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VIII
<br />TASI M II. - Radii, Ordinates and Deflections. Chola -100 ft.
<br />Dec.
<br />Radius
<br />Mid.
<br />I Ord.
<br />Tan.
<br />Dist.
<br />Def.
<br />Dist.
<br />De'
<br />ifot•
<br />Deg.
<br />Radius
<br />Mid.
<br />Ord.
<br />Tan.
<br />Dist,
<br />Det.
<br />Dist.
<br />,Def.
<br />1[or
<br />toI. 15
<br />t.
<br />181.34 1° 59'
<br />2° 25'• 3° Io'
<br />3° 58'
<br />101.33
<br />34°
<br />t.
<br />it.
<br />ft.
<br />It.
<br />36°
<br />0'10'
<br />34377.
<br />.036
<br />.145
<br />.291'0.05
<br />153.58 2° 20'
<br />7°
<br />819.0
<br />1.528
<br />6.105
<br />12.2I
<br />2.10
<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 />30
<br />11459.
<br />.109
<br />'.436
<br />S73
<br />0.15
<br />30
<br />764.5
<br />1.637
<br />6.540
<br />13.08
<br />2.25
<br />.40
<br />859 4. 4
<br />.145
<br />.5S2
<br />1.464
<br />0.20
<br />40
<br />737.9
<br />1.673
<br />6.685
<br />13.37
<br />2.30
<br />-50
<br />6875.5
<br />.182
<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 />5720.6
<br />.218
<br />.873
<br />1.745
<br />0.30
<br />20
<br />688.2
<br />1.819
<br />7.266
<br />14.53
<br />2.;.0
<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 />14.83
<br />2.55
<br />20
<br />42197.3
<br />.291
<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 />303819.8
<br />.327
<br />1.309
<br />2.618.0.45
<br />9
<br />637.3
<br />1.965
<br />7.846
<br />15.09
<br />2.70
<br />40
<br />3137.0
<br />.304
<br />1.454
<br />_2.000
<br />0.50
<br />20
<br />614.6
<br />2.037
<br />8.136
<br />10-27
<br />2.S0
<br />50
<br />:312.1.4
<br />.400
<br />1.600
<br />3.2DO
<br />0.55
<br />30
<br />603.8
<br />2.074
<br />8.281
<br />10,56
<br />V. So
<br />2 •
<br />2864.9
<br />•436
<br />1.745
<br />3.400
<br />0.60
<br />40
<br />593.4'
<br />2.110
<br />6.426
<br />16.85
<br />2.90
<br />10
<br />.2G14.,,
<br />.173
<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 />2155.7
<br />.509
<br />2.036
<br />4.072
<br />0.70
<br />30
<br />516.4
<br />2.29'2
<br />9.150
<br />18.30
<br />3.15
<br />30
<br />2292.0
<br />.545
<br />2.181
<br />4.363.0.75
<br />11
<br />521.7
<br />2.402
<br />9.085
<br />19.16
<br />3.30
<br />40
<br />2148.8
<br />.5.92
<br />2.327
<br />4.653'0.80
<br />30
<br />489.1
<br />2.511
<br />10.02
<br />'20.04
<br />3.45
<br />50
<br />2022.4
<br />.618
<br />2.472
<br />4.045
<br />0.85
<br />12
<br />478.3
<br />2.620
<br />10.45
<br />20.91
<br />3.60.
<br />3
<br />1910.1
<br />.655
<br />2.618
<br />5.235
<br />0.90
<br />30
<br />439.3
<br />2.730
<br />10.89
<br />21.77
<br />3.75
<br />10
<br />1809.6
<br />.69
<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 />2:008
<br />5.817
<br />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 />64 108
<br />14
<br />410.3
<br />3.058
<br />12.18
<br />24.37
<br />4.20
<br />40
<br />1562.9
<br />.800
<br />3.199
<br />6.398
<br />1.10
<br />30
<br />396.2
<br />3.168
<br />12.112
<br />25.24
<br />4.35
<br />50
<br />1105.0
<br />.836
<br />3.345
<br />6.1189
<br />1.15
<br />10
<br />383'.1
<br />3,277
<br />13.05
<br />26.11
<br />4.50
<br />!
<br />1132.7
<br />'.873
<br />3.49.0
<br />6.980
<br />1-.20
<br />30
<br />370.8
<br />3.387
<br />13.49
<br />26.97
<br />4.65
<br />10
<br />1375.4
<br />.909
<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 />3.728
<br />7!561
<br />1.30
<br />30
<br />348.5
<br />3.606
<br />14.35
<br />28.70
<br />4.95
<br />30
<br />1273.6
<br />.982
<br />3.026
<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 />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 />50
<br />1185.8
<br />t.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 />1146.3'1.091
<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 />10
<br />1109.3
<br />1.127
<br />4.507
<br />9.014
<br />1.55
<br />21
<br />27.1.4
<br />4.594
<br />18.22
<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 />4.814
<br />19.08
<br />35.16
<br />6.60
<br />30
<br />1042.1
<br />1.20D
<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
<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 />50
<br />982.6
<br />1.273
<br />5.085
<br />10.18
<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 />5.234
<br />10.47
<br />1.80
<br />26
<br />222.3
<br />5.697
<br />22.50
<br />4.1.99
<br />7.811
<br />10
<br />929.6
<br />1.346
<br />5.379
<br />10.76
<br />1.85
<br />27
<br />214.2.018
<br />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 />2S
<br />266.7
<br />.139
<br />24.19
<br />48.38
<br />8.40
<br />30
<br />881.9
<br />1.418
<br />5.669
<br />11.34
<br />1.95
<br />29
<br />199.7,6.360
<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 />30
<br />193.2
<br />6.5S3
<br />25.88
<br />51.76
<br />9.00
<br />The middle ordinato in inches for any cord of length (C) is equal to 0412 C'
<br />multiplied by tho middle ordinate taken from the above table. Thus, if it
<br />Sesirod to bond a 30 ft. rail to fit a 10 degreo,curve, ite middle ordinate should
<br />be .U012X0WX2.183 ar 2.:36 inches.
<br />TABLE III. Defections for Sub Chords for Sli'ort,Radius Curves.
<br />Degree
<br />of
<br />Radius � sub chord
<br />50 R -sin of s' clef. angle
<br />length
<br />a arc
<br />Curve
<br />sin. }def.ang. t2,5 Ft.
<br />15 Ft. 20 Ft.
<br />25 Ft.
<br />for 100 ft.
<br />30°
<br />193.18 1° 51'
<br />2° 2 58'
<br />-3° 43'
<br />toI. 15
<br />32°
<br />181.34 1° 59'
<br />2° 25'• 3° Io'
<br />3° 58'
<br />101.33
<br />34°
<br />171.01 2°06'
<br />2° 33' 3° 2I'
<br />4° I2`
<br />1a[.48
<br />36°
<br />161. So 2° 13`
<br />z° 41' 3° 33'
<br />l° 26'
<br />iol .66
<br />380
<br />153.58 2° 20'
<br />2° 49' '3° 44'
<br />4° 40'
<br />1ol.8,5
<br />400 .
<br />146.ig 2° 27'
<br />2° 57' 3' 55'
<br />4° 54'
<br />1o2.o6
<br />4a°
<br />139.52 2' 34'
<br />3° 05' 4° 07'
<br />08
<br />102.29
<br />440
<br />133.47 2° 41'
<br />:3° 13' 4° 18'
<br />5° 22'
<br />102.53
<br />46°
<br />127.97 2° 48'
<br />3° 21' 4° 29'
<br />5° 36
<br />102.76
<br />48°
<br />122.92 2° 55'
<br />3° 29' 4° 40'-
<br />5° 50
<br />iO3.00
<br />50°
<br />II.8.31 3°42'
<br />3° 38' 4° 51'6°
<br />04'
<br />103-24
<br />52°
<br />i r4. n6 3° 09'
<br />3° 46' S° 02'
<br />6° 11'
<br />1113,14
<br />54°
<br />110.11 3° 16
<br />3° 54' 5° 13'
<br />6° 31`
<br />103. 84
<br />56°
<br />Io6.5o 3° 22'
<br />4° 02 5° 23'"
<br />6° 44'
<br />104 14
<br />58°
<br />103. t4 3° 29'
<br />4° 10' S° 34'
<br />6° 57'
<br />104.43 .
<br />6o°
<br />100.00 3°35'
<br />4° 18 5° 44'
<br />7° 11'
<br />` 104.72
<br />f
<br />Ix
<br />CURVE_ FORMULAS
<br />R tan ' 1 , I R = T cot. I. chord'
<br />,5o tan
<br />f. # Chord=def. = R
<br />` Sin. ? D 1� = 50
<br />Sin. i D = 5o Sin. I >J No. chords = I
<br />�. It E = k ex. sec I D
<br />Sin. 2' D = 5o tai I E = 7' tan I Tan. def. = z chord def.
<br />The square of any distance, divided by twice the radius, will equal
<br />a the distance from tangent to curve, very nearly.
<br />To find angle for a given distance and dcflcctiou. `
<br />Rule I. Multiply the given distance by .01745 (def+ for I° for i It.
<br />see Table II.), 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 defection for a given angle and distance. Multiply the angle
<br />by ..01745, and the product by the distance,
<br />GENERALDATA
<br />!tions AYGLE TRIANGLES. Square the altitude, divide by twice the
<br />base. Add quotient to base for hypotenuse..
<br />Given Base loo, Alt. Io.Wo 20o=.5. 100 --.5=rao.5 hyp.
<br />Given Hyp. ton, Alt. 25.25'=200=3.125. 100-3.125=96.875=11ase.
<br />Error in first example, .002:,in last, .045.
<br />To find Tons of bail in one mile of track: nudtiply weight per yaid
<br />by 11, and divide by 7.
<br />LEVELING. The correction for curvature and refraction, in fert-
<br />rnd decimals of feet is equal to 0.574d2, where d is the distance in'uliles.
<br />The correction for curvature alone is closely, dz. The combined cor-
<br />rection is negative.
<br />PROBABLE ERROR. If dl, dz, da, etc. are the discrepancies -of various
<br />results from the mean; and if Ede=the sum of the squares of these differ-
<br />ences and n=the number of observations, then the probable error of the
<br />mean = - dI
<br />-0.6745
<br />SOLAR EPnEMERls. Attention is called to the Solar Ephemeris for ,
<br />the current year, published by Keuffel & Esser Co_, and furnished upon
<br />request. This handy booklet, 38x61 in., has about 190 pages of data very
<br />useful to the Surveyor; such as the adjustments of transits, levels and solar
<br />attachments; directions and tables for determining the meridian and the
<br />latitude from observations on the sun and Polaris; stadia measurements;
<br />magnetic declination; arithmetic constants, etc.
<br />'FABLE IV. -Minutes in Decimals of a Degree.
<br />I'
<br />..0167
<br />11'
<br />.1833
<br />21'
<br />5500
<br />31'
<br />.5167
<br />41'
<br />.6833
<br />51'
<br />.8500
<br />' 2
<br />.0333
<br />12
<br />2000
<br />22
<br />.31167'
<br />- 32
<br />.5333
<br />42
<br />:7000
<br />52
<br />.8667
<br />3
<br />.0500
<br />13
<br />.2167
<br />23
<br />.3833
<br />33
<br />.5500
<br />43
<br />.7167
<br />53
<br />.8833
<br />4
<br />.0667
<br />14
<br />2333
<br />24
<br />.4000
<br />34
<br />.5667
<br />44
<br />.7333
<br />54
<br />.9000
<br />a
<br />.0833
<br />15
<br />2500
<br />25
<br />.4167
<br />35
<br />.3833
<br />45
<br />.7.50n
<br />55
<br />.9167
<br />6
<br />.1000
<br />16
<br />.2667
<br />26
<br />4333
<br />36
<br />.6000
<br />46
<br />.7667
<br />56
<br />.933.1
<br />7
<br />.1157'
<br />17
<br />.2833
<br />27
<br />.4500
<br />37
<br />.6167
<br />47
<br />.78:38
<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
<br />.3167
<br />29
<br />.4833
<br />39
<br />.6500
<br />49
<br />.8167
<br />59
<br />.q;Xi
<br />10
<br />1 .1667 11
<br />20
<br />1 x3333 11
<br />30
<br />1 .5000
<br />40
<br />1 .6667 11
<br />56
<br />1 .8333 11
<br />60
<br />11 -noon
<br />Tanr,i� V.- Inches in Decimals of a boor.
<br />1-16 3-32 ys 7-]6 1,q `-16 3g " 3e 34 `F
<br />0052- .0078 .0104 Al�i6 o? .0260 613 .0417 -0021 fH 25 0720
<br />3 1 :i ii 7 S 9 SL l]
<br />.0833 1fi1A .2600 ,:3330 .4{G7 .1000 ::3aa .6tiG7 .7500 . ci3i x!167
<br />
|