|
VIII
<br />TABLE IL - Radii, Ordinates. and Deflections. Chord =100 ft.
<br />1 -Deg.
<br />Radius
<br />Ordd..
<br />Dat,
<br />Dist
<br />° r
<br />1 Ft.
<br />--Deg..:
<br />Radius
<br />`
<br />'Mrd.
<br />Dist
<br />Des
<br />Dor
<br />1 Ft.
<br />?7,;_.
<br />ft..
<br />t.
<br />IOI.15
<br />32
<br />-,19318
<br />181,39
<br />1 59
<br />t:t...
<br />._
<br />3 10
<br />I ft.
<br />ft.
<br />34°
<br />0°10'
<br />34377.
<br />.036
<br />.145
<br />'.291
<br />0.05
<br />7°.
<br />819.0
<br />1.528
<br />6.105.12.21
<br />;3°
<br />2:10
<br />20'17189
<br />_ 38°
<br />:073
<br />.291'.
<br />.582
<br />0.10
<br />20'
<br />781.8
<br />1.600
<br />16.395
<br />12.79
<br />2,20
<br />30,'11459
<br />. , 4°. 54' .
<br />:109
<br />.436
<br />'. .873
<br />0.15
<br />30
<br />764.5
<br />1:637
<br />6.540
<br />13.08.2.25
<br />133.47'
<br />40
<br />8594 4
<br />.145
<br />.582
<br />.1.164
<br />0 20
<br />40
<br />747.9
<br />1.873
<br />6.685
<br />13.37
<br />2.30
<br />" 50''
<br />6875.5
<br />,.182
<br />.727
<br />.1:454
<br />0.25
<br />8
<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 />1819
<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 />15:1 1
<br />2.60
<br />Io4:72
<br />3819.8
<br />.327
<br />1.300
<br />2.618
<br />0.45
<br />. 9
<br />637.3.1.965
<br />7.846,15.69
<br />2.70
<br />.30
<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
<br />16.56
<br />2.85
<br />2 i
<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 />"
<br />2644.6
<br />:473.1.891'
<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 />1,5
<br />25.7
<br />:509
<br />2.036
<br />4.072
<br />_
<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 />I1
<br />2.402
<br />521.7
<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 />2:51-1
<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 />2091
<br />3.60
<br />a 1
<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 />=:691'2.763
<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
<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 />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 />450
<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
<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 />.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.,29.56
<br />5.10
<br />40.'
<br />1228.1
<br />1.0184.071
<br />8.1'43
<br />1.40
<br />'18
<br />319.6
<br />3.935
<br />15.64 '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 />302.0
<br />':155
<br />16.51
<br />33.01
<br />5.70
<br />s
<br />1146.31:091
<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 />-
<br />1.60
<br />22� -
<br />262.0
<br />4:814
<br />19.08
<br />38116
<br />6.60
<br />30;
<br />1042.1
<br />1.200
<br />4.798
<br />9..596
<br />1.65..23`
<br />•,.250.8
<br />5.035
<br />19.94.
<br />39.87.6.90
<br />40
<br />1011.5
<br />1.237.4.943
<br />9,.886
<br />1.70.
<br />.24,
<br />240.5
<br />5,:255
<br />20..79,-41.58
<br />7.20
<br />50
<br />982:6
<br />1..273
<br />5.088
<br />10:18 .1.75
<br />.25 =;
<br />231.0
<br />5.476.21.64°
<br />43.28
<br />7.50
<br />6.
<br />055.4.1.309.5.234
<br />10.47,
<br />1.80:.,
<br />26
<br />222.3
<br />5,.697
<br />22.50:4499.7.80
<br />10
<br />929.6
<br />1.346
<br />5.379
<br />10.76
<br />1:85
<br />271
<br />214:2
<br />5.918
<br />23.35
<br />4669
<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_6.139
<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 />199.76.360
<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 />The middle ordinato }'n inches for any cord of length (0) is equal to .0012 C'
<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, i
<br />TABLE III. , Deflections for Sub Chords for Shoit Radius Curves.
<br />Degree
<br />of
<br />Curve
<br />Radius
<br />50
<br />M sub chord sin of
<br />t R = $def. angle
<br />Length
<br />of arc
<br />for 100 ft.
<br />sin. i def. ang.
<br />12.5: Ft.
<br />15 Ft.
<br />23 Ft. '•
<br />25 Ft.
<br />Joe
<br />511
<br />10.5?x.....20
<br />?7,;_.
<br />20 58,x.
<br />.. 3_43 .
<br />IOI.15
<br />32
<br />-,19318
<br />181,39
<br />1 59
<br />2 25
<br />._
<br />3 10
<br />305 8
<br />101'.33
<br />34°
<br />171.01
<br />-2° o6'
<br />2° 33'
<br />3° 21'
<br />4° 12'
<br />101.48
<br />36°
<br />161.8o '
<br />20 13'.
<br />z° 41.:
<br />;3°
<br />4* 26'
<br />Io1.66
<br />_ 38°
<br />153.58..
<br />20 20'
<br />20 49
<br />3°_44'
<br />40 40'.
<br />ioi.85 ,
<br />:40°
<br />146 '1'9
<br />2° 27'
<br />2° 51'
<br />30: 55' .
<br />. , 4°. 54' .
<br />102. o6 ..
<br />420
<br />139 52'
<br />'° 34'
<br />...
<br />3° 051
<br />4° 07'
<br />50 08
<br />162:29
<br />44°
<br />133.47'
<br />2° 4?'
<br />3° 13',..
<br />4°.18'`
<br />5° 22'
<br />102;53
<br />46°
<br />127;97; ..
<br />?° 48'
<br />3°=21''.:.
<br />?° 29'
<br />5° 36'
<br />io2:76
<br />:48° .
<br />12292,
<br />• 2° 55,
<br />3° ?9,.
<br />4° 40, .
<br />5° 50,
<br />iO3.00
<br />_ 50°
<br />.118.31=;
<br />3o O2, =
<br />. 3° 38, -
<br />_4° 51, :
<br />°04' :'
<br />: 6004 1
<br />:. 103.24..
<br />.52
<br />J 114.06.
<br />3° 09,
<br />3°-46'•
<br />5° 02'.
<br />6'.17' :
<br />103-54
<br />54°
<br />f IIO. I_I;
<br />3° 16'
<br />3' 5q'..
<br />5° 13'.
<br />6°:31''
<br />.:1o3 84...
<br />56° ,
<br />.. 106:50'•
<br />3° 22'
<br />4° 02' '
<br />' 5° 23'
<br />6°:44'
<br />104 I.4
<br />°
<br />.58
<br />103. 1.4
<br />3° 29'
<br />� 4°.10,
<br />5° 34,
<br />- •6°,57' '
<br />'- 104 43 ..
<br />6o°
<br />100.00
<br />3° 35'
<br />4° 18'-
<br />50 44.1
<br />70 11,
<br />Io4:72
<br />IX
<br />CURV E -FORM ULAS
<br />T= R tan Y'1 I R_ = T cot. 1 I. chord'
<br />I 5otan 2. -•- Chord def. = R
<br />Sitn 2 D R = 50
<br />5o Sin. A ll I
<br />Sm, , D K No. chords, D
<br />E _ ' R ex. sec I
<br />Sin.1 I) _ 5o tarn 's I E =X tan I. Tan. def. = 2 chord def.
<br />The -square of any distance, divided by tidice the radius, .will equal
<br />''fhe 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 :01745 (def. f6r- I for z 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 finddeflection for a given angle and distance. Multiply the angle
<br />-631 X01745, and the product by the distance.
<br />GENERAL DATA
<br />RIGHT ANGLE, TRIANGLES. ; Square the altitude, divide by twice .the
<br />abase. Add quotient to base for hypotenuse.
<br />Given Base ioo, Alt. 10.102-200=.5. IOO+-5=IOO.5 hyp.
<br />Given H' Joo, Alt..25.25'=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 0.574d2, where d is the distance in. miles.
<br />The correction . for . curvature alone is . closely, ;d?. The combined cor-
<br />rection is negative..
<br />PROBABLE,ERROR. . If di, d2, ds, _etc:. are the discrepancies of various
<br />results from the mean, and'if ±d2.=the sum of the squares of�these differ-
<br />ences.and ri=the number of observations, then the probable error of the
<br />"mean= Ede - -
<br />(0.6745 n(n-I)
<br />SOLAR EPIIEMER1s. '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 />1'
<br />'•-- -
<br />11'
<br />-Inches to Decimals of a rout.
<br />21'
<br />3500
<br />311
<br />.5167
<br />41'
<br />.6833
<br />511
<br />.8500
<br />".,2
<br />.0167
<br />' 12
<br />.1833
<br />22
<br />"3667
<br />32
<br />_.5333
<br />42,
<br />.7000
<br />52
<br />.8667
<br />_
<br />�3
<br />.0333
<br />13
<br />.2000
<br />-.2167
<br />23
<br />'.3833
<br />33
<br />.5500
<br />41
<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 />55
<br />-9000
<br />„ 5 -
<br />-
<br />.0833.
<br />15
<br />.2500.
<br />25
<br />-26
<br />.4167
<br />-.4333
<br />35
<br />36
<br />..5833
<br />45
<br />46
<br />.7500
<br />.7667
<br />56
<br />.9167
<br />- .9333
<br />6
<br />71.
<br />A 000
<br />`-.1167
<br />16
<br />17
<br />.2667
<br />.2833
<br />27-
<br />.4500
<br />37
<br />.6000
<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 />49
<br />.8000
<br />58
<br />59
<br />.9667
<br />9-
<br />-1
<br />.1500
<br />'19
<br />.3167-
<br />29
<br />30
<br />.4833
<br />:5000
<br />39
<br />40 '
<br />.6500
<br />.6667
<br />50
<br />.8167
<br />.8333,
<br />60
<br />.9833
<br />1.0000
<br />10'-
<br />.1667'
<br />20
<br />T.3333 11
<br />o.= •-'
<br />'•-- -
<br />-TABLE- V.
<br />-Inches to Decimals of a rout.
<br />-
<br />1-16
<br />3-32
<br />3-16
<br />%
<br />5-16
<br />%
<br />+
<br />%
<br />�
<br />YS
<br />.0729
<br />.0052'
<br />.0078
<br />-.0104 -.0156
<br />.0208_1
<br />.0260
<br />.0313
<br />.0417 I .0521 I
<br />,Of25 I
<br />1
<br />-.0833
<br />2
<br />I ._ 1667 I
<br />3
<br />.2500 1
<br />4
<br />.3333
<br />5
<br />.4167
<br />6
<br />.5000
<br />7 I
<br />.5833
<br />8 9
<br />.6667 .7500
<br />10
<br />.5333
<br />- 11
<br />.9167
<br />
|