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<br />VIII
<br />TA131M II. - Radii, Ordinates and. Deflections. Chord =100 ft.
<br />Deg. -
<br />Radius
<br />Slid.
<br />Ord.
<br />Tan.
<br />Dist.
<br />Def,
<br />Dist.
<br />Def.
<br />' lfor
<br />Deg. '.
<br />Radius
<br />h1id.
<br />Ord.
<br />Tan.
<br />Dist.
<br />Def.
<br />Det.
<br />Def.
<br />- Ft.
<br />3° 10'
<br />ft.
<br />ft.
<br />ft.
<br />ft.
<br />2 06
<br />33.
<br />ft, -
<br />ft.
<br />it.
<br />[t
<br />16i.So
<br />0'10'
<br />34377.
<br />.036
<br />.145.291
<br />lot. 66
<br />0.05
<br />- 7°
<br />819.0
<br />1.525
<br />6.105
<br />12.21
<br />2.10
<br />20
<br />17189.
<br />.073
<br />.291
<br />.552
<br />0.10
<br />20'
<br />751.5
<br />1.'000
<br />6.395
<br />12.79
<br />2.20
<br />1. 30^
<br />11459:-
<br />.109
<br />.436
<br />S73
<br />0.15
<br />30
<br />764.5
<br />1.637
<br />6.540
<br />13.03
<br />2.25
<br />40
<br />8594.4
<br />1145
<br />.5S2
<br />1.164
<br />0.20
<br />40.
<br />747.9
<br />1.673
<br />6.635
<br />13.37
<br />2.30
<br />50
<br />•6875.5
<br />.152
<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 />.S73
<br />1.745
<br />0.30
<br />20
<br />GS3.2
<br />1.519
<br />7.206
<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. S2
<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 />1:1.11
<br />2.60
<br />30
<br />. 3519.5
<br />.327
<br />1.309
<br />2.615
<br />0.45
<br />9
<br />G37.3
<br />1.965
<br />7.S46
<br />15. 69
<br />2.70
<br />40
<br />3437.9
<br />.304
<br />1.454
<br />2.009
<br />0. 0
<br />20
<br />614.6
<br />2:037
<br />5.136
<br />1G.2-
<br />2.50
<br />50
<br />3125:4
<br />.400
<br />1.600
<br />3.200
<br />0.55
<br />30
<br />G03.8
<br />2.074
<br />S.2S1
<br />16.56
<br />2.55
<br />2
<br />2864.9
<br />.43G
<br />1.745
<br />3.490
<br />0.60
<br />40
<br />593.4
<br />2.113
<br />8.426
<br />16.8:;
<br />2.90
<br />10
<br />2634.6
<br />.473
<br />1.591
<br />3.781
<br />0.65
<br />10
<br />573.7.
<br />2.1S3
<br />5.716
<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 />2.2D3
<br />9.1;0
<br />1S. 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 />2145.8
<br />.552
<br />2.327
<br />4.654
<br />O.SO
<br />30
<br />:-99.1
<br />2.511
<br />10.02
<br />20.04
<br />3.45
<br />50
<br />2022.4
<br />.613
<br />3.472
<br />'4.945
<br />0.85
<br />12
<br />47 S.3
<br />2. G20
<br />10.45
<br />20.91
<br />3.60
<br />3
<br />1910.1
<br />.655
<br />2. KS'
<br />5.235
<br />0.00
<br />30
<br />459.3
<br />2.730
<br />10.S9
<br />31.7;
<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.S39
<br />11.33
<br />22.6-4
<br />3.90
<br />20
<br />1719.1
<br />.727
<br />2.903
<br />5.817
<br />1.00
<br />30
<br />425.4
<br />2.949
<br />11.75
<br />2;.51
<br />4.05
<br />30
<br />1637.3
<br />.764
<br />3.0"
<br />6.108
<br />1.05
<br />11
<br />410.3
<br />3.053
<br />1;3.18
<br />9_t.37
<br />4.20
<br />40
<br />1562.9
<br />.500
<br />3.199
<br />6.398
<br />1.10
<br />30
<br />30.2.3.16S
<br />13.62
<br />25.24
<br />4.&i
<br />50
<br />1495.0
<br />.SMG
<br />'3.345
<br />6.659
<br />1.15
<br />15
<br />383.1
<br />3.277.1:3.05
<br />26.11
<br />4.50'
<br />4
<br />1432.7
<br />.873
<br />3.400
<br />6.950
<br />1.20
<br />30
<br />370.8
<br />3.337
<br />13.49
<br />20.07
<br />4.65
<br />10
<br />1375.4
<br />.900
<br />:3.6:i3
<br />7.271
<br />1.25
<br />16
<br />359.3
<br />3.4106
<br />13.02
<br />27.5.1
<br />3.80
<br />20
<br />1322.5
<br />.045
<br />:3.713
<br />7.:561
<br />1.30
<br />30
<br />343.5
<br />3.G06,
<br />14.35
<br />28.70
<br />4.95
<br />'30
<br />1273.6
<br />.982
<br />3.926
<br />7.552
<br />1.35
<br />17
<br />335.3
<br />3.716
<br />14.73
<br />29.53
<br />5.10
<br />40
<br />1225.1
<br />1.01S
<br />4.071
<br />5.143
<br />1.40
<br />1.8
<br />319.6
<br />3.935
<br />15.64
<br />3!.21)
<br />5.30
<br />50
<br />11S5.S
<br />1.055'4.217
<br />8.333
<br />1.45
<br />19
<br />302.E
<br />4.3.55
<br />16.51
<br />'3.01
<br />5.70
<br />5
<br />1146.3
<br />1.091
<br />4.302
<br />8:724
<br />1.50
<br />20
<br />2S7.9
<br />4.374
<br />17.37
<br />34.73
<br />6.00
<br />10
<br />1109:3
<br />1.127
<br />4.507
<br />9.01»
<br />1.55
<br />21
<br />274.4
<br />4.50.4
<br />1S.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 />4.514
<br />19.05.
<br />34.16
<br />0.60
<br />80
<br />1042.1
<br />1.200
<br />4.795
<br />,9.593
<br />1.65
<br />23
<br />'250.5
<br />5.035
<br />10.0-1
<br />39. S7
<br />0.90
<br />'40
<br />1011.5
<br />1.237
<br />4.9.43
<br />0:550
<br />1.70
<br />24
<br />240 5
<br />5.255
<br />20.79
<br />41.53
<br />7.30
<br />'50
<br />932.6
<br />1.273
<br />5.OSS
<br />WAS
<br />1.75
<br />25
<br />231.0
<br />5.476
<br />21.64
<br />43.2,-,
<br />7.50
<br />0
<br />955.4
<br />1.300
<br />5.234
<br />10.47
<br />1.S0
<br />26
<br />^22.315.07122.50
<br />44.99
<br />7.50
<br />1.0
<br />.929.6
<br />1.34E
<br />5.379
<br />10.70
<br />1.85
<br />27
<br />214.2
<br />5.918^3.33
<br />•10.C9
<br />3.10
<br />20
<br />9011.1
<br />1:3,S215
<br />.52.4
<br />11.05
<br />1.90
<br />28
<br />206.7
<br />G.1:i9
<br />14.19
<br />!s. 0
<br />3.,0
<br />30
<br />SSL 9
<br />1.415
<br />GCO
<br />11.3.1
<br />1.95
<br />^9
<br />109.7
<br />(1.360
<br />25.04
<br />50.01
<br />5.70
<br />40
<br />859.0
<br />1.455
<br />5.314
<br />11.63
<br />2.00
<br />1 30
<br />103.2
<br />fi.5S3
<br />25.85
<br />51, .70
<br />9.60
<br />jr•� The middle.ordinau3 in inches for any cord of length (0) is e+l1nal to .00 -2G -
<br />OO.Li;'multipliedbythe middle orclirato- taken from the above table. Tl:tts,;f It
<br />multiplied by the
<br />desired to bend a 20 ft. rail to fit it 10 deerec curve, ks middle ordinate sLould
<br />ly ! k bo .00124,9005<2.183 or 2.3G inches.
<br />" ! f TABLE III. Deflections for Sub Chords for Short Radius Curves.
<br />Degree Radius ?�subchord Lenge'.+
<br />= em c f X def. angle
<br />of 50 n of arc
<br />Curve sin. def. - forlGOft.
<br />( o 1 i 12.5 ht. 15 rt. 1.9 Ft. I 25 Ft.
<br />30°
<br />193. IS
<br />I° 51'
<br />^' 17
<br />2' 58
<br />3' 43'
<br />IOI.I"
<br />!' ;!Ill'. - 32°
<br />131.39
<br />1' 5e1'
<br />° 25,
<br />3° 10'
<br />3° 58'
<br />101.33
<br />34.
<br />171.01
<br />2 06
<br />33.
<br />3 2I
<br />I2
<br />1eI.4S
<br />36°
<br />16i.So
<br />2° 13
<br />2.° 41
<br />3° 33'
<br />1. 26'
<br />lot. 66
<br />a 111• 310°
<br />"
<br />133.510
<br />2° 20'
<br />2° 49'
<br />3° 4T'
<br />4° 0'
<br />IOI.85
<br />I; !' 40°
<br />146.19
<br />2° 27'
<br />2° 57'
<br />3° 55'
<br />4° 54
<br />102. oG
<br />42'
<br />139.52
<br />2° 34'
<br />3' O5'
<br />4' 07'
<br />S' 08,IO2.29
<br />°
<br />44
<br />133.47
<br />°
<br />2 41
<br />°
<br />3 13
<br />°
<br />4 110
<br />° 22'
<br />Io2.53
<br />460
<br />11,
<br />127.97
<br />20 48
<br />3' 21�.
<br />40 29'
<br />�0 36/
<br />Ion, 76
<br />48
<br />122.92
<br />2 55
<br />3 29
<br />4 40'
<br />S 50
<br />103.00
<br />1 50°
<br />]IS -3I
<br />3' 02'
<br />. 3° 38, .
<br />4° 51'
<br />6° 04'
<br />1o3.24
<br />I;! 52°
<br />114.06
<br />3° 09'
<br />3' 46'
<br />5' 02'
<br />66 17'
<br />103.54
<br />540
<br />110.11
<br />30 16'
<br />3-° 54'5
<br />° 13'
<br />6031 t
<br />103-84
<br />56°
<br />io6.5o
<br />3° 22'
<br />4' 02'
<br />5° 23'
<br />6° 44'
<br />104.14
<br />1 580
<br />103.14
<br />30 29'
<br />4' 10'
<br />50 34'
<br />6' 57'
<br />104.42
<br />+j 6o
<br />Ioo.Oo
<br />3. 35
<br />4 18
<br />5 44
<br />7 11
<br />.:
<br />104.7
<br />IX
<br />CURVE FORMULAS
<br />T= R tan ; I R=. T cot. ' I chord2
<br />T _ 56 tan I Chord def _ =R
<br />Sin. j} D R _ 50
<br />Sin.
<br />1z D
<br />Sin } D _ 5o _7c,,, chords
<br />R = I
<br />E = Rex. sec 1-1 D
<br />5o tan e I , 1
<br />Sin. } D = T E = T tan j I Tara. def. = l chord def:
<br />The square of any distance, divided by twice the radius, will equal
<br />the distance from tangent to -curve, very nearly.
<br />To find angle for a given distance and deflecticri.
<br />Rule I. Multiply the given distance by .or743; (def. for I° for I ft.
<br />see Table II.), and divide given deflection by the product.
<br />Rule 2. Multiply given deflection by J7.3, and divide the product by
<br />the given distance.
<br />To find deflection for a given angle and distaa=. 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 Lase loo; Alt. Io.102=200=.5. 100"}-.5=100.5 hyp.
<br />Given Hyp. 100,A1t.25.252=200=3.125. rco-;3.12,3=96.875=Base.
<br />Errcr in fart example, .00-; In last, .047.
<br />To find Tons of Rail in one mile of track: n!ukiply v:eiglit per yard
<br />by I I, and divide by 7.
<br />LE4ELING. The correction for curvature and refraction, in feet
<br />and decimals of feet is equal to 0.574de, where d is the distance in miles.
<br />The correction for curvature alone is closely, UI-. The ccmbined cor-
<br />rection IS negative.
<br />Pro : BLL1 ERROR. Ii d,, &, da, etc. are the discrepancies of various
<br />res111ts from the mean, and if 1d -=the sum of the squares of these differ-
<br />ences and n=the number of observations, then the probable error of the
<br />me�11=
<br />5 I ` S -d2
<br />SOLAR ErLr_�iri ts. Attention is called to the. Solar E hemeris for
<br />the current year, published by Keuffcl fi Esser Co_ and furnished free of
<br />charge upon request, which is 3;;}x5j in., with abou t 90 pages Of data very
<br />Useful to t'1e Surveyor; 'S'uch as the adjustments of trar_sAs, levels and
<br />solar attachments; directions and -tables for determining the meridian
<br />and the latitude from observations on the sun ands Polaris; stadia meas-
<br />urements; magnetic declination; arithmetic constar...ts; English and Metric
<br />conversions' trigonometric f ormulas; Natural and Logarithmic Functions;
<br />and Logarithms of Numbers.
<br />TABLE IV. = 1\iinutes in Decimals o[ a Degree..
<br />1' .01617 11' 1533 :Li' .3500 31' .5167 It' .6833 51' .5500
<br />2 .0333 12 .2000 "': .3667 32 .5353 62 ' .7000 52 .8667
<br />3 .0500 13 .2167 21 .3333 33 .5500 43 :7167 53 5833
<br />4 .0667 14 .2333 24 .4000 34 .5657 44 .7333 :r1 .9000
<br />5 .0533 15 .2500 25 .4167 35 .5333 45 .7500 55 .9167
<br />6 .1000 10 .2667 26 .4333 3G .6000 46 .7667 56 .9333
<br />7 .1107 1-, .2$33 27 .4300 37 .0167 47 7333 57 .9500
<br />8 .1333 is .3000 28 .4067 39 G333. 48 .1000 58 .9667
<br />9 .1500 19 .3167 29 .4533 39 G500 49 0167 59 .9333
<br />10 .1667 20 .3333 30 .5000 40 .6667 .50 .`3331 CO 1.0000
<br />TA$Lr✓ V. - Inches in Decimals of a hoot.
<br />1.16E
<br />14 3-16 1a 5-1G 3y a§ is 35 i3
<br />0052..OID4 0756 .0203 .0260 .0313w17 .0521 OG25 .0721 3 . 4 5 G 7 S 9 10 11
<br />3 .2500 .3333 .4167 .5000 .5S33 .5367 .7:100 .8333 .0167
<br />
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