|
VIII - -
<br />TABLE II. - T{adii,' Ordinates and'Deflections. Chord' 100 ft.
<br />_
<br />-
<br />Radius
<br />Mid.
<br />Ord.-
<br />Tan.
<br />Dist.
<br />pef•.Det.
<br />Rist.
<br />for
<br />1 Ft.
<br />Deo..'fRadius
<br />k
<br />Mid.
<br />Qrd.
<br />Tan.
<br />Dist.
<br />Det.
<br />Dist.
<br />Def.
<br />for i
<br />I FE.
<br />3°. 17,
<br />ft.it.
<br />3° 43,.
<br />' R.
<br />ft.
<br />!
<br />7 5(j
<br />€t,
<br />It.
<br />It.
<br />it.
<br />34°
<br />0"10'
<br />34377.
<br />036
<br />.145
<br />.291
<br />0.05,
<br />7°
<br />819'.0
<br />1.528
<br />6.103
<br />12.21
<br />2,10
<br />20
<br />17189.
<br />K3
<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 />.573
<br />0.15
<br />30
<br />764.5
<br />1.637:
<br />6.540
<br />13.05
<br />2.25
<br />40
<br />8594.4
<br />.145
<br />.552
<br />1:164.0.20
<br />46
<br />40
<br />747.9
<br />1.673,
<br />6.685
<br />1.3.37
<br />2.30
<br />110
<br />. 6875.5
<br />.182
<br />.727
<br />1.451
<br />0.2.1
<br />S
<br />716.8
<br />,1.746
<br />6.07.0
<br />13,95
<br />2.40
<br />1'
<br />5729.6
<br />,2i8
<br />.873
<br />1.745
<br />0.30
<br />20
<br />633.2
<br />1.510
<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 />90
<br />674.7
<br />1.855
<br />7.411
<br />14.82
<br />2.55
<br />20
<br />4297.3',.201
<br />4.° 1o'
<br />1,.164
<br />2.327
<br />0.40.'
<br />-40
<br />661.7
<br />I.S92
<br />7.556
<br />15.11
<br />3.60
<br />30
<br />3819.8
<br />.327
<br />1.309
<br />2.615
<br />0.45"
<br />9'
<br />637.3
<br />1.960
<br />7.846
<br />15.69
<br />2.70
<br />40
<br />3437.9
<br />.364
<br />1.454
<br />2.909.0.50,
<br />20
<br />614.0
<br />2.037
<br />.8.136
<br />16.27
<br />2.50
<br />50
<br />3125.4
<br />_ .400
<br />1:600
<br />3.200
<br />0.55
<br />30
<br />G03.S
<br />2.074
<br />8.251
<br />16.56
<br />2.85
<br />2.
<br />2864.9
<br />.436
<br />1.746
<br />3.400
<br />0.60
<br />40
<br />503.4
<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 />{.ZO
<br />2455.7..509
<br />2:03G
<br />4.073
<br />0.70.-.
<br />- 30'
<br />546.4
<br />2.292-0.150
<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 />9.58:5
<br />19.10
<br />3.30
<br />40
<br />2148.8
<br />=.582
<br />2;327
<br />4.654
<br />0.80-
<br />30
<br />199.1
<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 />0-8.5
<br />12�
<br />478,3
<br />2:620
<br />10,45
<br />20.91
<br />3.60
<br />S
<br />1910.1
<br />.653
<br />2;618
<br />5.235
<br />0.90
<br />.30
<br />459.3
<br />2.73010.89
<br />21.77
<br />3.75
<br />10
<br />1809.6
<br />.091
<br />2°763
<br />5.526
<br />0'.05
<br />-13 -,
<br />441.7
<br />2'S'10
<br />11.32
<br />22.61
<br />3.90
<br />20
<br />1719.1
<br />.727,2.903
<br />5.817,
<br />7.00
<br />'30
<br />425.4
<br />2.949
<br />11.75
<br />23.51
<br />4.05
<br />30
<br />1537.3
<br />.764.3.054
<br />6.103
<br />1-05'
<br />14'' ,
<br />410.3
<br />3.05S
<br />12.1.8
<br />24.37
<br />4.20
<br />,40
<br />1562.9
<br />-800
<br />3.109
<br />6.398
<br />1.70
<br />-30
<br />396.2
<br />3.103
<br />12.62
<br />25,24
<br />4.35
<br />50
<br />1495.0
<br />.830
<br />3.345
<br />6.659
<br />1.15
<br />15
<br />333.1'
<br />3.277
<br />13.0.5
<br />26.11
<br />4.50
<br />4'
<br />1432.7
<br />.8733.490
<br />6.980
<br />1,20.
<br />30
<br />370.8
<br />3.33713.49
<br />26.97
<br />4.65
<br />10
<br />1375.4
<br />.009
<br />3.635.
<br />7.271
<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
<br />,945
<br />3.713,
<br />7.561
<br />1,30
<br />30
<br />348.5
<br />3.606
<br />14.35
<br />2S.70
<br />4.9.5
<br />30
<br />.1273.6
<br />:932
<br />3.926,
<br />7.852
<br />1.33
<br />.1.7
<br />33S.3
<br />3.71G
<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 />3.035
<br />15.64
<br />,-,,1:29
<br />5.40
<br />50
<br />1185.8
<br />1.055
<br />4.2171
<br />8.433
<br />1.45
<br />1.9 .
<br />•302.9
<br />4.155
<br />16,51
<br />33,01
<br />5.90
<br />S
<br />1146.3
<br />1.091
<br />4.362
<br />6.724
<br />1.50
<br />20•
<br />287.3
<br />4.374
<br />17.37
<br />34.73
<br />G.00
<br />110
<br />1I09.3
<br />1.127
<br />4.507.
<br />9.014
<br />1.55
<br />21'
<br />274.4
<br />4.504.18.22
<br />"6.4.1
<br />6.30
<br />20
<br />1074,7
<br />1'.IG4
<br />4:653'
<br />0.805
<br />1_.60
<br />-3
<br />262:0
<br />4.314
<br />10,03
<br />35.16
<br />6.60
<br />30,
<br />1042:7
<br />1.200
<br />4.798
<br />0:506
<br />1.65.
<br />'23:
<br />250.5
<br />5.035
<br />10.94
<br />39.87
<br />6.00
<br />40
<br />.1011 ,5
<br />1.237
<br />4,.943
<br />9,586
<br />1.70
<br />24
<br />240.5
<br />5.255
<br />20.79.
<br />41.53
<br />7.20
<br />50'
<br />982.6
<br />1.273
<br />5-0,911110,111,
<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 />5.23410,47.
<br />1.80
<br />20, ,222.3
<br />8.697,
<br />23..50
<br />44,99
<br />7.80
<br />- 10
<br />929:G
<br />1':346
<br />5.379
<br />10;76'
<br />1.85
<br />27
<br />214.2
<br />5.915.23-35
<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 />206.7
<br />6.130
<br />24.19
<br />48.38
<br />8.40
<br />30
<br />581.9
<br />1,418
<br />5.669
<br />11,34
<br />1.95
<br />29
<br />199.7
<br />6.360
<br />2:5,04
<br />50.07
<br />8.70
<br />40
<br />839.9
<br />1.455
<br />5.814
<br />11,63
<br />2.00
<br />30
<br />193.2
<br />6.53
<br />25.88
<br />31.70
<br />9.00
<br />` The middle ordinate in inches for any cora of longth (C) isequal to .0012C'
<br />multiplied by the middle ordinate taken from the aboi•.e table. Thus, if it
<br />desired to bend a 30 ft. rail to fit a 10 degree curve, its middle ordinate should
<br />be .0012X90OX2.183 or 2,3Ginches.
<br />TABLE Ili. Deflections for Sub Chords for Short Radius Curves.
<br />Degree
<br />of
<br />Curve
<br />Radius -
<br />50
<br />Y2 slab chord ' ,
<br />h _ = sin of a def. ang.e
<br />Ler
<br />of
<br />far..1
<br />sin, s' def. a«g.
<br />12.5, lit.
<br />151+t.
<br />20 Ft.
<br />25 Ft.
<br />30°,
<br />193.13.
<br />I' 51'
<br />3°. 17,
<br />e° 58, ,
<br />3° 43,.
<br />101
<br />' 32
<br />; 181:39
<br />7 5(j
<br />2 25'
<br />3 70
<br />3 580
<br />lot
<br />34°
<br />171.0I
<br />2° 06'
<br />2° 33`.
<br />3° 21
<br />4° I2'\
<br />zoI
<br />36'
<br />161.80
<br />2' 13
<br />2' 41'
<br />3° 33':
<br />r° 26'
<br />101
<br />38'
<br />i,53. 58'20
<br />2O'
<br />2. 49'
<br />3° 44
<br />4° 40'
<br />loI
<br />40'
<br />146.19 ,.,
<br />a° 27'
<br />2° 57'
<br />3° 5,5
<br />(1° 54'
<br />zo2
<br />42
<br />139.52
<br />2° 34'
<br />30 05'
<br />.
<br />4' 07'
<br />S° 03
<br />102
<br />44'
<br />133.47
<br />2° 41
<br />3° 13'
<br />4' 18'
<br />S° 2''
<br />102
<br />46
<br />1227.97
<br />2° 43'
<br />3° 21'
<br />4° 29
<br />S° 36
<br />102
<br />¢8°
<br />122.92
<br />2° 55'
<br />30 29'
<br />4' 4.J
<br />5° 50'
<br />103
<br />50°
<br />118.31
<br />3°02''
<br />3°3S'
<br />4'5z'
<br />�° 04'.
<br />103
<br />52°
<br />114.c6
<br />3° 09'
<br />3..16 1
<br />5°o2'
<br />6° 17'
<br />103
<br />5¢°
<br />110.11
<br />3° 16'
<br />J° 54'
<br />.i° I".
<br />6° 31'
<br />1o3
<br />56°
<br />106.5o
<br />3 ° 2e'
<br />4° 02'
<br />5° 23'
<br />6° 4.1'
<br />104
<br />58°
<br />103.14
<br />3° 29
<br />4.° 1o'
<br />5° 34'
<br />6° 57
<br />104
<br />60°
<br />LQD,.00r
<br />�° 35
<br />¢° I$' -
<br />. J° -414'
<br />7° I1'
<br />504
<br />gth
<br />)O,ft.
<br />.I5
<br />.08
<br />.66
<br />.85
<br />.o6
<br />.29
<br />.53
<br />.76
<br />-00
<br />.24
<br />.54
<br />.84
<br />.14
<br />•43
<br />72
<br />7
<br />IX
<br />.. 'CURV,E- FORM i LP,S „• .'
<br />T = 72 tan I . - - •- - - -
<br />I. = T cot. ' 1 chord"
<br />-__ 5o tan # T�. . 2 ...Chord def. =
<br />T Sn:ll _® R
<br />5o R Sin: a D I
<br />Sin. ID N . chords = -
<br />"j" R L= R cs.scc 4 I p
<br />_
<br />5' tan I I
<br />1 E =.T tan I Tam. clef. =' chord deE;
<br />The square of. any distance,' divided by tivice t'�e'radius, '"rill equal
<br />the distance from tangent to curve, very near1k.
<br />To find annle far. agiven distance and deliectiaa.
<br />Ruled. 101iltiply the. given distance by,.01 4S (def, for i° for I ft:
<br />see Table II.);.aitd divide given deflection.by the pinduct. -
<br />Rule 2..- kfultiply 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 .oi745, and. the product. by the distance.
<br />GENERAL, DATA
<br />RIGHT ANGLE TRIANGLES.' Square the altitude,, ,d1vlde by. twice the'
<br />base. ' Add quotient to base for hypotenuse:
<br />Given' Base loo, Alt. Io.i6"-.2oo--.5.-1oo+.5=100.5 hyp.
<br />Given Tlyp.'loo,Alt. 25.25?=200=3 z2j,.loo-3.725=96.875=Base.
<br />- ' Error in first example, .002; In last, ;245.:
<br />To find Tons of Dail -in one mile of trach: multiply weight per yard
<br />by ti, and divide by 7.
<br />LEVELI-NG, -The correction for curvature aTul refraction, ,ia feet
<br />and decimals of feet is equal to 0.574 d2, where d is the distance in miles.
<br />The correction for curvature alone is 'clo.9 ly, sd-. The eoinbined crir-
<br />rection is negative. .
<br />PRODABLn ERROR. If d„ d.,, d„ etc. are the discrepancies of various
<br />results from the mean, and if idl=the sum of the squares of these differ-
<br />ences and n=the number of observations, then -the probable error of the
<br />mean= ode
<br />0.6743
<br />SOLAR Ei-Hrii1 ms. Attention is called to -the. Solar Ephemeris for
<br />the current year, published.by Keuffel & Esser Co., and furnislhed- free -of
<br />charge upon request, which is 3,x5, in:, with about :90 pages of data very
<br />useful to the :Surveyor; such -as the adjustments of transits, levels and
<br />solar attachments; directions and tables for det&mining the meridian .
<br />and the latitude from observations .on the sun and :Polaris; stadia, meas-
<br />urements;inagnetiedeclination;arithmetic constant; English and 1111etric
<br />conversions; trigonometric f ormulas; Natural and Logarithmic Functions;
<br />and Logarithms of Numbers.
<br />" TABLE IV. - Minutes.in T)eri7na1a of -, TVo-rep,
<br />1'
<br />.0167
<br />11'
<br />.1833
<br />21'
<br />.3500
<br />31'
<br />.5167
<br />41'
<br />.6533
<br />51'
<br />'.8500
<br />.0333
<br />12
<br />.2000
<br />22
<br />.ZG67
<br />32.
<br />.5333
<br />42'•
<br />-7000
<br />52
<br />.8667
<br />21
<br />.0500
<br />13
<br />.2167
<br />23
<br />."833
<br />33
<br />5
<br />43
<br />-7167
<br />53
<br />.8833
<br />4
<br />,06Gi'
<br />11
<br />.2333
<br />?.4
<br />.4000'
<br />34
<br />.5500
<br />41
<br />fr6C7
<br />54
<br />.5333
<br />fi
<br />0833
<br />15
<br />.2500
<br />25
<br />.4167
<br />33
<br />-5667
<br />45
<br />.7333
<br />7500
<br />55
<br />.9000
<br />.9167
<br />.1000
<br />1G
<br />.2667
<br />26
<br />.4333
<br />3G
<br />.5533
<br />.6000
<br />lit
<br />.7667
<br />5G
<br />.9333
<br />B
<br />17
<br />,2833
<br />'27
<br />.4500
<br />37'
<br />17
<br />7833
<br />57
<br />.9500
<br />.133319
<br />[20
<br />.3000
<br />28
<br />.4667'
<br />38
<br />.6167
<br />.6333
<br />4S
<br />58
<br />.9667
<br />9
<br />10
<br />.150019
<br />.31(7
<br />20
<br />.4833
<br />39
<br />,6500
<br />49
<br />.8000
<br />.8167
<br />59
<br />.9833
<br />16'7.
<br />.S.W.
<br />30
<br />.5000
<br />40
<br />6667 11
<br />50
<br />F,333
<br />60
<br />1.0000
<br />TA13LE V. - Inches in Decimals of,a Foot.
<br />1-1G
<br />00-130101
<br />.0156
<br />.0208
<br />.026G
<br />313.
<br />_04L7
<br />21
<br />.0625
<br />.0725
<br />I
<br />OS3g
<br />2
<br />3
<br />4
<br />5
<br />G
<br />'.5000
<br />7
<br />8
<br />9
<br />10
<br />11
<br />,1667
<br />•2500
<br />3333
<br />.4167
<br />.5333
<br />fr6C7
<br />7500
<br />.5333
<br />:9167
<br />
|