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VIII
<br />TABLE IL - Radii,- Ordinates and Deflections. China =160 ft.
<br />Deg.
<br />'Radius
<br />Mid.
<br />Ord.
<br />Tan.
<br />Diet.
<br />Def.
<br />Dist.
<br />Der.
<br />for
<br />1 Ft.
<br />Deg.
<br />Itndiue
<br />Mid
<br />Tan.
<br />Dfat,
<br />Def. Def'
<br />Diet. for
<br />1 Ft.
<br />300
<br />L
<br />EL
<br />2° 17'
<br />it.
<br />3° 43' -
<br />101,15
<br />320.
<br />ft.
<br />rt.
<br />ft..
<br />9110'
<br />311377.
<br />,036
<br />.145
<br />.291
<br />0,05
<br />7"
<br />819.0
<br />1.528
<br />;6.105
<br />12.21 2..10
<br />'20
<br />17780.
<br />,073
<br />.291
<br />.582
<br />0,10
<br />20'
<br />781.8
<br />1.600
<br />6.395
<br />12.79 2.20
<br />30
<br />11 59.
<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 />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 />0,20
<br />8
<br />716,8
<br />1,746
<br />6.-976
<br />13,05.2:40
<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 2.LU
<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 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 />7.556:15:11
<br />2.60
<br />30
<br />3319.8
<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 2.70
<br />40
<br />3137.9
<br />.364
<br />1.454
<br />2:909
<br />0.50
<br />20
<br />614.6
<br />2.037
<br />8,136
<br />10.27 2.80
<br />50
<br />3123,4
<br />,400
<br />1.600
<br />3:200.0.55
<br />30
<br />603.8
<br />2.074
<br />8.281
<br />16, 50.2,85
<br />2
<br />2864.9
<br />.43G
<br />1.745
<br />3.490
<br />0:60
<br />40
<br />593.4
<br />2.110'
<br />18,426
<br />16.85 2.00
<br />10
<br />264.4.6
<br />.473
<br />1.891
<br />3.781
<br />6.63
<br />10
<br />573.7
<br />2.183
<br />8.716
<br />17.43 3.00
<br />20,
<br />'2155.7
<br />.509
<br />2.036
<br />4.072
<br />0.70
<br />30
<br />516.4
<br />2.292
<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 />11
<br />521.7
<br />2,402
<br />9.585
<br />19A 0 3.50
<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
<br />6.85:
<br />12
<br />478.3
<br />2.620
<br />10:45
<br />20.31 3.60
<br />3
<br />1910.1
<br />.655
<br />2.618
<br />5.235
<br />0:90,
<br />30.459.3
<br />2.730
<br />10.89
<br />21.77 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 />22.61 3,90
<br />20.
<br />1719,E
<br />.727
<br />2.908
<br />5.817.1.00
<br />30
<br />425.4
<br />2.949
<br />11.75
<br />23.51 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 4.20
<br />40
<br />1562.0
<br />.800
<br />3.199
<br />6,398
<br />1.10
<br />30
<br />395.2
<br />3.168
<br />12.Q
<br />25-.24 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 '26.11
<br />4.50
<br />4
<br />1432.7
<br />.873
<br />3.490
<br />6.950
<br />1.20
<br />30
<br />370.8
<br />3.387
<br />13.49
<br />26.97 4.65
<br />10
<br />1375.4
<br />,909
<br />3.635
<br />7.271
<br />1.25
<br />18
<br />359.3
<br />3.496
<br />E3.92
<br />27:84 4, MY
<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.
<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
<br />29.56 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 />16.64
<br />31.29 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 />33.0L 5.70
<br />8
<br />1146.3
<br />1.091
<br />4,362
<br />8.724
<br />L.50
<br />20
<br />287.9
<br />-1.374
<br />17.37
<br />34.73 6.00
<br />10
<br />1709,3
<br />1.127
<br />4.507
<br />9.014
<br />L.55
<br />21
<br />27.1.4
<br />4.594
<br />18.22
<br />36.44 0.30
<br />20,
<br />1074.7
<br />1.164
<br />4.653
<br />9.305'1'60
<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 />4.708
<br />9-:59G
<br />1.65
<br />23.
<br />250.8
<br />5.035
<br />19194 ,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 7.20
<br />50
<br />,;982.6
<br />1.273
<br />5.088
<br />10:18
<br />1, 7.5
<br />26
<br />231.0
<br />5.476
<br />21.64
<br />43.28 7.00
<br />95 411.309
<br />5.234
<br />10.47
<br />1.80
<br />26
<br />222.3
<br />x:697
<br />22.50
<br />41.99 7:80
<br />10
<br />929.6
<br />1.346
<br />5.379
<br />10,70
<br />-1.85
<br />27
<br />214.2
<br />4.918
<br />23.33
<br />46.69 8.10
<br />20
<br />905.111-3S2
<br />5.524
<br />11.05
<br />1.90
<br />28
<br />206.7
<br />6.139
<br />24.19
<br />48.38 8.40
<br />3o
<br />'881.911,419
<br />5.660
<br />11.34
<br />1.05
<br />29
<br />199.7
<br />6,360
<br />25,04
<br />50.07 8.70
<br />40
<br />'859.911.465
<br />5.814
<br />11.63
<br />2.00
<br />30
<br />193.2
<br />6,583
<br />25.88
<br />51.76 9.00
<br />The middle ordinate in inches for any cord of length ((7) is equal to0012 C7'
<br />multiplied by the middle ordinate taken from the above table, Thus, if it
<br />,16dred to bend &.30 ft. rail to fit a 10 degreo 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 />Degree
<br />g
<br />of
<br />, Radius
<br />50
<br />}� sub chord
<br />=sinoF }def. angle
<br />11
<br />Length
<br />of arc
<br />Carve
<br />sin. Is def. ang.
<br />17,5 'Ft.
<br />15 Ft,
<br />20 Ft.
<br />25 A.
<br />for 100 it.
<br />300
<br />193.19-
<br />1° 51'
<br />2° 17'
<br />2° 58' '
<br />3° 43' -
<br />101,15
<br />320.
<br />.181.39
<br />1° 59'
<br />2° 25'
<br />3° lo'
<br />3° 58'
<br />101'33
<br />34°
<br />171,01
<br />2° 06'
<br />2° 33'
<br />3° 21'
<br />4° 12'
<br />101,48 -
<br />360
<br />161:8o
<br />2° 13'
<br />2° 41'
<br />3° 3.3'
<br />4° 26'
<br />101.66
<br />38°
<br />153 58
<br />20 20'
<br />2° 49
<br />3° 44'
<br />4° 40'
<br />1o1.85.
<br />40°
<br />146.19
<br />2° 27'
<br />20 57'
<br />3° 55'
<br />4° 54'
<br />102.o6
<br />42°
<br />139.52;
<br />2' 34'
<br />3°05'
<br />4°07'.
<br />5°08
<br />192.29
<br />44'
<br />X133 47
<br />2° 41'•
<br />3° 13'
<br />4° 18'..
<br />5° 22'
<br />102.53
<br />46°
<br />1127.97'
<br />2° 48'
<br />3° 21'
<br />4° 29'
<br />5° 36'
<br />102-76-
<br />48
<br />122:92
<br />.2° 55
<br />3°29'
<br />4° 4a'
<br />5° 50'
<br />I03,00 .
<br />50°
<br />118.31
<br />3° 02
<br />3° 38'
<br />4° 51'
<br />6° 04'
<br />103-24:
<br />52°
<br />114.06
<br />3° 09'
<br />.i° 46'
<br />5° oz'
<br />6° 17'
<br />103,.54
<br />54°
<br />:l lo. i1
<br />3° 16'
<br />3° 54'
<br />70 13'
<br />6°.31'
<br />:03.34
<br />56° _
<br />1o6. 50
<br />3° 22
<br />4° 02'
<br />S° 23'
<br />6° 44'
<br />104. 14'
<br />58°
<br />103.14
<br />3° 29'
<br />4° Io'
<br />5,34 '
<br />6° 57'
<br />104.43
<br />60°
<br />100.00.
<br />3° 35'
<br />4° 18'
<br />5° 44�.
<br />7° 1i'
<br />104.72
<br />Ix
<br />CURVE FbkMULAS
<br />'T.= K tan 2 I R= 1 cot. i I chord'
<br />*'i ^ 5o tan 2 1 Chord def. = It
<br />Sin. 50
<br />Sin, m D-= 50 Sin. 21 17 No. chords = I
<br />12 E = R ex: sec''-,-, I D
<br />Sin, a I7 = 50' '.an 2 I L' = T tan I Tan. def. _ '7 chord def,
<br />Z'
<br />The square of any (Iistanee, divided by twice the radius, will equal
<br />the,distance from tangent to curve, very.nearly-
<br />To find ankle'for a given distance and deflection.
<br />Mule I. Multiply the given distance by .01745 (clef. for 1a for I ft.
<br />see.Table 1I.), and divide given deflection by the product.
<br />Rule 2. Multiply given deflection by 57:3; and divide the product by
<br />tile'given distance.
<br />To.find deflection fora. given angle 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.io'=2oo=,5. i0o-I--5 100.5 hop.
<br />Given Hyp, 100, Alt..too= Base.
<br />Error in first 'example, .002; in last, -.045.
<br />To find Tons of Rail in one mile of track: multiply ]vuight, per yard
<br />liy i E, and divide by 7.
<br />LEVEL146. The correction% for curvature and refraction, in ,feet
<br />and decimals of feet is equal to 0.574d2, where d is the distance in milt -s.
<br />The correction for curvature alo6e is closely,' d2. The combined cor-
<br />rection is negative.
<br />PROBABLE Es8O11. If dl, d,, da, etc. are the discrepancies of various
<br />results from the mean, arid_ if _-da=the sum of the squares of these differ-
<br />erices and n=the number of observations, then the probable error of the
<br />mean= vd2
<br />t0.G745 n(n-1).
<br />SOLAR EPHEa1E:111s. Attention is called to the Solar Ephemeris for
<br />the current year, published by Keufiel & Esser Co., and furnished upon
<br />.request. This handy booklet, 328x6 in., has about 190 pages of data very
<br />useful to the Surveyor; such as the adjustments of transits, lci-els and solar
<br />attachments; directions and tables for determining the meridian and the
<br />Iatitude from observations on the sun arid Polaris; stadia measurements;
<br />magnetic declination; arithmetic constants, etc.
<br />TABLE IV. -Minutes in Decimals of a Degree.
<br />1/
<br />TAp1,E; V, --Inches in Decimals of a 1•oot., -
<br />11'
<br />:1833
<br />21'
<br />.3500
<br />IV
<br />.5167
<br />41'
<br />.6833
<br />511
<br />.8500
<br />12
<br />.0167
<br />12
<br />.2000
<br />22
<br />.3667
<br />'32
<br />.5333'
<br />42
<br />.7000
<br />52
<br />.8667
<br />3
<br />.0333
<br />13
<br />:2167
<br />23
<br />.3833
<br />33
<br />.5500
<br />43
<br />.7167
<br />53
<br />.8833
<br />4
<br />.0500
<br />14
<br />.2333
<br />24
<br />.4000
<br />34
<br />.5667
<br />44
<br />.7333
<br />54
<br />.9000
<br />5
<br />.0667-
<br />15
<br />.2500
<br />25
<br />.4167
<br />.35
<br />.5833
<br />45
<br />.7500
<br />55
<br />.0167
<br />6
<br />.0833
<br />I6
<br />.2667
<br />26
<br />.4333
<br />36,
<br />.6000
<br />46
<br />.7667
<br />56
<br />0333
<br />7
<br />.1000
<br />17
<br />.2333
<br />27
<br />.4500
<br />37
<br />.6167
<br />47
<br />.7833
<br />57
<br />0.100
<br />8,
<br />.1167
<br />.1333
<br />18
<br />.3000
<br />28
<br />-.4607
<br />38
<br />.6333
<br />48
<br />.€000
<br />58
<br />.9667
<br />9
<br />19
<br />.3167
<br />29
<br />.4833
<br />39
<br />.6500
<br />49
<br />.9167
<br />59
<br />.9833
<br />.10
<br />.1500
<br />.1687 11
<br />20
<br />1 .3337 11
<br />30
<br />1 .5000 11
<br />40
<br />.6667
<br />1 50
<br />1 -8333
<br />H 60
<br />1.0000
<br />TAp1,E; V, --Inches in Decimals of a 1•oot., -
<br />1-16 3-32
<br />r1052 .9.078
<br />yg
<br />.0104
<br />3-18
<br />.0156
<br />!a
<br />.0208
<br />;-I6
<br />.0260
<br />';•5
<br />.0313
<br />is
<br />.0-117
<br />Ss x's
<br />.0.521 1 .062:;
<br />n729
<br />1 2
<br />OE333 .1667
<br />3
<br />.2500
<br />4
<br />.3333
<br />:>
<br />.4167
<br />6
<br />.500(
<br />7
<br />533:1
<br />-3
<br />.6,667
<br />9 I 10
<br />.7500 I .8333
<br />11
<br />91t•,7'
<br />
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