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VIII
<br />TABLE IL - Radii, Ordinates and Deflection. Chord =100 ft.
<br />Dom''RadianOrd.
<br />Radius
<br />50
<br />11id.
<br />Tea
<br />Dist.
<br />Def.
<br />Dist.
<br />De'
<br />1fotr
<br />Deg.
<br />Radius
<br />Med.
<br />Did.
<br />Tau
<br />Dist.
<br />Def,
<br />Dist.
<br />Def.
<br />if r
<br />0'10'
<br />t.
<br />34377.
<br />'.036
<br />-
<br />.145
<br />.291
<br />0.05
<br />71
<br />t.
<br />819.0
<br />1.52$
<br />t.
<br />6:105
<br />t.,
<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 />109
<br />.436
<br />' .873
<br />0 1;
<br />30
<br />764.5
<br />1. .637
<br />6.540
<br />13 08
<br />2.2;
<br />40-
<br />-Sri91.4
<br />.145
<br />.582
<br />;1'.164
<br />0.20
<br />40.
<br />747.9
<br />1.673
<br />6.685
<br />t3 37
<br />2.30
<br />50
<br />6879.5
<br />..182
<br />-.727
<br />1.454
<br />0 23;
<br />8
<br />716.8
<br />1:746
<br />6.976'13:9
<br />5' 36'
<br />2.60
<br />1
<br />;720.6
<br />•.218
<br />.873
<br />1.745
<br />0.30
<br />20
<br />688.2
<br />1.819
<br />7.260
<br />14.53
<br />2.5.0
<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 />-4297.5
<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 />,301
<br />3810.8
<br />-.327
<br />1.309
<br />2.618
<br />0.45 -.
<br />9
<br />637.3,1.965
<br />3°35'
<br />7.840
<br />15.69
<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 />2.037
<br />8.136
<br />16.27
<br />2-80
<br />50-
<br />3125.4
<br />- .400
<br />t.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 />2364.9
<br />.4313
<br />1.745
<br />13.400
<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 />19
<br />573.7
<br />2.183
<br />8.716
<br />17.43
<br />3:00
<br />20
<br />2155.7
<br />.509
<br />2.036
<br />-4:072
<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 />0.75
<br />11
<br />521.7
<br />2.402
<br />9.585
<br />19.16
<br />3.30
<br />40
<br />2148.5
<br />,'.582
<br />2,327
<br />_4.363
<br />4.651
<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 />478.3'2.620
<br />10.45
<br />20.91
<br />3 -GO
<br />S. °
<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 />0.05
<br />13
<br />441.7
<br />2.889
<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.,940
<br />11:75
<br />23.51
<br />4.Qa
<br />30
<br />1637.3
<br />.704
<br />3.054
<br />6'..108
<br />I.o5 '
<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 />396.2'3.168
<br />12.02
<br />25.24
<br />4.35
<br />50
<br />1495..0
<br />.836
<br />3.345
<br />G.680
<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 />/G.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 />17.271
<br />1.25
<br />16
<br />359.3
<br />3.496
<br />13.92
<br />27.84
<br />4.80
<br />20_
<br />'1322.5,'..945
<br />3.718
<br />7.5611
<br />1:30
<br />30
<br />348.'5
<br />3.606
<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
<br />29.56
<br />5.10
<br />,40
<br />1228'.1'
<br />1.018
<br />4.071
<br />8._1431.40
<br />-
<br />319.6
<br />3-935
<br />15.64
<br />31.295.40
<br />50
<br />11S5.8'1.055
<br />4.217
<br />'8.433
<br />1.45
<br />.18
<br />10
<br />302.9
<br />,155
<br />16:51
<br />33.01
<br />5,70
<br />5
<br />1146.3
<br />1.091
<br />4.362
<br />8.724
<br />1.50
<br />211
<br />287.9'4.374
<br />17.37
<br />34.73
<br />6.00
<br />10
<br />.1109.3
<br />1.127
<br />4.607
<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 />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 />0.590
<br />1.65 „
<br />23
<br />250.8'5:035.19.94
<br />30.87
<br />6.90
<br />.40
<br />1011.5
<br />1,237
<br />4.943
<br />9.880
<br />1.70
<br />24
<br />240.5
<br />5.255
<br />20-79
<br />41.58
<br />7.20
<br />50
<br />082.6
<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 />tl
<br />955.4
<br />1.300
<br />5.234
<br />10.47
<br />1.80
<br />26
<br />222.3
<br />5.697
<br />22.50
<br />44.99
<br />7.80
<br />t0
<br />929.6
<br />1.346
<br />5.379
<br />10.70
<br />1.85
<br />27
<br />214.2
<br />5.918
<br />23.35
<br />46.69
<br />8.10
<br />20
<br />905.1.1.382
<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 />5.669
<br />11-34
<br />1.95
<br />29
<br />199.7
<br />6.300
<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.!8
<br />51.76
<br />9.00
<br />The middle ordinaW 'n incites for any cord of length (C) is equal to .0012 C'
<br />J multiplied by the nlidd�o ordinate taken from the above table. Thus, if it
<br />l desired to bend a 30 ft. rail to fits, ]0 degree curve, its middle ordinate should
<br />be ,0012X000X2.183 or 2.36 inches.
<br />TABLE III. 'Deflections for Sub Chords for short Radius Curve&
<br />Degree'
<br />of
<br />Curve
<br />Radius
<br />50
<br />V2 sub chord
<br />R =sin of }def. angle '
<br />Len th
<br />of arc
<br />_for 100 ft.
<br />sin. ¢ def. ang.
<br />12.5 Ft,
<br />15 Ft.
<br />20 Ft.
<br />25 Ft.
<br />300
<br />193.18
<br />1° j1'
<br />2° 17'
<br />2° 58'
<br />30 43'
<br />101.15
<br />32°
<br />181.39
<br />10 59'
<br />20 25'
<br />3° 10'
<br />3°.58'
<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 />2° 13
<br />2° 41`
<br />3° 3'3'
<br />4° 26'.
<br />101.66
<br />38°
<br />153.58
<br />2° 20'
<br />2° 49'
<br />3° 44`
<br />4° 40'
<br />101.85
<br />40° _
<br />146. 19
<br />2° 27'
<br />2° 57'
<br />30 55`
<br />4° 54,
<br />-ib2.o6
<br />42°139..52
<br />25
<br />2° 34'
<br />3° 05'
<br />. 4° 07'
<br />9'.08
<br />102.29
<br />44° i
<br />133:47
<br />2° 41'
<br />3° 13'
<br />4° 18'
<br />5''22'
<br />102.53
<br />460
<br />127.97
<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° 40'
<br />51 5o'
<br />103.©0
<br />50°
<br />118.31
<br />30 02'3°
<br />38'
<br />4° 51'
<br />6' 04'
<br />103.24
<br />520
<br />1i4.06
<br />3° 09'
<br />3° 46'
<br />3° 02'
<br />6° 17'
<br />103.54
<br />54°110.11
<br />58
<br />3° 16'
<br />3° 54'
<br />-5° 13' .
<br />6-31,
<br />103 , 84
<br />56°
<br />106.50
<br />3° 22'
<br />4° 02'
<br />S° 23'
<br />6° 44'
<br />104.14
<br />58'
<br />t0,3. 14
<br />3° 29'
<br />4' to'
<br />50 34'
<br />6°.57',
<br />104-43
<br />6o°
<br />100.00
<br />3°35'
<br />4°18'
<br />5°44
<br />7°I1'
<br />104.72
<br />]!]C
<br />CURVE FORMULAS
<br />I`. T 5tan 2I R - T cot. s I Chord def. Chord'
<br />S _
<br />J- R T 50
<br />a Sin. 1,D 0 Sin. I D No. chards = I
<br />2.E= R ex. sec 4 1 D
<br />1 a'D 5o tan .z
<br />Sin. I 1 Tan. clef. = a chord def.
<br />= 1. E _ '1' tan 1
<br />The square of any distance, divided by twice the radius, will equal
<br />the distance from of,
<br />to curve, very nearly.
<br />To find angle for a given distance and deflection.
<br />Rule 1.. Multiply the given distance by .01745 -(def. for I° for I ft.
<br />see Table If.),.and divide given deflection by the product.
<br />Rule 2. Multiply given deflection by j7.3, and divide the product by
<br />tlic given distance.
<br />To'find deflection for a given angle and distance. Multiply the angle
<br />by .oi745, 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 too, Alt. 10.][02 -200=.5. 100-.5=100.5 hy'p.
<br />Given fly -p. too, Alt. 25.252=200=3.125. 100 -3.125=96.875= -Base.
<br />Error in first example, .002; in last, .645.
<br />To. find Tons of Rail in one mile of track: multiply weight per yard
<br />by 1 I, and divide by 7.
<br />LEvBl,1NG. " 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 alnne is closely,, ad'. The combined cor-
<br />rection is negative.
<br />' PROVABLE ERROR.. Ifdl, d2, d3,' etc. are.the discrepancies of various
<br />results -from the mean, and if Ed'=the.sum of the squares of these differ-
<br />ences and nTthe.number of observations, then the probable error of the
<br />mean= Edz.
<br />-0.6745: it(n-I)
<br />5501.4E EPHEMERIs. 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, 3''x6 in., has about 160 pages of data very
<br />useful fo 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 />11
<br />.0167
<br />11'
<br />.1833
<br />21'
<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 />.7t67
<br />53
<br />.8833
<br />4
<br />.0667
<br />14
<br />.2333
<br />24
<br />.4000
<br />34
<br />.5GG7
<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 />.7.500
<br />55
<br />.9167
<br />6
<br />'.1000
<br />16.2667
<br />26
<br />.4333
<br />36
<br />.6000
<br />46
<br />.7667
<br />56
<br />.0333
<br />7
<br />.1167
<br />17
<br />2833
<br />27
<br />.4500
<br />37
<br />.6167
<br />47
<br />.7833
<br />57
<br />.9.500
<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 />10
<br />:1667
<br />20
<br />:3333
<br />30
<br />5000
<br />40
<br />.6667
<br />50
<br />.8333
<br />60
<br />1.0000
<br />TABLE V.
<br />-Inches in Decimals of a Foot.
<br />1-16
<br />3-323-16
<br />%
<br />5-16
<br />y
<br />?e
<br />is
<br />.0052
<br />-0078
<br />.0104
<br />.01,56
<br />.0208
<br />.0260
<br />.0313
<br />.0417
<br />.0521
<br />.0625
<br />0729
<br />I
<br />�
<br />I �
<br />�
<br />I
<br />_ -0833
<br />.1667
<br />.2500
<br />1833
<br />.41'67
<br />.5000
<br />.5833
<br />.6667
<br />.7500
<br />.8333
<br />4167
<br />
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