|
VIII
<br />TAimEIL-Ridii,'Ordinates'and.Deflections. Chord 100 ft.
<br />Deg. - :
<br />Radius
<br />Mid.
<br />Ord.'-
<br />Tan.
<br />Dist.'
<br />. Def.
<br />Dist.
<br />Dor'
<br />1Ft.
<br />:Deg.
<br />Radius
<br />• Mid..
<br />Ord.
<br />Tan.
<br />Dist.
<br />Def.
<br />Dist.
<br />D f
<br />"1 Ft.
<br />2° 58''3°43'
<br />.0167-
<br />0333
<br />101.15-
<br />...320.,...
<br />. 181.39._--
<br />._..1°.591---
<br />20 25'. ..-
<br />.3°.10,_ ...
<br />_3°.58' ...,101--
<br />33. .
<br />340
<br />171.01
<br />0°10''34377.
<br />2° 33'
<br />.036
<br />-:145
<br />:291
<br />0:05
<br />:.7"
<br />819.0.1.528
<br />29 41'
<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 />'.409
<br />'.43G
<br />::873
<br />0,15
<br />30"
<br />764.5
<br />1:637
<br />6.540
<br />13.08.2.25
<br />2° 41' .
<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 />.185
<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 />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 />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 />.364.1.454
<br />'2:909
<br />0:50
<br />720
<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- -
<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,'3.781
<br />0.65.
<br />10 '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 />30'546.4
<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 />it
<br />521.7
<br />2.402
<br />0.585
<br />19:16
<br />3.30
<br />40-
<br />2148:8
<br />.582
<br />2.a27
<br />-4.654
<br />0.80
<br />30
<br />499..1
<br />2.511.10.02
<br />20:04
<br />3.45
<br />50'•
<br />2022.4
<br />-.618
<br />2.472
<br />4.045
<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 />22.64
<br />3.90
<br />20
<br />1719.1:'.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 />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 />,.14
<br />1.10
<br />,
<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 />10.1375.4
<br />'.909
<br />3.635
<br />.7•.271
<br />1.25•
<br />16,
<br />359.3
<br />3:406
<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":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 />1.018
<br />4.071
<br />8.143
<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 />302.9
<br />4:155
<br />16.51-.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 />4.507
<br />9.014
<br />1.55
<br />.21,
<br />274.4-4.594
<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 :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
<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 />1.309.5.234
<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 />.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 />6.669'11.34
<br />1.95
<br />29:
<br />199.T6.360
<br />25.04
<br />50107
<br />8-70
<br />40
<br />'859.9
<br />1.455
<br />6.814
<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 }}'n inches for any cord of length (0) is equal to .0012 C'
<br />multiplied by the rRiddle 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 .0012X900X2183 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.'' def. ang.
<br />1 Y2 sub chordLengt
<br />R =' sin of a def. angle
<br />of arch
<br />for 100 ft.
<br />12.5- Ft.
<br />'15 Ft.
<br />q 20 Ft. '
<br />25 Ft.
<br />3010
<br />193.18
<br />1°51'
<br />2°17'
<br />2° 58''3°43'
<br />.0167-
<br />0333
<br />101.15-
<br />...320.,...
<br />. 181.39._--
<br />._..1°.591---
<br />20 25'. ..-
<br />.3°.10,_ ...
<br />_3°.58' ...,101--
<br />33. .
<br />340
<br />171.01
<br />2° 06'
<br />2° 33'
<br />3° 21'
<br />¢° 12'
<br />101.48
<br />360
<br />161.8o _'
<br />2° 13.
<br />29 41'
<br />3° 33,
<br />4°.26'
<br />101.66
<br />38°
<br />153.58
<br />2° 20'
<br />z° 49
<br />3° 44'
<br />4° 40'-
<br />'101.8.5
<br />o --
<br />40
<br />1¢6.19
<br />,- o , -
<br />z 27 ,
<br />-
<br />20 57'
<br />- -
<br />3o 55'
<br />-
<br />- 4o 54 -_
<br />' 102.06 -.
<br />42o
<br />X39; 52
<br />20 34':
<br />36 05,..
<br />40 01'
<br />50 08'102:29
<br />45
<br />-44*'-
<br />133:47-
<br />2° 41' .
<br />3°'13'
<br />4° 18' '
<br />5° 22'_
<br />162.53
<br />46' `_`
<br />127.9T:
<br />2° 48'
<br />3°.21'..
<br />40 29- ,
<br />' .5° 36'
<br />J02.76
<br />-48°: • .
<br />-122.92
<br />2°• 55'
<br />'30.02'•
<br />3° 29'
<br />4° 40'
<br />5°:50'
<br />-103.00
<br />.500..
<br />I 18.31
<br />: :
<br />3o 381
<br />40 5 C -
<br />.. , 60 04'
<br />- I03 :.24
<br />;52 ° ,
<br />.. 114:o6
<br />3°'09'
<br />3° 46' ',
<br />5° 02'
<br />6° i7'
<br />103-54-
<br />54° .1
<br />-110. Il
<br />3°.16'
<br />3° 54' ;
<br />, 5°• 131-
<br />6° 31' "
<br />' - 03, 84
<br />56° t;
<br />: 106. So .
<br />3° 22'
<br />4° 02'
<br />5° 23''
<br />6044'
<br />10¢..1¢ .
<br />58,..
<br />-103. 14.
<br />.3*. 219'
<br />4° 10,.
<br />5° 34'
<br />6° 57''
<br />,..104.43
<br />:600
<br />100.00.
<br />. 3°35'
<br />4°18'
<br />S°44'
<br />70 -11'
<br />104. 72
<br />IX
<br />CURVE FORMULAS
<br />T R tan 2 I R= T cot. 2 I chord'
<br />T,,, 5o tan 21'-I Chord def. = R .
<br />Sin. I D R = 50
<br />5o Sin, 2_D I
<br />Sin. 21 D =No. chords D
<br />='
<br />E R ex. sec m'I D
<br />Sin: 12 D = 50 t 1. z •I E T tan } I Tan. def. = Z chord def.
<br />The squai-e'of any distance, divided' by twice the radius, will equal
<br />=the distance from tangent to'curve, eery nearly.
<br />To find angle -for a given distance -and -deflection.
<br />Rule -i. :Multiply the given distance by .01745 (def. for I' for I ft-
<br />-see Table 11.), and divide given deflection by'the product.
<br />Rule 2. Multiply given deflection by 57.3, and divide the product by
<br />.the_givendistance. . , -
<br />To find deflection for a given' angle and distance. Multiply the angle
<br />'by :oiA5,: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. I0.10'=200=.5. lc;O+.5=I60:5 hyp.
<br />Given Hyp.:I oo, Alt. 25.252 _200 =3-I 1 25. 100-
<br />.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 r, and divide by 7.
<br />LEVELiN6. The correction for curvature .and refraction; in feet
<br />anddecimalsof 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 />'PROAABLE'ERROR. If d1, 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:- Ede
<br />• _ 't0.6745�
<br />SOLAR EP14snlElils:•- •Atterltion is' called- to the Solar Ephemeris for
<br />the current year, published by :Keuffel & Esser Co:,. and 'furnished upon
<br />request. .This handy booklet; 3!x6 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 Aetermining, the meridian and the
<br />latitude from observations oil the sun=and Polaris; stadia measurements;
<br />magnetic-dectination; arithmetic constants, etc. .
<br />Teixr.F'TV'=Minutes in Decimals of a Decree.
<br />7
<br />,;;' TABLE V. -Inches in Decimals of a root.
<br />1-16 3-32 Y 3-16 '/y 5-16 % M
<br />.0052 I .0078 I .01304 I .0156 .0208 I .0260 I , .0213 I .0417 I .0 821 .06025 I .Ol 29
<br />.0833 .1667 .2500 .3333 .4167 .5000 5833 .6667 .7000 .8333 .9167
<br />111
<br />.1833
<br />21/
<br />-.3500
<br />311'
<br />..5167
<br />411
<br />.6833
<br />51/
<br />.8500
<br />.11
<br />2
<br />.0167-
<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 />'..050013
<br />-2167.
<br />23'
<br />"_.3833
<br />33
<br />..5500
<br />43
<br />.7167
<br />53
<br />.8833
<br />- 4
<br />•
<br />14
<br />24
<br />.4000
<br />34
<br />.5667
<br />44
<br />.7333
<br />54
<br />.9000
<br />5
<br />.0667
<br />15
<br />_ .2333
<br />25
<br />.4167
<br />35
<br />.5833
<br />45
<br />.7500
<br />55
<br />.9167
<br />6
<br />.0833
<br />16'
<br />.2500
<br />26.
<br />.4333
<br />35
<br />.6000
<br />46
<br />.7667
<br />56
<br />.9333
<br />7-.1167,.
<br />.1000
<br />17
<br />.2667'.
<br />.2833
<br />2T
<br />.4500
<br />37
<br />.6167
<br />47
<br />.7833
<br />57
<br />.9500
<br />8
<br />18
<br />28
<br />.4667
<br />38
<br />.6333
<br />48
<br />.8000
<br />58
<br />.9667
<br />- 9 `
<br />..1333
<br />.1500
<br />19 •
<br />.3000
<br />'.3167'
<br />29-
<br />.4833
<br />39 '
<br />.6500
<br />49
<br />.8167
<br />59
<br />.9833
<br />10...
<br />1 1.1667:1120
<br />1 .3333.11
<br />30.
<br />1 .5000 11
<br />40
<br />.6667
<br />50
<br />.8333
<br />60
<br />1.0000
<br />,;;' TABLE V. -Inches in Decimals of a root.
<br />1-16 3-32 Y 3-16 '/y 5-16 % M
<br />.0052 I .0078 I .01304 I .0156 .0208 I .0260 I , .0213 I .0417 I .0 821 .06025 I .Ol 29
<br />.0833 .1667 .2500 .3333 .4167 .5000 5833 .6667 .7000 .8333 .9167
<br />
|