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I.
<br />TABLE II._- Radii, Ordinates and- Deflections. Chord 100 ft.
<br />Deg.
<br />Ila ius
<br />Mid
<br />Ord. •
<br />Tan. "
<br />Dista,
<br />Def.
<br />Dista
<br />Def.
<br />for
<br />1 Ft.
<br />Deg. ".
<br />iia les
<br />Mid.
<br />OcJ.
<br />Tan.
<br />Dist.'
<br />Def.
<br />Dist.
<br />Del.
<br />Icr
<br />1 Ft.
<br />2°17'
<br />ft.ft.
<br />3°4j'-
<br />t.
<br />ft.
<br />i
<br />1°59'
<br />ft.
<br />it.
<br />ft,
<br />ft.
<br />34'
<br />0°10'
<br />34377.
<br />036
<br />'-:145
<br />:291
<br />0.03'
<br />T
<br />519.0
<br />1.525
<br />6.105
<br />12.21
<br />2.10
<br />20
<br />17159.
<br />073
<br />.291.
<br />.552
<br />0.10
<br />20'
<br />7S1.8
<br />1.600
<br />0.39:5
<br />12.79
<br />2.20
<br />30
<br />11459.
<br />.109
<br />.43G.
<br />-.873
<br />0.15'
<br />30'
<br />764.5
<br />1.637
<br />G. 540
<br />13-.08
<br />2.25
<br />40
<br />8594.4
<br />.145.
<br />.552
<br />-1.164
<br />0.20
<br />40
<br />747.9
<br />1.673
<br />G:GS5
<br />13.37
<br />2.30
<br />50
<br />GS75.5
<br />.132
<br />.727
<br />1 A54
<br />0.25
<br />8
<br />716.8
<br />1.746
<br />6.97E
<br />13.95
<br />2.40
<br />1
<br />5729.6
<br />•.218
<br />.S73.
<br />1.745
<br />0.30
<br />20
<br />GSS.2
<br />1.819
<br />7.203
<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 />1.555
<br />7.411
<br />14.52
<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 />1.592
<br />7.550
<br />15.11
<br />2.60
<br />'30
<br />3S19.S
<br />.327
<br />1.309
<br />2.618
<br />0.45
<br />9
<br />637.3
<br />1.9G.5
<br />7.546
<br />15.60
<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.S0
<br />50
<br />3125.4
<br />.400
<br />1.600
<br />3.200
<br />0.55
<br />30
<br />603.8
<br />2.074
<br />8.281
<br />16.56
<br />2.55
<br />2'
<br />28Crt.9.436
<br />1.745
<br />3.490
<br />0.60
<br />40
<br />593.4
<br />2.113
<br />8.426
<br />16.55
<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 />2.1S3
<br />8.716
<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 />540.4
<br />2.202
<br />91150
<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 />9.555
<br />i9.16
<br />3.30
<br />40
<br />214S.8'
<br />.592
<br />2.327
<br />4.654
<br />O.SO
<br />30
<br />_99.1
<br />2.511
<br />10.02
<br />20.04
<br />0.45
<br />50
<br />2022.4
<br />.615
<br />2.472
<br />4.945
<br />0.85
<br />12
<br />478.3
<br />2.620
<br />10.45
<br />20.91
<br />GO
<br />3
<br />1910.1
<br />.655
<br />2.618
<br />5.235
<br />0.00
<br />30••159.3
<br />3.730
<br />10.89
<br />21.77
<br />3.75
<br />10
<br />1509.6
<br />.691
<br />2.763
<br />5.526
<br />0.95
<br />13.
<br />441.7
<br />'2.839
<br />11.32
<br />22.64
<br />3.90
<br />`20
<br />1719.1
<br />.727
<br />9.903
<br />5.817
<br />1.00
<br />30
<br />125.4
<br />2.049
<br />11.75
<br />23.51
<br />4.. 05
<br />30
<br />1637.3
<br />.764
<br />3.054
<br />6.10S
<br />1.05
<br />14 -
<br />410.3
<br />3.05S
<br />12.15
<br />24..37
<br />•3.20
<br />40
<br />1562.9
<br />.800
<br />3.199
<br />6.308
<br />1.10
<br />30
<br />^96.2
<br />3.168
<br />12.62
<br />225.24
<br />4.35
<br />50
<br />1495:0
<br />.S36
<br />3.345
<br />6.6SJ
<br />1:15
<br />15
<br />353.1
<br />3.277
<br />13.05
<br />2G. I1
<br />•1.50
<br />4
<br />1432:7
<br />.S73
<br />3.490
<br />G.9SO
<br />1.20
<br />• 30
<br />370.3
<br />3. SS-
<br />13.49
<br />26.97
<br />•1.65
<br />10
<br />1375.4
<br />•.909
<br />3.6'35
<br />7.271
<br />1.25
<br />16
<br />359.3
<br />3.496
<br />13.92
<br />21.84
<br />-3.50
<br />20
<br />1322.5
<br />.945
<br />3.71E
<br />7.561
<br />1.30
<br />30
<br />34S.5
<br />3.60G
<br />14.35
<br />25.70
<br />4.05
<br />30'
<br />1273.6
<br />.OS2
<br />3.9'-6
<br />7.852
<br />1.35
<br />17
<br />338.3
<br />3.716
<br />14. 7S
<br />29.56
<br />5.10
<br />40
<br />1228.1
<br />1.0184.071
<br />5.143
<br />1.40
<br />18
<br />319.6
<br />3.935
<br />15.64
<br />31.29
<br />5.47
<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 />1.6.51
<br />33.01
<br />5.70
<br />S
<br />1146.3
<br />1.091
<br />4.30^_
<br />3.723
<br />1.50
<br />20
<br />257.9
<br />3,37,1
<br />17.37
<br />34.73
<br />G.00
<br />10
<br />1109.3
<br />1.127
<br />4.507
<br />9.011
<br />1.55
<br />21
<br />274.4
<br />4.,504
<br />18.22
<br />36.4.1
<br />G.3J
<br />20
<br />107.1.7
<br />1.164
<br />4.653
<br />9.305
<br />1.60
<br />22
<br />262.0
<br />4.814
<br />19.03
<br />38.1G
<br />G.60
<br />30
<br />1042:1
<br />1.200
<br />-1.703
<br />9.596
<br />1.65
<br />23
<br />250.5
<br />5.035
<br />19.04
<br />39.87
<br />6.90
<br />40
<br />1011.5
<br />1.237
<br />4.943
<br />0.88G
<br />1.70
<br />24
<br />240.5
<br />5.253
<br />20.79
<br />41.53
<br />7.20
<br />50
<br />-082.6
<br />1.273
<br />5.083
<br />10.18
<br />1.75
<br />25
<br />231.0
<br />5.476
<br />21.64
<br />43. 2Q
<br />7.50
<br />6
<br />955.4
<br />1.309
<br />5.234
<br />10.47
<br />1.50
<br />26
<br />222.3
<br />5.697
<br />32.50
<br />44.99
<br />7.50
<br />10
<br />929.6
<br />1.346
<br />5.379
<br />10.70.
<br />1.S5
<br />27
<br />214.2
<br />5.915
<br />23. S5
<br />46. 69
<br />`1.I0
<br />20
<br />905.1
<br />1.352
<br />5.524
<br />11.05
<br />1.90
<br />23
<br />206.7
<br />G13J
<br />21.19
<br />48.33
<br />S.40
<br />3O
<br />SS1.9
<br />1.415
<br />5.669
<br />11.34
<br />1.95
<br />'9
<br />199.7
<br />6.. 360
<br />25.0.1
<br />50.07
<br />S.70
<br />40-559.9
<br />1.455
<br />5.814
<br />11.63
<br />2.00
<br />30
<br />10:3.2
<br />6.553
<br />1 '5.SS
<br />51.76
<br />9.00
<br />,:
<br />length -al 0__ G
<br />The middle ortliva , in'nches for any cord of e th C is equal to .0
<br />T tc 1 ( )
<br />s
<br />- "' 'L' It
<br />i c U � ordinate From the table. hum..
<br />mult PLe 1 � the middle or L to tai.en f ., above T
<br />desired to bend a 30 ft. rail to fit a 10 degree curve, its middle ordinate sliould
<br />be .0012X90OX2.1S3 or 2.36 inches.
<br />TABLE III. Deflections for Sub Chords for Short Ra4itls-Curves.
<br />Degree
<br />of
<br />Carve
<br />R.Sius
<br />�'sebchord
<br />r = sin of z def. angle
<br />Length
<br />of arc
<br />for 160 it.
<br />sin.: vet. ang.
<br />12.5 Ft.
<br />15 Ft.
<br />20 Ft.
<br />25 Ft.
<br />30°
<br />193:15
<br />1°51'
<br />2°17'
<br />_'.58' _
<br />3°4j'-
<br />101.15
<br />320
<br />151.39
<br />1°59'
<br />2°-5'
<br />3° 10'
<br />3°58'
<br />161.33
<br />34'
<br />171.01
<br />2°o6'
<br />2° 33'
<br />3°2I'
<br />4°12'
<br />101.48
<br />36°
<br />161.8o
<br />2° 13'
<br />2° 41'
<br />3° 33'
<br />a° 26'
<br />fo1.66
<br />38°
<br />153.58
<br />2° 20'
<br />2° 49'
<br />3° 44'.
<br />4°.40' .
<br />IoI.85
<br />40°
<br />146. i9
<br />2° 27
<br />2° 57'
<br />3° 55'
<br />4' S4
<br />lo2.o6
<br />42'
<br />139.52'°
<br />34'
<br />30 0-1
<br />}° oi'
<br />S° 03
<br />102.29
<br />44°
<br />133.47
<br />2° 41'
<br />3° 13'
<br />4° 18'
<br />5° 22'
<br />102.53
<br />46°
<br />127.97.
<br />' 20 48'
<br />3° 21'
<br />4° 29'
<br />S° 36'
<br />102.76
<br />4S°
<br />122.92
<br />z° 55'
<br />3° z9'
<br />4° 40,
<br />5°_50,
<br />103.00
<br />50°
<br />118.31..
<br />3° O2,
<br />3,38,:
<br />4; 51,
<br />6° 04,
<br />103.24
<br />52°
<br />114.06.
<br />3° 09'
<br />3' 46'
<br />S° oz'
<br />6° 17' .
<br />103.54
<br />540
<br />110.11
<br />3° 16'
<br />3° 54'
<br />.5° 13'
<br />60 31',
<br />103.84
<br />56°
<br />106.50
<br />3° 22'
<br />4° 02'
<br />5° 23'
<br />6° 44'
<br />104.14
<br />58°
<br />103.14
<br />30 29'
<br />4' 10f.
<br />5° 34'
<br />6° 57'
<br />104.43
<br />60°
<br />Ioo. oO
<br />30 35
<br />4° IS'
<br />5° 44'
<br />70 11'
<br />104- 72
<br />IX
<br />CURVE FORMULAS
<br />T= R tan 2 I R= T cot. 2 I chords
<br />T _ 5gtan 4.I Chord clef. _ ..R
<br />Sin. kD : 50
<br />R =
<br />>o Z :Sin. 1 , D I,
<br />'R Nc. chords= -
<br />` . . E = R ex. see I D
<br />5o tan• j I def. = a
<br />Sin. j D' _ ,I, E = T tan. 4 Tan: I chord def.
<br />The square of any distance, divided by twice the radius, will equal
<br />the distance frons tangent to curve, very nearly.
<br />To find angle for a given distance and deflection.
<br />Role I. • Multiply. the given distance by .01745 (def. for I° for i ft.
<br />see Table IL), and divide given deflection by the.product.
<br />Rule 2. Multiply 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 .01745, and the product by the distance.
<br />GENERAL DATA
<br />RIGHT ANGLE TRLANGLES. Square the altitude, divide by twice the
<br />base. Add quotient to base for hypotenuse.
<br />_Given Base too, Alt. 1o.io2-2oo=.5. 100-}-.5=100.5 hvp.
<br />Given Hyp. ioo, Alt. 25.252=200=3.125. 100-3.125=96.875=Base.
<br />Error in first example, .002; 1n last, .045.
<br />To find Tons of Rail in one mile of trach.: multiply weight per yard
<br />by it, and divide by 7.
<br />LEVELING. The correction for curvature and refraction, in' feet
<br />and decimals of feet is equal to 0.574d2, where d is the distance in files.
<br />The correction for curvature alone is closely, 3d=. The combined cor-
<br />rection is negative.
<br />Pr.ODADLr, Error. If dl, d., d, , etc. are the discrepancies of v rlolis
<br />resu1t3 from the mean, and if Yd= -the sum of the squares of these differ-
<br />ences and n=the number of observations, then the probable error of the
<br />lneaa=45 I id'
<br />1 n (n-1)
<br />SOL:1R. EPHE*,*Eris. Attention is called to tileC ,.,olar h � .nemerls for
<br />the current year, published by'Keuffel & Esser Co., and furnished free of
<br />charge upon request, which. is 3.}x418 in., �vith about 90 pages of data very
<br />useful to, the Surveyor; such as the adjustments of transits, levels and
<br />solar attachments; directiors.and tables for determining the meridian
<br />and the latitude from observations, on the sun and Polaris; stadia nieas-
<br />tirements; ipavneticdeclinatio_a; arithmetic constants; English and Metric
<br />conversions; trigonometric f ormulas; Natural and Logarithmic run ctions;
<br />and Logarithms of numbers.
<br />TABLE IV. - Minutes in Decimals of a Degree.
<br />1'
<br />.0167
<br />11'
<br />.1833
<br />21'
<br />.3500
<br />31'
<br />oIG7
<br />41'
<br />.6533
<br />51'
<br />.8500
<br />d
<br />.0333
<br />12
<br />.2000
<br />122
<br />'.3667
<br />32
<br />:.333
<br />42
<br />.7000
<br />52
<br />.8667
<br />S
<br />0500
<br />13
<br />.2167
<br />23
<br />.3S33
<br />33
<br />.5500.
<br />43
<br />.7167
<br />53
<br />.8833
<br />4
<br />.OG67
<br />14
<br />.2333
<br />21
<br />.4000
<br />3i
<br />5007
<br />44
<br />.1333
<br />:i4
<br />.9000
<br />G
<br />OS33
<br />15
<br />.2500
<br />25
<br />.41G7
<br />35
<br />5"33
<br />15
<br />.7500
<br />55
<br />.9167
<br />G
<br />.1000
<br />10 .
<br />.2667
<br />26
<br />.-1333
<br />30
<br />GOOO
<br />16
<br />.7667
<br />5G
<br />.9333
<br />7
<br />.1167
<br />17
<br />.2533
<br />27
<br />.4500
<br />37
<br />.0167
<br />17
<br />.7S33
<br />57
<br />.9500
<br />8
<br />.1333
<br />13
<br />.3000
<br />28
<br />.4667
<br />33
<br />G333
<br />6000
<br />58
<br />.9667
<br />9
<br />.1500
<br />19
<br />.3167
<br />29
<br />.4533
<br />39
<br />ri500
<br />148
<br />49
<br />'1G7
<br />59
<br />.9833
<br />10
<br />.16167 i
<br />20
<br />.3333
<br />3fl
<br />I 5000 11
<br />40
<br />GfiG7
<br />50
<br />X333
<br />ri0
<br />1.0000
<br />TABLE V. - Inches in Decimals of a root.
<br />1-16
<br />3-32
<br />is
<br />3-16
<br />%
<br />5-1Gi
<br />3's
<br />r2 is
<br />% I
<br />/i
<br />0052
<br />.0075
<br />.0104
<br />.0156
<br />.0 08
<br />.0200
<br />.0:>I3
<br />.0417 .0521
<br />.0625
<br />1
<br />2
<br />3
<br />4
<br />5
<br />G
<br />7
<br />6 9
<br />10
<br />11
<br />0833
<br />.1067
<br />2500
<br />.3333
<br />.4167
<br />.5000
<br />.5533
<br />.6667 .7500
<br />.5333
<br />.9167
<br />
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