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TABLE II. - Radii, Ordinates and Deflection. Chord= 100 ft.
<br />beg.
<br />I'.adius '
<br />Mid.
<br />Ord.
<br />Tan.
<br />Dist.
<br />Def.
<br />I Dista
<br />1. f rcf-
<br />1 FI
<br />Deo..
<br />Radius
<br />lfid.
<br />Ord.
<br />Tan.
<br />List,
<br />Dcf.
<br />Dist.
<br />fcr
<br />1 rt.
<br />^' 17'
<br />t.
<br />ft.
<br />ft.
<br />ft.
<br />I
<br />I° 59'
<br />it.
<br />ft.
<br />it.
<br />ft.
<br />34'
<br />36'
<br />2'10'
<br />34377:
<br />.036
<br />.145
<br />.291
<br />0.05,
<br />7'
<br />819.0
<br />1.525
<br />6.105
<br />12.21"2:10
<br />4' 40'
<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 />"so
<br />11-159.
<br />.109
<br />.43G
<br />. :573
<br />0.15
<br />30
<br />764.5
<br />1.637
<br />6.540
<br />13.08
<br />2.25
<br />40
<br />8591.4
<br />.145
<br />.582
<br />1.IGI
<br />0.20
<br />40
<br />7.17.9
<br />1.673
<br />6.GS5
<br />13.37
<br />2.30
<br />50
<br />6875.'5
<br />.152
<br />.727
<br />1.454
<br />0.2.5)8
<br />.
<br />103.24
<br />716.8
<br />1.746
<br />6.976
<br />13.95
<br />2.40
<br />11'
<br />5729.6
<br />.213
<br />-.873
<br />, 1.74.5
<br />0.30
<br />20
<br />638.2
<br />1:819
<br />7.266
<br />14.53
<br />2.50
<br />10
<br />4911.2
<br />,255
<br />1.018
<br />2.030
<br />0.35
<br />30
<br />674.^r
<br />1.855
<br />7.411
<br />14.82
<br />2.55
<br />20
<br />4297.3
<br />.291
<br />1.1&1
<br />2.327
<br />2.40
<br />10
<br />661.7
<br />1.S92
<br />7.556
<br />15.11
<br />2.60
<br />•30
<br />3819.5
<br />.327
<br />1.309
<br />2.018
<br />0.43
<br />9
<br />637:3
<br />1.965
<br />7.846'15.69
<br />2.70
<br />.x.40
<br />3437.9
<br />'.364
<br />1.454
<br />- 2.909
<br />0.50
<br />20
<br />G14.G,2.037.
<br />8.136
<br />16.27
<br />2.80
<br />X50
<br />3125.4
<br />.400
<br />1.600
<br />3.200
<br />0.55'
<br />30
<br />003.8
<br />2.074
<br />8.251
<br />16.56
<br />2.85
<br />2.
<br />2864.9
<br />.436
<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 />10
<br />2644.6.473
<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 />20
<br />2455.7
<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 />7392.0
<br />.545
<br />2.181:
<br />4.303
<br />0.75
<br />11 ,
<br />521.7
<br />2.403
<br />9.585'19.16
<br />3.30
<br />40
<br />2148.8
<br />.582
<br />2.327
<br />4.654
<br />0:80
<br />30
<br />399.1
<br />2:511
<br />10.02
<br />20.0.1
<br />3.45
<br />50
<br />2022.4
<br />.618
<br />2.472
<br />4.945
<br />0.85
<br />12
<br />478.3
<br />2.G20
<br />10.45
<br />20.91
<br />3.60
<br />S1910.1
<br />•.655
<br />2.615
<br />5.235
<br />0.90
<br />.30
<br />459.3
<br />2.730
<br />10.59
<br />21.77
<br />3.73
<br />l0
<br />1509.6
<br />.601
<br />2.763
<br />5.526
<br />0.95
<br />'13
<br />441.7
<br />2.839
<br />11.32
<br />22.61
<br />3.90
<br />20
<br />1719.1
<br />.727
<br />2.903
<br />5.817.1.00
<br />30
<br />425.4
<br />2.949
<br />11.75
<br />23.51
<br />4.05
<br />30
<br />1637.3
<br />.764
<br />3.054
<br />, 6.105
<br />1.05
<br />14
<br />410.3
<br />3.055
<br />12.15
<br />24.3T4.20
<br />40
<br />.1562.9
<br />.800
<br />3.199
<br />6.398
<br />1.10
<br />30
<br />396.2
<br />3.163
<br />12.62
<br />25.24
<br />4.35
<br />50
<br />1495.0
<br />.83G
<br />3.345
<br />G.GS9
<br />1.15
<br />15 '
<br />353.1
<br />3.277
<br />13.05
<br />26.11
<br />4.50
<br />4
<br />1433.7
<br />.873
<br />3.490
<br />6.950
<br />1.20
<br />30
<br />370.5
<br />3.357
<br />13.49
<br />26.97
<br />4.65
<br />10
<br />1375.4
<br />.009
<br />3.635
<br />7.271
<br />1.2.5
<br />10
<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 />345.5
<br />3.606
<br />14.35
<br />28.70
<br />4.95
<br />30
<br />1273.6
<br />.952
<br />3.9226
<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 />1225.1
<br />1.018
<br />4.071
<br />8.143
<br />1.40
<br />18
<br />319.G
<br />3.935
<br />15.64
<br />31.29
<br />5.40
<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 />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 />20
<br />257.9
<br />4.374
<br />17.37
<br />34.73
<br />6.00
<br />10
<br />:.1109.3
<br />1.127
<br />4.507
<br />9.014
<br />1.55
<br />21
<br />274.4
<br />4.594
<br />18.22
<br />36.44
<br />6.30
<br />2U
<br />1074.7
<br />1.164
<br />4.65 3
<br />9.305
<br />1:60
<br />22
<br />262.0
<br />4.814
<br />19.08
<br />38.16
<br />fi:60
<br />-30
<br />1042.1
<br />1.200
<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 />.40
<br />1011.5.1.237
<br />4.943
<br />9.8336
<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 />5.088
<br />10.18.
<br />1.75
<br />25
<br />231.0
<br />5.476
<br />21.64
<br />43.2S
<br />7.50
<br />is .
<br />955.4
<br />1.309
<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.SO
<br />10
<br />929.6
<br />1.346
<br />5.379
<br />10.76
<br />1.85
<br />,'.7
<br />214.2
<br />5.918
<br />23.35
<br />46.69
<br />5.10
<br />20
<br />905.1
<br />1.352
<br />5.524
<br />11.05
<br />1.90
<br />2S
<br />206.7
<br />6.139
<br />24.19
<br />48.38
<br />3.40
<br />30
<br />831.0
<br />1.418
<br />5.G69
<br />11.34
<br />1.95
<br />29
<br />199.7.
<br />6.360
<br />25.04
<br />50.07
<br />5.70
<br />40
<br />559.9
<br />1.455
<br />5.814
<br />11.63
<br />2.00
<br />30
<br />193.2
<br />6.583
<br />25.83
<br />51.76
<br />9.00
<br />The middle ordinate in inches for any card of length (C) is egnal to .0012 C''
<br />mnitiplied by the middle ordinato taken from the above table. Thus, if it
<br />desired to bend a 30 ft. rail to fit a 10 degrea curve, its middle ordinate'shonld
<br />M .0012X90OX2.183 or 2.36 ilaellcs.
<br />TABLE III. Deflections for Sub Chords for Short Radius Curves.
<br />Degree
<br />of .
<br />Curve
<br />Radius
<br />50
<br />A sub chord = sin of ' def. angle
<br />P. a
<br />1 ength
<br />of arc
<br />for 100 ft.
<br />sin. It def. an.-.
<br />12.5 Ft.
<br />15 Ft.
<br />20 Ft.
<br />25 Ft.
<br />.30'
<br />193.13
<br />I' 51'
<br />^' 17'
<br />3° 58'3'
<br />43'
<br />.101.15
<br />32°
<br />181.39
<br />I° 59'
<br />25'
<br />'
<br />3' Io'
<br />3' 58'
<br />1:01.33
<br />34'
<br />36'
<br />171.01
<br />161.80
<br />2' 06'
<br />2' 13
<br />33'
<br />3' 41'
<br />3' 21'
<br />3' 33'
<br />4' 12'
<br />,' 26'
<br />I01.48
<br />Ioi.66
<br />238'
<br />1J3.58
<br />2° 20
<br />? 49'
<br />3' 44'
<br />4' 40'
<br />101.85
<br />40'
<br />146. f9
<br />^° 27
<br />2'57'
<br />3' 55'
<br />4' .94"
<br />IO2.o6
<br />42
<br />139:52
<br />2°34'
<br />3°05'
<br />4°07'
<br />5'08
<br />102.29
<br />44'
<br />133.47
<br />3-' 41`
<br />3° 13'
<br />4° IS
<br />S° 22'
<br />-102.53
<br />46'
<br />127-97
<br />20 486
<br />3' 21'
<br />4° 29,
<br />5' 36'
<br />102 76
<br />4S°
<br />122.0-2
<br />2' 55�
<br />3' 29'
<br />4' 40'
<br />5o 50'
<br />iog.Oo
<br />50°118-31
<br />118.31
<br />3° 02'
<br />3° 38'
<br />1' 51'
<br />6' 04'
<br />.
<br />103.24
<br />52°
<br />114. c
<br />I
<br />3° 09'
<br />3° r,6'
<br />S° C2'
<br />6° 17'
<br />103.51.
<br />54'
<br />110.1.'l
<br />3° 16'
<br />3' S4'
<br />:;° 13'
<br />6° 31' -
<br />163.84
<br />56°
<br />io6. 5O
<br />3° 22'
<br />4° 02'
<br />5' 23'
<br />6' 4T'
<br />104-14
<br />580
<br />IO3. 1
<br />30 29'
<br />40 10'.
<br />50 34�
<br />60 57'
<br />104.43
<br />60
<br />100.00'
<br />3 05
<br />4 18
<br />5044
<br />7 11,
<br />104-72
<br />CURVE FORMULAS .
<br />T =.R tan � I R = T cot. 1 I chorda
<br />_ 5o.tan I I Chord def. =
<br />R
<br />R
<br />T Sin. I D 50
<br />Sin. s •D - •io - Sin. D No. chords
<br />= I
<br />R E= R ex. sec I.
<br />5o tan z I r
<br />1
<br />t -
<br />Sin. � D - .1 E ='1' tan � I Tan. def. = z chord def.
<br />The square of any distance, divided by twice the radius, will equal
<br />elle clistance frons tangent to curve, very nearly.
<br />To find angle for a.given distance and deflection.
<br />Rule I. Multiply the given distance by .01745 (clef. for I° for l ft7
<br />see Table II.), and divide given deflection by the product.
<br />Rule 2.-' Multiply given deflection by 57.3, and dividetheproduct-by
<br />the given distance.
<br />To find deflection for a given angle and distance. -Multiply the -angle
<br />by .0.1745, 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. 1O.1O2_200=.5, ioo+.5=100.5 hyp.
<br />Given Hyp. 7oo,Alt. 25.252-200=3.125.I0O-3:125=96.875=Base.
<br />Error in first example; .002; in last, -.o45.
<br />To find Tons of Rail in one mile of track: multiply weight per yard
<br />by I I, 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 miles.
<br />The'correction for curvature alone is closely, Jda. The combined cor-
<br />rection is negative.
<br />PROBABLE ERROR. If dl, d., da, etc. are the discrepancies of.various
<br />results from the mean, and if Xd2=the sum of the squares of these differ-
<br />ences and n=the number of observations, then the probable error of the
<br />mean= 0.6745 Ida
<br />n (n-1)
<br />SOLAR EPHEMERIS. Attention is called to the Solar Ephemeris for
<br />the current year, published by Keuffel cC Esser Co., and furnished free of
<br />charge upon request, which is 34x5) 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 determining the meridian
<br />and the latitude from observations on the sun and Polaris; stadia meas-
<br />urements; magnetic declination; arithmetic constants; English and Metric
<br />conversions; trigonometric formulas; Natural andLogarithmic Functions;
<br />and Logarithms of Numbers.
<br />TABLE IV. - Minutes in Decimals of a Degree.
<br />1' .0167 11' .1833 21' .3500 311, .5167 41' .6833 by .8500
<br />2 .0333 12 ,2000 22 .3667 32 .5333 4v .7000 52 .8667
<br />8 .0500 13 .2167 23 .3833 33 .5500 43' .7167 53 .5833
<br />4 .0667 14 ,2333 '24 .4000 34 .5667 44 .7333 64 .9000'
<br />b .0533 16 ,2500 25 .4167 35, .8833 45
<br />TABLE V. -
<br />inches in Decimals of a Foot.
<br />• ' 1-16
<br />1 2
<br />?/g
<br />3-lri
<br />/}
<br />:i -]G
<br />i3
<br />ig
<br />1.
<br />.0052
<br />.0078
<br />.Ola,
<br />.01.56
<br />.0208
<br />.036D
<br />J6
<br />.6313
<br />.0117 .0521
<br />.0625
<br />_07!a-
<br />0721•
<br />1 ,
<br />2
<br />3
<br />4
<br />5
<br />7
<br />8 9
<br />10,
<br />11
<br />.0833
<br />.1667
<br />.2500
<br />.3333
<br />.4167
<br />.5000
<br />.5833
<br />.fi567 .7500 ,.8333
<br />.9167
<br />.7500
<br />55
<br />.9167
<br />6
<br />:1000
<br />16
<br />.2667
<br />26
<br />4333
<br />36
<br />.6000
<br />4G
<br />.7G67
<br />56
<br />.0333
<br />7
<br />.1167
<br />11
<br />.2833
<br />27
<br />.4500
<br />37
<br />.6167
<br />47
<br />.7533
<br />57
<br />.9500
<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 />19.3167
<br />29
<br />4533
<br />39
<br />.0500
<br />49
<br />.8167
<br />b0
<br />.9333
<br />10
<br />.16167
<br />20
<br />,3333
<br />g0
<br />.5000
<br />40
<br />rGG7
<br />50
<br />.8333
<br />60
<br />1.0000
<br />TABLE V. -
<br />inches in Decimals of a Foot.
<br />• ' 1-16
<br />1 2
<br />?/g
<br />3-lri
<br />/}
<br />:i -]G
<br />i3
<br />ig
<br />1.
<br />.0052
<br />.0078
<br />.Ola,
<br />.01.56
<br />.0208
<br />.036D
<br />J6
<br />.6313
<br />.0117 .0521
<br />.0625
<br />_07!a-
<br />0721•
<br />1 ,
<br />2
<br />3
<br />4
<br />5
<br />7
<br />8 9
<br />10,
<br />11
<br />.0833
<br />.1667
<br />.2500
<br />.3333
<br />.4167
<br />.5000
<br />.5833
<br />.fi567 .7500 ,.8333
<br />.9167
<br />
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