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VIII-
<br />TeaLe.II. 77 Radii, Ordinates and,:Deflectione. Chord 3100 ft.
<br />Deg
<br />Rediae
<br />Mid.
<br />Ord.
<br />Tan.
<br />Dist.
<br />Def.
<br />Dist.
<br />De'
<br />Ifot.,
<br />'
<br />Deg:
<br />Radigs
<br />Mid.
<br />Ord.
<br />:Tan.
<br />' Dist.
<br />Def. Def'
<br />.Dist. If r
<br />t.
<br />2° 17'
<br />t.
<br />3° 43'101.15
<br />.
<br />32°
<br />181.39-.
<br />10 59'
<br />t.
<br />t.
<br />-t
<br />t.
<br />0'10'
<br />34377.
<br />.036
<br />.145
<br />;291
<br />0.05
<br />7.'
<br />S10.0
<br />1.52f3
<br />6.105
<br />12.21 2.10
<br />20
<br />17189.
<br />.073
<br />.291
<br />.582
<br />0.10
<br />20'
<br />781.81.600
<br />40 40'
<br />6.395
<br />12,79,2-20
<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 2-2.,
<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 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 2 40;
<br />i
<br />5729.6
<br />.218
<br />.873
<br />.1.745
<br />0,30
<br />20
<br />688.2
<br />1.810
<br />7.266
<br />11,53 2_510
<br />10.
<br />4911.2
<br />.255
<br />7..018
<br />•2.036
<br />0.35
<br />30
<br />674.7
<br />1.855
<br />7.411
<br />14.82 2.55,
<br />20
<br />4297.3
<br />.291
<br />1:164
<br />2.327
<br />0:40
<br />40
<br />661.7
<br />I. 892
<br />7.556
<br />1:7.1.1 2.601
<br />5° 34f
<br />C33L0L':8,-.327.1..309
<br />104.43
<br />60°
<br />loo. o0
<br />3° 35
<br />- 9
<br />637.3
<br />1.965
<br />•7.846
<br />15.69 2.70.
<br />_30_
<br />40
<br />3187.9
<br />.364
<br />1.453
<br />_2.616.•O,A5_
<br />2.909
<br />0:50
<br />20
<br />614.6
<br />2.037
<br />8.136
<br />16-27 2-80
<br />50
<br />'
<br />3123:4
<br />.400
<br />1,600
<br />3.200
<br />0.55
<br />30
<br />603.8.2.074
<br />8.281
<br />16.56 2-85
<br />t
<br />2864.9
<br />.436
<br />1.745'"3.490
<br />0.60
<br />40
<br />593.4
<br />2.110
<br />8:426
<br />16.85 2-90
<br />LO
<br />2644.6
<br />.473.1.89L
<br />3.781
<br />0:65.
<br />10 .'
<br />573.7
<br />2.183
<br />.8.716
<br />17.43 3.00
<br />20
<br />2455.7
<br />r. 509
<br />2.036
<br />4.072
<br />0.70
<br />', 30
<br />5111A
<br />2.202
<br />9.150
<br />18.30 3.15
<br />30
<br />2292.0
<br />.545
<br />2,181
<br />4.363
<br />0.75
<br />31
<br />521-7
<br />2.402
<br />9.585
<br />19.16 3.;10
<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 3.45
<br />50
<br />2022.4
<br />.618
<br />2.472
<br />4.945.0:85
<br />12 L
<br />478.3
<br />2.620
<br />10.45
<br />20.'91 3.60
<br />3
<br />1910.1
<br />.655
<br />2.618
<br />5.235
<br />0.90.
<br />' -30
<br />450:3
<br />2.730
<br />10.80
<br />21.77 3.70
<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 3.90
<br />20
<br />1719:11
<br />.727
<br />2.908
<br />5,817
<br />1.00
<br />30
<br />425.4
<br />2:940
<br />11.75
<br />23.51 9.05
<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 4.20
<br />40
<br />1562.9
<br />.800
<br />3.199
<br />6,398
<br />1.10
<br />30'396.2
<br />3.168
<br />12.62
<br />25.24 4..35
<br />50
<br />1495.0
<br />.836
<br />3.345
<br />6.689
<br />1.15
<br />t5
<br />383,L
<br />3.277
<br />13.05
<br />26.11 4.50
<br />4
<br />1432.7
<br />.873
<br />3.490
<br />6?980
<br />1.20
<br />1 ' 30.370.8
<br />387
<br />13.49
<br />26.97 4.0&
<br />10
<br />1375.4
<br />.909
<br />3.635
<br />71.271
<br />1.25
<br />16
<br />359-3
<br />3.496
<br />3.606
<br />13.92
<br />27,84 4.80
<br />20
<br />1322.5
<br />.945
<br />3.718
<br />7.561
<br />1.30
<br />30.348-5
<br />14.35
<br />28.70 4.95
<br />30
<br />1273.6
<br />.982
<br />3.926
<br />7.852
<br />1.3.5
<br />17
<br />338-3
<br />3.716
<br />14.78
<br />29.:;6 5.1U
<br />40
<br />1228.1
<br />1.018
<br />4.071
<br />18.143
<br />1.40
<br />18
<br />319.6
<br />3.935
<br />16..64
<br />31.29 5.40,
<br />50
<br />1185.8
<br />1.055
<br />4.217.!8.433
<br />1.45
<br />19
<br />302.9.4.155
<br />16.51
<br />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 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 6.30
<br />20
<br />1074.7
<br />1.164
<br />4.653
<br />0.305
<br />1".60
<br />22 ,_
<br />262:0
<br />4-814
<br />19.08
<br />38.16 6.60
<br />30
<br />1042.1
<br />1.200
<br />4.798.
<br />9.5961.65
<br />23
<br />250.8.5-035'19.94
<br />39.87 6.90
<br />40
<br />1011.5
<br />1.237
<br />4.943
<br />9.886
<br />1.70
<br />_
<br />24
<br />240.5
<br />5,255
<br />20:79
<br />41.58 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 />43.23 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 7.SO
<br />10
<br />929.6
<br />1.346
<br />5.379
<br />10.76
<br />1.85
<br />27
<br />214.2
<br />,018
<br />23.35
<br />46.69 5.10
<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 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 />.360
<br />25,04 '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 />23.88
<br />51.76 9.00
<br />Tha middle ordinate }n inches for any cox I of length (C) is equal to .0012 C'
<br />nnultipiied by the middle ordinate taken from the above table. Thus, if it
<br />desired to bends 30 ft. rail to fit 10 degree curve, its middle ordinate should
<br />be .0012X90OX2.183 or 2.36 inches.
<br />TABLE 111. Deflections for Sub Chords For Short Radius Curves.
<br />Degree
<br />of .
<br />Curve .
<br />Radius
<br />5U
<br />sin, 1. def. ang.
<br />34 sub chord =sin of z def. angle
<br />R
<br />f ength
<br />of are
<br />For 100 ft.
<br />12,5 Ft.
<br />15 Ft.
<br />20 Ft.
<br />25 6t.
<br />30°
<br />1 193.18
<br />1° 51'
<br />2° 17'
<br />2° 58`•
<br />3° 43'101.15
<br />.
<br />32°
<br />181.39-.
<br />10 59'
<br />2° 25'
<br />3° 117'
<br />3' 58'
<br />101.33
<br />340
<br />171.01
<br />2° 06'
<br />2'33'
<br />3°z1'
<br />4° 12'
<br />lot, 48
<br />360
<br />161.80
<br />2',13'.
<br />2° 41'
<br />3° 331
<br />4° 26'
<br />1o1.66
<br />38°
<br />153.58.
<br />2° 20'
<br />2° 49'
<br />3° 44'
<br />40 40'
<br />.101..8;
<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 />2' 34'
<br />3' 05'
<br />4° 07'
<br />g° 08
<br />102.29 .
<br />44°
<br />133.47
<br />2° 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 />102.76
<br />48°
<br />122.92
<br />28 55'.
<br />3° 29'
<br />4° 40'
<br />S' 60'
<br />103.00 '
<br />50°
<br />118.31.
<br />3° 02,'
<br />3° 38
<br />4° 51
<br />6' 04' .
<br />103.24
<br />52°
<br />114-o6
<br />3° 09'
<br />3° 46'
<br />,5° 02'
<br />60.17''
<br />103' 14 '
<br />54'
<br />110.11
<br />3° 16'
<br />3° 54'
<br />.
<br />6° 31'
<br />fo3. 84
<br />56°
<br />Io6!50
<br />3° 22'
<br />4° 02'
<br />.5'13'
<br />S° 23
<br />6° 44'
<br />104.14
<br />58'
<br />1D3�14
<br />3' 29'
<br />4' 10
<br />5° 34f
<br />60 57.
<br />104.43
<br />60°
<br />loo. o0
<br />3° 35
<br />4° 14
<br />5° 44`
<br />I 7° 11'
<br />1D+•- 72
<br />4- CURVE' FORMULAS
<br />I = R tan, I .R = T cot. '.' I. r.hord2
<br />T 5o tan >; I Chord' def. = It
<br />Sin. D R 50... .
<br />Sin. z D 11 Sin. ; D No. chards
<br />1 £ =Rex. sec ; [ ' D W71
<br />Sin. 2 D S0 t1I E= T tan } i Tan. def. - 1 chord de
<br />The square of any distance, divided: by twice the radius, wi11 equal
<br />the distance, from tangent to curve, very nearly.
<br />Tor find angle' for a'given distance and deflection.
<br />Rule I. Multiply -the giveii distance,by .0,1745 {def. for 1° for.l ft.
<br />see Table,] 1.), 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 and distance. Multiply the angle
<br />by .01745i and the product by the distance.
<br />. 90-rJt-aa
<br />GENERAL DATA
<br />RIGHT ANGLE TK1.a. GLEs. Square:the altitude,, divide by'twice the c
<br />base. Add quotient to base for.hypotenuse: :-
<br />Given Base loo, Alt. 10.10'=200 =.5. I0O+-5=100.15 hyp:
<br />Given Hyp. loo, Alt. 25.252_200=3. 125. 100-3.125=96.875=Base.
<br />Error in first example, .002,; in last, .045.
<br />To find Tons of Rail in one mile of ,track:'multiply- «,eight' per yard
<br />by 1 i, and divide by 7.
<br />LEVELING. The- correction fdr curvature and refraction, in feet
<br />and decimals of feet is equal to 0.574d2,.wherc d is the.distaniv in miles..
<br />The correction for curvature -alone is,closely, ;d?: The combined cor-
<br />rection is negative.
<br />PROBABLE ERROR. If d1, d2, da, etc. are the discrepancies of various
<br />results front the mean, and if 2;d2=the sum of the squares`ofithcse differ-
<br />ences and n=the number of observations, then the.prot�able error'of the
<br />mean= , EdI
<br />10.6745 n{n-l) i 3 Ls',
<br />C, S1 -
<br />I b, 47
<br />SOLAR. EPHEUI.,RIs. Attention 1 ¢callc`d to the Solar Ephemeris for
<br />the current year, published by Ke ffel & 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 constant's, etc. ,
<br />T. nr v TV -L- ATimltes in Dv6mals of a Degree.
<br />11
<br />11 f
<br />21'
<br />.3500
<br />MY
<br />.5167
<br />411
<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 />3
<br />.0333
<br />13
<br />.2000
<br />23
<br />.3833
<br />33
<br />5500
<br />43
<br />.7167
<br />53
<br />.8833
<br />4
<br />.0500
<br />14
<br />.2167
<br />24
<br />.4000
<br />34
<br />.5667
<br />44
<br />.7333
<br />54
<br />.(1000
<br />5
<br />.0667
<br />15
<br />.2333
<br />25
<br />.4167
<br />35.
<br />.5833
<br />45
<br />.7500
<br />55
<br />A167
<br />6
<br />-0833
<br />16
<br />.2500
<br />_2667
<br />26'
<br />.4333
<br />36
<br />.6000
<br />46
<br />.7667
<br />56
<br />51333
<br />7
<br />-1000
<br />17
<br />27
<br />.4500
<br />37
<br />.6167
<br />47
<br />.7833
<br />57-
<br />1.1-500
<br />8
<br />.1167
<br />'.1333
<br />LS
<br />.2833
<br />28
<br />.4667
<br />38
<br />.6333
<br />48
<br />.8000
<br />58
<br />.9667
<br />9
<br />'.1500
<br />l9
<br />.3000
<br />.3167
<br />29
<br />.4833
<br />39
<br />.6500-
<br />49
<br />.8167
<br />59
<br />.9833
<br />Ip
<br />.1667
<br />20
<br />.3333
<br />30
<br />.5000
<br />40
<br />'.6667
<br />1 50
<br />.833.1
<br />60
<br />1.00011
<br />-1-AFILE,v.1-inches in 1.1cc1mais 01 a rook.
<br />1-16 3-32 yA 3 -Irl �,a 5-16 3a ;; Sa ?< '`
<br />.x1052 .0078 .0101 0f 56 .0208 I .0260 .0313 .0417 .0:;21 .0622 .0729
<br />1 ° 3 4 6 7 8 3 10 11
<br />-_0833 .I6ti7 .2500 .3333 .4167 .SUull -:>83:1 X-667 .751111 .8333 .9167.
<br />
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