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r
<br />Y TABLE IL -Radii, Ordinates I and Deflections. Cho rd=100 ft.
<br />Deg..
<br />Radius
<br />Mid.
<br />Ord.
<br />Tan,
<br />-Dist.
<br />. Def.
<br />Dist.
<br />Def,
<br />for .
<br />1 Ft.1
<br />Deg.'
<br />Radius
<br />Mid.
<br />Ord,
<br />Tan.
<br />Dist,
<br />Def.
<br />Def.
<br />for
<br />Ft.
<br />`,.1
<br />27' ._
<br />t,
<br />34377.
<br />t..
<br />036
<br />ft.
<br />.145
<br />t.
<br />,291
<br />/
<br />0.05:
<br />7°
<br />ft.'
<br />819.0
<br />ft _
<br />1.528
<br />ft ,0°10'
<br />6,105
<br />101.33 '
<br />2:10
<br />20
<br />17189.
<br />073
<br />'.109
<br />.2g1
<br />,582
<br />0.10
<br />20'
<br />781.8
<br />1,600
<br />8,395
<br />3° 33' .
<br />2.20
<br />30
<br />40•
<br />11459.
<br />.153 , 58 _.
<br />.436
<br />.873
<br />0.15•
<br />30-
<br />764.5'
<br />1,637
<br />6,540
<br />2° 27'
<br />2.25
<br />50
<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 />44
<br />46'
<br />2.30
<br />1
<br />6875.5
<br />'
<br />.182'
<br />.727
<br />" .454
<br />0.25
<br />-S •
<br />716.8
<br />1.746
<br />6',976
<br />59 36'
<br />.,50.50'
<br />2,40
<br />10
<br />5729.6
<br />,218
<br />.873
<br />11.745
<br />0.30
<br />20
<br />688.2
<br />1.819
<br />7;266
<br />14.53
<br />2.50
<br />W.
<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 />3
<br />4297.3
<br />.291
<br />'•,327
<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 />40
<br />3819.8
<br />,3437.9
<br />4° to'
<br />1.309
<br />:2.618
<br />0.45
<br />9,
<br />637.3
<br />1.965
<br />7:846
<br />15.69
<br />2:70
<br />60
<br />60
<br />:.364
<br />1.454
<br />2.909
<br />0.50
<br />20'
<br />614.6
<br />2.037
<br />$.136
<br />16.27
<br />2,80
<br />3125:4.400
<br />'.436
<br />1.600
<br />3.200
<br />0.55
<br />30
<br />603.8
<br />2.074
<br />81281
<br />16:56
<br />2.85
<br />10
<br />2804.9'
<br />'.473.
<br />1.745
<br />,3'.490
<br />0.60
<br />-40
<br />593.4
<br />2.110
<br />8.426
<br />16,85
<br />2.90
<br />20
<br />.2644.6
<br />'.509
<br />1.891.3.781
<br />0.65
<br />10
<br />573:7.2:183
<br />8.716
<br />17.43
<br />3.00
<br />30
<br />2455.7
<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 />40
<br />2292,0.582
<br />2.181'
<br />4363
<br />0.75_
<br />il`
<br />521.7
<br />2.402
<br />9.585
<br />19'.16
<br />3.30
<br />50
<br />2148.8
<br />.
<br />2.327,
<br />4..545
<br />.654
<br />0:80
<br />: 30
<br />499.1
<br />2.511
<br />10'.02
<br />20.04
<br />3.45
<br />S.
<br />2022,4
<br />,618'2.472
<br />4.945
<br />0.85•
<br />12=
<br />478.3
<br />2.620
<br />10.45
<br />20.91
<br />3.60
<br />10
<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 />21.77'3.75
<br />20
<br />1809.6
<br />.691
<br />'.727
<br />2.763
<br />5,526
<br />0.95
<br />13
<br />441.7
<br />2.839
<br />11.32,
<br />22.64
<br />3.90
<br />80
<br />1719.1
<br />_1637.3
<br />2.908'
<br />5,817.1.00
<br />30
<br />425.4
<br />2.949
<br />11.75
<br />23.51
<br />4.05
<br />40
<br />.764
<br />3.054
<br />6.108
<br />1.05
<br />-14
<br />410.3
<br />3.058.12:18.
<br />24.37
<br />4.20
<br />50
<br />.1562,9
<br />,800
<br />3.199
<br />6,398
<br />1.10
<br />-30
<br />396.2
<br />3.168
<br />12,62
<br />25.24
<br />4.35
<br />`
<br />.1495.0
<br />..836
<br />3,345
<br />6,689,
<br />1.15.
<br />15
<br />383.1
<br />3.277.13.05
<br />26:11
<br />4.50
<br />10
<br />1432.7
<br />..873
<br />3.490
<br />6:980
<br />1.20,
<br />' 30
<br />370:8
<br />3;387
<br />13.49
<br />26.97
<br />4:65
<br />20
<br />1375.4
<br />:.909,3.635
<br />7,271
<br />1.25
<br />'16'
<br />359.3
<br />3,496
<br />13:92
<br />27.84
<br />4.80
<br />30.
<br />1322.5
<br />-1273.6
<br />.945
<br />3.718
<br />7.561
<br />1.30
<br />30
<br />`17
<br />348.5
<br />3.606
<br />14.35
<br />28.70
<br />4.95
<br />-.982
<br />3.926
<br />7.852
<br />1.35
<br />-
<br />338.3
<br />3,716
<br />14.78'
<br />29.56
<br />5.10
<br />40
<br />'50
<br />-1228.1
<br />1,018
<br />4,071
<br />8.143
<br />1.40
<br />.18
<br />319.6
<br />3.935
<br />15.64'
<br />31'.29,
<br />5.40
<br />f
<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 />33,01
<br />5.70
<br />10
<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
<br />6,00
<br />20
<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
<br />6:30
<br />i 30
<br />.;1074.7
<br />-1042,1
<br />1,164
<br />1,200
<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 />40
<br />-1011.5
<br />4.798
<br />9.596
<br />1.65,
<br />23•
<br />250.8
<br />5.035
<br />19:94
<br />39:87
<br />6,90
<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
<br />7,20
<br />Q 50
<br />982.6
<br />1273
<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 />10
<br />955.4
<br />1:309-5.234
<br />10.47
<br />1,80
<br />26
<br />222.3
<br />5.697
<br />22.50
<br />44`.99
<br />7.,80
<br />20
<br />929.61,346
<br />6.379
<br />10.76
<br />1,85
<br />27!
<br />214.2
<br />5.918
<br />23.35,
<br />46.69
<br />8,10
<br />30
<br />;905.1
<br />'881.9
<br />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 />1,418
<br />5.669
<br />11,34.
<br />1,95
<br />29:
<br />199.7
<br />6.360
<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 />1 30'
<br />193.2
<br />6,583
<br />25.88
<br />51.76
<br />9,00
<br />The middle ordinate in inches for any cord of length (a) is equal to ,0012 C'
<br />multiplied by the middle ordinate taken from the above table, Thos, if it
<br />desired to bend a 30 ft, rail to fit a 10 degree curve,- its middle ordinate should
<br />be .0012X900X2.183 or 2.36 inches.
<br />TABLE IIL 'Deflections for Sub Chords for S&ort Radius Curves.
<br />Degree
<br />of
<br />Curve
<br />Radius
<br />50
<br />aubR chord = sin of I def. angle
<br />Lenof gth
<br />for 100 ft.
<br />sin. l def. ang,
<br />12.5: Ft.
<br />1'5 Ft.
<br />20 Ft.
<br />25 Ft.
<br />31'
<br />,5167
<br />1°51.'
<br />`,.1
<br />27' ._
<br />2° 58'-
<br />3° 43' "
<br />.101,15 -=
<br />32
<br />181.39
<br />10 59'
<br />2° 25'
<br />_
<br />3° Io'
<br />3° 58'
<br />101.33 '
<br />340
<br />171.0I
<br />z° 06'
<br />2° 33 ' _
<br />'
<br />3° 21'
<br />4 ° 12'
<br />101,48
<br />350
<br />i61,. 80.
<br />2° 13'
<br />z° q 1'.
<br />3° 33' .
<br />4° 26'
<br />101'.66
<br />380--
<br />.153 , 58 _.
<br />_ 2°.20'
<br />20 49' _
<br />3° 44' -
<br />4' 40' :
<br />. 101-85
<br />407
<br />146.'19.
<br />2° 27'
<br />2° 57'
<br />3° 55'
<br />4° 54'
<br />102.o6
<br />420;_.
<br />. 139.52
<br />2°.34''
<br />3° 05'.
<br />4' 07'
<br />5° 08' .:
<br />102.29..
<br />44
<br />46'
<br />133.47
<br />2°.41'
<br />3° 13'
<br />4° 18'
<br />S° 22'
<br />'1'02.53
<br />48° '
<br />127.97
<br />'
<br />2° 48'
<br />3° 21'
<br />4° 29'
<br />59 36'
<br />.,50.50'
<br />102.76 -
<br />50°
<br />1'22.92
<br />20 55'
<br />3° 29'
<br />4° 40'
<br />.
<br />103,00
<br />11 8.31 :
<br />3° 02'
<br />30 38'
<br />40 51':
<br />60 04'
<br />.103, 24, .
<br />52°
<br />54a
<br />114.06
<br />30.09'
<br />30 46''.
<br />5° 02'
<br />6° 17'
<br />103:54
<br />38
<br />110:1"I
<br />3° 16'
<br />30 54'.
<br />50 13'
<br />6' 31,
<br />103:84
<br />.56°
<br />58
<br />io6.5o.
<br />30 22'.
<br />40 02,.
<br />5°.23'
<br />6° 44'
<br />104,14_.
<br />60°
<br />I.o3 14
<br />3, �9,..
<br />4° to'
<br />S° 34'
<br />6° 57'
<br />104.43. .
<br />.3333
<br />lo0..00
<br />3°35'
<br />4°18'
<br />5°44'
<br />7°_11'
<br />104.72
<br />It
<br />'CURVE. FORMULAS
<br />T = R tan A I R= T cot. 2 I Chord def, = chords
<br />,l, -50 tan J.I 60 . - R
<br />Sin.. 13 R =
<br />50 ;Sin. 2 a D No. chords = �:
<br />R E =,R ex. sec a I '
<br />_;5o tan I a
<br />.Sin. } D - T , E T tan_8 I _ . .Tan. def. = 2 chord def.
<br />The:square,of any &4nce,'divided by twice the radius, will equal
<br />the distance from tangent to curve, very nearly.'
<br />To find angle fora given distance and deflection.
<br />Rule'i. .Multiply the given distance by .01745 (def. for I° for I ft.
<br />see 'Table II.), and divide'given. deflection by the product.'
<br />Rule'2. Multiply -given deflection' by g7.3, and divide the product by
<br />thegiven distance:
<br />Td 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 loo, Alt. 10.102=200=.5. Ioo+.5=IOO.5 hyp•
<br />Given. Hyp. loo, Alt. 25.252'=too=3,125, -3.125
<br />Given
<br />Error in first example, .002; in last, .045•
<br />To`fi'iid _Tons of, Rail'in one mile of track: multiply, weight per yard
<br />: by' ii, and divide by q.
<br />LEVELING, The correction for curvature and refraction, in feet
<br />and.decimals'of feet is equal to 0.574 d3,where d is the. distance in miles.
<br />The. correction. for curvature alone is closely, Jd2:: The combined cor-.
<br />rection is negative.
<br />. PROBABL$ ERROR. If d�, d„ da, etc. are the discrepancies of various
<br />results from the mean; and if ld2.=the sum of the squares of these dificr-
<br />enees and n=the number 0f. observations;'then the -probable error of the,
<br />mean= + 0.6745 n(n-1)
<br />SOLAR EPHEMERIS. Attention' is called to the Solar Ephemeris ,for
<br />the *current year, published by Keuffel & Esser'Co., and furnished free' of
<br />charge upon request, which' is 34x58 -in., with about 90 pages of data very
<br />useful -to the Surveyor; such as the adjustments of transits, levels and
<br />Polar attachments; directions and tables for, determining the meridian
<br />and the latitude from observations on thesun and Polaris;. stadia meas-
<br />urements; magnetic declination arithmetic constants; English and Metric
<br />conversions; trigonometric f ormulas; Natural and Logarithmic Functions;
<br />and Logarithms of Numbers.
<br />TABLE IV.'- Minutes
<br />in Decimals of a De ee.
<br />1'
<br />.0167
<br />11'
<br />.1833t27
<br />.3500
<br />31'
<br />,5167
<br />41'
<br />,6833
<br />51'
<br />.8500
<br />2
<br />.0333
<br />12
<br />.2000.3667
<br />32
<br />.5333
<br />42
<br />.7000
<br />52
<br />.8667
<br />it
<br />.0500
<br />'13
<br />.2167,3833
<br />33
<br />,5500
<br />43
<br />.7167
<br />53
<br />.8833
<br />d
<br />.0667
<br />14
<br />.2333.4000
<br />34
<br />.5667
<br />44
<br />.7333
<br />54
<br />.9000
<br />5
<br />.0833
<br />15
<br />.2500,4167
<br />35
<br />.5833
<br />45
<br />.7500
<br />55
<br />.9167
<br />6
<br />,1000
<br />16 .
<br />.2667.4333
<br />36
<br />.6000
<br />46
<br />.7667
<br />56
<br />.9333
<br />.7
<br />'.1167
<br />17
<br />.2833.4500
<br />37
<br />,6167
<br />47
<br />.7833
<br />57
<br />.9500
<br />8
<br />.1333
<br />1S
<br />.3000.4667
<br />38
<br />.6333
<br />48
<br />.8000
<br />58
<br />.9667
<br />9•'
<br />.1500
<br />19
<br />'.3167:4833
<br />39
<br />.6500
<br />49
<br />.8167
<br />59
<br />.9833
<br />10
<br />.1667
<br />20
<br />.3333
<br />5000
<br />40
<br />.6667
<br />50
<br />1 .833311
<br />60
<br />1,0000
<br />TABLE V. - Inches in Decimals of a Foot.
<br />1-16 3-3231 3-18 5-lfi % 34 s/a71
<br />:0052 -,0078 .0104.: ,0156 .0208 .0260 .0313 1 .0417 LC521 10625 .0729
<br />1 2 34 5 6 7 8 9 10 11
<br />.0833. .1667 .2500 .3333. .4167 1 .5000 1 .5833 1 .6667 .7500 1 .8333 .9167.
<br />A
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