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VIII - -
<br />TABLE IL -Radii, Ordinates and Deflections. Ch6id_=100 ft.
<br />;Deg.'
<br />Radius
<br />Mid
<br />Ord
<br />Tan.
<br />Def.
<br />Dist.
<br />f.
<br />Dor
<br />1 Ft
<br />Deg
<br />Radius
<br />Mid.
<br />-Ord.
<br />Tan„
<br />Dist.
<br />Def.
<br />Dist:
<br />Dor•
<br />:Dist.
<br />7 Ft.
<br />2° 17'
<br />2° 58':
<br />30 43'
<br />!01.15
<br />_320.. _
<br />-..-_181.39
<br />_ !°..591
<br />t.
<br />t.
<br />t.
<br />t.
<br />34°
<br />0°101
<br />34377.=-
<br />.038
<br />;145
<br />;231
<br />0.05
<br />7'
<br />819.0
<br />1:528
<br />6:10512.21
<br />3°33'
<br />2:10
<br />20
<br />17189.
<br />.073
<br />.291
<br />:582
<br />0.10
<br />20'
<br />781.81:600
<br />0.. --....
<br />40..-
<br />6.395
<br />12.79
<br />2.20
<br />30.
<br />11459.
<br />.109
<br />.436;
<br />1.873
<br />0.15
<br />30
<br />764.5
<br />1.637
<br />6.540
<br />13.08
<br />2.25
<br />:=•40'
<br />8594.4'•'.145
<br />4° 18'
<br />.582
<br />'1.164
<br />0.20''
<br />40
<br />747.9
<br />1:673
<br />6:685
<br />•13.37
<br />2.30
<br />-50'
<br />6875.5.
<br />.182
<br />.727
<br />4.454
<br />0.25
<br />8 "
<br />716.8
<br />1:746
<br />.6.976`13.95
<br />3. 38
<br />2.40
<br />1 -
<br />5729.6
<br />•.218
<br />.873,'-1.745
<br />3°,091
<br />0.30
<br />20
<br />688.2
<br />1.819
<br />7.266
<br />14.53
<br />2.50
<br />10
<br />4911.2
<br />.255
<br />1.018
<br />2.036
<br />0.35
<br />30
<br />674.7
<br />1.855
<br />7.411
<br />14.82
<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 />1.892
<br />7.556
<br />15.11
<br />2.60
<br />30
<br />3819.8
<br />•.327
<br />1`.300':2:618
<br />0.45.
<br />` 9
<br />637.3
<br />1.965
<br />7:846.15.69
<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°16.27
<br />2.80
<br />50
<br />3125.'4,,.400
<br />1.600
<br />3.2000
<br />.55
<br />30
<br />603.8
<br />2.074
<br />8.281'16.56
<br />2.85
<br />2
<br />2864.9,'.436
<br />1.745
<br />3.490
<br />0.60
<br />40:
<br />593:4
<br />2.110
<br />8:426.16.85
<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 />" 20
<br />2455.7.
<br />.509
<br />2.036
<br />4c 072
<br />0.70
<br />30'
<br />546.4
<br />2.292
<br />9:1.50
<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 />9.585
<br />19.16
<br />3.30
<br />,.40..
<br />2148.8
<br />:582
<br />2.327
<br />4:654
<br />0.80.
<br />- 30
<br />499.1
<br />2.511
<br />10.02:
<br />201,04
<br />3.45
<br />50
<br />2022.4'-.618
<br />2.472
<br />_4:945
<br />0.85
<br />12
<br />478.3 ,2:620
<br />10.4 5
<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 />459.32:730
<br />10.89
<br />21.77.3.75
<br />10
<br />1809.6
<br />•.691
<br />2.763
<br />5.526
<br />0.95
<br />13.
<br />441.7
<br />2.839
<br />11.327,
<br />22.64
<br />3.90
<br />20
<br />1719.1
<br />;.727
<br />2.908
<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 />6.108
<br />1.05
<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 />12.62
<br />25.24
<br />4.35
<br />50.
<br />1495.0
<br />:836
<br />3.345
<br />6.689
<br />1.15
<br />15,
<br />383.1
<br />3.277
<br />13.05
<br />26:11
<br />4.50
<br />S
<br />1432.7
<br />.873
<br />3_1.490
<br />6.980
<br />1.20
<br />30
<br />370.8
<br />3.387
<br />13.49
<br />26.97
<br />4.65
<br />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 />27:84'4.80
<br />20
<br />1322.5
<br />_.945
<br />3.718'
<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 />3.926
<br />7.852
<br />1.35'
<br />17
<br />338.3
<br />3.716
<br />14.78-;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 />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 />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 />274.4
<br />4.594
<br />18.22 .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 />1.814
<br />19.08
<br />38:16
<br />6.60
<br />30 "
<br />1042.1
<br />1.200.4.798
<br />-9.596
<br />1.65
<br />23
<br />250.8
<br />5:035
<br />19..94.-39:87
<br />6.90
<br />.', 40,
<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 />_1011.5
<br />982.6
<br />1'.273
<br />6.088
<br />10.18
<br />1.75
<br />25
<br />231.0
<br />5.476
<br />21:64
<br />43.28
<br />7:50
<br />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 />44.99:7.80
<br />10
<br />929.6
<br />1.346
<br />5.379,
<br />10.76
<br />1.85 '-27
<br />214.2
<br />:918
<br />23.35 '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 />.139
<br />24.19
<br />48.38
<br />8.40
<br />30
<br />$81.9
<br />1.418
<br />b.869
<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 />30
<br />193.2
<br />6.583
<br />25.88
<br />51:76
<br />9.00
<br />The
<br />inultiulied
<br />middle ordinate
<br />by the middle'ordinate
<br />ll'n inches for any cord.of length (0) is sq mal to .0012 C'
<br />taken from the ahnve to hla- ' Thnp: if it
<br />desired to bends 30ft. rail to fit 10 degree curve, its middle.ordina,te should
<br />be .0012X900X2.183 or 2.36 inches..
<br />TABLE III. a Deflections'for Sub Chords for Short Radius Curves.
<br />Degree
<br />of
<br />Curve
<br />Radius
<br />50
<br />V2 sub chord ,
<br />R = sin of a def. angle -
<br />Length
<br />of arc
<br />for 100 ft.
<br />sin. i def. ang.
<br />12.51 Ft.
<br />15 Ft:
<br />20 Ft. '
<br />25 Ft.
<br />300
<br />193.181°511
<br />.8500
<br />2° 17'
<br />2° 58':
<br />30 43'
<br />!01.15
<br />_320.. _
<br />-..-_181.39
<br />_ !°..591
<br />20 ?5r_
<br />..3° 101.
<br />30.58,.
<br />101.33
<br />34°
<br />171.01
<br />2°'06'
<br />2° 331
<br />3°.211
<br />4° 12'
<br />101.48
<br />360
<br />161:80,;.--
<br />2°131,
<br />2°-411.
<br />3°33'
<br />4'26'
<br />1ol.66
<br />380
<br />153, 58
<br />20 20'
<br />2° 49'
<br />3° 44'
<br />40 40'
<br />101.8,5
<br />0.. --....
<br />40..-
<br />?46.19
<br />o ' --
<br />2 27
<br />" 1 -
<br />?:57
<br />o 1
<br />3 55
<br />0
<br />4.54
<br />102,06 `
<br />42°
<br />139; 52
<br />'-° 34' ..
<br />30 05'
<br />4° 07'
<br />5° o8
<br />102.29.
<br />-44°
<br />133.47•
<br />2° 41:
<br />3° 13'
<br />4° 18'
<br />S° 22'
<br />102.53
<br />'460 ''
<br />127 97::
<br />20 48'
<br />30.21'
<br />4 29�
<br />50 36'.
<br />16_2,:76
<br />;480'
<br />iz2:92
<br />20 55',.
<br />3° 29 ...
<br />40 49
<br />50-50
<br />-103.00,.
<br />600..a
<br />"' 118:3!
<br />3 _02
<br />3. 38
<br />4 51
<br />6 04
<br />!03.24
<br />520
<br />1�4' 06..,
<br />3°,091
<br />" 3o 46'
<br />50 0i':, '
<br />_ '6° 17'
<br />103.54
<br />54°�;
<br />-110- � I.,
<br />3°_16' ..
<br />3°.54';'
<br />50 131
<br />60 311
<br />103.84
<br />56 7
<br />. !06.50
<br />.`3°.22'
<br />4°:O2.
<br />5° 23'
<br />6° 44'
<br />104'. 14
<br />580
<br />100.60
<br />3a-29'
<br />4o'!8,lo,
<br />.3333
<br />30
<br />.5000
<br />60:'
<br />,100.00
<br />3 35 -
<br />� 4.
<br />5° 441
<br />7° 1I'
<br />404. 72
<br />y
<br />IX
<br />CURVE FORMULAS
<br />T __ 56_ tan 1:1 R = T cot. ; I Chord def. chord'
<br />1:
<br />T_ S Z p R '50 R .
<br />t
<br />Sin. 12 D = R Sin. , D No. chords I
<br />,:.. K' E R ex: sec z. I D
<br />Sm. D = 56_ tan z I- E _ _T tan } 1 Tan. def. = !chord def.
<br />T .•
<br />- The -square 'of 'any -distance, divided by twice the radius, will equal
<br />the distance from tangent to curve; very nearly.
<br />To find angle for 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 5y-3, and divide the product by
<br />the given -distance.
<br />To find deflection fora given angle and distance. Multiply the angle
<br />by, bi-745;•and the product by the distance.
<br />GENERAL DATA
<br />RIGHT'ANGLE TRIANGLES. Square the altitude,. divide by twicethe
<br />base. Add quotient to base for hypotenuse.
<br />Given-BaseYoo; Alt.'Io.Io2-Zoo=.S._Ioo+.5=1oo.5 hyp.' ..
<br />Given. Hy,P.
<br />>oo, Alt. 25.252=260-3.125. 100-3.125=86.875=Base.
<br />Error in first example, .002; in last, .045:
<br />To find Tons of Rail in one ,dile of track:, multiply weight per yard
<br />by i't,`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'coriection for -curvature alone is closely, ,;d2. The combined cor-
<br />reciion ie'negative. '
<br />:.- BABLE:ERROR. If dt;�dz, d2, `etc. atethediscrepancies of various _
<br />'results-from'the mean, and,if"Ed2=the sum -of the squares. of these differ -
<br />.i s' it=the number of"observafions,:'then the -probable error of the
<br />mean=
<br />`t0 6745 n(n-1)
<br />.-SOLAR- EPHEMERIS. Attention is called to the Solar' Ephemeris for
<br />the
<br />-current -year, published. by Keuffel & Esser Co., and furnished upon
<br />,request.; .This handy booklet, 38x6 in., has about 190'pages of data very
<br />usefol-to the: Surveyor; such as the adjustments of transits, levels and solar
<br />attachments; -directions and table's. for 'determining..the meridian and the
<br />'latitude from observations on the sun and Polaris;, stadia measurements;
<br />magnetic declination; 'arithmetic constants; etc.
<br />TABLE IV. -Minutes; in Decimals of a Degree.
<br />" 11"
<br />.0167"
<br />111
<br />.1833 '
<br />' 211
<br />.3500
<br />"311'
<br />.5167
<br />411
<br />.6833
<br />511
<br />.8500
<br />2,
<br />.0333
<br />12
<br />.2000
<br />22
<br />.3667
<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 />5 '
<br />'.0833
<br />15
<br />.2500
<br />25
<br />.4167
<br />35
<br />:5833
<br />45
<br />.7500
<br />55
<br />.9167
<br />61
<br />.1000
<br />16
<br />.2667
<br />26'
<br />-.4333
<br />36
<br />.6000
<br />46
<br />.7667
<br />56
<br />.9333
<br />7.
<br />:.1167
<br />17
<br />.2833
<br />27 ,
<br />.4500
<br />37
<br />'.6167
<br />47.
<br />.7833
<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 />'.9833
<br />10
<br />:1667
<br />20
<br />.3333
<br />30
<br />.5000
<br />40
<br />.6667
<br />50
<br />.8333
<br />60
<br />1.0000
<br />TABLE V. -Inches in Decimals of a Foot.
<br />1-16 3-32 jj 3-16 '/s 5-16 Y2 % % 14
<br />.0052 .0078 .0104 .0156 .0208 .0260 .0313 .0417 .0521 .0625 .0729
<br />1 11
<br />.0833. 1667 .2:100 (.3333 .4167 I .5000 I .5833 I .6667 I .7900 .8333 .9167
<br />
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