|
VIII `�._. l ` .. , ♦ > P, .- h J'� - . a , i� ..... '" _
<br />TABLir1 IL Radii, Orliinatee anal Deflections Chord 100 ft.
<br />Deg:`-'Rdius`
<br />' Radius.
<br />+ 50 '
<br />Mid
<br />Ord.
<br />Tan.
<br />Dist:
<br />'Def.-
<br />DU
<br />_Dc
<br />for..
<br />ITt
<br />`-Deg.
<br />Radms
<br />hiid
<br />Oid.'
<br />Tan ,;
<br />Dist.
<br />Def.
<br />Dist.
<br />Def.
<br />for
<br />1 Ft.
<br />01,10',34377``
<br />2' 58' l
<br />:036
<br />x145
<br />j .231''0.051
<br />-193.
<br />i81.39
<br />.:7°,
<br />t,
<br />819:0
<br />ft.
<br />1'.52$
<br />it.
<br />6:105
<br />it,
<br />12.21
<br />2.10
<br />20.
<br />17189
<br />:073
<br />.291,.-582'0
<br />q° 12'
<br />l0
<br />20'
<br />781.8
<br />1..600
<br />6.395
<br />12:79
<br />2.20
<br />30:
<br />r40
<br />11459
<br />'-8594.4
<br />.169
<br />, .436
<br />1{ '; 873
<br />0 15
<br />30
<br />764.5,1'.637
<br />40° t
<br />'6.540
<br />13.08
<br />2.25
<br />-
<br />3°755' '
<br />-4°40_
<br />.-4°.5 f"
<br />':145
<br />, .582
<br />41,164
<br />4 20
<br />40'
<br />747.9
<br />1.673
<br />6.685
<br />13.37
<br />2.50
<br />501
<br />' 6875 5
<br />-.1S2
<br />:.727
<br />i 1.454
<br />0 2
<br />8
<br />716 8'
<br />1:746
<br />s 6,976
<br />13.95
<br />2.40
<br />1'
<br />5729,6
<br />- .218
<br />.873
<br />'1.745
<br />0: 31)
<br />F!'' 20
<br />688.5
<br />1:819
<br />17.266
<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;1,855
<br />103.54
<br />7.411
<br />14.82
<br />2.,5
<br />20,
<br />4297.3
<br />:291
<br />1.164
<br />"2.327
<br />0:401
<br />,.1'40'
<br />661:7
<br />1.592
<br />7.556
<br />15.11
<br />2.60
<br />30,•3819.8,,.327'1.309
<br />3° 29
<br />4° lo'
<br />5° 34'
<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 />,3137.9
<br />.:.364
<br />1.454
<br />'2.9D0
<br />0.50
<br />20
<br />614.6"2.037
<br />'8:130
<br />16.27
<br />2.80
<br />50
<br />.3125.4
<br />•.400,1.600
<br />;3.200
<br />0.55
<br />30
<br />603,8'2.074
<br />'8.281.16,56
<br />2.85
<br />• 2864.9
<br />'
<br />:.436
<br />1:745
<br />'3.400
<br />0 ,60,
<br />40
<br />533,.4
<br />2.'110
<br />"S: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 />573.712.183..8.716
<br />17.43
<br />3.00
<br />20
<br />2155:7
<br />.500
<br />2.036
<br />"4.072
<br />0',70'
<br />' 30
<br />5-16.4'2:292
<br />`9.150
<br />18.30
<br />S.15
<br />30
<br />2292.0
<br />.545
<br />2.181
<br />14.363
<br />0(75
<br />11
<br />521.7'2.402
<br />9.585
<br />19.ifi
<br />3.3o
<br />f40::2148.8
<br />-:5132
<br />2.327
<br />4.654
<br />0.80
<br />30
<br />499.21'2.511,
<br />10.02 '
<br />20.04
<br />3.45
<br />'50
<br />:2022.4.
<br />.618
<br />2.472
<br />4,945.0.85.1.13
<br />47S.32
<br />620
<br />1045.:20.01
<br />3.60
<br />8:-'..
<br />1910.1
<br />.6:15
<br />2.618
<br />•5,235
<br />0.90
<br />30
<br />459.3'2730
<br />ID. -SO
<br />21.77
<br />3.75
<br />'10
<br />.1809.6
<br />;691
<br />2.703
<br />• 5'.520
<br />0 95 1
<br />'•13
<br />441.71
<br />2.939
<br />11:32
<br />22.64
<br />3.90
<br />1 20
<br />1719.1
<br />.727
<br />2.908
<br />15.817:1.00.
<br />i7' 30
<br />425.4
<br />2.949;
<br />11.75
<br />23. a1
<br />4.05
<br />30'
<br />'1637.3
<br />::764
<br />3.054
<br />16.,108
<br />105.
<br />14
<br />410.3
<br />3,,058
<br />12,-lS_+
<br />24.37
<br />4.20
<br />40
<br />1562.9
<br />.800
<br />3.199
<br />16,398
<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 />10.689,
<br />1.15,
<br />15
<br />353.1
<br />3.277
<br />13.05
<br />26.1`1
<br />4.50
<br />4.'
<br />1452 7
<br />,:873
<br />3,'490
<br />6 280
<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 />3.035
<br />7.271'
<br />1 2516
<br />359.3'3.496
<br />13.92.
<br />27.84
<br />4.SO
<br />20,
<br />1322.5
<br />,045
<br />3.718
<br />{7.501'
<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 />3.920
<br />7.852
<br />1.35
<br />17
<br />338.3
<br />3:715
<br />14.78
<br />29..56'5.10
<br />40
<br />1228.1
<br />1:DIS
<br />4.071
<br />;8: 143
<br />,
<br />1:40
<br />.
<br />18
<br />819.6'3.935'15.64
<br />31.29
<br />5.40
<br />,so
<br />1185.8
<br />1.055
<br />4.217.
<br />8:433
<br />1.45 1
<br />"19 '
<br />302.0
<br />4:155
<br />16:51,
<br />33.01
<br />5.70
<br />5
<br />1146.3
<br />1.001
<br />4.362
<br />18.724
<br />1:50
<br />20
<br />287.0'4.374
<br />17..37-
<br />34.73
<br />6.00
<br />10
<br />•.1100.3
<br />1.127
<br />4.507
<br />9.014
<br />1.55",21
<br />274:4
<br />4.594
<br />18.22.
<br />36.44
<br />6.30
<br />20
<br />c-1074.7
<br />1.164
<br />4.653
<br />;9.305.1.60',22
<br />262.0''4.814
<br />19.08 `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 />250:8'5.035
<br />1.9.94"
<br />39.87
<br />6.90
<br />40
<br />X1011.5
<br />1-.237
<br />4.943
<br />9.886
<br />1.70
<br />'24 '
<br />240.5;5.255
<br />20.79-.41.58
<br />7.20
<br />50-
<br />' 982.6
<br />3.273
<br />5.088
<br />10.18
<br />1.75
<br />25
<br />231.0,
<br />5.476,
<br />2164 :43.28
<br />7.50
<br />6.
<br />. 955.4
<br />1.309
<br />5.234
<br />10.47 .1.80'
<br />26
<br />222.3'5:697
<br />22.50 .44,09
<br />7.81)
<br />10
<br />929.6
<br />1.346
<br />5.379
<br />10.76 •
<br />E &i
<br />27
<br />211-2
<br />5, 018
<br />23,35-46-69
<br />8.10
<br />20
<br />905.1
<br />1.382
<br />5.524
<br />•1.1.05
<br />1.90
<br />28
<br />206.71
<br />,139
<br />24.19
<br />48.88
<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 1
<br />193.216.583
<br />25.88,
<br />51.76
<br />9.00
<br />Th middlo ordinate in inches for any cord_ of length (U) is equal to .001.2 U'
<br />multiplied by the Middle ordinate taken from the above .table. Thee, if it
<br />desired to Venda 30 ft. rail to fits 10 degree curve, its middle ordinate should
<br />be .0012X900X2.183 or 2.36 inches. t
<br />TABLE III.. Deflections for Sub Chords for Short Radius Curves.
<br />Degree
<br />of •
<br />Curve
<br />' Radius.
<br />+ 50 '
<br />3,6sub chord = sin of def: angle
<br />R'
<br />Length
<br />of arc
<br />for 100 ft.
<br />sin.1 def, ang.12:5
<br />F t.
<br />15 1 t.
<br />20 Ft. '
<br />25 F't.
<br />300
<br />z8,
<br />10 6I P
<br />2° 17, .:
<br />2' 58' l
<br />3° -43'
<br />101.15
<br />32°-"
<br />-193.
<br />i81.39
<br />i°59'
<br />2' -25'
<br />3°.10,._-
<br />3°-58'-.-107-33
<br />52
<br />34°
<br />171.01
<br />20 o6'
<br />2° 33'
<br />3° 21
<br />q° 12'
<br />I0I.48
<br />.36°
<br />i6z.8o' '"
<br />z°"13'
<br />2001''1''
<br />' 3° 33'_,
<br />1° 26'-r
<br />.rot .66
<br />0067
<br />,14
<br />20'
<br />2°.-49'n
<br />3°4'
<br />T
<br />101.85
<br />40° t
<br />-,153 ,5
<br />: 146.Itj.
<br />_2°
<br />2°�7r
<br />.9000
<br />-
<br />3°755' '
<br />-4°40_
<br />.-4°.5 f"
<br />Io2.66
<br />..42°
<br />139.52.
<br />z° 34�
<br />3° 05'
<br />4° 67'
<br />5° o8
<br />io2.z9
<br />44`
<br />133.47
<br />2° 41
<br />3° 13
<br />, :4°: i8.
<br />.5° 22'
<br />102.53
<br />q6°.--
<br />;
<br />,:: 127,977
<br />2° 48
<br />3° 21'
<br />4° 29'• ;
<br />. •5°.36'
<br />102,76
<br />480
<br />1,22.92.
<br />2° 55,
<br />3° 29,
<br />4° 40' .
<br />5° 50'
<br />103, 00
<br />. 5o°,
<br />:'I 18 31..
<br />3° 02'
<br />3- 38' '
<br />4°. 51'
<br />6° 04'
<br />103.24 .
<br />S3°.
<br />114-o6
<br />3° 09
<br />3° 46° .
<br />5° 02'
<br />17
<br />103.54
<br />54'
<br />Iio. ra/
<br />3° 16'
<br />3° 54, .
<br />5° 13'
<br />6°.31'
<br />103..84
<br />56'- ;-
<br />- 106.52-
<br />3° 22'
<br />4° 02'
<br />5' 23.
<br />6`44"
<br />' 104. 14
<br />58°1
<br />103. t.4
<br />3° 29
<br />4° lo'
<br />5° 34'
<br />6°'57'
<br />104.43
<br />60°
<br />100.00
<br />3035'
<br />4° 18'
<br />5° 44'
<br />%°'1I'
<br />104.72
<br />+l�k
<br />CURVE FORMULAS '
<br />T'� It tan z I R. T Cot. 2 I, chord°
<br />- Chord def. R _
<br />Stn D - KA- 50
<br />Sin'I'D 50 Sm '$ ,ll' No, chords = ll
<br />K E Rex sec ; I,'
<br />Stn 2'D 50 a .I
<br />, tan .,: Tan, def, _ I chord def.
<br />�. T' T tan. T
<br />t The square_ of an} -distance, divided' -by twice the radius', will equal
<br />the distance from tangent twcdrve; very; Nearly _ '
<br />-1J.1fo-fiiid angle for'a,giveli"distance-and deflection: '
<br />'Rule'i. Multiply' the•given distance by .01745 (def. for I° for I ft.
<br />see'1'able II.),:and divide given deflection by the product.
<br />'Rule -'2.' -Multiply given dcflectiori by 57.3, and divide the product by
<br />the givemdistance.= ;
<br />To finde
<br />d flection for a. a. given angle and distance. Multiply the angle
<br />by&f74,5, and the product.b'y the distance.
<br />w G>✓lv'>✓RAi: DaTA
<br />RIGHT• ANGLE TRIANGLES: Square the altitude, divide by,twice the
<br />base., • Add:quotient to base for hypotenuse
<br />Given Base,ioo;'Alt. Io.IO2=200=,5, 106+.5-10o.5 hyp...'' ;
<br />-Given Hyp. ioo, Alt. 2�.252=206'=3.125. 100 -3.125=96.875 -Base.
<br />Error in first example, .002; in last, .045: -
<br />To:find Tons of Rail in one mile of track: multiply a•eight,per yard
<br />by I,I, and divide by 7. -
<br />G-VELIPiG', ' The, correction.,, for curvature and. 'refraction, in feet
<br />and decimals of'feet is equal' to, 4:574d?, where `d is the distance in miles.
<br />The 'Correction_for`,curvature alone is 'closely"3d'. The combined cor-
<br />rection is negative
<br />PR_o$nBls ERR6lz ' If dl; d,, da;.etc. are'the discrepancies of" various
<br />results:from the,mean,Iand.if Tda-the 'sum of the squares of these differ-
<br />ences and"n-the;nilmbe'r of observaiinns, then the probable error -of the
<br />mean- adz
<br />SOLAR EmHk4kms. -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, 38x6 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, determin i ng the lneHilian and the
<br />latitude from observations on the -sun and Polaris; stadia measurements;
<br />magnetic declination; arithrnetic constants, etc.
<br />TABLE 1V. --Minutes in Decimals of a Degree.
<br />-11,
<br />-
<br />111
<br />.1833
<br />211
<br />.3500
<br />.311
<br />-:5167
<br />4i�.
<br />.6833
<br />51�
<br />.8500
<br />:.j2.
<br />.0167
<br />'.0333
<br />12
<br />.2000
<br />22
<br />.3667
<br />32
<br />.5333
<br />42
<br />.7000
<br />52
<br />.5667
<br />3,':0500-
<br />0521
<br />13
<br />.2167
<br />23
<br />.3833
<br />33
<br />.5500
<br />43
<br />.7167
<br />53
<br />.8833
<br />4
<br />0067
<br />,14
<br />.2333
<br />24
<br />.4000
<br />34
<br />:5667
<br />44
<br />.7333
<br />54
<br />.9000
<br />"5
<br />.9167
<br />- 15,
<br />.2500
<br />25
<br />.4167
<br />35
<br />.5833
<br />45
<br />.7500
<br />55
<br />.9167
<br />i-6
<br />.0833
<br />:1000
<br />16
<br />:2667
<br />26
<br />.4333
<br />36
<br />.6000
<br />46-
<br />.7667
<br />56
<br />.9333
<br />-.1167
<br />:17
<br />2833
<br />27
<br />.4500
<br />37
<br />.6167
<br />47
<br />.7833
<br />57
<br />.9500
<br />_g
<br />18
<br />-3000
<br />28•
<br />.4667
<br />38
<br />.6333
<br />48
<br />.8000
<br />58
<br />.9667
<br />9
<br />.1333
<br />19
<br />.3167
<br />29
<br />.4833
<br />39.6500
<br />;49
<br />..5167,
<br />59
<br />.9833
<br />'10
<br />.1500
<br />.1667
<br />20
<br />.3333.
<br />30
<br />.5000
<br />90
<br />.6667
<br />50
<br />.8333
<br />60
<br />1.0000
<br />-
<br />TABLE V.
<br />-Inches in* Decimals of a POOL.
<br />1-10'
<br />3-32
<br />y
<br />3-16-
<br />.00.52 .
<br />,0078•
<br />.0104
<br />.0156
<br />.0208
<br />.0260.
<br />.0313.
<br />.0417
<br />0521
<br />.0625
<br />.0729
<br />J
<br />1
<br />2
<br />3
<br />4
<br />5
<br />6'
<br />7
<br />S
<br />9
<br />10
<br />I1
<br />.0833
<br />.1667
<br />•.2500
<br />.3333
<br />9167
<br />.5000-
<br />..5833
<br />.6667
<br />.7500
<br />.833.3
<br />.9167
<br />
|