. Attention is calle'i3 to the Solar F_phemeris for
<br />the current year, published by KeuffO & Esser Co., and furnished upon
<br />request, This handy booklet, 3gx6.in., has about 190 pages of data very
<br />d 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 frons observations on the sun and Polaris; stadia measurements;
<br />1 magnetic declination; arithmetic constants, etc.
<br />f TABLE IV. -Minutes in Decimals of a Degree.
<br />1f
<br />.0167
<br />11
<br />1833
<br />211
<br />.3500
<br />31"
<br />.5167
<br />411
<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 />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 />44.7333
<br />.583:1
<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 />1.167
<br />6
<br />.1000
<br />I6
<br />.2667
<br />26
<br />.4333
<br />36
<br />.6000
<br />46
<br />.7661
<br />56
<br />.0333
<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 />.1.667
<br />20
<br />.3333
<br />30
<br />.5000
<br />40
<br />.661617
<br />50
<br />.8333
<br />60
<br />1.0006
<br />fAg1,r•. 1'. --Inches
<br />in Decimais of it hoot.
<br />1-16
<br />3-32
<br />Y
<br />3-16
<br />1';
<br />5-16
<br />%
<br />;i
<br />34
<br />%
<br />,p
<br />-0052
<br />',0078
<br />.01D4
<br />.0156
<br />.0208
<br />.0260
<br />.0313
<br />.0417_
<br />.0521 I
<br />.06'_5
<br />.0729
<br />�
<br />1
<br />2
<br />3'
<br />'a
<br />:7
<br />�
<br />6
<br />�
<br />7
<br />�
<br />.3
<br />�
<br />9 !
<br />10
<br />11
<br />.0833
<br />.1667
<br />2.500
<br />.3333
<br />.4167
<br />-5000
<br />.583:1
<br />.B667
<br />.7500 I
<br />.8333
<br />9167
<br />
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