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®YIY -
<br />TABrz IL,- Radii, Ordinates and Deflections, Chord 100 ft.
<br />Deg.
<br />.Radius
<br />Mid
<br />Ord:
<br />Tan.
<br />Dist,
<br />Def.
<br />Dist.
<br />Dor ,
<br />1Ft.
<br />..Deg.
<br />Radius
<br />Mid.
<br />Ord.
<br />Tan
<br />.Dist.
<br />Def.
<br />Dist.
<br />Def.
<br />for
<br />° ,
<br />?. 17
<br />t. - _
<br />t. -
<br />t.
<br />ft.
<br />!
<br />1° 59'
<br />it.
<br />ft.,
<br />ft,
<br />ft.
<br />i
<br />0"`.10!
<br />34377.
<br />036
<br />•.145
<br />,291
<br />0.05',
<br />'7"
<br />819.0
<br />1•:528
<br />6.105
<br />12.21
<br />2.10
<br />20
<br />17189.'
<br />,073
<br />.291
<br />.582
<br />0.10
<br />20'
<br />781.8.1.600
<br />-
<br />40146.19:'
<br />,6.395
<br />12.79
<br />2.20
<br />= 30
<br />11459.
<br />7.109
<br />.436
<br />,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° 1$'
<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 />1.454
<br />0.25
<br />8
<br />716.8
<br />1:746
<br />6:976
<br />13.95
<br />2.40
<br />fl '
<br />5729.6-,218
<br />52°
<br />.873
<br />1.745
<br />0.30
<br />20'
<br />688:2
<br />1:819
<br />54°
<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 />,7.266
<br />1.411
<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 />:.3271:309
<br />`2:618
<br />0.45
<br />'9 -
<br />637:3
<br />1':965
<br />.7.846
<br />15.69
<br />2.70
<br />`•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 />2,80
<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 />2.85
<br />8 "
<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
<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 />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 />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 />14.654
<br />0.80;
<br />30
<br />499.1
<br />2.511
<br />10.02
<br />20.04
<br />3.45
<br />50,
<br />20224
<br />_618
<br />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 />8
<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
<br />3.75
<br />10'.1809.6
<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 />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 />80
<br />1637.3
<br />'..764
<br />3.0541
<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 />15383.1
<br />3.277.
<br />13.05
<br />26.11
<br />4.50
<br />a, '
<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 />10
<br />1375.4.909,3.635
<br />7.271
<br />1.25
<br />16:
<br />359.3
<br />3:496
<br />13.92.
<br />27.84
<br />4.80
<br />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
<br />29.56'5.10
<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 />31.29.5.40
<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.-1109:3
<br />1.227
<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"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 />38.16
<br />6.60
<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
<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 />5.088
<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"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 />- 10'
<br />.929.6
<br />1.346
<br />5:37$
<br />10:76
<br />1.85
<br />27
<br />214.2
<br />5.918
<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 />28';
<br />206.7
<br />6.139
<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
<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 middle ordinate in'inches for any cord of length (C) is equal to .0012 C'
<br />multiplied by the middle iordinate' taken from the above table. Thus, 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.: j
<br />TABLE III. ' Deflections'for Sub Chords for Short Radius Curves.
<br />Degree
<br />of
<br />Curve
<br />Radius
<br />56
<br />j f sub:chord
<br />R = sin of $ def. angle '
<br />Length
<br />of arc
<br />for 100 ft.
<br />sin. I def. ang.
<br />12.5 Ft.
<br />15 Ft.
<br />20 Ft. ':
<br />25 Ft.
<br />o
<br />30 -
<br />193.18
<br />° • ,
<br />_ z 51
<br />° ,
<br />?. 17
<br />o , ,
<br />_2 58 ,'
<br />° ,
<br />__3 -43
<br />101.15
<br />3a°
<br />181,39
<br />1° 59'
<br />z° 25'
<br />3° lo'
<br />3° 58'
<br />101.33
<br />34°
<br />191,01
<br />2° 06'
<br />I
<br />20 33'
<br />3° 21'
<br />4° 12'
<br />101.48
<br />360
<br />161:86_ :.
<br />2' 13'
<br />2° 41' _`
<br />30.33'
<br />4' 26'
<br />Ioz.66
<br />380--
<br />- ?53 58__.
<br />2° 20,-.,
<br />`?0 49'_
<br />-.3° 44'- -
<br />4° 40'
<br />IOI.85
<br />-
<br />40146.19:'
<br />-
<br />o r`
<br />a 27
<br />o ,
<br />z 57�'
<br />o;
<br />3 55.
<br />4 54
<br />IO2.o6
<br />4:2
<br />- 139.52..
<br />2° 34'-
<br />3° 05'
<br />4°.07'-
<br />5° o8'
<br />102.29
<br />44°
<br />133.47.
<br />''2°.41�� .
<br />3° 13''.
<br />4° 1$'
<br />5° 22'
<br />102.53
<br />46?. •
<br />- ,129.97
<br />2° 48!
<br />30 21,..:
<br />4° 29'.
<br />.. -5° 36'
<br />102.76
<br />48° .
<br />.122.92:
<br />2°'55'
<br />','3' �9'
<br />4° 40,
<br />5° 50'
<br />103.00
<br />50'
<br />- 118.31.
<br />3° 02'
<br />3° 38'
<br />4° 51,
<br />6° 04,
<br />Io3.24
<br />52°
<br />i14.06
<br />3° 09'
<br />- 3° 46'
<br />5° o2'
<br />6° 17'
<br />103.54
<br />54°
<br />I IQ. II
<br />3° 16' _
<br />: 3° 54'
<br />5' �3'
<br />60 31�
<br />103.84
<br />56°
<br />106.50
<br />3°22'
<br />'Ao oz'
<br />5°23'
<br />6°44'
<br />104,14
<br />58°
<br />103:14 '
<br />_ 3° z9'
<br />4° Io'.
<br />5° 34'
<br />6° 5T
<br />104.43
<br />60°
<br />Ioo.00
<br />3° 35
<br />4° 18'
<br />S° 44'
<br />9° ii'
<br />104.72
<br />: CURVE "FORMULAS
<br />T o tan � I R= T cot. l I Chord def. = chord2
<br />Z .= 5 r 50 R
<br />Sin. 1) .. _ _. R. _ a
<br />Sin. D_ = 50 i Sin. s D No. chords = I
<br />R '" E =. R ex, sec z I �•
<br />5o tan I I
<br />Sin. j D T E= T tan I I Tan. def. = a chord def..
<br />The.square of any distance, divided by twice the radius, will equal
<br />the distance from tangent to curve, very nearly.
<br />To find angle for given'distance and deflection.
<br />Rule 1. r Multiply.' the given distance by .01745 (def. for I° for i ft.
<br />see Table II.),` and divide given deflection by the product.
<br />_
<br />Rule 2. Multiply given -deflection by 57,3; and divide the product by
<br />the given distance:
<br />To find deflection for' a' given angle and distance. Multiply the angle
<br />by .01745, and the product by the distance.
<br />GENERACDATA
<br />RIGHT ANGLE TRIANGLES. Square the altitude, divide by twice, the
<br />base. Add quotient to base'for hypotenuse. "
<br />Given Base loo; Alt. lo.i62 200=.5..1 +.5=100.5 hyp.
<br />.Given Hyp. ioo, Alt. 25.25$-200=3.125. 106-3-125=96.875 =Base.
<br />.Error in first example, .o62; in last, ..o45,. ,
<br />To find Tons .of, Rail` in one, mile of track: multiply weight per yard
<br />by II and,divide by 7.
<br />LEVELING. The correction for curvature and refraction, in 'feet
<br />and decimals of feet is equal to 0.574 da, where d is the. distance in miles.
<br />The correction for curvature alone is closely, *dac The combined cor-
<br />rection is negative."
<br />PROBABLE ERROR. If. d,, de; d8, etc: are- the discrepancies of various
<br />results from the mean; -and if.Ida=the sum of the squares of these dWor-
<br />ences and n=the number of observations, then the probable error of the.
<br />mean=- 0.6745. Xds
<br />n (n-1)
<br />SOLAR EpnEmFRls. Attention is called to the Solar Ephemeras ,for,
<br />the *current year, published by.Keuffel & Esser Co.; and furnished free of
<br />charge upon request, which is 3jx58 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 f ormulas;;Natural andLogarithmic F tinction;
<br />and Logarithms of Numbers::
<br />TABLE IV. _ Minutes in Decimals of a Degree. _
<br />1' .0167' IV- •1833 211-, -.3500 31' .5167 41' .6833 51' .8500
<br />2 .0333 12 , ;2000 22 .3667 32 .5333 42 .7000 52, .8667
<br />b .0500 13 ,2167 23 .3833 33 .5500 43 .7167 53 .8833
<br />.4 .0667- 14. ,2333 24 .4000 34 .5667 44 .7333 54 .9000
<br />5 ':0833 15 ,2500, 25 .4167 35 .5833 45 .7500 55 .9167
<br />6 .1000 16 .2667 26'' .4333 36 .6000 46 .7667 56 .9333
<br />7 .1167• 17 .2833• 27 .4500 37 '.6167 47 .7833 57 .9500
<br />8 .1333 18 .3000 28 .4667 38 .6333 48 .8000 58 .9667
<br />10 ,1500 19 3167 29 -4833 39 .6500 49 .8167 59 ,9833
<br />1667 20 ' .3333 30 .5000 40 .6667 50 .8333 60 1.0000
<br />- TABLE -V.-= Inches in Decimals of- a Foot.
<br />716 3-32 Y8 3-18 1 y 5-16 % q % Y. 31
<br />0052 •,0078 .,0 04 -•.0156' .0208 .0260 '.0313 :0417 .0521 '.0625 ,0729
<br />•0833 .1667 .2500 :3333 .4167- .5000 1 .5833 1 .6667 .7500 .8333 .9167
<br />
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