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VIII
<br />TABLE IL - Radii, Ordinates and Deflections. Chord =100 ft.
<br />Deg''
<br />'liadius
<br />Mid.
<br />Ord. -
<br />Tau
<br />Dist..
<br />Def.
<br />Dist.
<br />De'
<br />for
<br />1 Ft
<br />Deg.
<br />g
<br />Radius
<br />Mid.
<br />Ord.
<br />Tan
<br />Dist.
<br />Def.
<br />Dist.
<br />Def.
<br />for
<br />1 Ft.
<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
<br />12.21
<br />2.10
<br />20
<br />17189c,
<br />.073.291
<br />3° 21'
<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 />0.15
<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 />0.25
<br />8. ..
<br />716.8
<br />1.746
<br />6.976
<br />13.95
<br />2.40
<br />1' " -
<br />5729.6.218
<br />20 55'
<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 />1:309
<br />2:618
<br />0.45
<br />9
<br />637:3
<br />1.965
<br />'7.846.15:69
<br />51' 44'
<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 />2037.
<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 />8.281'16.56
<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 />2.292,9.150
<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 />. 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 />10.4520:91
<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 />, 1809.6.691
<br />2.763
<br />.'5.526
<br />0.95.
<br />13
<br />441.7
<br />2.839.
<br />11:32.
<br />22.6'4
<br />3.90
<br />20
<br />1719,.1.
<br />.727
<br />2.908
<br />5.817
<br />1.00.E
<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
<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 />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 />161 •'
<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 />30
<br />348.5
<br />3.606
<br />14.35
<br />28:70.4.95
<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
<br />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
<br />31.29
<br />5.40
<br />50
<br />1185.8
<br />1.055
<br />4.217
<br />$: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
<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 />'9.596
<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 />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 />..273
<br />1'
<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 />V'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 />P.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. 713
<br />24.19
<br />48:38
<br />8.40
<br />30
<br />1881.9
<br />1.418
<br />5.669
<br />11.34
<br />1.95
<br />29
<br />199.7.6.360
<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 />The middle ordinate•u inches for any cord of length (0) is equaLto .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.
<br />TABLE III. Deflections'for Sub Chords for Short Radius Curves.
<br />De� ree
<br />Curve
<br />Radius
<br />SOus
<br />3a sub chord _ sin of I def. angle
<br />Length
<br />of arc
<br />for 100 ft.
<br />sin. a def. ang.
<br />12.5 Ft.
<br />15 Ft.
<br />20 Ft.
<br />25 Ft.
<br />30'
<br />193.18
<br />10'51'
<br />2° 17
<br />2° 58
<br />30 43'
<br />101.15
<br />'32*'
<br />.. 181:39.
<br />1 59 ..
<br />2 2
<br />10
<br />.7000
<br />„.33...
<br />340
<br />171.01
<br />2°'o6'
<br />2° 33'
<br />3° 21'
<br />4° 12'
<br />101.48
<br />36°
<br />161;.80 '
<br />- 2° �3
<br />2° 41,
<br />3° 33'
<br />4° 26' ..
<br />,ioi.66
<br />38°
<br />153.58
<br />2° 20'
<br />2° 49
<br />3° 44'
<br />4° 46''
<br />`-101.85
<br />•40° :
<br />146.19
<br />2° 27,
<br />2°-57,
<br />3° 55'.
<br />4°.54'
<br />-102,06
<br />42°
<br />139-52
<br />20 34a
<br />.3° 05,..
<br />4° 07
<br />5008
<br />:I62.29
<br />449:
<br />: 133147;
<br />2141 '
<br />3° 13'49
<br />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 />30 29'.
<br />4049'
<br />5° 50'
<br />103:00 ,
<br />5�°
<br />118.31 ...
<br />' 3° 02'
<br />3° 38'
<br />40.51, ..
<br />6° 04
<br />103.24
<br />52°
<br />°
<br />114.06, .
<br />r: .3°.09' .
<br />3° 46'
<br />5° 02'
<br />'6° 17'
<br />103.54
<br />54
<br />110.11
<br />.30 16'•
<br />3° 54' ,
<br />' '5° 13'
<br />6° 31
<br />103': 84
<br />56°..
<br />106.56
<br />.3° 22' .
<br />4° 02'.'
<br />50 23'..
<br />'6° 44'
<br />104-14
<br />580
<br />103.14. '
<br />30 29'
<br />4° 10'
<br />° 34'
<br />5
<br />- 6 ° 57
<br />1 0 4:43
<br />•600
<br />IOO.00
<br />30 35'
<br />4° 18':
<br />51' 44'
<br />_
<br />.7°.-I1'
<br />104-72..
<br /> . - - I IX
<br />CURVE FORMULAS
<br />T= K tanI R= T cot. Z I chord=.
<br />T -- 50 tan 2 I Chord def.
<br />_ Sin.- D _ _ R 50 _R_ Y
<br />3 _
<br />D = 50 Sin- 2_D No. chords = I
<br />R E= R ex. sec a I D
<br />1
<br />go tan i I 3
<br />Sin. z D T 'E = T tan } I Tan. def. = 2 chord def.
<br />The' square sof any .distance, divided by twice the _radius, will equal
<br />,the distance from. tangent, to curve, very nearly.
<br />-To find'angl'e for- a given distance and 'deflection. -
<br />Rule -1 Multiply the given distance by .01745 (def. for i° f0r•i 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 fora giveniangle and distance.' Multiply the angle
<br />by :01745, 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 loo, Alt. lo.102=200'=.5:.I0'0+-5=1oo.5 hyp.
<br />Given Hyp. ioo, Alt.,25.252=200=3.125.'100=3:125=96.875=Base.
<br />Error in first' example, .602; 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 />rection is negative.
<br />._ PROBABLE -ERROR. If d1, d2, ds, etc. are the discrepancies of various
<br />-results-from-the mean, and if Ed2=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 />='46745
<br />N n.(471) .
<br />SOLAR EPHEMERIS. Attention iscalledto 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• themeridian 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 />41F
<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 />:.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
<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 />' 9:
<br />.1500
<br />19
<br />.3167
<br />29'
<br />.4833
<br />39
<br />.6500
<br />49
<br />.8167
<br />59
<br />'.9833
<br />1:10 -.
<br />..1667
<br />20
<br />:3333
<br />1 30
<br />.5000
<br />40
<br />.6667'
<br />50
<br />.8333
<br />60
<br />1.0000
<br />- -. TABLE V. -Inches in Decimals of a Foot. .
<br />1-16 3-32 Y. 3-16 Y4 546 � % % % ?�
<br />0833 .70668 2;00 I .30333 -4167 I .b000 I, .5833 .6667 I .7900 I .8333 I .9167
<br />
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