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VIII
<br />T"LE IL , Radii-, Ordinates and Deflections. Chord 100 ft. .
<br />Dag .
<br />Aadiue•
<br />Mid .
<br />Ord.
<br />Tan.
<br />Diet.
<br />Def.
<br />Dist.
<br />for.
<br />1 or.Ft-
<br />Deg.
<br />Radies
<br />Mid
<br />Ord...
<br />Tan
<br />Dist.
<br />Def.
<br />Dist.
<br />Def -
<br />] r t.
<br />- 193.18
<br />1° 51'2°
<br />. 17'
<br />z° 58'
<br />3° 43'
<br />101-15
<br />320
<br />181.39
<br />I°° 59'
<br />2° �5-
<br />3° 10
<br />3° 58'-
<br />0'10'
<br />34377.
<br />036
<br />.145
<br />'..291
<br />O°05
<br />7-
<br />819.0
<br />1.528
<br />.6.105
<br />1221
<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 />3D,
<br />11459.
<br />.109
<br />.430
<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
<br />,,145
<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 />1.404
<br />0.25
<br />a
<br />716.8
<br />1.146
<br />-6.976
<br />13.9.5
<br />2.4D
<br />1
<br />5729.6.218
<br />6-04 '
<br />.873
<br />1.745
<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..550
<br />15.11
<br />2.60
<br />30''
<br />3819.8,
<br />.327
<br />1.309
<br />2.618
<br />0.45'
<br />9 "
<br />637.3
<br />1:965
<br />7.840
<br />15:60
<br />2.70
<br />40
<br />3137.9
<br />.364
<br />1.454
<br />2.909
<br />0.50
<br />20
<br />614.6
<br />2.037
<br />A. 136:
<br />16.27
<br />2.80
<br />50
<br />3125.4
<br />.400
<br />1.600
<br />3-200
<br />0.55
<br />_
<br />,30
<br />603-8
<br />2.074
<br />,8:281
<br />16.56
<br />2.85
<br />2: -.
<br />2364.9
<br />.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 />2155.7
<br />.509
<br />2.036
<br />4:072
<br />0.70
<br />30
<br />546.4
<br />2.292,9.150
<br />18-30
<br />3.15
<br />30
<br />2292.0
<br />.545
<br />2.181
<br />1'.363
<br />0.75
<br />11
<br />521.7
<br />2.402
<br />0.585
<br />19.16
<br />3.30
<br />40
<br />2148.8
<br />.562
<br />2.327
<br />4.654
<br />0.80
<br />30
<br />499.1
<br />2.511'10.02
<br />20.04
<br />3.45
<br />50
<br />:2022.4'=.618
<br />2.472
<br />4.945
<br />0.85
<br />-
<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 />?0
<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 .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 />16.
<br />383:1
<br />3.277
<br />13-05
<br />26.11
<br />4.50
<br />s: -
<br />1132.7
<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
<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 />1322.5.946.3.718
<br />,7:561
<br />1.30
<br />- 30
<br />348.5
<br />.606.14.35.
<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 />:716
<br />14.78
<br />29:56
<br />5.10
<br />4D,
<br />1228.1-1.018
<br />4.071
<br />'8:143
<br />1:40
<br />.18
<br />319.&
<br />:035
<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 />•-1°55
<br />16.51
<br />33.01
<br />5.70
<br />8.
<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 />'•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 />20.: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 />1.287
<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 />982.6.1-273
<br />5.088
<br />10.18
<br />1:75
<br />E6
<br />231.0
<br />6.476
<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
<br />7.80
<br />10
<br />929.6
<br />1.346
<br />5.379
<br />10.76
<br />1:85
<br />1:7
<br />214.2.918
<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 />.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 mlaate orawaten inches for any cord of length (0) is equal to .0012 C'
<br />multiplied by tho ]riddle ordinate, taken from the above table. Thus. if it
<br />desired to benda 30 ft. rail to fit 10 degree curve, its middle ordinate shoald
<br />be .0012X900X2.183 or 2.36 inches. ;
<br />TABLE HL Deflections for Sub Chorda for Short Radius Curves.
<br />Degree
<br />of
<br />Radius
<br />59
<br />- sub chord t
<br />R = sin of z def. angle
<br />Length
<br />- of arc
<br />Curve
<br />On. 'r dd. ang.
<br />12.5 Ft.
<br />15 Ft.
<br />20 Ft.
<br />25 Ft.
<br />for 100 ft.
<br />30°
<br />- 193.18
<br />1° 51'2°
<br />. 17'
<br />z° 58'
<br />3° 43'
<br />101-15
<br />320
<br />181.39
<br />I°° 59'
<br />2° �5-
<br />3° 10
<br />3° 58'-
<br />101.33
<br />34°
<br />171.01
<br />2 o6'
<br />2° 33'
<br />3° 2I`
<br />4° 12'
<br />lol', 48
<br />36°
<br />161.8o
<br />2° 13'
<br />2! 41'
<br />3° 33
<br />4° 26'
<br />ioi .66
<br />38°
<br />153.58
<br />20-20'
<br />2' 49
<br />3° 44
<br />4° 40
<br />101.85
<br />406,_
<br />146.i4'
<br />2° 27'
<br />2° 57'3°.55'
<br />15
<br />4° 54'
<br />102°06
<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 />2° 41
<br />3°. 13'
<br />4° 180•
<br />5° 22'
<br />io2.53
<br />46.0
<br />127.97
<br />2° 48'
<br />3° 21'
<br />,t° 29'
<br />5° 36'
<br />102.76
<br />48°
<br />122-9z
<br />2° 55'
<br />3° 29'
<br />4° 40'
<br />5° 50'-
<br />-103.00
<br />50°
<br />11:8.31
<br />3° 02'
<br />3- 38
<br />4° 51,'
<br />6-04 '
<br />I03 , 24
<br />52°
<br />11.4.06
<br />3°'09` .
<br />3° 46'
<br />S° 02,
<br />60 17'
<br />103.54
<br />54°
<br />110.11
<br />3° 16''
<br />3° 54'
<br />5° 13'
<br />60 3i'
<br />163. 84
<br />560
<br />106.5o
<br />3° 22'
<br />4° 02'
<br />S ° 23'
<br />60 44'
<br />1'04.14
<br />593-14
<br />20
<br />3°29'
<br />4° 10'
<br />5° 34'
<br />60 57'
<br />104.43
<br />600
<br />100.00
<br />3°35'
<br />4° i8'
<br />5° 44'
<br />7° i1'
<br />104.72
<br />NZ
<br />CURVE FORMULAS
<br />T = EZ tan a i . R•T cot. ' 1 'chorda
<br />.1. ='So tan z I Chord def. _
<br />Sin. z U I1 = '50 k'•
<br />Sin. -In D- = So ; Sin. $ D No. chords = 'I
<br />IZ t E ="R ex° sec ; I D
<br />Sin. ; p = 50 t 7 I E. _ `I tan } I Tan. def. = ; chord def.
<br />The square of any distance, divided by twice the radius, will equal
<br />the distance from tangent to curve, very nearly. •i
<br />To find angle for a given distance'and deflection.
<br />Rule t. Multiply the given distance by .017}45 (clef: for i °. for i, -ft:
<br />see Table II.), and divide given deflection by Che product.
<br />Rule 2: Multiply given deflection by 57.3, and divide.the•product by
<br />thegiven 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 TizIANIiLES. Square the altitude,. divide by twice the
<br />base.,- Add quotient to base for hypotenuse. 4
<br />Given. Base loo, Alt. io.iol-Zoo=.5.4.6b+'5=ioo.5 hyp. .
<br />Given Hyp. too, Alt. 25.255 --a00 =3.125°,100-3:125=q6°875=Base.
<br />Error in first example, .002; in ,last, :045. I
<br />.To find Tons of Rail in one mile; of track: multiply .weight per yard
<br />lay i i, and divide by 7.
<br />LEVELING. The . correction- for -curvature and: refraction, in feet
<br />and decimals of feet is equal to` 0.574d', where: d-isthe distance in miles.
<br />The correction for, curvature alone is closely, d 1. The : combilied: _cor-
<br />rectinn is negative. .
<br />,PROBABLE. ERROR. If-d�, d2, de, 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= Ed 2
<br />f0.fi745 n(n-1)
<br />SOLAR EPHEMERIS. • 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, 3$x6 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 />TABLE W. -Minutes in Decimals of a Deirree.
<br />It
<br />.0167
<br />11'
<br />.1833
<br />21f
<br />.3500
<br />31/
<br />.5167'
<br />411
<br />.6833
<br />51'
<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 />.2187
<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 />S.
<br />0833
<br />15
<br />.2500
<br />25
<br />.4167
<br />35
<br />-5833
<br />45
<br />.7500
<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 />.9333
<br />7
<br />.1167
<br />17
<br />.2833
<br />27
<br />.4500
<br />37
<br />.6167
<br />X47
<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 />3000
<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 />69
<br />.9333
<br />1'0 J
<br />.1667
<br />20
<br />.3333
<br />30
<br />.5000
<br />40
<br />.6667
<br />50
<br />.8333
<br />60
<br />1.0000
<br />T:kat-E V.---fnches
<br />in Decimals of a Foor.
<br />1-I6
<br />3-32yg
<br />3-16
<br />ii
<br />5-16
<br />1.1
<br />3a
<br />%
<br />,
<br />.0052
<br />.0078
<br />.01'0.1
<br />.0156'
<br />-0208
<br />l
<br />-0260
<br />..0313
<br />.0117
<br />.0-521
<br />.06'_'-1
<br />.0729
<br />1
<br />l
<br />3
<br />I
<br />4
<br />i
<br />6
<br />7
<br />8
<br />9
<br />10
<br />1.1
<br />.0833
<br />.1667
<br />.2500
<br />.3333L
<br />.5167
<br />.:;UUO
<br />.:183:3
<br />.r.667
<br />.7500
<br />.8333
<br />
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